Investigation of Adaptive Base Isolation System Utilising Magnetorheological Elastomer · 2017-12-01 · Investigation of Adaptive Base Isolation System Utilising Magnetorheological

Investigation of Adaptive Base Isolation System Utilising Magnetorheological

Elastomer

By: Xiaoyu Gu

A thesis submitted in partial fulfilment of the requirements for

the degree of Doctor of Philosophy

University of Technology, Sydney

Faculty of Engineering & IT

April 2017

Certificate Of Authorship/Originality

I

To my dearest parents

Certificate Of Authorship/Originality

II

CERTIFICATE OF AUTHORSHIP/ORIGINALITY

I certify that the work in this thesis has not previously been submitted for a degree nor

has it been submitted as part of requirements for a degree except as fully acknowledged

within the text.

I also certify that the thesis has been written by me. Any help that I have received in

my research work and the preparation of the thesis itself has been acknowledged. In

addition, I certify that all information sources and literature used are indicated in the

thesis.

Signature of Candidate

Date

Acknowledgement

III

ACKNOWLEDGEMENT

I am truly fortunate to have spent four years at the Centre for Built Infrastructure

Research (CBIR) at University of Technology, Sydney (UTS) that provided me the

great opportunity to accomplish my graduate studies in a friendly but highly

competitive environment. I would first like to thank my PhD supervisors, Prof.

Jianchun Li and Dr Yancheng Li who guided, mentored and encouraged me throughout

my whole PhD study with their knowledge, jovial disposition and patience.

I would like to acknowledge the members of CBIR Dynamics and Control Group, in

particular, Richard Turnell for his generous help during my experimental tests and

valuable guidelines about student life in UTS and Australia. Also, I cannot thank

enough Dr Yang Yu for his time spent with me for strengthening fundamental concepts

on numerical modelling.

I am also indebted to my true friends who gave me so many helps in different ways

during my study at UTS. My special thanks go to Jing Wu, Lian Zhang, Ruoshi Xu, Dr

Mehrisadat Makki-Alamdari, Dr Mohsen Askari, Dr Saad Mahbub Subhani. It is my

great pleasure to meet you and have you in my life.

Last, but not the least, I want to thank my family for their support through my entire

life. Your raised me up to the person I am now and your support helps me overcome all

the difficulties during my study. In addition, my special appreciation goes to my

boyfriend, Hao Jiang, without whose motivation and encouragement, completion of this

degree would be impossible.

List Of Publications Related To This Thesis

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LIST OF PUBLICATIONS RELATED TO THIS THESIS

Refereed Journal Articles

1. Gu, X., Li, Y. & Li, J., 2016. Investigations on response time of magnetorheological

elastomer isolator for real-time control implementation. Smart Materials and

Structures. 25(11), p.11LT04.

2. Gu, X., Li, J., Li, Y. & Askari, M., 2016. Frequency control of smart base isolation

system employing a novel adaptive magneto-rheological elastomer base isolator.

Journal of Intelligent Material Systems and Structures. 27(7), pp.849-858.

3. Gu, X., Yu, Y., Li, J., Li, Y., & Alamdari, M. M. 2016. Semi-active storey isolation

system employing MRE isolator with parameter identification based on NSGA-II

with DCD. Earthquakes and Structures, 11(6), 1101-1121.

4. Gu, X., Yu, Y., Li, J. & Li, Y. 2017. Utilising optimal general regression neural

network (GRNN) inverse model for modelling and control of magnetorheological

elastomer base isolation system. Journal of Sound & Vibration. (Accepted)

5. Yu, Y., Li, Y., Li, J. & Gu, X., 2016. Self-adaptive step fruit fly algorithm

optimized support vector regression model for dynamic response prediction of

magnetorheological elastomer base isolator. Neurocomputing. 211, pp.41-52.

6. Yu, Y., Li, Y., Li, J. & Gu, X., 2016. A Hysteresis model for dynamic behaviour

of magnetorheological elastomer base isolator. Smart Materials and Structures.

25(5), p.055029.

7. Yu, Y., Li, Y., Li, J., Gu, X. & Royel, S., 2016. Dynamic modelling of

magnetorheological elastomer base isolator based on extreme learning machine.

Mechanics of Structures and Materials: Advancements and Challenges. pp. 703-

List Of Publications Related To This Thesis

V

708. CRC Press.

8. Askari, M., Li, J., Samali, B. & Gu, X., 2016. Experimental forward and inverse

modelling of magnetorheological dampers using an optimal Takagi–Sugeno–Kang

fuzzy scheme. Journal of Intelligent Material Systems and Structures. 27(7),

pp.904-914.

Conference Paper

1. Gu, X., Li, J. & Li, Y. 2014. Adaptive base isolation system with magneto-

rheological elastomer base isolators: numerical investigations. Proceeding of the

sixth World Conference on Structural Control and Monitoring (6WCSCM),

Barcelona, Spain.

2. Gu, X., Li, J., Askari, M. & Li, Y. 2014. Semi-active control of an innovative adaptive base isolation system. 14th International Conference on ER Fluids and MR Suspensions (ERMR2014).Spain.

3. Gu, X., Li, J. & Li, Y., 2014. Innovative semi-active storey isolation system

utilising novel magneto-rheological elastomer base isolators. Proceeding of 23rd

Australasian Conference on the Mechanics of Structures and Materials

(ACMSM23). Byron Bay, Australia

Table Of Contents

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TABLE OF CONTENTS

CERTIFICATE OF AUTHORSHIP/ORIGINALITY ....................... II ACKNOWLEDGEMENT..................................................................... III LIST OF PUBLICATIONS RELATED TO THIS THESIS ............. IV TABLE OF CONTENTS ...................................................................... VI LIST OF FIGURES ............................................................................... XI LIST OF TABLES ........................................................................... XVIII ABSTRACT ........................................................................................... XX CHAPTER 1 INTRODUCTION .......................................................... 1 1.1 Background And Motivation Of This Research ................................................. 1 1.2 Objective Of The Present Research .................................................................... 8 1.3 Organisation Of This Thesis ............................................................................... 9 CHAPTER 2 LITERATURE REVIEW ........................................... 12 2.1 Preface............................................................................................................... 12 2.2 State-Of-Art Of The Conventional Base Isolation............................................ 14

2.2.1 Working principle of base isolation ...................................................................................... 14 2.2.2 History and Development of Base Isolation ......................................................................... 14 2.2.3 Contemporary Base Isolation Devices .................................................................................. 17 2.2.4 Categorisation of conventional base isolation techniques ..................................................... 28 2.2.5 Issues Related to Conventional Base Isolation...................................................................... 28

2.3 Ideas Of “Smart” Isolation System ................................................................... 29

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2.4 Present “Smart” Base Isolation ......................................................................... 30 2.4.1 Active Base Isolation System ............................................................................................... 31 2.4.2 Semi-active Base Isolation System ....................................................................................... 32 2.4.3 Issues Related to Present Hybrid Base Isolation Systems ..................................................... 36

2.5 MRE Vibration Isolation................................................................................... 37 2.5.1 Brief Description of MRE Material ...................................................................................... 38 2.5.2 MRE vibration isolator in mechanical engineering ............................................................... 40 2.5.3 MRE base isolator in civil engineering ................................................................................. 43 2.5.4 Control Application of MRE Isolators .................................................................................. 50

2.6 Research Gaps And Challenges ........................................................................ 55 CHAPTER 3 MRE BASE ISOLATION AND HYSTERESIS

MODELLING ........................................................................................ 58 3.1 Chapter Outline ................................................................................................. 58 3.2 Introduction and Background ........................................................................... 59

3.2.1 MRE base isolator ................................................................................................................. 59 3.3 Forward Model of MRE Base Isolator.............................................................. 61

3.3.1 Generalised Bouc-Wen Model .............................................................................................. 61 3.3.2 Strain-Stiffening Model ........................................................................................................ 74 3.3.3 Comparison of Bouc-Wen Model and Strain-Stiffening Model ........................................... 91

3.4 Inverse Model of MRE Base Isolator ............................................................... 92 3.4.1 Introduction ........................................................................................................................... 92 3.4.2 Experimental Setup and Training Data ................................................................................. 94 3.4.3 Inverse Modelling of MRE Base Isolator ............................................................................. 96 3.4.4 MRE Base Isolator Inverse Model Based on FOA-Optimised GRNN ............................... 100

3.5 Summary ......................................................................................................... 103 CHAPTER 4 INVESTIGATION OF RESPONSE TIME OF MRE

ISOLATOR FOR REAL-TIME CONTROL ................................... 105 4.1 Chapter Outline ............................................................................................... 105 4.2 Background ..................................................................................................... 106

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4.3 Response Time Definition .............................................................................. 108 4.4 Response Time Calibration Of MRE Base Isolator ........................................ 110

4.4.1 Input Excitations ................................................................................................................. 110 4.4.2 Experimental Setup ............................................................................................................. 111 4.4.3 Measured Response Time ................................................................................................... 112

4.5 Approaches To Minimise Response Time ...................................................... 113 4.5.1 Optimal Controlled PWM Servo Current Source................................................................ 113 4.5.2 Modification to The Solenoid Circuit ................................................................................. 120 4.5.3 Field-Quenching Coil Configuration .................................................................................. 122

4.6 Response Time Under Different Configurations ............................................ 125 4.6.1 On Current and Force Responses ........................................................................................ 125 4.6.2 Performance evaluation for real-time control implementation ........................................... 127

4.7 Summary ......................................................................................................... 131 CHAPTER 5 SEMI-ACTIVE CONTROL OF MRE BASE

ISOLATION SYSTEM ....................................................................... 133 5.1 Chapter Outline ............................................................................................... 133 5.2 Design and Identification Of The MRE Base Isolation System ..................... 134

5.2.1 Three-storey Building Model Design .................................................................................. 134 5.2.2 System Identification .......................................................................................................... 137

5.3 Experimental Setup And System Description................................................. 146 5.4 Control Algorithms ......................................................................................... 150

5.4.1 LQR Control with GRNN Inverse Model ........................................................................... 151 5.4.2 GA Optimised Fuzzy Logic Control ................................................................................... 154 5.4.3 Lyapunov-Based Control .................................................................................................... 163 5.4.4 Frequency Control .............................................................................................................. 171

5.5 Comparative Investigation Results And Discussion ....................................... 175 5.5.1 Earthquake Records ............................................................................................................ 176 5.5.2 Evaluative Indices ............................................................................................................... 179 5.5.3 Comparison between Numerical and Experimental Results ............................................... 181 5.5.4 Peak Responses ................................................................................................................... 186 5.5.5 Evaluative indices comparison ............................................................................................ 201

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5.5.6 Time Histories ..................................................................................................................... 209 5.5.7 Control Force and Current Comparisons ............................................................................ 224 5.5.8 Comparative Evaluation between Different Control Methods ............................................ 233

5.6 Summary ......................................................................................................... 234 CHAPTER 6 INNOVATIVE STOREY ISOLATION UTILISING

SMART MRE ISOLATION SYSTEM ............................................. 236 6.1 Chapter Outline ............................................................................................... 236 6.2 Background And Introduction ........................................................................ 237 6.3 System Description ......................................................................................... 240 6.4 Optimal Current Selection Of The MRE Isolator ........................................... 243

6.4.1 Five-Storey Benchmark Building Model ............................................................................ 243 6.4.2 Optimisation Problem Statement ........................................................................................ 244 6.4.3 Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) with DCD ............................... 245 6.4.4 Parameter Identification Based on NSGA-II with DCD ..................................................... 247

6.5 Control Method ............................................................................................... 250 6.6 Numerical Investigation .................................................................................. 251 6.7 Summary ......................................................................................................... 268 CHAPTER 7 CONCLUSIONS AND FUTURE RESEARCH ...... 269 7.1 MRE Base Isolator Modelling ........................................................................ 269 7.2 Response Time Of MRE Base Isolator Investigation ..................................... 271 7.3 Control Algorithm For MRE Base Isolation System ...................................... 271 7.4 Experimental Realisation Of MRE Base Isolation System ............................ 272 7.5 Storey MRE Isolation System ......................................................................... 274 7.6 Suggestions For Future Work ......................................................................... 275

7.6.1 Optimisation of Coil Configuration for Further Response Time Reduction ....................... 275 7.6.2 Further Development of Control Algorithm ....................................................................... 276 7.6.3 Optimisation of MRE Isolator Placement in Storey Isolation System ................................ 277

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7.6.4 Experimental Investigation of the MRE Base Isolation System on Full-Scaled Civil

Infrastructures .................................................................................................................................. 277 REFERENCE ....................................................................................... 279 APPENDIX ........................................................................................... 293 Appendix A Peak Responses Under Four Earthquakes ........................................ 293 Appendix B Evaluative Indices ............................................................................ 296 Appendix C Selected Time History Responses .................................................... 300 Appendix D Control Force And Corresponding Current ...................................... 306

List Of Figures

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LIST OF FIGURES

Figure 2.1 Laminated rubber bearing: (a) composite and sectional details; (b) schematic diagram ........................................................................................................................ 17 Figure 2.2 Lead core rubber bearing (New Zealand rubber bearing): (a) composite and sectional details; (b) schematic diagram ...................................................................... 20 Figure 2.3 Pure friction (PF) bearing: (a) composite and sectional details; (b) schematic diagram ........................................................................................................................ 21 Figure 2.4 EDF base isolation system: (a) composite and sectional details; (b) schematic diagram ........................................................................................................................ 22 Figure 2.5 Resilient friction base isolation (R-FBI) system: (a) composite and sectional details (Mostaghel 1987); (b) schematic diagram ........................................................ 23 Figure 2.6 Sliding resilient friction base isolation (S-RF) system: (a) composite and sectional details; (b) schematic diagram ...................................................................... 24 Figure 2.7 Friction pendulum base isolator: (a) external view; (b) composite and sectional details; (c) schematic diagram ...................................................................... 25 Figure 2.8 Categorisation of conventional base isolation techniques .......................... 27 Figure 2.9 Schematic diagram of (a) hybrid isolation system combining passive base isolation with supplementary dampers; (b) “smart” base isolation system with controllable isolators .................................................................................................... 30 Figure 2.10 Schematics of variable-orifice damper ..................................................... 34 Figure 2.11 Schematics of a controllable MRF damper .............................................. 35 Figure 2.12 Shear stress-strain curves under different magnetic field (Li, Li & Samali 2012) ............................................................................................................................ 40 Figure 2.13 Design of the MRE vibration isolation mount (Kavlicoglu et al. 2011) .. 41 Figure 2.14 Sketch of the MRE-based vibration isolator (Liao et al. 2012) ................ 42 Figure 2.15 (a) Cross-section view of MRE isolator; (b) Vibration model of the MRE seat suspension system with human body .................................................................... 42 Figure 2.16 Structure model coupled with an MR elastomer-based base-isolation system (Jung et al. 2011) ............................................................................................. 43 Figure 2.17 Cross-section view and photo of variable stiffness and damping isolator (Behrooz, Wang & Gordaninejad 2014b) .................................................................... 44 Figure 2.18(a) Phenomenological Bouc-Wen model of VSDI; (b) On-state and off-state shear force deformation characteristics of VSDIs (Behrooz, Wang & Gordaninejad 2014a) .......................................................................................................................... 45

List Of Figures

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Figure 2.19 Photo and cross-section view of the laminated MRE base isolator (Li, Li, Li, et al. 2013) .............................................................................................................. 47 Figure 2.20 Photo and cross-section view of the highly adjustable laminated MRE base isolator.......................................................................................................................... 47 Figure 2.21(a) Force-displacement relationships of the MRE base isolator at quasi-static testing (f=0.1Hz, Δ=8mm); (b) force-displacement loops at different amplitudes (2mm, 4mm and 8mm) excitation at 0.1 Hz and 3A (Li, Li, Tian, et al. 2013) ........... 47 Figure 2.22 Laminated negative stiffness MRE isolator (Yang et al. 2014) ............... 49 Figure 2.23 Different working modes of hybrid magnetic system (Yang et al. 2014) 50 Figure 2.24 Multiple short-type floating slab track magneto-rheological system model (Li et al. 2016).............................................................................................................. 54 Figure 3.1 Experimental setup for training data acquisition and power equipment (Li, Li, Tian, et al. 2013)..................................................................................................... 59 Figure 3.2 MRE isolator’s stiffness and damping dynamics with different current input...................................................................................................................................... 60 Figure 3.3 Schematic diagram of the proposed Bouc-Wen model for MRE isolator .. 62 Figure 3.4 Comparison between experimental data and forecast values from the proposed model with different excitation amplitudes (1Hz-3A) ................................. 63 Figure 3.5. Comparison between experimental data and forecast values from the proposed model with different applied currents (1Hz-4mm) ...................................... 64 Figure 3.6 Comparison between experimental data and forecast values from the proposed model with different excitation frequencies (4mm-1A) ............................... 64 Figure 3.7 Parameter identification results: (a) k0 vs current; (b) c0 vs current; (c) α vs current; (d) A vs current; (e) β vs current; (a) γ vs current Based on the observations in Table 3.1 and Figure 3.4 to Figure 3.6, it can be assumed that the values of parameters are more affected by applied current rather than the excitation frequency and amplitude. Hence, an average of parameter values under different excitation scenarios when applied current is 0A, 1A, 2A and 3A, respectively, is taken as the parameter at the corresponding current level. Next, a curve fitting is conducted to explore the definitive correlation between the parameter of interest with applied current. Figure 3.7 shows the fitting curve of all six parameters, among which k0, c0, A, β, and γ have a linear relation with current while α and current have a quadratic relation. The fitted functions of parameters are expressed by Eq 3.2. ............................................................................ 67 Figure 3.8 k0 dependent responses of the generalised Bouc-Wen model: (a) force-displacement loops; (b) force-velocity loops ............................................................... 69 Figure 3.9 c0 dependent responses of the generalised Bouc-Wen model: (a) force-displacement loops; (b) force-velocity loops ............................................................... 69

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Figure 3.10 α dependent responses of the generalised Bouc-Wen model: (a) force-displacement loops; (b) force-velocity loops ............................................................... 70 Figure 3.11 A dependent responses of the generalised Bouc-Wen model: (a) force-displacement loops; (b) force-velocity loops ............................................................... 71 Figure 3.12 β and γ dependent responses of the generalised Bouc-Wen model: (a) force-displacement loops of changing β; (b) force-velocity loops of changing γ ................. 71 Figure 3.13 Comparison between experimental force and predicted force by Bouc-Wen model with random displacement input ....................................................................... 72 Figure 3.14 Comparison between experimental force and predicted force by Bouc-Wen model with El Centro earthquake displacement input ................................................. 73 Figure 3.15 Break-down of the hysteresis of MRE base isolator ................................ 75 Figure 3.16 Schematic diagram of the proposed strain-stiffening model for MRE isolator.......................................................................................................................... 75 Figure 3.17 Comparison between experimental data and forecast values from the proposed model with different excitation amplitudes (1Hz-3A) ................................. 77 Figure 3.18 Comparison between experimental data and forecast values from the proposed model with different applied current (2Hz-4mm) ........................................ 78 Figure 3.19 Comparison between experimental data and forecast values from the proposed model with different applied current (1A-4mm) .......................................... 79 Figure 3.20 k0 dependent responses of the generalised strain-stiffening model: (a) force-displacement loops; (b) force-velocity loops ............................................................... 80 Figure 3.21 c0 dependent responses of the generalised strain-stiffening model: (a) force-displacement loops; (b) force-velocity loops ............................................................... 80 Figure 3.22 α dependent responses of the generalised strain-stiffening model: (a) force-displacement loops; (b) force-velocity loops ............................................................... 83 Figure 3.23 F0 dependent responses of the generalised strain-stiffening model: (a) force-displacement loops; (b) force-velocity loops ..................................................... 83 Figure 3.24 Correlations between parameter values and applied current with different excitation frequencies .................................................................................................. 84 Figure 3.25 Correlations between parameter values and excitation frequency with different applied current ............................................................................................... 85 Figure 3.26 Correlations between parameter values and applied current with different excitation amplitudes ................................................................................................... 86 Figure 3.27 Relationships between model parameters and applied current as well as absolute maximal displacement ................................................................................... 87 Figure 3.28 Comparison between experimental force and predicted force by strain-stiffening model with random displacement input (I = 0A) ........................................ 89

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Figure 3.29 Comparison between experimental force and predicted force by strain-stiffening model with random displacement input (I = 3A) ........................................ 90 Figure 3.30 Experimental setup for MRE inverse model identification ...................... 95 Figure 3.31 Training data for GRNN inverse model ................................................... 96 Figure 3.32 Schematic diagram of inverse model based on GRNN .......................... 101 Figure 3.33 Performance of the GRNN inverse model (a) comparison between measured current and GRNN output; (b) regression analysis of results .................... 103 Figure 4.1 Circuit diagram of the solenoid with current and voltage sources ........... 108 Figure 4.2 Definition of response time at rise edge and fall edge ............................. 110 Figure 4.3 Illustration of input displacement and current excitations ....................... 111 Figure 4.4 Experimental setup of current and force response testing ........................ 112 Figure 4.5 Original current and force response of MRE isolator .............................. 113 Figure 4.6 Schematics of a typical servo system ....................................................... 114 Figure 4.7 Definition of duty cycle ............................................................................ 114 Figure 4.8 PWM signal governed current source: (a) schematic diagram; (b) transfer function block diagram .............................................................................................. 116 Figure 4.9 Working principle of a PWM servo current drive responding under a step command .................................................................................................................... 118 Figure 4.10 Circuit description of isolated IGBT drive driven by PWM signal........ 119 Figure 4.11 Circuit description of power supplies used in IGBT switch system ...... 119 Figure 4.12 Schematic diagram of MRE isolator with multi coils ............................ 122 Figure 4.13 Circuit description of split coil system ................................................... 124 Figure 4.14 Circuit diagram of split coil system........................................................ 124 Figure 4.15 Current response curves under different coil configurations ................. 125 Figure 4.16 Current and force response time under different displacements ............ 126 Figure 4.17 Final current and force responses with field-quenching coil configuration.................................................................................................................................... 127 Figure 4.18 Response time comparison under El-centro earthquake ........................ 129 Figure 4.19 Response time comparison under Kobe earthquake ............................... 129 Figure 4.20 Response time comparison under Hachinohe earthquake ...................... 130 Figure 4.21 Response time comparison under Northridge earthquake ...................... 130 Figure 5.1 Schematic diagram and dimensioning drawing of the three-storey shear building model ........................................................................................................... 135 Figure 5.2 Photos of three-storey shear building model and connections in the structure.................................................................................................................................... 136 Figure 5.3 Modal testing experimental setups of fixed base building and base isolated structure...................................................................................................................... 138

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Figure 5.4 Flowchart of experimental modal analysis / statistical modal analysis module in DIAMOND (Doebling, Farrar & Cornwell 1997) ................................................. 139 Figure 5.5 Experimental dynamic mode shapes (along softer direction): (a) first mode shape; (b) second mode shape; (c) third mode shape ................................................ 141 Figure 5.6 Comparison between experimental and predicted top floor displacement in fixed base building ..................................................................................................... 142 Figure 5.7 Comparison between experimental and predicted top floor displacement in base isolated building ................................................................................................. 146 Figure 5.8 Experimental setup schematics of comparative testing of proposed MRE base isolation system.................................................................................................. 146 Figure 5.9 Photo of experimental setup: (a) front view; (b) side view ...................... 148 Figure 5.10 Laser sensor and sensor adapter ............................................................. 148 Figure 5.11 Power supplies and data acquisition system with dSPACE ................... 149 Figure 5.12 Block diagram of a general semi-active structural control problem ...... 151 Figure 5.13 Semi-active control strategy of MRE base isolation system with GRNN inverse model ............................................................................................................. 152 Figure 5.14 Schematic diagram of inverse model based on GRNN .......................... 153 Figure 5.15 Schematic diagram of the RBF based NFLC ......................................... 156 Figure 5.16 Fuzzy rule base matrix at hidden layer ................................................... 157 Figure 5.17 Schematic diagram of one chromosome with encoded NFLC parameters.................................................................................................................................... 160 Figure 5.18 Flow chart of NSGA-II with DCD ......................................................... 161 Figure 5.19 NSGA-II optimised membership function for top acceleration and base displacement .............................................................................................................. 162 Figure 5.20 Schematics of the dynamic system ......................................................... 164 Figure 5.21 Stiffness ON-OFF control (Liao et al. 2012).......................................... 169 Figure 5.22 Flow chart of the feed-forward frequency control system (Gu et al. 2016).................................................................................................................................... 172 Figure 5.23 Time histories of evaluative indices and corresponding control command.................................................................................................................................... 174 Figure 5.24 Earthquake time histories and pseudo-acceleration spectra (damping ratio=5%) ................................................................................................................... 177 Figure 5.25 Experimental and numerical relative displacement responses of Passive-on system (0.15 Hachinohe) ........................................................................................... 181 Figure 5.26 Experimental and numerical absolute acceleration responses of Passive-on system (0.15 Hachinohe) ........................................................................................... 183 Figure 5.27 Peak responses with four different earthquake magnitudes of El-Centro earthquake .................................................................................................................. 187

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Figure 5.28 Peak responses with four different earthquake magnitudes of Kobe earthquake .................................................................................................................. 188 Figure 5.29 Peak responses under four earthquakes (scaling factor = 15%) ............. 189 Figure 5.30 Peak inter-storey drift ratio under four earthquakes (inter-storey drift ratio = inter-storey drift/floor height (0.04m); earthquake scaling factor= 15%) .............. 191 Figure 5.31 Peak floor acceleration under four earthquakes (earthquake scaling factor = 15%) ........................................................................................................................ 194 Figure 5.32 Peak relative displacement under four earthquakes (earthquake scaling factor = 15%) ............................................................................................................. 196 Figure 5.33 Peak floor shear/Seismic weight W under four earthquakes (W = 912.57N (fixed base building)/1402.58N (base-isolated building) ; earthquake scaling factor = 15%) ........................................................................................................................... 198 Figure 5.34 Evaluative indices J1 ~ J6 under four earthquakes (earthquake scaling factor = 15%) ........................................................................................................................ 202 Figure 5.35 Evaluative indices J7 ~ J9 at worst case scenario (earthquake scaling factor = 15%) ........................................................................................................................ 203 Figure 5.36 Time history of top floor acceleration with different control algorithms (0.15 El-Centro) ......................................................................................................... 212 Figure 5.37 Time history of top floor acceleration with different control algorithms (0.15 Kobe) ................................................................................................................ 213 Figure 5.38 Time history of top floor acceleration with different control algorithms (0.15 Hachinohe)........................................................................................................ 214 Figure 5.39 Time history of top floor acceleration with different control algorithms (0.15 Northridge) ....................................................................................................... 215 Figure 5.40 Time history of base displacement with different control algorithms (0.15 El-Centro) .................................................................................................................. 216 Figure 5.41 Time history of base displacement with different control algorithms (0.15 Kobe).......................................................................................................................... 217 Figure 5.42 Time history of base displacement with different control algorithms (0.15 Hachinohe) ................................................................................................................. 218 Figure 5.43 Time history of base displacement with different control algorithms (0.15 Northridge) ................................................................................................................. 219 Figure 5.44 Time history of base acceleration with different control algorithms (0.15 El-Centro) .................................................................................................................. 220 Figure 5.45 Time history of base acceleration with different control algorithms (0.15 Kobe).......................................................................................................................... 221 Figure 5.46 Time history of base acceleration with different control algorithms (0.15 Hachinohe) ................................................................................................................. 222

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Figure 5.47 Time history of base acceleration with different control algorithms (0.15 Northridge) ................................................................................................................. 223 Figure 5.48 Time history of control force with different control algorithms (0.15 El Centro) ....................................................................................................................... 226 Figure 5.49 Time history of control force with different control algorithms (0.15 Kobe).................................................................................................................................... 227 Figure 5.50 Time history of control force with different control algorithms (0.15 Hachinohe) ................................................................................................................. 228 Figure 5.51 Time history of control force with different control algorithms (0.15 Northridge) ................................................................................................................. 229 Figure 5.52 Control force and corresponding control current with NSGA-NFLC (Earthquake scaling factor = 15%) ............................................................................ 230 Figure 5.53 Control force and corresponding control current with Lyapunov control (Earthquake scaling factor = 15%) ............................................................................ 231 Figure 5.54 Control force and corresponding control current with frequency control (Earthquake scaling factor = 15%) ............................................................................ 232 Figure 6.1Sketches of: (a) fixed base building; (b) base-isolated building; (c) storey isolated building ......................................................................................................... 240 Figure 6.2 Schematic diagrams of: (a) fixed base building model; (b) storey-isolated building model ........................................................................................................... 242 Figure 6.3 Photo and typical floor plan of the 5-storey benchmark building model (Wu & Samali 2002) .......................................................................................................... 243 Figure 6.4 Illustration of Pareto frontier (Barraza et al. 2017) .................................. 246 Figure 6.5 Time history of top floor acceleration under El Centro earthquake ......... 252 Figure 6.6 Time history of top floor acceleration under Kobe earthquake ................ 253 Figure 6.7 Time history of top floor acceleration under Hachinohe earthquake ....... 254 Figure 6.8 Time history of top floor acceleration under Northridge earthquake ....... 255 Figure 6.9 Comparison of top floor acceleration between optimised SI and controlled SI ................................................................................................................................ 256 Figure 6.10 Peak floor acceleration response under four earthquakes ...................... 257 Figure 6.11 Peak inter-storey drift ratio response under four earthquakes (drift ratio = inter-storey drift/floor height; floor height = 600mm) ............................................... 258 Figure 6.12 Peak relative displacement response under four earthquakes ................ 259 Figure 6.13 Control current of different storey under El Centro earthquake ............. 261 Figure 6.14 Control current of different storey under Kobe earthquake ................... 262 Figure 6.15 Control current of different storey under Hachinohe earthquake ........... 263 Figure 6.16 Control current of different storey under Northridge earthquake .......... 264

List Of Tables

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LIST OF TABLES

Table 2.1 Inference rule of the fuzzy logic control algorithm (Yang et al. 2016) ....... 54 Table 3.1 Identified parameter values for Bouc-Wen model under different excitation scenarios ....................................................................................................................... 65 Table 3.2 Identified parameter values for strain-stiffening model under different excitation scenarios ...................................................................................................... 81 Table 3.3 Final identified parameter values of strain-stiffening model ....................... 88 Table 3.4 Comparison results between Bouc-Wen model and strain-stiffening model...................................................................................................................................... 91 Table 4.1 Original current and force response time (4mm displacement) ................. 112 Table 4.2 Final current and force response time (4mm displacement, field-quenching configuration) ............................................................................................................. 127 Table 5.1 Detailed designated parameters of each component .................................. 136 Table 5.2 Comparison of natural frequency and damping ratio between numerically predicted and modal analysis results.......................................................................... 140 Table 5.3 Mode shape vectors from modal analysis results ...................................... 140 Table 5.4 Parameter values of MRE base isolator’s Bouc-Wen model ..................... 143 Table 5.5 Identified structural parameters of the base isolated building model ........ 145 Table 5.6 Evaluative indices for NSGA II ................................................................. 162 Table 5.7 NSGA-II optimised weights for NFLC ..................................................... 163 Table 5.8 Benchmark earthquakes information ......................................................... 178 Table 5.9 Evaluative indices description ................................................................... 180 Table 5.10 Comparative peak responses of experimental and numerical results (0.15 El Centro) ....................................................................................................................... 184 Table 5.11 Comparative peak responses of experimental and numerical results (0.15 Kobe).......................................................................................................................... 184 Table 5.12 Comparative peak responses of experimental and numerical results (0.15 Hachinohe) ................................................................................................................. 185 Table 5.13 Comparative peak responses of experimental and numerical results (0.15 Northridge) ................................................................................................................. 185 Table 5.14 Reduction of peak floor responses of different isolation scenarios ......... 199 Table 5.15 Evaluative indices value .......................................................................... 204 Table 5.16 Comparison of five controllers ................................................................ 233 Table 6.1 Parameter values of MRE isolator model .................................................. 241

List Of Tables

XIX

Table 6.2 Structural parameters of the 5-storey model .............................................. 243 Table 6.3 Optimisation current solutions and corresponding objective values ......... 249 Table 6.4 Evaluative indices description ................................................................... 265 Table 6.5 Values of evaluative indices J1~J6 under four earthquakes with different isolation scenarios ...................................................................................................... 266 Table 6.6 Values of evaluative indices J1~J6 under four earthquakes with different isolation scenarios (Cont’d) ....................................................................................... 267

Abstract

XX

ABSTRACT

Most of current researches on controllable or “smart” base isolation systems have been

based on the hybrid of conventional base isolation system with active or semi-active

dampers. Although supplementary dampers may help to reduce maximum

displacement of base isolation systems and provide adjustable damping to suppress

vibrations of the protected structure, it suffers some setbacks such as introduction of

undesirable acceleration, limited performance due to the passive nature of base

isolation, etc. Moreover, those “smart” supplementary dampers failed to add

“smartness” or controllability toward working mechanism of isolation systems, i.e.

decoupling ground motion from superstructures. In recent years, the development of

adaptive base isolator utilising magnetorheological elastomer (MRE) shed light on

“truly” smart base isolation systems in which isolators’ lateral stiffness can be

controlled in real time by varying applied current. To this end, the MRE base isolation

system exhibits a promising potential for ultimate seismic protection of civil

infrastructures due to its ability to maximise, in real time, level of decoupling between

ground motion and the superstructure. However, there have been only limited

researches reported in this area. In addition, there is lack of throughout investigations,

especially experimental investigation, on critical issues and feasibility related design

and implementation of such MRE-based smart base isolated system, which is much

needed for future development and application.

This thesis is aimed at filling aforementioned research gap in development and

application of MRE-based smart base isolated system by contributing new knowledge

in the fields in terms of: i) modelling of the MRE isolator to capture its forward and

inverse dynamic characteristics; ii) comprehensive investigation on the response time

of MRE isolator and exploration of approaches to minimise the lag; iii) overcome

Abstract

XXI

obstacles in experimental realisation of smart base isolation system; iv) other

innovations in seismic protection of civil infrastructures employing MRE isolator.

First, the modelling of the MRE isolator is conducted for dynamic response prediction

of the device. Two forward models of the isolator are proposed and compared, namely,

a phenomenological model based on hysteresis Bouc-Wen model and innovative strain-

stiffening model identified by least square (LS) function. Performance evaluation of the

model has been conducted based on the experimental testing data from MRE isolator.

Furthermore, due to the inherent nonlinearity and hysteretic characteristics of the

devices, it is challenging to obtain a less complicated mathematical model to describe

the inverse dynamics of MRE base isolators and hence to perform control synthesis of

the MRE base isolation system. Therefore, an optimal general regression neural

network (GRNN) inverse model has been proposed to depict the inverse dynamics of

the isolator. With the inverse model, the nonlinearity and phenomenological hysteresis

brought into control system by the MRE isolator can be neutralised for the classic

control algorithm like LQR to be feasible.

Real-time control of the MRE isolators holds the key to unlock MRE materials’ unique

characteristics, i.e. instantly changeable shear modulus in continuous and reverse

fashion. However, one of the critical issues for the applications of real-time control is

the response time delay of MRE vibration isolators, which has not yet been fully

addressed and studied. Therefore, the next topic of this thesis is to identify the inherent

response time of the MRE isolator and explore feasible approaches to minimise the

response time delay. The definition and experimental measurement of the response time

of MRE isolator is presented, followed by three response time reduction approaches,

i.e. PWM servo current drive, modification of isolator’s solenoid and innovative

configuration of solenoid excitation.

A three-storey shear building model is then designed as the testing bed of proposed

MRE base isolation system. Various control algorithms are proposed, developed and

formulated to explore the capability of the smart isolation system, includingnon-

Abstract

XXII

dominated sorting genetic algorithm optimised neural fuzzy logic control

(NSGA-NFLC), Bang-Bang control, LQR control with GRNN inverse model,

frequency control and Lyapunov-based current selection control. Comprehensive

investigation of seismic protection performance of the MRE isolation system has been

conducted numerically and experimentally. Promising vibration suppression

performance has been observed in most controlled solation scenarios, particularly in

NSGA-NFLC and Lyapunov controller.

Finally, an innovative storey isolation system utilising MRE isolator has been proposed

and numerically evaluated. The advantage of storey isolation system lies in that it can

distribute the deformation of base isolation system into different levels, leading to

effective solution of extensive base displacement issue faced by conventional base

isolation system. The NSGA-II is utilised to seek for the optimal placement of isolators

and current input of each device. The Lyapunov-based current selection control is

employed for the control of the storey isolation system. A comprehensive numerical

testing compares the seismic responses of bare building, building with passive

controlled MRE base isolation system, building with optimal MRE storey isolation

system and controlled storey isolation system. Simulation results indicate that the

controlled storey isolation system is capable of significantly mitigating the floor

acceleration and base displacement as well as avoiding whipping effect problem in

passive storey isolation system.

Introduction

1

CHAPTER 1

INTRODUCTION

1.1 BACKGROUND AND MOTIVATION OF THIS RESEARCH

Earthquake is known to cause the biggest loss of human life apart from epidemics and

wars. In fact, on average, there are more than 15,000 earthquakes per year with different

magnitude happening around the world and to a degree depending on the magnitude,

some of them can be disastrous. For structures in high seismicity regions, earthquake

loading is considered the most significant and possibly the most destructive external load,

particularly for low- to medium-rise buildings whose fundamental frequency normally

falls into the range of the predominant frequency of earthquakes, resulting in a hazardous

influence on buildings worldwide. Moreover, a substantial proportion of the world’s

population lives in regions of seismic hazard, at risk from earthquakes of varying severity

and varying frequency of occurrence. Earthquakes cause significant loss of life and

damage to property every year. Everyone has probably witnessed through television and

other media the vast destruction of infrastructures and tragic loss of life caused by the

Kobe earthquake in Japan in 1995 claiming over 5,400 lives and the Sichuan Earthquake

in China in 2008 in which over 67,000 people lost their lives.

In the structural engineering field, one of the constant challenges is to find new and better

means to protect structures and constructed facilities from the damaging effects of

destructive environmental forces. A passive control system in the form of a base isolation

system, using elastomeric or sliding bearings to serve as a foundation to the buildings, is

Introduction

2

a milestone in the development and evolution of earthquake-resistant designs and

technologies. The application of base isolation for earthquake resistance is a radical

departure from the traditional approaches used by structural engineers. In a conventional

fixed-base design, strengthening a structural system to provide superior seismic

performance leads to a stiffer structure attracting more forces to the building and the

contents of the structure since a fixed-base building tends to amplify the ground motion.

To minimise this amplification, the structural system must either be extremely rigid or

have a high level of damping. At best, rigidity leads to the non-structural elements

experiencing amplified ground accelerations, which may hurt sensitive equipment and

vulnerable elements. Damping at a high level, on the other hand, means either damage to

the system or expensive design and construction cost.

Base isolation allows the engineers to control damage during moderate and large

earthquakes for both the structural and non-structural elements in the building and the

cost can be significantly reduced. The concept of base isolation had been controversial

for a long time but has been gradually accepted by many countries. Several types of

isolation systems have been put into use and various isolation devices have been invented

by structural engineers.

Briefly, a base isolation system is formed by interposing a soft layer whose horizontal

stiffness is much lower than that of the structure. Therefore, when built on top of a base

isolation system, the building obtains a fundamental frequency much lower than its fixed-

base frequency and, consequently, lower than the predominant frequencies of the

earthquake. Thus, the first dynamic mode of the isolated building involves the

deformation only in the isolation system, leaving the structure above remaining almost

rigid. Higher modes which will produce deformation in the structure are orthogonal to

the first mode and thus to the ground motion. As a result, these higher modes usually have

low participation factors so that if there is high energy in the ground motion at the higher

mode frequencies, the energy cannot be transmitted into the structure. In this way, the

Introduction

3

base isolation system cuts off the energy transmission path and protects the building from

earthquake damage.

Such a simple but effective working principle makes ‘isolation’ a very attractive approach

to protect important buildings housing expensive and sensitive equipment and it is no

surprise that the technology has been applied to infrastructures such as hospitals,

computer centres, and so on. The mechanism of the isolation system is independent from

damping, although some damping is beneficial to suppress resonance due to long-period

motion at the frequency of the isolation system, but damping at a high level is not

favorable in isolation systems for coupling issues in that high levels of energy dissipation

lead to smaller displacements at the isolation system but higher accelerations in the

superstructure (Kelly 1999; Narasimhan et al. 2006; Ramallo, Johnson & Spencer Jr

2002).

However, while the use of the base isolation techniques has achieved significant success

in reducing the structural damage to buildings from earthquake attacks for several

decades, there are still some constraints in the practical implementation remaining,

including large relative displacements at the isolation level and the possibility of uplift of

the isolators under severe earthquakes. Moreover, traditional passive base isolation

systems are also proven to be vulnerable when facing unpredictable and versatile

earthquakes because, once implemented, the parameters of the passive base isolation

system may never be changed, which leaves the building in great danger when an

undesignated earthquake attacks the building.

A great number of researchers have been dedicated to the resolution of this issue and

many of them have proposed innovative designs. Among them, the so-called hybrid

control base isolation system, a combination of passive base isolator with active or semi-

active damping devices, is the most attractive one (Saaed et al. 2015). Spencer, Johnson

& Ramallo (2000) discussed a base isolation system using hypothetical “smart” dampers

that can adapt to and protect against seismic excitation of different characteristics and

Introduction

4

tested a family of controllers for the smart damper to find the optimal isolation system

over the suite of ground motions considered. Following this research, Yoshioka, Ramallo

& Spencer Jr (2002) further analysed the “smart” base isolation strategy employing a

sponge-type magnetorheological damper as a smart damper in the system. The

effectiveness of the proposed smart base isolation system is demonstrated for both far-

field and near-field earthquake excitations. In order to further understand the

characteristics of a hybrid base isolation system, Li & Ou (2006) comprehensively studied

the hybrid isolation systems comprising mainly a base isolation system and semi-active

dampers or active controllers and analysed the control force and the active controllers’

characteristics. Lin, Roschke & Loh (2007) developed a hybrid base isolation system with

a magneto-rheological (MR) damper and applied fuzzy control algorithm to the system.

Kim et al. (2006) designed a Neuro-fuzzy model of hybrid isolation system by integrating

a passive base isolation system, FPS bearings and MR dampers. Such a system proved

effective by extensive simulation and experimental testing. In recent years, such hybrid

isolation systems have drawn increasing attention as an option for a seismic protection

strategy.

Nevertheless, incorporating a passive base isolation system with complementary

damping, no matter passive, active or semi-active, doesn’t change the inherent passive

nature of the isolator. In other words, such a system is incapable of changing the stiffness

of base isolator and thus the fundamental frequency of the structure to isolate earthquake

energy at different frequencies. Additionally, extra damping has drawbacks in

transmitting energy at high modes into the superstructure, and augmenting dampers also

brings about problems such as low cost-efficiency and dubious reliability and

sustainability. Therefore, a novel base isolation system, whose lateral stiffness can be

easily controlled in a real-time fashion, is highly desired to endow the structure with the

ability to instantly decouple earthquake excitation at any time instant. However, due to

the lack of the required adaptive stiffness structural element, such an idea was not

Introduction

5

explored.

In this regard, a smart material named magneto-rheological elastomer (MRE) became

rather appealing owing to its feature of controllable shear modulus subject to different

applied magnetic field. Inspired by the uniqueness of the material, several MRE vibration

or seismic isolators have been proposed (Li et al. 2014), among which the highly

adjustable MRE base isolator has drawn considerate attention in the area. Li, Li, Li, et al.

(2013) designed and manufactured a full-scale device with laminated MRE layers and

steel plates by imitating the classic laminated rubber bearing. In order to improve the

performance of the MRE isolator, i.e. compose it with a large range of stiffness increase

under limited applied magnetic field, researchers improved the design by employing a

new MRE material and ameliorating the manufacturing process. Results of experimental

testing indicate that this novel MRE base isolator exhibits satisfactory performance with

a considerable increase of stiffness under applied magnetic field. In order to fully exploit

the special properties of the MRE base isolation, innovative control system especially

designed for the adaptive base isolator is urgently needed. Moreover, comprehensive

experimental testing on a MRE base isolated structure has yet to be conducted for a

convincing demonstration of the effectiveness and versatility of the seismic protection

strategy under various seismic activities.

As discussed earlier, the emergence of the MRE base isolator has provided a completely

different angle to address the aforementioned issues associated with passive and hybrid

base isolation systems. Hence, this research is dedicated to the experimental proof-the-

concept and realisation of the MRE base isolation system as a proactive exploration of

the application of the MRE base isolation system in the real world. To this end, several

obstacles need to be overcame in this research, i.e. i) acquire precise models of MRE

isolator which depict the forward and inverse dynamics of the device with high accuracy

and computational efficiency as the premise of control system development; ii) establish

the MRE base isolation system, which includes design and identification of the primary

Introduction

6

testing structure and inauguration of optimal experimental setup; iii) develop appropriate

control strategies to take the most advantage of the MRE base isolation system.

The characterisation of the MRE base isolator has to be firstly completed to enable the

precise description of both forward and inverse dynamics of the device. The forward

modelling of base isolator requires accurate recurrence of generated force, reasonable

computational complexity and versatility under a wide range of random external inputs.

In the semi-active control of the proposed isolation system, it is not enough to merely

grasp the forward model of the MRE isolator, the reason being semi-active control

utilising classic optimal control methods such as LQR, LQG and sliding mode control,

calculates desired control force and emulates the real system to an idealised reference

system and control current command is required for an MRE isolator to generate the

calculated control force. Hence, MRE base isolation systems adopting such control

algorithms typically have two controllers, i.e. i) a primary controller which computes the

desired control force required for given conditions; ii) an MRE base isolator

voltage/current controller which regulates the MRE base isolator to produce the control

force calculated by the first controller. To this end, an inverse model which can describe

the correlation between input current and desired control force as well as the system

feedback information is of great interest.

Another critical factor influencing the performance of the control system is the time delay

in the entire system. Studies have demonstrated that the current response time of the MRE

isolator when subjected to varying control commands contributes to most of the time

delay in the system. Hence, the investigation of the causes for the excessive response time

and approaches to minimise it are also required. Moreover, the design and optimisation

of the experimental system deserves comprehensive research, which includes the primary

testing structure design, input excitation selection, data acquisition system setup,

feedback signal transmission and processing.

Most importantly, due to the distinctive working principle of the base isolation system,

Introduction

7

innovative control algorithms need to be developed so as to exploit the uniqueness of the

MRE base isolator. In the development of control strategies, the high nonlinearity and

hysteresis of the MRE isolator need to be accommodated or offset by the algorithm. For

instance, fuzzy logic control is famous for high tolerance of uncertainty in the system so

it can be a suitable candidate in the control of the proposed system. Moreover, the control

system can also be proposed by combining a classic optimal controller like LQR with the

inverse model discussed previously to counterweigh the nonlinearity of the isolator. More

control strategies can also be explored by investigating the system stability with

Lyapunov function. Furthermore, since the working principle of MRE isolator is to

deflect earthquake energy by shifting natural frequency of the isolated structure, a novel

control algorithm can be developed by adjusting the stiffness of MRE isolator and thus

the structural frequency to maintain the isolated structure at a non-resonance state at any

time instant.

Subsequently, other innovations employing MRE base isolator for structural vibration

control is also a topic worth looking into, such as storey isolation system or segmental

structures with smart isolations. In this type of control, optimisation of structure is another

issue which has an important effect on structural control performance. In structural

control, the type, location and number of active/semi-active control devices should first

be optimally determined for the building. As a result, the optimised control signals are

sent to the control devices to change their parameters to achieve beneficial control forces

by which the maximum building response reduction can be achieved. This way of

designing helps to decrease the amount of load on the members and protect them from

damage.

Advances in the aforementioned areas can provide a platform for the next generation of

smart structures where structural control is integrated with an intelligent adjustable base

Introduction

8

isolation system.

1.2 OBJECTIVE OF THE PRESENT RESEARCH

This research aims at developing and investigating an innovative adaptive base isolation

system utilising MRE material to meet the challenge in traditional base isolation system.

To achieve this goal, characterisation and modelling of the MRE isolator will firstly be

conducted. Experimental investigation of smart MRE base isolation systems will then be

established utilising different control algorithms. The seismic protection performance

will be evaluated numerically and experimentally with comprehensive shake table testing.

Finally, innovative application of the MRE isolator on other seismic protection strategy

will be proposed

Specifically, the objectives of this research are as follows:

1) To develop novel parametric forward models (e.g. Bouc-Wen Model, strain-

stiffening model) and non-parametric inverse model to describe the field-

dependent nonlinear hysteretic characteristics of the MRE seismic isolator in

both forward and inverse fashion.

2) To investigate the current and force response time of the MRE isolator and

explore practical approaches to minimise the response time for better control

performance.

3) To design and manufacture the primary structure as the testing bed of the MRE

base isolation system and obtain the identification of designated testing structure,

MRE isolator and integrated MRE base isolation system

4) To develop various control algorithms for smart base isolation system employing

MRE base isolator to realise the real-time control of the isolation system.

5) To conduct investigation of the robustness and seismic protection performance

of the proposed control method and system with numerical and experimental

examinations.

Introduction

9

6) To propose an innovative storey isolation system employing the MRE base

isolators and to compare the seismic protection performance of the bare building,

passive base-isolated building, passive storey-isolated building, optimised

storey-isolated building and controlled storey-isolated building.

1.3 ORGANISATION OF THIS THESIS

This thesis has been organised into seven chapters. The introduction, motivation and

innovation of this research are presented in the current chapter. It is worth pointing out

that, since the current dissertation is a multi-disciplinary study, besides Chapter 2 which

presents the literature review governing the whole research, the literature review relevant

to each discipline area is conducted and provided in the corresponding chapter. Hence,

the overviews of the other six chapters are as follows.

Chapter 2 presents a comprehensive literature review of previous research work with

emphasis on the evolution of the base isolation system using different base isolation

devices, its advantages and drawbacks as well as the urgent problems facing the

traditional passive base isolation system. Meanwhile, a detailed review about the present

“smart” base isolation, which combines a passive isolator with active or semi-active

damping devices, is also included in this chapter to explore the possibility of using

existing control algorithms for smart base isolation systems and potential innovative

control methods derived from all the previous research achievements. Next, a brief

description about MRE material and a state-of-art review of the isolation devices utilising

the material are affirmed. In the end, the challenges and research gap at present are

summarised, serving as the basis of the research presented in the following chapters

Chapter 3 proposes two innovative models to describe the forward dynamics of MRE

isolator invented by Li et al. (2013a) and one novel non-parametric model for inverse

dynamic characteristics based on neural network. This chapter starts from a briefing of

the smart rubber named MRE and the preparation of the soft MRE material adopted in

Introduction

10

this study. Following the description of the material is the design and characterisation of

the MRE base isolator. Next, two parametric models, namely, Bouc-Wen model and

strain-stiffening model, are proposed and analysed to capture the forward dynamic

properties of the device. The two models are then compared in regard to the model

complexity, prediction accuracy and identification running time. Following the forward

modelling, an inverse model of MRE base isolator is developed based on general

regression neural network (GRNN). The non-parametric model is trained by the fruit fly

optimisation algorithm (FOA) for robust performance.

Chapter 4 investigates the current- and force- response time of the MRE isolator. The gap

of recognition of response time delay caused by the MRE isolator device itself in existing

research is firstly stated. Then, the response time in MRE base isolator is defined and

quantified experimentally. Finally, feasible approaches to reduce the response time have

been explored so as to provide the possibility for the realisation of real-time control based

on the MRE isolators.

Chapter 5 systematically expounds the experimental realisation and evaluation of the

MRE base isolation system. The design of a three-storey building model with a

fundamental frequency of 1.913Hz is firstly presented as the primary testing structure.

The identification of the three-storey building, MRE base isolator and the integrated smart

base isolation system was then conducted. To prove the versatility of the proposed smart

isolation system, four benchmark earthquakes, El Centro 1940, Hachinohe 1968, Kobe

1995 and Northridge 1994, are adopted as the ground motion, among which El Centro

and Hachinohe records represent far-fault earthquakes while Kobe (Sylmar) and

Northridge records stand for near-fault earthquakes. A shake table is employed to

regenerate the earthquake acceleration records without distortion. The seismic protection

performance of the proposed MRE base isolation system has been demonstrated through

a comparative case study of fixed base building, passive-on and passive-off base isolation

system, MRE base isolation system with diverse controllers, i.e. Bang-Bang control, LQR

Introduction

11

control with GRNN inverse model, neural fuzzy logic controller, frequency controller

and Lyapunov-based current controller.

Chapter 6 proposes an innovative storey isolation system employing MRE isolators for

seismic protection. The stiffness of each level in the proposed isolation system can thus

be changed according to characteristics of the MRE isolators. Non-dominated sorting

genetic algorithm type II (NSGA-II) with dynamic crowding distance (DCD) is utilised

for the optimisation of the parameters at isolation level in the system. To control the storey

isolation system, a Bang-Bang controller is utilised at each isolation level. Extensive

comparative simulation study is then conducted using a 5-storey benchmark model to

evaluate the performance of the proposed isolation system under different earthquake

excitations. Simulation studies compare the seismic responses of bare building, building

with passive controlled MRE base isolation system, building with passive-controlled

MRE storey isolation system, building with optimised storey isolation system and

building with controlled storey isolation system.

Chapter 7 summarises the contents of all the chapters together with concluding remarks.

Some future works are also suggested in this chapter.

Literature Review

12

CHAPTER 2

LITERATURE REVIEW

2.1 PREFACE

Since the dawn of history, earthquakes have claimed the lives of thousands of people and

led to huge loss of property, leaving the survivors grieve-stricken. Utilising advanced

science and technology to fight against the power of nature and save lives from natural

disasters has always been the main motivation impelling structural researchers all around

the world. Over the years, many aseismic construction designs and technologies have

been developed in attempts to protect civil infrastructures from the devastating effects

caused by earthquakes, which have given rise to base isolation or seismic isolation, the

most widely recognised and adopted seismic protection strategy for civil infrastructures.

Essentially, a seismic isolation system works by a principle to decouple the structure and

its contents from damaging ground or support motions induced by earthquakes. The

decoupling is achieved by increasing the flexibility of the isolation system. Since most of

the seismic isolation systems are mounted under the superstructure, this seismic

protection strategy is referred to as base isolation system.

However, despite being the most mature and accepted seismic protection strategy, the

traditional base isolation system is still faced with some serious challenges. Among all

the challenges, lack of adaptability required to deal with the diversity and unpredictability

of earthquakes is on the top of the list (Narasimhan et al. 2006). In other words, the

conventional base isolation system with its passive nature is rather vulnerable when

facing the unpredictable and diverse nature of earthquakes. That is to say, once designed

Literature Review

13

and installed, the passive base isolation system is incapable of adjusting its own properties

to cope with the changes of either the structure or the earthquake (Spencer Jr &

Nagarajaiah 2003). More discussions on challenges faced in current research and practice

of base isolation will be elaborated in the following sections. To address the challenges,

researchers have been looking into means to provide adaptability to the system, i.e.

development of intellectual structure or “smart” base isolation systems in the scope of

structural control.

In this chapter, a comprehensive literature review will be presented to depict the origin,

development and application of the base isolation system, followed by a detailed

summary of conventional base isolation devices and previously reported research on

various types of “smart” base isolation systems which have been categorised as hybrid

base isolation systems to differentiate them from the new stiffness controllable base

isolation systems. Next, a state-of-art of the base isolators with controllable stiffness

utilising magneto-rheological elastomer (MRE) is elaborated as well as the control

applications of the MRE base isolators. The emphasis is laid on three aspects: (1) the

inherent disadvantages of and challenges faced by conventional base isolation devices

despite of their popularity in engineering practice for seismic protection; (2) the inherent

shortcoming in the hybrid isolation system that combines a passive isolation system with

either active or semi-active supplementary dampers; (3) the reasons that enable a smart

base isolation system with controllable stiffness to be a superior solution in addressing

the challenges confronted with present base isolation systems. Finally, the gaps and

challenges between the present research and practical implementation of the real-time

Literature Review

14

controlled smart base isolation system are articulated and discussed.

2.2 STATE-OF-ART OF THE CONVENTIONAL BASE ISOLATION

2.2.1 Working principle of base isolation

The working principle of a base isolation system for seismic protection can be explained

in a simple term, i.e. “decouple”. The base isolation system decouples the building or

structural elements from lateral movement of the ground motion by interposing isolators

with low lateral stiffness between the structure and its foundation. The low lateral

stiffness of the isolators helps to shift (or lower) the overall fundamental frequency of the

isolated structure outside the predominant frequencies of the ground motion, which

results in “decoupling” of the superstructure and ground motions. The first dynamic mode

of the isolated structure involves deformation only at the isolation level, while the rest of

the structure, to all intents and purposes, is kept relatively rigid. The higher modes of

vibration, however, are orthogonal to the first mode and, consequently, to the ground

motion. These higher modes have less participation in the vibration of the structure, so

that the energy in the ground motion with the higher frequencies are less likely to be

transmitted into the structure. As a matter of fact, the isolation system does not absorb the

earthquake energy, but deflects it through the dynamics of the system. This effect does

not depend on damping, but a certain level of damping is beneficial to suppress

displacement responses to some extent.

2.2.2 History and Development of Base Isolation

Frank Lloyd Wright was the first person known to apply the base isolation system on a

real structure with his design of the Imperial Hotel completed in Tokyo in 1921 (Kelly

1985). This design was extremely controversial since it was in complete contrast to any

accepted practice at that time. When looking at the construction site, Wright discovered

Literature Review

15

there were 8 layers of fairly good soil and a layer of soft mud beneath that, which has

appeared to Wright as “a good cushion to relieve the terrible shocks. Why not float the

building on it” (Kelly 1986). He tied the building to the upper layer of the good soil by

closely penetrating the short piles as far as the top of the soft mud. The building’s

extremely good performance in the devastating 1923 Tokyo earthquake dispelled all the

doubts and has drawn people’s attention to the intuitive idea of floating the building, as

“a battleship floats on the ocean”. Though this building was a highly decorated building

with appendages of many kinds, which usually gets badly damaged in earthquakes, the

only damage to the building was to statuary in the courtyard of the hotel (Reitherman

1980).

However, the fortuitous layers of soft mud are unlikely to happen to appear at every

construction site, other ways to produce an “artificial soft mud” are to be sought by

engineers. In the late twenties and thirties, the concept of the flexible first storey was

proposed by structural engineers (Green 1935; Jacobsen 1938). In this approach, the

lateral stiffness of the columns of the first storey would be designed to be much lower

than that of the columns above, which will concentrate the deformation in these first-

storey columns under earthquake loadings. However, to be effective in reducing

accelerations at the upper level, the displacements in the first-storey columns would be

quite large, and the effect of vertical load could produce severe damage to the columns

on this sideways movement of the columns. To modify the approach, a soft first-storey

method (Fintel & Khan 1969) was proposed to so the first storey columns would yield

during an earthquake to produce an energy-absorbing action and control the

displacements. Nevertheless, the displacements would still need to be several inches to

produce enough damping and a yielded column greatly reduces the buckling load

capacity, which would lead to column instability and building collapse (Chopra, Clough

& Clough 1972).

While the soft storey can protect the upper level, the price of potential destruction of the

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first- level columns will arise. Therefore, an continuing search for a mechanism that can

overcome the dilemma has been carried out and many types of roller bearing systems

have been proposed, patented and tested on the top of it (Ryuiti 1941). Since the ground

movement can be in any direction, it is necessary to use spherical bearings or two crossed

layers of rollers. These kinds of rollers are very low in damping and have no inherent

resistance to wind. As a result, other mechanisms which provide wind restraint and

energy-absorbing capacity are needed. Meanwhile, the possibility of a permanent offset

after an earthquake also exists since there are no restoring forces. When pressed against

the steel for a long time, steel will face the possibility of cold welding which would result

in the system becoming rigid after some time, which will affect the lifespan and reliability

of the system.

The first use of rubber for earthquake protection was in an elementary school in Skopje,

Yugoslavia (Seigenthaler 1970). The building was a three-storey structure in concrete and

was completed in 1969. It rests on large blocks of natural rubber. Unlike more recent

rubber bearings, these blocks were completely unreinforced so that the weight of the

building easily caused the sway of the structure. The vertical stiffness of the system is

about the same as the horizontal one so that the building will bounce and rock backwards

and forwards during an earthquake. This method is unlikely to be used again thanks to

the development of reinforcing rubber blocks with steel plates.

The development of multilayer elastomeric bearings is a milestone in the history of base

isolation, which makes the century-old concept practicable and opens up new possibilities

for design and application (Derham & Plunkett 1976). The concept of seismic isolation

has become a practical reality within the last 20 years with the development of these kinds

of bearings, which are made by vulcanisation bondings of sheets of rubber to thin steel

reinforcing plates. With the steel plates, these bearings can be very stiff in the vertical

direction and are able to carry the vertical load of the building. In the horizontal direction,

they are very flexible due to the rubber plates, thereby enabling the building to move

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laterally under strong ground motion and concentrating the deformation in the bearings.

2.2.3 Contemporary Base Isolation Devices

After the decades of early trials and developments, practical and reliable contemporary

base isolation systems have been gradually formed and matured. The milestone of modern

seismic isolation technique is the invention and application of laminated rubber bearing

and polythene friction plates. Various base isolation devices have been developed and put

into service since then thanks to researchers and engineers’ persistent endeavours (Patil

& Reddy 2012). Representative isolators will be introduced in the following sections.

2.2.3.1 Laminated rubber bearing

Figure 2.1 Laminated rubber bearing: (a) composite and sectional details; (b) schematic diagram

As mentioned, one of the early stage uses of base isolation is to insert a rubber layer under

the structure to provide relatively low horizontal stiffness. Such attempts have

encountered the issue of a lack of vertical capacity, which is critical in civil engineering

practice. To resolve this issue, the laminated rubber bearing was invented and came into

service. Laminated rubber bearings were initially used to provide vibration isolation for

apartment blocks, hospitals and concert halls built over subway lines or mainline

railroads. In 1975, Derham suggested that such bearings could be used to protect

buildings from earthquake ground motions (Derham & Plunkett 1976) and since then,

intensive research on the LRBs has continued worldwide.

As shown in Figure 2.1(a), two thick steel endplates are installed to the bottom and top

m

Top plate

Laminated rubber and steel sheets

Bottom plate

(a) (b)

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surface of the laminated rubber bearings, ensuring that the isolator is firmly connected to

the foundation below and the superstructure above. Thin steel shims and rubber sheets

are vulcanised and bonded together to form a sandwich structure under pressure and heat.

Inner thin steel plates can provide vertical load capacity and stiffness and prevent the

lateral bulging of the rubber. Particularly, the steel plates laterally constrain the rubber

sheets when a vertical load is applied to the elastomeric bearings, providing the vertical

stiffness. Horizontal flexibility is achieved by the shearing deformability of the rubber

sheets in between every two steel plates. In other words, due to its unique structure, LRB

possesses both horizontal flexibility and high vertical stiffness with a restoring force as

well. Tests also have shown that the mechanical properties of LRB are generally not

influenced by temperature, aging and rate of history of loading (Komodromos & Stiemer

2001). As can be seen in Figure 2.1(b), a LRB can be modelled as a pair of parallel

connected spring and dashpot.

A number of advantages of LBR have been observed, such as effective isolation

performance, stable characteristics over a long working life, capability of deformation

recovery aftershock; good vertical tension and compression capacity. However, the low

damping provided by the rubber may lead to excessive base displacement (Ramallo,

Johnson & Spencer Jr 2002). Generally, the damping provided by LRB ranges between

2% to 3% at 100% shear strain. Extreme base displacement is the root of instability and

even the overturning of the structure.

2.2.3.2 High Damping Rubber Bearing (HDRB)

To overcome the low damping issue of LRB, the high damper rubber bearing (HDRB) is

then developed by substituting the ordinary elastomer sheets in LRB with high damping

rubbers. High-damping rubber is a filled rubber compound with inherent damping

properties due to the additional special fillings, such as carbon and resins (Hwang & Ku

1997). Experimental studies of the property of HDRBs (Naeim & Kelly 1999) have

verified the anticipated energy dissipation capacity, which is, typically, equivalent to

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about 15% damping ratio of equivalent linear elastic models. However, HDRB may not

provide the necessary initial rigidity under service loads and minor lateral loads, although

some initial rigidity is provided by high-damping rubber compounds which exhibit higher

stiffness under small strains. A structure isolated with such bearings has a constant, large

fundamental period due to the flexibility of the isolation system, which makes the

structure vulnerable to wind action with dominant frequencies close to the fundamental

frequency. In other words, HDRB may experience stability problems when very large

horizontal displacements happen, durability problems of some rubber materials, and

excess deformation at the serviceability limit state (Mazzolani 2001). In addition, HDRB

subjected to cyclic loading dissipates energy in the form of heat, which means the

damping and mechanical properties of the HDRB appear to be temperature dependent

due to the material sensitivity to temperature changes (Abrishambaf & Ozay 2010).

2.2.3.3 New Zealand (NZ) Rubber Bearing (Lead Core Rubber Bearing)

Another device adding initial stiffness and supplementary damping on the basis of LRB

is a lead core rubber bearing which was invented in New Zealand in 1975 (Robinson

1982). It is also named as New Zealand rubber bearing (NZRB) and has been adopted

widely in New Zealand, Japan and the United States. The composition of NZRB is similar

to LRB featuring laminated rubber and steel structure except for containing one or more

lead plugs inserted into holes in the middle of the rubber bearing, as shown in Figure 2.2

(a). The steel plates in the bearing force the lead plug to deform in shear. The lead core

must fit tightly in the laminated bearing, which is achieved by forcing a lead plug slightly

larger in diameter into the hole.

Lead is a crystalline material whose structure can be changed temporarily under

deformations beyond its yield point and regained as soon as the deformation is removed

by the restoring force in the rubber. As the lead deforms plastically in shear by being

forced by the steel plates, once it has exceeded its yield stress, the energy inside will be

dissipated significantly. Therefore, the presence of the lead core reduces displacement of

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the isolator and the isolator essentially works as a hysteretic damper device, which can

be observed in Figure 2.2 (b).

Figure 2.2 Lead core rubber bearing (New Zealand rubber bearing): (a) composite and sectional details; (b) schematic diagram

The lead rubber bearing system is easy to install, manufacture, analyse and design.

Furthermore, the lead plug reduces the displacement of the structure, produces an increase

in damping, from 3% critical damping to about 10-15% and also increases the resistance

to wind load. Thanks to the advantages of NZRB, it is possibly the cheapest solution to

the problems of base isolation in that the one unit supports the base-isolated structure,

provides an elastic restoring force and also, by the selection of the appropriate size of lead

plug, produces the required amount of damping (Robinson & Tucker 1981). Nevertheless,

the non-linearity brought by the lead plug deformations, although providing damping,

may also induce resonances in higher modes of the structure. The continuous sudden

changes of stiffness of LCRBs may excite higher model responses, lowering the

anticipated reductions of the accelerations of the structural masses. Moreover, damages

to the lead core in the NZ rubber bearing after extreme displacement cannot be detected

from outside and thus may affect after-shock serviceability.

2.2.3.4 Pure Friction (PF) base isolation system

Another category of base isolation devices is sliding bearings, which utilise the friction

between sliding surfaces to dissipate energy and hence protect the superstructure. As a

matter of fact, the earliest and simplest sliding base isolation system is pure-friction (PF)

m

Top plate

Laminated rubber and steel sheets

Lead plug

Bottom plate

(a) (b)

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base isolation. As can be seen from Figure 2.3, a typical PF type base isolator consists of

developing a frictional force by providing a sand layer or rollers at the base, which will

dissipate the energy of earthquake force. The system is developed in China for low-rise

structures. The system is useful for a wide range of frequency input (Patil & Reddy 2012).

The cost of the PF system is very low and it can be utilised in a wide range of sites.

Another merit is that it is effective for a wide range of frequency, and the torsional effects

by the asymmetric building can be diminished. However, the main disadvantage is that it

is unable to recover from excitation and is sensitive to foundation settlement due to lack

of restoring force, which is a common issue faced by most sliding bearings. Hence, a PF

base isolation system may suffer from large sliding and residual displacement due to

geometry of the sliding surface.

Figure 2.3 Pure friction (PF) bearing: (a) composite and sectional details; (b) schematic diagram

2.2.3.5 Electricite de-France (EDF) system

Based on the pure friction bearings, another friction type base isolator has been developed

under the auspices of Electricite de-France (EDF) and hence is named as EDF base

isolation system. This system is standardized for nuclear power plants in regions of high

seismicity and is constructed by the French company Framatome (Su, Ahmadi &

Tadjbakhsh 1989). The schematic diagram of an EDF isolator is shown in Figure 2.4. As

can be observed, the EDF isolator consists of a steel reinforced laminated Neoprene pad

which provides horizontal flexibility as the laminated rubber structure in LRB and a lead-

bronze plate in between the Neoprene pad and a steel plate anchored to the superstructure.

The lead-bronze plate is in frictional contact with the steel plate and the frictional relative

m

Polished surface interface

(a) (b)

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movement on the sliding surface can serve as energy dissipation when the

superstructure’s displacement is too large. The friction surfaces are designed to have a

coefficient of friction of μ = 0.2 during the service life of the base isolation system.

Figure 2.4 EDF base isolation system: (a) composite and sectional details; (b) schematic

diagram

It can be seen from the schematic diagram in Figure 2.4 (b) that the EDF base isolator

essentially uses an elastomeric bearing and friction plate in series. By doing so, the EDF

is endowed with merits of both types of isolators in that when lower amplitude ground

motion strikes, the Neoprene pad provides the horizontal flexibility and when the seismic

excitation gets higher, sliding occurs at the lead-bronze frictional surface and provides

extra protection for the structure, which is counted as a double safety mechanism (Fan &

Ahmadi 1990). It is also claimed that the EDF system guarantees a maximum acceleration

transmissibility of μg (Gueraud et al. 1985). Thus, the power plant and its contents may

be designed on that basis. However, owing to the presence of the frictional surface, it is

inevitable for the EDF system to have the issue of potential permanent displacement after

drastic ground excitation since it lacks a restoring force.

2.2.3.6 Resilient Friction Base Isolation (R-FBI) System

Mostaghel et al. have proposed a base isolation system named resilient friction base

isolator (R-FBI) composed of layers of sliding elements with rubber cores (Mostaghel,

Hejazi & Khodaverdian 1986; Mostaghel & Khodaverdian 1987). The sectional view and

schematic diagram of R-FBI are illustrated in Figure 2.5. As shown, the R-FBI consists

mSteel reinforced laminated

Neoprene pad

Sliding surface

Steel plate

Lead-bronze plate

(a) (b)

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of a series of flat rings which can slide on each other and a central rubber core and several

peripheral rubber cores implemented in the flat rings. A soft rubber cover is mounted

around the sliding rings to protect them from dust and corrosion. To reduce the friction,

the sliding rings are Teflon coated.

Figure 2.5 Resilient friction base isolation (R-FBI) system: (a) composite and sectional details

(Mostaghel 1987); (b) schematic diagram

As shown by the schematic diagram, the system possesses parallel actions of friction,

damping and restoring spring forces. The friction comes from sliding elements, which is

the major energy dissipater in the device, while the rubber cores distributes the horizontal

displacement and velocity along height of the isolator. To this end, the R-FBI system is a

combination of elastomeric bearing and sliding isolator on a firm sense. Meanwhile, since

the vertical loading is all carried by the sliding plates, the rubber cores do not share any

vertical loading, which ensures the rigidity in the vertical direction. Moreover, the sliding

movement is restrained by the rubber cores, which provide a certain level of restoring

force and hence prevents residual deformation of the isolator to some extent. The

variation of the vertical load is of much higher frequencies as compared to the horizontal

load. This should lead to a high degree of decoupling between horizontal and vertical

responses. However, when the ground motion is too vigorous, the rubber will be damaged

and thus R-FBI is still not a complete resolution for permanent displacement. Also,

according to Muscolino, Pirrotta & Ricciardi (1997), R-FBI provides less cantering force

m

1. Top cover plate Top connecting plate

Rubber cover

Central rubber core

Peripheral rubber cores

Bottom cover plateBottom connecting plate

Sliding rings

(a) (b)

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compared to LRB.

2.2.3.7 Sliding Resilient Friction (S-RF) Base Isolation

Combining the desirable features of EDF system and R-FBI system, a base isolator named

sliding resilient friction (S-RF) base isolator is proposed (Su, Ahmadi & Tadjbakhsh

1989). In the S-RF base isolator, the Neoprene pads of EDF system are replaced by an R-

FBI. To put in another way, the upper surface of R-FBI is substituted by a friction plate

as shown in Figure 2.6.

With such arrangement, the S-RF base isolation system is also a double safe mechanism

similar to EDF: the device behaves in the manner of a R-FBI when the seismic excitation

is at a relatively low level; only when a very high level of ground motion strikes the site,

the sliding will happen at the top level of the isolator and will provide extra protection.

Despite all the advantages, as explained previously, the S-RF system still has permanent

displacement in the sliding layer due to the introduction of the frictional layer.

Figure 2.6 Sliding resilient friction base isolation (S-RF) system: (a) composite and sectional

details; (b) schematic diagram

2.2.3.8 Friction Pendulum System (FPS)

So far, all the friction type or sliding type base isolators are suffering from the residual

permanent deformation due to the lack of restoring force. To resolve this issue, the friction

pendulum base isolator has been come up with and intensive investigations have been

conducted on the friction pendulum system (FPS). Traditionally, the FPS consists of a

m

1.

R-FBI unit

Friction plates

(a) (b)

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spherical stainless steel surface and a slider, covered by a Teflon-based composite

material. During ground motion, the slider moves on the spherical surface lifting the

structure and dissipating energy by friction between the spherical surface and the slider,

as shown in Figure 2.7. As an advanced version of the PF system which overcomes the

main drawback of non-restoring force, the response characteristics of the FPS are

influenced by the curvature of the spherical sliding surface and vertical loading on the

bearing (Jangid 2005). Therefore, the frequency ratio is then determined by the radius or

shape of the sliding surface’s curvature, which leads to the inadaptability to diverse types

of earthquakes.

Figure 2.7 Friction pendulum base isolator: (a) external view; (b) composite and sectional

details; (c) schematic diagram

To resolve this issue, researchers have focused on the development of FPS with variable

frequency, such as with variable frequency pendulum isolators (Pranesh & Sinha 2000),

variable curvature pendulum systems (Tsai, Chiang & Chen 2003), double concave

friction pendulum system (Fenz & Constantinou 2006), triple friction pendulum bearing

(Fenz & Constantinou 2008). Nevertheless, despite possessing multiple frequencies or

curvatures, the passive FPS cannot cover the entire seismic frequency range, leading to

vulnerability of an isolated structure confronted with unpredictable earthquakes.

2.2.3.9 Other types of base isolators

Besides the classical categories of base isolations, i.e. elastomeric bearing and sliding

bearings, a diversity of base isolations has been invented and put in service thanks to

mInner slider

Articulated slider

Top plate

Articulated sliderBottom plate

(a) (b) (c)

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researchers’ unremitting efforts. Five types of isolators, namely, spring type system,

sleeved pile isolation system, rocking system, BS cushion, isolation using geo-synthetic

materials, will be briefly introduced as following.

The spring isolation system is composed of springs which are flexible in both horizontal

and vertical directions, where vertical frequency is normally between three and five times

the horizontal frequency. Hence, the spring type isolators are widely used when three-

dimensional isolation is required.

The sleeved pile isolation system is suitable for the soft soil condition which has large

depths and where provision of pile foundation is necessary. The system consists of a

casing around the pile and a gap maintained between the pile and the casing so as to sway

the structure under earthquake. This system was implemented in the Union house in

Auckland, New Zealand in the year 1983 (Kelly 1990).

The rocking system, although it is not a usual usage of base isolation technique, is suitable

for the slender structures that may develop overturning moments and tensions in the

foundations. The rocking system allows lifting force of columns or walls from the

foundation (Gelagoti et al. 2012). However, the method is not used because of the

complexities involved in analysis and design.

The BS cushion system was first patented in China (Chinese Patent Number

ZL99202381.5), which is also known as treated asphalt-fibre seismic base isolation

cushion (Patil & Reddy 2012). The advantage of the system is its low cost and safety but

the performance is moderate.

In 2004, Yegian and Kadakal presented a base isolation technique utilising a geo-

synthetic material (Yegian & Kadakal 2004), which is a high strength, non-woven

geotextile placed over an ultra-high molecular weight polyethelene (UHMWPE) liner.

The geo-synthetic material placed underneath a foundation of a structure and over a liner

allows the dissipation of earthquake energy in sliding friction.

27

Figure 2.8 Categorisation of conventional base isolation techniques

Conventional base isolation techniques

Early stage attempts

Elastomeric bearing

Sliding bearing Others

Mud layer

Flexible first storey

Roller bearing

Rubber layer

Laminated rubber bearing (LRB)

High damping rubber bearing

(HDRB)

New Zealand bearing (NZ)

Resilient-friction base isolation (R-FBI)

Pure friction (PF) bearing

Friction pendulum bearing

Electric de-France system (EDF)

Sliding resilient-friction system (S-RF)

Spring type system

Rocking system

BS cushion

Sleeved pile isolation system

Base isolation using Geo-Synthetic materials

Laminated rubber bearing (LRB)

High damping rubber bearing

(HDRB)

New Zealand bearing (NZ)

Pure friction(PF) bearing

Adding damping

Ensure vertical capacity

Combine features of elastomeric bearing and friction mechanism

Combination

Restoring force

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2.2.4 Categorisation of conventional base isolation techniques

As discussed, the base isolation techniques can be divided into the following four

categories: early stage use, elastomeric bearings, sliding bearings and other techniques.

The early stage use of base isolation, including mud layer, flexible first storey, roller

bearing and rubber layer beneath structure, is a successful exploration of this technique

and verified the feasibility of the concept. The most significant device in the elastomeric

bearing category is a laminated rubber bearing, which adds vertical capacity to the rubber

bearings and ensures the practicability of isolators in civil infrastructures. To solve the

excessive base displacement issue, HDRB and NZ rubber bearings have been proposed.

As a combination of merits of both elastomeric and PF bearings, R-FBI and EDC system

presents rather promising seismic protection effectiveness. S-RF is then proposed to

further enhance the strength of R-FBI and EDF systems. Due to the existence of a

frictional sliding surface, a permanent displacement will occur in the aforementioned

friction type isolators, which is then overcome by the invention of FPS. The

categorisation and interrelation between the isolators are shown in Figure 2.8.

2.2.5 Issues Related to Conventional Base Isolation

From the literature review of all the conventional base isolation approaches, it can be

concluded that extensive research and development on traditional base isolation system

have bred a mature and diverse collection of base isolators. Each type of isolator has been

developed based on needs in applications but also inherits shortcomings. Therefore, it is

fair to draw a conclusion as follows: practical base isolation design is achieved through

the optimisation of characteristics of the designated superstructure, type of the soil or

foundation, common earthquake witnessed by the site, etc. Such optimisation, on the

other hand, hinders the system to achieve the best isolation results in order to provide

safer and robust performance for the isolated structure. For instance, the near-fault

seismic activities, which features intense long-period velocity waves (usually with an

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amplitude of 0.5m/sec and period range between 2-4sec) (Hall et al. 1995), can be

detrimental and induce excessive displacement response in the conventionally base-

isolated structures with a period in this range (Lu & Lin 2009). One approach to allocate

large displacement is to use larger base isolators, which is quite commonly implemented

in Japan, which is effective but not economical (Kelly 1999). Another usual approach is

to use high damping isolators, i.e. high damping rubber bearing (HDRB) and NZ rubber

bearing or additional viscous dampers in the base isolation system. However, high

damping system that can cope with large displacement may cause large acceleration

response and be less effective under moderate earthquakes (Jangid & Kelly 2001). As a

matter of fact, minimising the structural acceleration and displacement is recognised as

an irreconcilable conflict, of which excessive displacement relates to structural damage

while acceleration introduces condensed damage to the non-structural elements, such as

instruments (Kelly 1990). Hence, it is beneficial if there is a type of base isolator that can

adjust itself in real time for optimal performance at any given time instant without

compromising either or both of the responses. Additionally, application of the classic

elastomeric base isolation is restricted to low- to medium-rise, more rigid buildings, as a

result of possible uplifting forces in the isolators when the superstructure is tall and

slender. The reason is, if the building is tall enough, the horizontal acceleration of floors

will produce inevitable overturing moment and thus potentially introduce a large tension

in the isolation system (Kelly, Leitmann & Soldatos 1987).

2.3 IDEAS OF “SMART” ISOLATION SYSTEM

To address the issues in the passive base isolation system, researchers started seeking

solutions from the perspective of structural control. Figure 2.9 illustrates two typical

“smart” isolation systems under extensive research. Figure 2.9 (a) shows the schematic

diagram of a hybrid isolation system combining passive base isolation with

supplementary dampers while Figure 2.9 (b) displays the smart base isolation system with

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controllable isolators, which allows direct control and changes on the properties of the

isolation components. As can be seen from the schematic diagrams, both “smart” isolation

systems employ a sensing network, signal processor and control decision unit. For an

analogy, if the structure is the human body, the sensing network provides senses of sight,

hearing and touch; the signal processor is the body’s neural network; while the control

unit serves as the brain and endows the structure with intelligence. The control effects are

applied on the structure by either supplementary dampers or isolation itself. The state-of-

the-art review, advantages and disadvantages of the two “smart” isolation systems are

introduced in the following two sections.

Figure 2.9 Schematic diagram of (a) hybrid isolation system combining passive base isolation

with supplementary dampers; (b) “smart” base isolation system with controllable isolators

2.4 PRESENT “SMART” BASE ISOLATION

As explained, most of present “smart” base isolation systems are actually a hybrid of

passive base isolation and controllable active or semi-active damping devices (Yoshioka,

Ramallo & Spencer Jr 2002). The schematic diagram of such a smart isolation system is

illustrated in Figure 2.9 (a). Normally, such isolation system should be categorised as

hybrid control system in the disciplines of structural control. According to the type or

Passive isolator

Connectingdampers

Controlcomputer

Damperdriver

Sensingsystem

Controlcomputer

Sensingsystem

Isolatordriver

Adjustable isolator

(a) (b)

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characteristic of the auxiliary device, current control of base isolation system can be

classified as active control and semi-active control.

Next, this section will introduce several typical examples of the hybrid “smart” base

isolation systems.

2.4.1 Active Base Isolation System

The active base isolation system is designed by supplementing the passive base isolation

with devices controlled by active strategies (Johnson et al. 1998). Active control strategies

have been long developed as one means by which to minimise the effects of

environmental loads such as wind load and seismic excitations (Housner, Soong & Masri

1996). Active control systems operate by using external energy supplied by actuators to

impart forces on the structure. The appropriate control action is determined based on

measurements of the structural responses.

Many active control methods and mechanisms have been adopted by structural engineers

and several active base control systems have been proposed and studied (Kelly, Leitmann

& Soldatos 1987; Reinhorn et al. 1989; Reinhorn, Soong & Wen 1987; Schmitendorf,

Jabbari & Yang 1994; Yang et al. 1996; Yoshida, Kang & Kim 1994). Reinhorn, Soong

& Wen (1987) studied the properties of structures undergoing inelastic deformations and

proposed the shape control of such kinds of structures through the use of an active

pulse/force system. Kelly, Leitmann & Soldatos (1987) proposed the use of robust control

in conjunction with base isolation to minimise the absolute displacement and velocity.

The control forces are designed to overcome only the forces which would be generated

by the isolation system at the base of the structure. Through simulations, Yoshida, Kang

& Kim (1994) investigated the use of LQG and H∞ control strategies with hybrid base

isolation systems.

Additionally, several small-scale experiments have been performed to verify the

effectiveness of these systems in reducing the structural responses. Schmitendorf, Jabbari

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& Yang (1994) proposed a robust control theory to obtain active controllers that are

suitable for practical implementation on full-scale civil structures. Control methods for

seismic-excited buildings isolated by a frictional-type sliding-isolation system are

presented by Yang et al. (1996) based on the theory of continuous sliding-mode control.

Reinhorn & Riley (1994) performed analytical and experimental studies of a small-scale

bridge with a sliding hybrid isolation system in which a control actuator was employed

between the sliding surface and the ground to supplement the base isolation system.

However, even though a large amount of analytical and experimental research has been

conducted in the last 30 years, and a number of full-scale structures in Japan have been

equipped with active control systems, there are no full-scale, active control

implementations employing base isolation systems around the world, mainly due to the

lack of real-time controllable isolation devices and some other challenges, including high

capital cost and maintenance, great reliance on external power, system reliability and

robustness and lack of acceptance of non-traditional technology.

2.4.2 Semi-active Base Isolation System

As discussed in the last section, the major challenge faced with active control is the large

requirement of external power to drive the actuators. Hence, to address the issue of energy

consumption of active control system, another type of hybrid base isolation system has

been proposed and explored by the researchers to reduce the seismic response of a

building by adding supplementary semi-active energy-dissipation or displacement control

members. In recent years, semi-active control devices have received a great deal of

attention because they offer the adaptability of active control devices without requiring

the associated large power sources. In fact, many can operate on battery power, which is

critical during seismic events when the main power source to the structure may fail.

According to presently accepted definitions, a semi-active control device is one that does

not increase the mechanical energy in the controlled system, i.e. including both the

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structure and the device, but has properties which can be dynamically varied to optimally

reduce the responses of a structural system. Therefore, in contrast to active control

devices, semi-active control devices do not have the potential to de-stabilise the structural

system. Preliminary studies indicate that appropriately implemented semi-active systems

perform significantly better than passive devices and have the potential to achieve

satisfactory performance without the cost of high energy input as fully active control

system, thus allowing the possibility of effective response reduction during a wide array

of dynamic loading conditions. Examples of such devices include variable orifice fluid

dampers, controllable friction devices, variable stiffness devices, controllable liquid

dampers and controllable fluid dampers (Ramallo, Johnson & Spencer Jr 2002; Sack &

Patten 1994; Shinozuka, Constantinou & Ghanem 1992; Symans & Constantinou 1996;

Symans & Constantinou 1999; Yoshioka, Ramallo & Spencer Jr 2002). Because all of

these semi-active devices are intrinsically nonlinear, one of the main challenges is to

develop control strategies that can optimally reduce structural responses. Various

nonlinear control strategies have been developed to take advantage of the particular

characteristics of the semi-active devices, including adaptive nonlinear control

(Kamagata & Kobori 1994), fuzzy control methods (Patten et al. 1994), bang-bang

control (McClamroch & Gavin 1995), and clipped-optimal control (Dyke et al. 1996).

Among all the semi-active dampers, the electromechanically-variable orifice hydraulic

damper and magnetorheological fluid (MRF) damper are the most popular devices and

have drawn greatest attention.

2.4.2.1 Variable Orifice Hydraulic Damper

One means of achieving a variable damping device is to use an electromechanically-

variable orifice to alter the resistance to the flow of a conventional hydraulic fluid. Hence,

the output force of the damper is controlled by the valve. A schematic of such a device is

given in Figure 2.10. The concept of applying these types of variable damping devices to

control the motion of structures experiencing seismic motion was first discussed by

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Kawashima, et al. (Kawashima, Unjoh & Shimizu 1992). Experiments were conducted

in which a hydraulic actuator with a controllable orifice was implemented in a single-lane

model bridge to dissipate the energy induced by vehicle traffic (Kuehn, Song & Sun 1999;

Neff Patten et al. 1999; Sack & Patten 1994).

This kind hydraulic damper has also been adopted in the seismic protection of building

structures. In 1998, a semi-active damping system utilising variable orifice dampers was

installed in the Kajima Shizuoka Building in Shizuoka, Japan. The hydraulic dampers are

installed inside the walls on both sides of the building serving as a disaster relief base in

post-earthquake situations (Kobori 1998; Kurata 2001). Moreover, an experimental study

of a base-isolated three-storey steel frame is presented with equipment of a variable-

orifice fluid damper system (Wongprasert & Symans 2005). Numerical simulation and

shake table experimental tests demonstrate that the proposed system demonstrates a good

protection performance for the structure.

Figure 2.10 Schematics of variable-orifice damper

2.4.2.2 Magneto-Rheological Fluid (MRF) Damper

Another popular semi-active device is a controllable fluid damper developed with

magnetorheological (MR) fluids. The essential characteristic of controllable fluids is their

ability to reversibly change from a free-flowing, linear viscous fluid to a semi-solid with

controllable yield strength in milliseconds when exposed to a magnetic field. One type of

controllable fluid damper is shown conceptually in Figure 2.11 and such dampers have

Variable-orifice valve

Load

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attracted a considerable amount of interest. One of the outstanding strengths of the MRF

damper is that it doesn’t contain any moving parts other than the piston, which assures

the simplicity in design and reliability during service. Thanks to its practical advantages,

the control and applications of the MRF damper have been intensively explored.

Figure 2.11 Schematics of a controllable MRF damper

Dyke et al. (1996) proposed a clipped-optimal control (COC) strategy on the MR fluid

damper and numerical results indicate that the proposed system can acquire significant

vibration reduction during earthquake attack. Experimental verification of the base

isolation system augmenting MR damper was conducted by Yi et al. (2001) based on a

six-storey testing structure with multiple MR dampers. Results indicate that high

performance can be achieved by the system. Yoshioka, Ramallo & Spencer Jr (2002)

carried out the experiment of intelligent base isolation system on a 2 DOF system, with

the MR damper attached on the base mass block. COC force selecting strategy with

optimal linear control algorithm was adopted and it was proven that the proposed system

could mitigate vibrational response for a wide range of excitation conditions. The seismic

protection of a “smart” base isolation system with MR dampers was also examined

numerically on a nonlinear 20-storey benchmark building by Yoshida & Dyke (2004). A

three-dimensional nonlinear dynamic analysis of a base isolation system with smart

damper was also published by Nagarajaiah & Narasimhan (2006) on an L-shaped

benchmark building. Application-wise, Fujitani et al. (2003) developed a 400kN MR

fluid damper with a stroke of 950mm, which enables the application of MRF dampers in

Load

MR fluid

Accumulator

ControllableValve

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real base-isolated buildings.

2.4.3 Issues Related to Present Hybrid Base Isolation Systems

As mentioned, all the present “smart” base isolation systems accomplish a certain level

of “smartness” in the system by adding supplementary variable damping via active or

semi-active dampers to a passive base isolation, which is recognised as a hybrid control

system. The hybrid control strategy has been proved to be effective in terms of seismic

protection throughout comprehensive numerical and experimental testings (Dyke et al.

1996; Nagarajaiah & Narasimhan 2006; Yi et al. 2001; Yoshida & Dyke 2004). However,

the role of damping in seismic isolation has been comprehensively studied by Kelly

(1999) and results demonstrate that use of supplementary dampers in seismic isolation is

a misplaced effort and will cause undesirable side effects. It is well known that damping

is able to primarily control vibration responses under the circumstances of steady-state

resonance and free vibration stage (Crandall 1970). Nevertheless, when confronted with

impact load, which is particularly featured in near-fault earthquakes, not enough time is

allowed for the damping to dissipate vibrational energy. Since the hysteresis nature of

damping is not changed, it is worth questioning whether or not the semi-active or “smart”

damping can cope with the sudden change in external load or structure. Moreover, despite

the fact that the supplementary damping may forcefully confine the base displacement of

the passive base isolation system (Inaudi & Kelly 1993), high-frequency accelerations as

well as increase of inter-storey drifts may be introduced to the superstructure by

augmenting damping (Tsai & Kelly 1993).

Hence, to achieve ideal isolation performance as well as avoid the issued brought by

augmenting additional dampers, the solution should focus on the adaptability of the base

isolator itself. To this end, the smart isolation system shown in Figure 2.9 (b) is proposed

in this study. Distinct from the hybrid isolation system, the control actions are applied on

the superstructure directly by varying the properties of the base isolation unit in real time.

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To realise this idea, the isolators in such a smart isolation system should possess

adjustable and controllable mechanical properties. The magnetorheological elastomer

(MRE) introduced in the following section has provided the possibility of such an

isolation system and the “smart” base isolation system in this thesis is developed on the

basis of the MRE base isolator. In a word, to overcome the drawbacks caused by the

inherent passive nature of the conventional base isolation system, the presently accepted

hybrid isolation system introduces control action to the system by augmenting active or

semi-active dampers to the structure. However, the supplementary dampers also bring

about some undesirable problems such as acceleration in higher modes and adding

damping does not affect the passive nature of base isolators. To this end, the proposed

“smart” base isolation system provides a solution to the problem without compromising

displacement and acceleration suppression performance by employing a property-

controllable MRE base isolator.

2.5 MRE VIBRATION ISOLATION

As mentioned, the passive isolators are usually able to achieve good performance for a

designated narrow band of excitation frequency. Nevertheless, the performance

deteriorates when external excitation frequencies are outside the designated range. The

effective range of a passive isolator is fixed based on the superstructure and design of the

isolator, which cannot adapt to changes on types of ground excitations or superstructures.

To capitalise the unique advantages of the working mechanism of a base isolation, new

type of smart base isolation endows adaptability and intelligence directly to the base

isolation itself and provides a completely different approach to address the

aforementioned issues. It can provide decoupling between the superstructure and

damaging ground motions from earthquakes by directly accustoming the stiffness of the

base isolation level in real time. In other words, the smart isolators are capable of

adjusting lateral stiffness of the isolation system in real-time to avoid transmission of the

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ground motion into the superstructure. Recently, use of magnetorheological elastomer

(MRE) in base isolation has been intensively researched and several designs have been

reported. To capture the latest development in this field, the following section will be

divided into four parts: i) a brief introduction about the MRE material; ii) MRE vibration

isolator in Mechanical engineering; iii) MRE base isolator in Civil engineering; iv)

control application of the MRE isolators.

2.5.1 Brief Description of MRE Material

The key material of the adaptive vibration isolator is a kind of intelligent rubber named

magneto-rheological elastomer (MRE), which is a class of solids consisting of a

polymeric matrix with embedded micro- or nano-sized ferromagnetic particles such as

carbonyl iron (Gong, Zhang & Zhang 2005). With such a composite microstructure, the

most prominent characteristic is the controllable rheological properties in the presence of

an external magnetic field. For instance, when applied with magnetic field, the

arrangement of ferromagnetic particles in MRE is changed hence affecting the shear

modulus of the material. In other words, since the ordered structure is embedded in its

matrix after curing, MRE materials’ mechanical, electrical and magnetism characteristics

can be controlled by the applied magnetic field. Moreover, as a solid analog of magneto-

rheological fluid (MRF), MRE possesses advantages of both magneto-rheological

material and elastomer (Guan, Dong & Ou 2008; Jolly, Carlson & Munoz 1996), such as

rapid response, good reversibility, strong controllability, etc. Meanwhile, it overcomes

the problems of sedimentation, poor stability and particle wearing of MRF (Zhou & Jiang

2004). Conventionally, matrix material, ferromagnetic particles dispersed in the matrix

and additives are the three major ingredients forming MREs (Jolly, Carlson & Munoz

1996). The most commonly adopted matrix materials are natural rubber and silicone

rubber. The silicone rubber surpasses natural rubber as a matrix material in many

situations because of the following advantages: 1) the precursor of the silicon rubber is

liquid, which makes it easier for the ferromagnetic particles to be uniformly distributed

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in the matrix; 2) the viscosity of silicone rubber is relatively low so that the magnetised

ferromagnetic particles can move easily to form a chain structure while curing in the

magnetic field; 3) the softness of silicone results in high MR effect of the composite

material (Böse & Röder 2009). Different soft magnetic materials can be used as the

ferromagnetic or polarised material, among which the spherical carbonyl iron particles

are usually used because it possesses high permeability, high saturation magnetisation

and low remnant magnetisation and coercivity (Boczkowska & Awietjan 2009). High

saturation magnetisation and high magnetic permeability provide greater attraction

between particles, which leads to higher MR effect while low remnant magnetisation

ensures that the particles will not stick together during the absence of magnetic field so

that the MR effect of the material is reversible (Lokander & Stenberg 2003). Moreover,

Silicone oil is the most widely adopted additive to improve the mechanical properties of

MREs (Lee & Medland 1978).

MR effect, with which the properties of the MR elastomer, especially the shear modulus,

can be alternated by simply adjusting the applied magnetic field, is fully utilised in the

design of the MRE base isolator. Usually, MR effect is evaluated by the ratio of increase

of modulus ∆G to the initial storage modulus G0. In order to achieve higher MR effect, a

series of material optimal designs have been conducted by researchers worldwide (Chen

et al. 2007; Hu et al. 2005; Sun et al. 2008; Tian et al. 2011; Wang et al. 2006; Zhang et

al. 2009; Zhang et al. 2010). Many factors contribute to the performance in MR effect of

MREs, such as alternation of matrix material, size of the ferromagnetic particles,

environmental factors during curing, process of preparation. The MRE base isolator

investigated in this thesis adopts a soft MRE material prepared by Li et al (Li, Li, Li, et

al. 2013; Li, Li & Samali 2012; Li, Li, Tian, et al. 2013). Comprehensive studies have

been conducted by the authors to optimise the material design and maximise the MR

effect so as to endow the MRE isolator with the largest stiffness range to meet the versatile

and adaptive working requirements. The characterisation of the material is then carried

on by the researchers and the strain-stress curves of the produced soft MRE sample in

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shear mode under various magnetic field strength are shown in Figure 2.12. Five magnetic

fields with different flux densities varying from 0 to 0.44T are applied to the sample and

the shear modulus of the material can be represented by the slope at each point. It can be

seen from Figure 2.12 that each strain-stress curve has a peak point, whose corresponding

abscissa is called yield shear strain. Under any magnetic field, the MRE sample exhibits

a linear relationship between the shear strain and stress within the yield strain, while

beyond the critical strain, it behaves with plasticity. Moreover, the shear yield stress also

increases with the increase of applied magnetic field, which also demonstrates the MR

effect in the material. More details about the preparation of the material will be introduced

in next chapter.

Figure 2.12 Shear stress-strain curves under different magnetic field (Li, Li & Samali 2012)

2.5.2 MRE vibration isolator in mechanical engineering

2.5.2.1 MRE Mount for Shock and Vibration Isolation

Kavlicoglu et al. (2011) proposed a MRE mount for shock and vibration isolation. The

schematic diagram of the MRE mount is shown in Figure 2.13. As can be seen from

Figure 2.13, the core part for variable stiffness of the mount is four pieces of MRE layers

with a thickness of 0.5 inch. The MRE layers are energised by two built-in electromagnet

coils. Two mounting plates are installed on the top and bottom of the MRE layers serving

0

5

10

15

20

25

30

0 50 100 150 200 250 300

Shea

r stre

ss (k

Pa)

Strain (%)

0 mT 110 mT220 mT 330 mT440 mT

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for both mechanical connection as well as part of the magnetic flux path. Besides

mounting plates, the electromagnet core and MREs together form the magnetic path.

However, magnetic path in this design is not a closed loop and thus the magnetic design

is not efficient, which greatly restricts the stiffness variation range and isolation

effectiveness of the device. The performance of the 2-layer MR elastomer mount is

characterised by compression, shear, vibration, and shock tests. Testing results show that

noticeable shock and vibration suppression performance has been verified.

Figure 2.13 Design of the MRE vibration isolation mount (Kavlicoglu et al. 2011)

2.5.2.2 Real-time MRE Tunable Stiffness and Damping Vibration Isolator

Liao et al. (2012) proposed a real-time tunable stiffness and damping vibration isolator

based on MRE material. The design sketch and illustration of different numbered parts

are shown in Figure 2.14 and similar designs have been configured in the research

reported in the years of 2001 and 2006 (Deng, Gong & Wang 2006; Ginder, Schlotter &

Nichols 2001). It can be seen from Figure 2.14 that the tunable stiffness and damping

vibration isolator mainly consists of eight parts, namely, base plate, magnetic coils,

magnetic conductor, shear plate, iron core, MREs, voice coil motor and mounting plate.

The stiffness elements in the device are four MRE samples working in shear mode and

the MRE samples are connected to the shear plate. Two closed C-shaped magnetic

circulates are formed by the base, iron core, magnetic conductor and part of the shear

MREsMREs

Electromagnetcore Electromagnet

coilElectromagnet

core

Mounting plate

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plate. A voice coil motor is fixed between the magnetic conductor and mounting plate,

which functions as a force generator outputting force proportional to the shear velocity.

Hence, with such configuration, the tunable stiffness is achieved by four MRE samples

while adaptive damping is realised by the voice coil motor.

Figure 2.14 Sketch of the MRE-based vibration isolator (Liao et al. 2012)

2.5.2.3 MRE Seat Suspension System

Figure 2.15 (a) Cross-section view of MRE isolator; (b) Vibration model of the MRE seat

suspension system with human body

Du, Li & Zhang (2011) and (Li, Zhang & Du 2012) proposed a MRE base isolator for a

seat suspension system for more comfortable ride experience and less potential of driver

fatigue. By altering the MR elastomer isolator’s stiffness through a controllable magnetic

field and selecting a suitable control strategy, the system’s natural frequency can be

changed to avoid resonance, which consequently reduces the vehicle’s vibration energy

input to the seat, and thus suppress the seat’s response. The schematic diagram of the

isolator is shown in Figure 2.15. As can be seen, this device is composed of core and base,

magnetic coil, non-magnetic rings and MR elastomer. The coil, core and base form the

magnetic path. The proposed seat isolator works in both shear and compressive mode.

CoreMRE

Core bracketRingCoilHousing

Base

Human body

Seat cushion

Seat frame

Cabin floor(a) (b)

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Experimental testing showed this device exhibited a clear increase in stiffness and

damping.

2.5.3 MRE base isolator in civil engineering

2.5.3.1 Conceptual study

The idea of utilising the Magneto-Rheological Elastomers (MREs) to provide adjustable

stiffness for the civil infrastructures have been firstly explored by Hwang, Lim & Lee

(2006) and Usman et al. (2009) numerically. Hwang, Lim & Lee (2006) has conducted a

conceptual study on the application of MREs to the base isolation systems and Usman et

al. (2009) investigated the feasibility of the novel idea by coupling a six degree-of-

freedom structural model with an MRE-based isolation system. Numerical testing results

reveal that the proposed system achieved considerable reduction of base displacement

and top floor acceleration under different types of earthquake excitations.

Figure 2.16 Structure model coupled with an MR elastomer-based base-isolation system (Jung

et al. 2011)

To further validate the feasibility and effectiveness of MRE base isolation, Jung et al.

(2011) evaluated the seismic performance of a smart base isolation system by

incorporating two MRE material blocks with a small-scaled single floor structure. The

testing schematics diagram is shown in Figure 2.16. A case study has been conducted by

testing the base isolated structure under sinusoidal loading and artificial earthquake

excitations. Three cases of magnetic field across the MRE blocks, namely 0.01T, 0.16T

Sensor

ControlComputer

MRE baseisolator

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and 0.52T, have been looked into and compared. Numerical and experimental testing

results indicate that it is feasible to utilise the smart base isolation system based on MRE

material as an alternative to a passive base isolation system for better seismic protection

performance. However, the testings reported in this study have yet to explore the control

algorithms of applied magnetic field so as to achieve controllable stiffness throughout the

external earthquake attacks.

2.5.3.2 Variable Stiffness and Damping Isolator (VSDI)

Figure 2.17 Cross-section view and photo of variable stiffness and damping isolator (Behrooz,

Wang & Gordaninejad 2014b)

Behrooz, Wang & Gordaninejad (2014b) have proposed a variable stiffness and damping

isolator (VSDI) which is designed based on MRE material. The cross-section view and

photo of VSDI is illustrated in Figure 2.17. As shown in the cross-section schematics,

two pairs of trapezoidal MRE blocks are placed in the middle of the device. Each of the

MRE pair is separated by a steel shim and rubber elements are used to embrace the MRE

pairs and fix the MRE pairs between two thick steel plates. An optimal design of magnetic

field is then realised by two identical steel caps each embedded with two coils of 800

turns of wires. Overall size of the isolator is 128 mm x 64mm x 110mm and power

requirement of each device is 234.2 W at 4A. The two caps are placed above and

underneath the MRE material while the power cords shown in Figure 2.17 realises

positive and negative currents in coils inside each cap so as to form a magnetic field

closed-loop. Therefore, highest possible magnetic field is guaranteed in each MRE,

resulting in large stiffness variation range. The role of the steel shim in between of the

MRE

Shim Coils

Elastomer

Shim

Elastomer

PowerCords

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MRE material blocks is quite important: the shim itself is for the magnetic flux

transmission, resulting in higher possible magnetic field across the MRE isolator; the high

strength of steel also prevents the rubber from tearing under large strains and hence

reduces the vulnerability of the VSDI.

To describe the dynamic characteristics of the VSDI, a phenomenological model is

proposed based on Bouc-Wen model, which is shown in Figure 2.18(a). The formula of

the model and values of the constant parameters in the model can be found in reference

(Behrooz, Wang & Gordaninejad 2014a). Figure 3(b) shows the comparison between

hysteresis correlations between shear force and displacement predicted by the proposed

model and measured experimentally. As can be observed in Figure 2.18(b), an increase

of approximately 57% is achieved in shear stiffness when current changes from 0 to 4A.

However, due to the design, the MRE and rubber elements become the weakest link in

the vertical direction. Therefore, the restricted vertical capacity becomes the major

limitation of this design, which is not favourable in civil engineering applications.

Figure 2.18(a) Phenomenological Bouc-Wen model of VSDI; (b) On-state and off-state shear

force deformation characteristics of VSDIs (Behrooz, Wang & Gordaninejad 2014a)

2.5.3.3 Highly adjustable laminated MRE base isolator

To overcome the issue of limited vertical loading capacity, Li et al. (Li, Li, Li, et al. 2013;

Li, Li, Tian, et al. 2013) have proposed the first laminated MRE base isolator inspired by

LRB. The photo and cross section view of the laminated MRE isolator is shown in Figure

FVSDI

k2

c2

km

cm

k1

v x

Bouc-Wen

0A experiment4A experimentAnalytical

Forc

e (N

)

Displacement (mm)

(a) (b)

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2.19. In the prototype, 46 layers of 1-mm-thick steel plates and 47 layers of 2-mm-thick

MRE sheets are placed alternately to form a laminated structure. All steel and MRE layers

are shaped into a cylinder with a diameter of 140mm and such arrangement results in a

total height of 140mm. As known, the laminated structure is widely accepted in base

isolator design in practice, the reason being i) the laminated structure guarantees large

vertical capacity brought by steel plates and at the same time maintains high horizontal

flexibility due to MRE layer; ii) steel plates can improve the magnetic conductivity

throughout the structure. The laminated structure together with two cylindrical steel

blocks vulcanised on the top and bottom of the laminated structure form the core of the

isolator. A cylindrical coil with an inner diameter of 196mm is mounted to embrace the

laminated MRE core so as to generate the magnetic field across the MRE material. The

space between the core and coil allows the core a maximum horizontal deformation of

26mm. To analyse the influence of air gap between core and coil on the magnetic field in

the MRE sheets, Li & Li (2015)) have investigated the distribution of magnetic field in

the MRE isolator under different deformation situations. It is discovered that, although

the magnetic field distribution is dependent on the motion of the isolator, the change of

the magnetic flux is relatively small and the flux line is still straight and uniform under

various deformation cases. Meanwhile, since the steel wall, top and bottom plates and

core of the isolator form a closed magnetic circuit, the influence caused by air gap which

allows deformation on the magnetic field can be neglected. A 2-mm-thick cylindrical

shaped wall made of epoxy material is utilised as the non-magnetic support to incorporate

the coil as well as the laminated MRE core. The steel yoke, coil and core are bolted on

the bottom plate while only the MRE core is bolted to the top plate. There is a gap between

the top plate and outer layer of the isolator in order to eliminate friction when the top

plate and core move horizontally. The estimated vertical loading capacity of the device is

370kg in the weakest case scenario, where the applied current is 0A (softest condition for

MRE) and horizontal displacement is the maximum (26mm). Experimental testing results

reveal that there are increases of 37% in effective stiffness and 44% in maximum shear

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force when a current of 5A is applied.

Figure 2.19 Photo and cross-section view of the laminated MRE base isolator (Li, Li, Li, et al. 2013)

Figure 2.20 Photo and cross-section view of the highly adjustable laminated MRE base isolator

Figure 2.21(a) Force-displacement relationships of the MRE base isolator at quasi-static testing (f=0.1Hz, Δ=8mm); (b) force-displacement loops at different amplitudes (2mm, 4mm and 8mm)

excitation at 0.1 Hz and 3A (Li, Li, Tian, et al. 2013)

Further research has been carried out by Li, Li, Tian, et al. (2013) seeking higher adjusting

range of the isolator’s stiffness for better adaptability and controllability. A highly

Top plate

Laminated MRE and steel layers

Gap

Coil

Steel yoke

Top plate

SolenoidSteel yoke

MRE laminated structure

-10 -8 -6 -4 -2 0 2 4 6 8 10-400

-300

-200

-100

0

100

200

300

Displacement mm

Forc

e N

Frequency=0.1Hz, I=0AFrequency=0.1Hz, I=1AFrequency=0.1Hz, I=2AFrequency=0.1Hz, I=3A

-10 -8 -6 -4 -2 0 2 4 6 8 10

-300

-200

-100

0

100

200

300

Displacement mm

Forc

e N

=2mm, f=0.1Hz, I=3A=4mm, f=0.1Hz, I=3A=8mm, f=0.1Hz, I=3A

Forc

e(N

)

Forc

e(N

)

Velocity (mm/s)Displacement (mm)(a) (b)

Displacement (mm)

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adjustable MRE base isolator was designed and manufactured with similar design to the

previous laminated isolator but with soft MRE material. The photo and schematic

diagram of the MRE isolator is shown in Figure 2.20. The laminated structure embedded

in this device consists of 25 layers of MRE sheets and 24 layers of steel plates arranged

alternately. Each layer is 1mm in height and 120mm in diameter. With the presence of a

3A current, great increases of more than 1600% in shear modulus and more than 1400%

in maximum shear force are achieved.

To characterise the MRE isolator, a series of experimental testings were conducted with

a broad range of inputs by Li, Li, Tian, et al. (2013). Sinusoidal waves with amplitudes

of 2mm, 4mm, and 8mm were applied on the MR elastomer isolator. The shear force

responses were measured with applied current of 0A, 1A, 2A and 3A under each

sinusoidal excitation. Figure 2.21(a) illustrates the force-displacement hysteresis loops at

different current inputs under a cyclic loading with amplitude of 8mm and frequency of

0.1Hz. Figure 2.21(b) shows the loops at different displacement amplitude when the

current is 3A and frequency is 0.1Hz. It is noteworthy that in single force-displacement

loop, the stiffness increases at large shear deformation, which is recognised as strain-

stiffening behaviour. Such behaviour has also been reported as the feature of passive

elastomeric bearings.

2.5.3.4 Laminated MRE Base Isolator with Negative Changing Stiffness

The pilot research of Li, Li, Tian, et al. (2013) about the laminated MRE base isolator is

widely recognised as a breakthrough on proof-of-concept and development of adaptive

base isolator employing MRE material. However, it is also faced with practical issues

about energy consumption. In civil engineering practice, it is required that the stiffness

should be high during normal service life for structural safety considerations and to resist

wind loads. When earthquake strikes, the MRE isolator should be softened to lower the

natural frequency of the system and hence decouple the superstructure from ground

motion. To realise such configuration, the MRE base isolator should be powered up for

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most of the operational time. To this end, Yang et al. (2014) have proposed an MRE

isolator that possesses reduced stiffness when the applied current is increased.

Figure 2.22 Laminated negative stiffness MRE isolator (Yang et al. 2014)

The photo and cross-section view of the negative changing stiffness isolator is shown in

Figure 2.22. As can be observed from Figure 2.22, the design of the device is very similar

to the stiffness hardening MRE base isolator. The MRE and steel laminated structure

consists of 10 layers of MRE sheets and 11 layers of steel sheets bonded together, each

of which is 1 mm thick and 35 mm in diameter. Instead of the steel block, two permanent

magnets are placed on the top and bottom of the laminated structure. Such magnets

placing arrangement generates an initial magnetic field across the MRE sheets and thus

provides a relatively high initial stiffness of the isolator. Depending on the current

direction, the electromagnetic coils can generate a magnetic field either in the same or

opposite direction of the magnetic flux of the permanent magnets. The schematics of the

magnetic field direction are shown in Figure 2.23. When the coil is applied with a positive

current, a magnetic field with the same direction as that of the permanent magnets will be

generated and the stiffness of the device is increased as a result; in contrast, if energised

by a negative current, the magnetic field of the permanent magnets is off-set and thus the

stiffness is decreased.

In 2016, Yang et al. (2016) equipped this isolator on a scaled three storey building and

demonstrated the concept of utilising the negative stiffness isolator for seismic protection

of the structure. However, the size as well as vertical capacity of the isolator is fairly

small and the required size of permanent magnets is enormous to generate considerable

magnetic field when the isolator is enlarged to meet the requirement of practical

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application. Meanwhile, there is no essential difference in principle of control algorithm

design between the stiffness hardening and softening MRE isolator. Hence, the MRE base

isolator designed by Li, Li, Tian, et al. (2013) is employed and the experimental

realisation of the smart base isolation system based on the isolator is discussed in this

thesis.

Figure 2.23 Different working modes of hybrid magnetic system (Yang et al. 2014)

2.5.4 Control Application of MRE Isolators

To exploit the unique properties of an MRE isolator to its maximum advantage, various

control methods have designed to regulate the applied current or voltage to the isolator

for ideal control performance. Three control applications, namely, Bang-Bang control,

fuzzy logic control and human simulation intelligent control (HSIC) are introduced in this

section, among which Bang-Bang control is the most popular approach in the MRE

isolator control application. Nevertheless, what is noteworthy is that most of the present

control applications are realised in mechanical engineering and the control application of

MRE base isolator in civil engineering is yet to be explored.

2.5.4.1 Bang-Bang (ON/OFF) Control

Bang-bang (on-off) control, which is a kind of optimal control, grew out of sliding mode

control (SMC) based on Lyapunov function. Generally, Bang-Bang control law can be

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expressed as following

Eq. 2.1

where g(t) is the switching function, i.e. when , the MRE isolator is at ON-state

and when , the MRE isolator is at OFF-state. The Bang-Bang control has its

own physical interpretation: when the structure’s displacement and velocity are with the

same sign, which means the superstructure is moving away from the equilibrium position,

the MRE base isolator provides additional stiffness for the system; in contrast, when the

displacement and velocity are with the opposite signs, which means the superstructure is

moving towards the equilibrium position, the isolator maintains the softest situation.

The Bang-Bang control is firstly utilised in the control of MRE vibration isolators in

mechanical engineering since the controlled system is normally modelled as a single

degree-of-freedom system and thus it is easier to apply the control law. Liao et al. (2012)

has firstly applied a combined ON/OFF control on a real-time tunable stiffness and

damping MRE vibration isolator. Under random excitation, the control law can be written

as Eq. 2.2. Experimental results indicate that the responses of the payload are suppressed

significantly in comparison to the passive system. The root mean square (RMS) value and

the maximum value of the displacement responses of the payload are decreased by 36.0%

and 50.0%, respectively. In addition, the RMS values and maximum values of the velocity

responses are decreased by 45.4% and 52.5%, respectively.

Eq. 2.2

The ON/OFF control was then employed for seat vibration suspension utilizing a MRE

isolator (Tao et al. 2012). A three degree-of-freedom system was considered to model the

g(t) 1

g(t) 0

Literature Review

52

system consisting of human body, seat cushion and seat frame isolated by the MRE

device. The current and effective stiffness control law can be expressed as

Eq. 2.3

where x2 is the relative displacement of the seat cushion. By applying the control

algorithm, the isolator’s stiffness is tuned to establish a non-resonant state against base

excitations, hence suppressing the seat’s responses.

To evaluate the performance of the laminated negative changing stiffness MRE base

isolator, Yang et al. (2014) conducted the experimental testing on a single degree-of-

freedom system whose vibration response was attenuated by the ON/OFF control logic.

Testing results demonstrated that the isolator possesses noticeable effectiveness in

vibration attenuation under ON/OFF control.

Despite the comprehensive studies and success using ON/OFF control, the control

performance of this method has yet to be tested under seismic loadings. Meanwhile, it is

difficult to decide which structural response signal to be chosen as the switching condition

when the superstructure is a large-scaled multiple level building.

2.5.4.2 Fuzzy Logic Control

Civil infrastructures embrace a substantial number of uncertainties caused by the

structure’s deterioration, aging, environmental noises, etc. As a result, how to

accommodate the uncertainties in the control system becomes one of the major challenges

in the civil control procedure. Furthermore, structures in the civil engineering discipline

include loaded structural elements and unloaded non-structural members. Normally, the

effects of non-structural elements are not taken into consideration when conducting the

Literature Review

53

structural design and calculation while the structural vibration control is mainly targeted

on the completed practical structure, where the non-structural elements and mass changes

have a considerable influence on the computational model. Therefore, applying fuzzy

logic control on a semi-active system becomes a heated research topic. Fuzzy logic

control method shows a high tolerance of nonlinearity and uncertainty in the control

system since it pursues significance rather than precision (Symans & Kelly 1999). More

specifically, a fuzzy controller does not rely on the analysis and synthesis of the

mathematical model of the process, so the uncertainties of input data from external loads

and structural response sensors are treated in a much easier way by the fuzzy controller

than with classical control theory. The designing process of a fuzzy controller begins with

choosing inputs and output, and defining the membership functions (MFs).

In the study exploring the feasibility of MRE base isolation in seismic protection of civil

structure, Jung et al. (2011) firstly used the fuzzy logic control to select the magnetic field

applied on the MRE blocks under the one degree-of-freedom structure. Three magnetic

flux amplitudes (0.01T, 0.16T and 0.52T) are provided for selection. Detailed control law

is not presented in this paper but testing results show that it is feasible and effective to

use fuzzy logic control for stiffness alteration of the MRE base isolation level.

Yang et al. (2016) have also applied fuzzy logic control algorithm in the development of

the laminated negative stiffness MRE base isolator. A scaled three-storey structure was

adopted as the testing bed. The inputs chosen are the relative displacement of the top floor

to the first level (x3 - x1), displacement of the first level and the velocity of ground

movement . The inference rule of fuzzy logic is listed in Table 2.1. In the table, each

input has two member functions which were abbreviated to: P-Positive, N-Negative. The

output is the current signal and the membership functions were defined as: L-Large, S-

x1

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54

Small.

Table 2.1 Inference rule of the fuzzy logic control algorithm (Yang et al. 2016)

Variable MF

x3 - x1 N N N N P P P P

N P N P N P N P

P P N N P P N N

Stiffness Soft Hard Soft Hard Hard Soft Hard Soft

Current L S L S S L S L

2.5.4.3 Human Simulation Intelligent Control (HSIC)

Figure 2.24 Multiple short-type floating slab track magneto-rheological system model (Li et al.

2016)

In recent years, MR isolators’ advantages of adjustable stiffness and damping have drawn

great attention in the vibration control of railway or subway tracks. Li et al. have proposed

a mechanism utilising MRE isolators for subway floating slab track to achieve vibration

isolation control in a wide frequency range (Li et al. 2016). Although it wasn’t explicitly

x1

RailFastener

Floating slabMR isolators

Rail 1 Rail 2

A-A schematic diagram

A-A

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55

stated in this paper which kind of MR isolator is utilised, this example is still included as

an application of MRE isolator due to the same working principle of utilising the

controllable stiffness of the isolator. The two-dimensional floating slab tracks studied are

selected as the research objective and modelled as in Figure 2.24. A novel control

algorithm, HSIC (human simulation intelligent control) minimising the overall energy

transfer is developed for the control of the system. The detailed control algorithm

derivation can be found in the reference (Li et al. 2016). The optimal real-time stiffness

and damping is achieved according to evaluation index based on multiple target

optimisations. The effectiveness of humanoid intelligent control is verified by simulation

results in magneto-rheological vibration isolation system design.

2.6 RESEARCH GAPS AND CHALLENGES

Based on the literature review, it can be concluded that the conventional base isolation

systems, although have been widely adopted in civil infrastructures for seismic

protection, has inherent problems due to its passive nature, such as excessive base

displacement, potential hazard of overturning, restriction to higher-rise structures,

inadaptability to earthquake excitations beyond the designated scope.

To resolve these issues, a concept of hybrid “smart” base isolation systems, combining a

passive base isolation system with active or semi-active damping systems, has been

explored. A great number of designs of this type of isolation system have been proposed

and validated numerically and experimentally. Nevertheless, in this type of isolation

system by augmenting dampers to the system, the passive nature of the base isolation

remains unchanged and hence the controllability and adaptable range of the hybrid system

is rather limited. Expressly, the hybrid isolation system’s performance is still restricted

by the design of the passive isolation components. Moreover, adding variable damping

into the system may introduce excessive accelerations in higher modes and besides extra

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56

damping do not help to suppress vibration responses under impact loading conditions.

To address the challenges, new generation of smart base isolation endowing the base

isolation itself directly with adaptability and intelligence has provided a completely

different angle in addressing the aforementioned issues. The representative design of such

an isolation system achieves controllable stiffness by employing a smart material named

MRE whose shear modulus can be controlled in real-time and reverse fashion by the

applied magnetic field. Many designs have been presented during the last five years.

However, in-depth understanding about the control of the MRE isolation system needs to

be acquired to exploit its unique characteristics as a tunable stiffness base isolation device.

Furthermore, comprehensive experimental testing on MRE base isolated structure has yet

to be conducted for a convincing demonstration of the effectiveness and versatility of the

seismic protection strategy under various seismic activities.

Therefore, several challenges need to be resolved on the way to realise the MRE base

isolation system practically. First of all, suitable models which possess both accuracy and

computational efficiency should be developed to describe the forward and inverse

dynamics of the MRE isolator for the sake of control synthesis and analysis. Secondly,

due to the enormous inductance of the solenoid utilised in all MRE base isolators, the

response time to the control command is hefty, which leads to large time delay in the

MRE base isolation control system. As known, exaggerated time delay may lead to

degradation of the control performance and even cause instability of the control system.

Therefore, an investigation should be conducted to define the response time of the MRE

isolator of interest and approaches to minimising the time delay should be explored.

Thirdly, to validate the seismic protection performance of the proposed MRE base

isolation system, thorough experimental testing should be conducted. This involves i)

proper design and modelling of the isolated structure as the testing bed and integration

and precise identification of the MRE base isolation system; ii) appropriate experimental

setup and configuration; iii) powerful shake table to accurately regenerate real earthquake

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57

excitations without distortion; iv) appropriate selection of various earthquake excitations

to prove the versatility of the MRE base isolation system; v) development of various

control strategies according to the unique features of the MRE isolator. Subsequently,

other innovations employing the MRE isolation system should be explored to broaden

the horizon of research in this technique. To this end, this thesis targets the

aforementioned challenges and explores the resolutions for each challenge in the

following four chapters.

MRE Base Isolation And Hysteresis modelling

58

CHAPTER 3

MRE BASE ISOLATION AND HYSTERESIS MODELLING

3.1 CHAPTER OUTLINE

In this chapter, the modelling depicting the forward and inverse dynamics of MRE base

isolator is discussed for control analysis and synthesis discussed in the following chapters.

The design, experimental setup for characterisation and dynamic features of the MRE

isolator are firstly introduced. Two parametric models, namely, Bouc-Wen model and

strain-stiffening model, are then developed, analysed and compared to describe the

forward dynamics of MRE isolators. The forward modelling emphasises accurate

description of strain-stiffening feature and highly nonlinear and hysteretic characteristics

of the isolator. The development of two forward models follows the same procedure, i.e.

proposal of mathematical expression, parameter identification, analysis of influence of

modal parameter on modal responses, experimental validation of model’s performance.

Next, a general regression neural network (GRNN) inverse model is proposed and

developed by employing fruit fly optimisation algorithm (FOA). Testing results show that

the GRNN inverse model can precisely recurrent the inverse dynamics of the MRE base

isolator by predicting applied current to the isolator based on desired control force

generated by the designated controller. Hence, the application of the inverse model in

control system has promising potential to overcome the challenges in the semi-active

control caused by high nonlinearity of the MRE base isolator and hence achieve


59

satisfactory control performance.

3.2 INTRODUCTION AND BACKGROUND

3.2.1 MRE base isolator

Figure 3.1 Experimental setup for training data acquisition and power equipment (Li, Li, Tian,

et al. 2013)

The MR elastomer base isolator employed in this experimentation is prototyped by Li et

al. (Li, Li, Tian, et al. 2013), which is introduced in Section 2.4.3.3. The photo and

schematic diagram of the MRE isolator is shown in Figure 2.20. As can be seen in the

graph, in the laminated MRE structure, 26 MR elastomer sheets with a thickness of 1mm

are vulcanised with 25 steel plates with the same thickness alternatively to form a

sandwich structure. With such layout, the steel plates can provide adequate vertical

loading capacity while the MR elastomer sheets can provide adaptive controllable

horizontal flexibility for the smart base isolator. A solenoid with a resistance of 40Ω and

inductance of 3.5H is mounted around the sandwich structure to energise the MR

elastomer in accordance to the applied control current. Two steel plates are fixed on each

side of the MR elastomer laminated structure to connect it with the top and bottom plates.

Furthermore, the size and location of the steel blocks and connecting plates are carefully

designated so as to form optimised magnetic circuit and thus guarantee maximum uniform

magnetic field throughout the laminated MR elastomer structure. More details about the


60

design can be found in reference (Li, Li, Tian, et al. 2013)

To evaluate and characterise the mechanical and dynamic properties of MRE base

isolator, a series of experimental tests were conducted utilising the experimental setup

shown in Figure 3.1. To apply accurate horizontal movement command, the UTS shake

table was used to provide horizontal loadings to the isolator either in the quasi-static mode

or in dynamic mode. The bottom plate of the MRE base isolator was mounted on the

shake table and moves along with the shake table motion while the top plate of isolator is

fixed to a reference frame so as to make sure that the displacement of shake table equals

to the horizontal deformation of isolator. Meanwhile, a load cell (Model No. STS-300-

B10, Sun Scale INC) is installed to the fixed reference frame to measure the lateral load

from the isolators. The key to the setup lies in that the top plate of isolator and load cell

remain relative static during the dynamic tests, hence avoiding undesirable inertia force

in the measurements. A DC power supply (DC Power Conditioner, SOLA Electric,

Division of SOLA Basic Australia) with capacity of 240 V and 5.3 A, as shown in Figure

3.1, provides DC current to energize the magnetic coil. A slider (Type: S-260-10,

Yamabishi Electric Co. Ltd, Tokyo, Japan) was used to adjust the applied current to the

magnetic coil, also shown in Figure 3.1.

Figure 3.2 MRE isolator’s stiffness and damping dynamics with different current input

In the dynamic tests, various harmonic displacement inputs have been selected to load

the MRE base isolator by shake table. In total, sinusoidal waves with three amplitudes of

-5 0 5

-200

-100

0

100

200

Displacement(mm)

Forc

e(N

)

-50 0 50-300

-200

-100

0

100

200

300

Velocity(mm/s)

Forc

e(N

)

0A1A2A3A


61

2mm, 4mm, 8mm and four frequencies of 0.1Hz, 1Hz, 2Hz and 4Hz were applied on the

MR elastomer isolator. As mentioned previously, the gap between the stainless steel wall

and the laminated core of the isolator is 15mm. Hence, the largest displacement amplitude

in the sinusoidal testing is determined to be 8mm, which is adequate in practical

application and can avoid buckling in the core structure. Therefore, there are altogether

12 displacement input scenarios. At each displacement scenario, the constant currents of

0A, 1A, 2A and 3A are applied on the MRE isolator. The displacement-force and

velocity-force responses with different current inputs are displayed in Figure 3.2 with the

sinusoidal excitation of 2Hz frequency and 4mm displacement.

3.3 FORWARD MODEL OF MRE BASE ISOLATOR

3.3.1 Generalised Bouc-Wen Model

3.3.1.1 Modelling Process of Bouc-Wen Model

It can be clearly observed from Figure 3.2 that the biggest challenge in the modelling of

MRE base isolator is to accurately depict the strain-stiffening feature in force-

displacement relation and highly nonlinear and hysteretic behaviour. Hysteresis, which is

a memory-dependent, multivalued relation between force and deformation, is often

observed in structural materials and elements, such as reinforced concrete, steel, base

isolators, dampers, and soil profiles (Song & Der Kiureghian 2006). Many mathematical

models have been developed to describe such behaviour for use in time history and

random vibration analysis, among which Bouc-Wen class model is the most popular

strain-stiffening model. Originally proposed by Bouc (1967) and later generalised by

Wen (1976), the Bouc-Wen model is versatile in describing various characteristics of

hysteretic behaviour, e.g., degrading of stiffness and strength and the pinching effect

(Baber & Noori 1983; Baber & Wen 1981; Noori, Choi & Davoodl 1986). Moreover, the

Bouc-Wen model is also favourable because of computational simplicity since only one


62

auxiliary nonlinear differential equation is needed to describe the hysteretic behaviour.

Therefore, the Bouc-Wen model is one of the ideal candidates to describe the forward

dynamics of MRE isolator. The schematic diagram of the model is shown in Figure 3.3.

It can be seen from Figure 3.3 that, the model is composed of a Bouc-Wen component,

which reproduces hysteresis loops, in parallel with a Kevin-Viogt element (Chen et al.

2011), which is a combination of paralleled spring and dashpot and describes solid-

material behaviours. Hence, the force of the proposed Bouc-Wen model can be expressed

by

Eq. 3.1

Figure 3.3 Schematic diagram of the proposed Bouc-Wen model for MRE isolator

where k0 is the stiffness of the spring; c0 represents the viscous coefficient indicating the

damping capacity of the system; α is the post- to pre-yielding stiffness ratio; z(t) is called

evolutionary variable, which directly describe the hysteretic features of the model. The

second function in Eq. 3.1 defines evolutionary variable z(t), in which A, β, and γ are non-

dimensional parameters which are responsible for the shape and the size of the hysteretic

loops. Furthermore, n is recognized to control the transition from linear to nonlinear

range. In this work, the value of n = 1 is considered to reduce the complexity of parameter

nn zxzzxxAzzxcxkF

100

Bouc-Wen componentx

F - F0

c0(I)

k0(I)


63

identification.

3.3.1.2 Parameter identification results

A genetic algorithm (GA) is adopted to identify the values for parameters in different

excitation scenarios. More specifically, 36 sets of parameters are identified under each

excitation scenario (applied current = 0, 1A, 2A, 3A; sinusoidal amplitude = 2mm, 4mm,

8mm; sinusoidal frequency = 1Hz, 2Hz, 3Hz). Detailed information about GA is

presented in Chapter 6. The identified parameter values are summarised in Table 3.1.

With the identified parameters, the measured and predicted hysteresis loops in some cases

are compared in Figure 3.4 to Figure 3.6.

Figure 3.4 Comparison between experimental data and forecast values from the proposed model

with different excitation amplitudes (1Hz-3A)

Figure 3.4 shows the comparison of measured and predicted force-displacement and

force-velocity curves with sinusoidal excitation amplitudes of 2mm, 4mm and 8mm when

applied current is 3A and excitation frequency is 1Hz. As can be seen from Figure 3.4,

the predicted curves present a good agreement with measured results, especially under

smaller excitation amplitudes. Moreover, with the increase of excitation amplitude, the

maximal shear force generated by the MRE isolator exhibits an obvious magnification.

However, the effective stiffness and damping coefficient, which are indicated by the slope

of the force-displacement curve and force-velocity curve, respectively, slightly decreases

when amplitude rises. Moreover, Mullins effect, which refers to an instantaneous and

-10 -5 0 5 10-400

-200

0

200

400

Displacement (mm)

Shea

r for

ce (N

)

-60 -40 -20 0 20 40 60-400

-200

0

200

400

Velocity (mm/s)

Shea

r for

ce (N

)

2mm-measured

2mm-predicted

4mm-measured

4mm-predicted

8mm-measured

8mm-predicted


64

irreversible softening of the force-displacement curve occurring whenever the load

exceeds the prior all-time maximum vlaue (Mullins 1948), can be well depicted by the

proposed model.

Figure 3.5. Comparison between experimental data and forecast values from the proposed

model with different applied currents (1Hz-4mm)

Figure 3.6 Comparison between experimental data and forecast values from the proposed model

with different excitation frequencies (4mm-1A)

Figure 3.5 compares the predicted and measured force-displacement and force-velocity

relations with applied current varying from 0A to 3A under the same sinusoidal excitation

with frequency of 1Hz and amplitude of 4mm. Normally, the increase of applied current,

which leads to escalation of applied magnetic field on MRE material, will result in the

amplification of strain-stiffening effect and nonlinearity of the device’s response as being

illustrated by Figure 3.5. Figure 3.6 displays the device’s hysteresis loops under different

frequencies of 1Hz, 2Hz and 4 Hz when the applied current is 1A and amplitude is 4mm.

-5 0 5-300

-200

-100

0

100

200

300

Displacement (mm)

Shea

r for

ce (N

)

-30 -20 -10 0 10 20 30-300

-200

-100

0

100

200

300

Velocity (mm/s)

Shea

r for

ce (N

)

0A-measured0A-predicted1A-measured1A-predicted2A-measured2A-predicted3A-measured3A-predicted

-5 0 5

-100

-50

0

50

100

Displacement (mm)

Shea

r for

ce (N

)

-100 -50 0 50 100

-100

-50

0

50

100

Velocity (mm/s)

Shea

r for

ce (N

)

1Hz-measured

1Hz-predicted

2Hz-measured

2Hz-predicted

4Hz-measured

4Hz-predicted


65

Interestingly, the force-displacement curves under different excitation frequencies are

rather identical to each other, which shows little dependence of the isolator’s dynamics

on excitation frequency. The distinctions between force-velocity loops under different

frequencies, however, are mainly due to the fact that amplitude of velocity equals to the

product of amplitude of displacement and frequency of the excitation.

It can be observed from Figure 3.5 and Figure 3.6 that the values of parameters are more

affected by applied current rather than the excitation frequency and amplitude. Hence, an

average of parameter values under different excitation scenarios when applied current is

0A, 1A, 2A and 3A, respectively, is taken as the parameter at the corresponding current

level. Next, a curve fitting is conducted to explore the definitive correlation between the

parameter of interest with applied current. Figure 3.7 shows the fitting curve of all six

parameters, among which k0, c0, A, β, and γ have a linear relation with current while α

and current have a quadratic relation. The fitted functions of parameters are expressed by

Eq 3.2.

Table 3.1 Identified parameter values for Bouc-Wen model under different excitation scenarios

Current 0A

Frequency 1Hz 2Hz 4Hz

Amplitude 2mm 4mm 8mm 2mm 4mm 8mm 2mm 4mm 8mm

k0 4.90 4.55 4.37 5.72 5.34 4.84 7.04 6.52 6.11 5.49

c0 0.31 0.31 0.25 0.20 0.21 0.13 0.12 0.14 0.14 0.20

α 1.68 1.27 3.49 13.63 1.09 10.54 2.23 16.50 12.19 6.96

A 2.50 1.30 2.64 0.13 0.08 0.71 3.10 0.22 0.59 1.25

β 5.89 2.08 4.88 3.70 7.30 4.15 5.78 6.99 1.29 4.67

γ 3.01 1.17 -1.02 0.22 2.52 -2.80 1.76 4.24 2.41 1.28


66

Table 3.1 Identified parameter values for Bouc-Wen model under different excitation scenarios (cont'd)

Current 1A



k0 22.81 16.41 13.49 25.13 17.43 15.38 24.94 19.09 15.68 18.93

c0 1.31 0.75 0.29 0.76 0.41 0.57 0.49 0.22 0.28 0.56

α 1.68 1.27 3.49 13.63 1.09 10.54 2.23 16.50 12.19 6.96

A 1.45 3.79 2.77 1.37 2.91 3.12 1.12 2.62 2.84 2.44

β 4.59 1.13 2.70 4.85 4.48 6.28 5.14 6.33 1.49 4.11

γ 0.76 3.37 0.34 -1.55 -1.88 3.03 2.37 1.92 1.77 1.12

Current 2A



k0 41.04 29.49 23.57 38.73 30.64 24.14 42.09 29.76 25.98 31.72

c0 1.99 0.86 0.39 0.94 0.70 0.56 0.65 0.58 0.46 0.79

α 48.18 19.22 26.32 17.74 19.67 26.93 24.18 22.96 41.27 27.39

A 2.20 5.57 6.71 5.23 5.95 2.52 2.48 4.29 4.02 4.33

β 2.15 4.52 3.33 2.61 4.91 3.68 3.31 5.64 2.62 3.64

γ 3.22 -1.63 -0.65 1.36 -0.69 -2.07 0.87 4.79 2.04 0.81

Current 3A



k0 53.96 37.01 30.75 51.73 40.18 30.60 48.69 37.77 33.00 40.41

c0 2.67 0.91 0.86 1.30 1.17 0.44 0.74 0.44 0.77 1.03

α 32.60 52.94 35.23 44.40 11.31 28.92 26.06 28.85 33.50 32.65

A 2.51 2.35 4.64 2.36 4.11 6.05 6.03 5.64 7.00 4.52

β 2.37 1.54 4.57 3.09 4.12 3.63 4.24 2.62 3.62 3.31

γ 2.03 1.13 -1.84 1.69 -1.66 -0.94 0.43 2.64 2.66 0.68


67

Figure 3.7 Parameter identification results: (a) k0 vs current; (b) c0 vs current; (c) α vs

current; (d) A vs current; (e) β vs current; (a) γ vs current Based on the observations in

Table 3.1 and Figure 3.4 to Figure 3.6, it can be assumed that the values of parameters

are more affected by applied current rather than the excitation frequency and amplitude.

Hence, an average of parameter values under different excitation scenarios when applied

current is 0A, 1A, 2A and 3A, respectively, is taken as the parameter at the corresponding

0 1 2 30

10

20

30

40

50

60

Current (A)

Para

met

er fo

r k0

Measured parameterAveraged parameterFitting curve

0 1 2 30

0.5

1

1.5

2

2.5

3

Current (A)

Para

met

er fo

r c0


(a) (b)

0 1 2 30

10

20

30

40

50

60

Current (A)

Para

met

er fo

r


0 1 2 30

1

2

3

4

5

6

7

8

Current (A)

Para

met

er fo

r A


(c) (d)

0 1 2 31

2

3

4

5

6

7

8

Current (A)

Para

met

er fo

r


0 1 2 3

-2

0

2

4

6

Current (A)

Para

met

er fo

r


(e) (f)


68

current level. Next, a curve fitting is conducted to explore the definitive correlation

between the parameter of interest with applied current. Figure 3.7 shows the fitting curve

of all six parameters, among which k0, c0, A, β, and γ have a linear relation with current

while α and current have a quadratic relation. The fitted functions of parameters are

expressed by Eq 3.2.

Eq. 3.2

3.3.1.3 Model Parameter Analysis

In order to better adopt the proposed model for its vibration control application, a

comparative study is conducted to analyse the influences of the model parameters on the

output responses of the model. In this case, the displacement and velocity data are

obtained from the test of 2Hz frequency excitation with 4mm amplitude and 2A supplying

current.

Figure 3.8 describes the resultant hysteresis loops with the changing value of k0. The

values of k0 are set to be 10, 20, 29.76, 40 and 50, among which 29.76 is the value

calculated by Eq 3.2 when the input current is 2A. It is seen that the maximum force and

effective stiffness change almost linearly with k0. Another phenomenon worth noting is

that all the loops intersect at two points, as pointed out in Figure 3.8 (a). Moreover, the

force-velocity loops also join together at two points in Figure 3.8 (b), where velocity

approximately reaches positive and negative maximum value. These positions are

deemed as the key points of strain stiffening since this unique behaviour turns to be more

evident from the points. For instance, the two points highlighted in Figure 3.8 (a) indicate

the critical points of strain stiffening. In the force-velocity responses, the enclosed area

289.12108.0617.44554.0

324.1109.1106.716.149.1

2329.02725.0053.676.11

20

0

IIII

IIAIII

IIcIIk


69

of every curve increases as the value of k0 grows.

Figure 3.8 k0 dependent responses of the generalised Bouc-Wen model: (a) force-displacement

loops; (b) force-velocity loops

Figure 3.9 c0 dependent responses of the generalised Bouc-Wen model: (a) force-displacement


The influence of value of parameter c0 on the output response of the device is given in

Figure 3.9. Unlike parameter k0, c0 has little effect on the maximal shear force and

effective stiffness of the isolator, which means that all the shear forces with different

values of c0 arrive at the maximums with the same value at two endpoints. Meanwhile,

the force-velocity curve also reflects that peak shear force occurs when the velocity is

zero and decreases to minimum at maximal velocity, which means the damping force has

little contribution to the total shear force. Such conclusion can be supported by the fact

-5 0 5-300

-200

-100

0

100

200

300

400

Displacement (mm)

Shea

r for

ce (N

)

k

0=10

k0=20

k0=29.76

k0=40

k0=50

-150 -100 -50 0 50 100 150-400

-300

-200

-100

0

100

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300

400

Velocity (mm/s)

Shea

r for

ce (N

)

Intersecting point

(a) (b)

-6 -4 -2 0 2 4 6-200

-150

-100

-50

0

50

100

150

200

Displacement (mm)

Shea

r for

ce (N

)

c

0=0.1

c0=0.2

c0=0.29

c0=0.4

c0=0.5

-150 -100 -50 0 50 100 150-200

-150

-100

-50

0

50

100

150

200

Velocity (mm/s)

Shea

r for

ce (N

)

(a) (b)


70

that identified value of c0 is rather small. It can also be observed that the changing in c0

results in slight difference between corresponding hysteresis loops, not to mention the

maximal shear force. However, it can still be seen from Figure 3.9 that the force-

displacement curve grows wider as the value of c0 increases, which leads to larger energy

dissipation capacity.

Figure 3.10 α dependent responses of the generalised Bouc-Wen model: (a) force-displacement


Figure 3.10 and Figure 3.11 illustrates the influence of parameters α and A, respectively,

on the dynamic response of the model. An obvious similarity between the two figures can

be observed, which indicates that one of the parameter can be replaced by the other if the

hidden relationship between these two can be found. It is not discussed in this work but

the proposed Bouc-Wen model can be improved from this point. As aforementioned, α is

post- to pre-yielding stiffness ratio, which represents the linearity level of the hysteresis

loops. As can be seen in Figure 3.10 (a) and Figure 3.11 (a), with the increase of α and A,

the strain-stiffening effect and nonlinearity of the response can be detected. Also, when

α = 1, the force-displacement curve is an ellipse, which shows no nonlinearity behaviour

-6 -4 -2 0 2 4 6-250

-200

-150

-100

-50

0

50

100

150

200

250

Displacement (mm)

Shea

r for

ce (N

)

=1=10=22.96=30=40

-150 -100 -50 0 50 100 150-250

-200

-150

-100

-50

0

50

100

150

200

250

Velocity (mm/s)

Shea

r for

ce (N

)

(a) (b)


71

of the model.

Figure 3.11 A dependent responses of the generalised Bouc-Wen model: (a) force-displacement loops; (b) force-velocity loops

Figure 3.12 β and γ dependent responses of the generalised Bouc-Wen model: (a) force-displacement loops of changing β; (b) force-velocity loops of changing γ

Paramters β and γ have been recognised to determine the shape of hysteresis loops. shows

the force-displacement correlations dependent on the change of β and γ, respectively. It

is seen from Figure 3.12 (a) that the nonlinearity tends to be more obvious as the value of

β gets smaller. On the contrary, when β grows, the hysteretic shapes are inclined to be

linear ellipses. It is noteworthy that an effective β should be kept positive. In other words,

β should fluctuate in an effective range for reproducing reasonable hysteretic shapes on

-6 -4 -2 0 2 4 6-250

-200

-150

-100

-50

0

50

100

150

200

250

Displacement (mm)

Shea

r for

ce (N

)

A=1.5A=3.0A=4.29A=6A=7.5

-150 -100 -50 0 50 100 150-250

-200

-150

-100

-50

0

50

100

150

200

250

Velocity (mm/s)

Shea

r for

ce (N

)

(a) (b)

-6 -4 -2 0 2 4 6-400

-300

-200

-100

0

100

200

300

400

Displacement (mm)

Shea

r for

ce (N

)

=2.5=3.0=4.48=8.0=10.0

-6 -4 -2 0 2 4 6-300

-200

-100

0

100

200

300

Displacement (mm)

Shea

r for

ce (N

)

=-3.0=-1.97=-1.0=1.=3.0

(a) (b)


72

condition that all the other referenced parameters are fixed. As for the influence of

Figure 3.13 Comparison between experimental force and predicted force by Bouc-Wen model

with random displacement input

parameter γ, the trend of hysteresis loops’ change subjected to the tuning of parameter

0 2 4 6 8 10-50

0

50

Time (s)

Forc

e (N

)

0A

Experimental data Predicted force

0 2 4 6 8 10-200

-100

0

100

200

Time (s)

Forc

e (N

)

1A


0 2 4 6 8 10-300

-200

-100

0

100

200

300

Time (s)

Forc

e (N

)

2A


0 2 4 6 8 10-400

-200

0

200

400

Time (s)

Forc

e (N

)

3A



73

value is quite similar to that of β. In the case when γ is negative, the nonlinearity level

Figure 3.14 Comparison between experimental force and predicted force by Bouc-Wen model

with El Centro earthquake displacement input

increases with the increasing absolute value of γ. Otherwise, the hysteresis loops progress

0 10 20 30 40 50-50

0

50

Time (s)

Forc

e (N

)

0A


0 10 20 30 40 50-200

-100

0

100

200

Time (s)

Forc

e (N

)

1A


0 10 20 30 40 50-300

-200

-100

0

100

200

300

Time (s)

Forc

e (N

)

2A


0 10 20 30 40 50-400

-200

0

200

400

Time (s)

Forc

e (N

)

3A



74

linearly. It is also noticed that, although the nonlinearity of model reduces with the

increase of both values of β and γ, the influence of parameter value’s change on the

hysteresis shape becomes rather limited when the parameter reaches certain value.

3.3.1.4 Modal Validation

Finally, to evaluate the performance of the generalised Bouc-Wen model of MRE base

isolator, the shear forces predicted by the proposed model and measured experimentally

are compared under two different displacement excitation scenarios, i.e. random

excitation with the maximum amplitude of 5mm and excitation frequency between 1Hz

and 20Hz and a magnitude scaled El Centro earthquake. The reason for choosing these

two displacement inputs is to demonstrate the feasibility and accuracy of utilising the

model in practical application under real environmental disturbance. As the frequency

and amplitude of displacement in these input situations varies throughout the record, the

time histories of predicted and measured shear force are compared instead of force-

displacement and force-velocity loops to evaluate the fitting performance of the proposed

model.

The time histories of force response under two excitation cases are shown in Figure 3.13

and Figure 3.14. Each displacement scenario is tested with four different applied currents

ranging as 0A, 1A, 2A and 3A. As can be seen from the graphs, the generalised Bouc-

Wen model can perfectly predict the shear force compared to the measured results even

under random or real earthquake displacement excitation scenarios, which indicates a

promising application in control system synthesis and analysis.

3.3.2 Strain-Stiffening Model

3.3.2.1 Modelling Process of Strain-Stiffening Model

Through the observation of dynamic characteristics of MRE isolator shown in Figure 3.2,

it can be concluded that the MRE base isolator presents two major dynamic features, i.e.


75

viscoelasticity and strain stiffening. In other words, the force-displacement hysteresis

Figure 3.15 Break-down of the hysteresis of MRE base isolator

Figure 3.16 Schematic diagram of the proposed strain-stiffening model for MRE isolator

loops can be recognised as the superposition of two typical curves as shown in Figure

3.15. The first curve is the hysteresis loop traditionally utilised to describe he viscoelastic

feature of rubbers while the other is a strain-stiffening curve representing the increase of

stiffness when the isolator experience large displacement at the presence of magnetic

field. The dynamic characteristics regarding to viscoelasticity of the device are

represented by the Kevin model (Christensen 2012), which consists of a linear spring and

a viscos dashpot. The strain-stiffening component, on the other hand, is represented by a

nonlinear spring. As a result, a strain-stiffening model is proposed by paralleling the

Kevin model and strain stiffening spring, as shown in Figure 3.16. The mathematical

xc xc= +

Hysteresis dynamicsof MRE base isolator

Viscoelasticitycomponent

Strain-stiffeningcomponent

Strain stiffening componentx

F - F0

c0

k0


76

expression of the model can be expressed by

Eq. 3.3

where c0 and k0 denote the damping and stiffness parameters in the Kevin model,

respectively; α is a coefficient for the power law element; F0 is the initial shear force

produced by the initial displacement of the device.

The following steps of modelling of strain-stiffening model are conducted similarly to

that of the modelling process of Bouc-Wen model: identification of parameters c0, k0, α

and F0; analysis of parameter identification results; analysis of influence of changing

parameters on the model; model validation using random displacement input.

By solving a related linear least square (LS) problem, the parameters in Eq. 3.3 can be

identified for the proposed model. In the LS solving process, the displacement x and

velocity of the device are supposed as constants at each time point t. Hence, Eq. 3.3

can be more explicitly illustrated by

Eq. 3.4

The vector consisting of parameters to be identified is then built as

Eq. 3.5

According to the reference (Stergioulas, Cebon & Macleod 2000), the normal equation

governing parameter vector can be written as

Eq. 3.6

where denotes the measurement vector (sample Yi taken at time

sample ti) , corresponding to collected shear force F(t) in this work; N is the number of

input-output pairs in one hysteretic loop; G is the design matrix of the LS fit, which can

GTG b GTY

110 NYYYY


77

be expressed by

Eq. 3.7

3.3.2.2 Parameter Identification Results

Same testing data as in Bouc-Wen modelling process is used in the identification of strain-stiffening model. The LS solution of model parameters is then calculated according to Eq. 3.6. 48 sets of parameters are identified under each excitation scenario (applied current = 0, 1A, 2A, 3A; sinusoidal amplitude = 2mm, 4mm, 8mm; sinusoidal frequency= 0.1Hz, 1Hz, 2Hz, 3Hz).

The identified parameter values are summarised in

Table 3.2. With the identified parameters, the measured and predicted hysteresis loops in

some cases are compared in Figure 3.17 to Figure 3.19.

Figure 3.17 Comparison between experimental data and forecast values from the proposed

model with different excitation amplitudes (1Hz-3A)

Figure 3.17 presents the comparison of the measured and predicted responses with

different loading amplitudes with an excitation frequency of 1Hz and the applied current

fixed to 3A. As observed, the maximal shear force and corresponding damping exhibit an

obvious magnification with the adding amplitude. Moreover, the phenomenon of Mullins

effect is also reasonably described by the proposed model as is in Bouc-Wen model

-10 -5 0 5 10-400

-200

0

200

400

Displacement (mm)

Shea

r for

ce (N

)

-60 -40 -20 0 20 40 60-400

-200

0

200

400

Velocity (mm/s)

Shea

r for

ce (N

)

2mm-measured

2mm-predicted

4mm-measured

4mm-predicted

8mm-measured

8mm-predicted


78

(Mullins 1948; Mullins & Tobin 1957).


model with different applied current (2Hz-4mm)

Figure 3.18 illustrates the force-displacement and force-velocity curves under different

applied current when the sinusoidal displacement excitation has a frequency of 2Hz and

amplitude of 4m. It is aforementioned that increasing applied current leads to an

amplification of effective stiffness and stain stiffening of the device responses. Four

groups of comparison results confirm the capacity of the proposed model to demonstrate

this phenomenon caused by the ascending current. It is noteworthy that, in every

hysteretic loop, the strain-stiffening model can perfectly depict the strain-stiffening

phenomenon of MRE isolator.

Figure 3.19 shows the comparative results between experimental measurements and

forecast forces from the proposed model when the loading amplitude is 4mm and the

applied current is 1A. It is noted that the force-displacement loop almost keeps unchanged

with different loading frequencies. Particularly, when the frequency is above 0.1Hz, the

shear force and effective stiffness, denoted by the slope of the force-displacement curve,

are independent of the excitation frequency.

-5 0 5-300

-200

-100

0

100

200

300

Displacement (mm)

Shea

r for

ce (N

)

-30 -20 -10 0 10 20 30-300

-200

-100

0

100

200

300

Velocity (mm/s)Sh

ear f

orce

(N)

0A-measured0A-predicted1A-measured

1A-predicted2A-measured

2A-predicted3A-measured3A-predicted


79


model with different applied current (1A-4mm)

3.3.2.3 Modelling Analysis

Similar to Bouc-Wen mdoel, a comparative study is conducted to analyse the influences

of the model parameters on the output responses of the model adopting the displacement

and velocity data obtained from the test of sinusoidal excitation with frequency of 2Hz

and amplitude of 4m and applied current of 3A. Figure 3.20 describes a series of force-

displacement/velocity responses in relation to different values of k0: 5, 23.1482, 40 and

60. Similar to k in Bouc-Wen model, increase of values of k0 leads to the growth of

effective stiffness as well as the maximal shear force, which linearly rises with the

increasing values of k0. The influence of value of parameter c0 on the output response of

the device is given in Figure 3.21. Unlike parameter k0, c0 has little effect on the maximal

shear force and effective stiffness of the isolator but gives rise to the obvious expansion

of the enclosed area in the force-displacement loops. Parameter α has acquired the

recognition for the strain stiffening of the hysteretic loops. Figure 3.22 shows four sets of

hysteretic loops with varied sizes and shapes with respect to different values of α. It is

noticeable that in the small displacement region, the force-displacement response almost

coincides with others with different α. However, when the adding displacement is more

than a specific value (1.5mm in this case), the strain stiffening behaviour becomes

-5 0 5

-100

-50

0

50

100

Displacement (mm)

Shea

r for

ce (N

)

-100 -50 0 50 100

-100

-50

0

50

100

Velocity (mm/s)

Shea

r for

ce (N

)

0.1Hz-measured0.1Hz-predicted1Hz-measured1Hz-predicted2Hz-measured2Hz-predicted4Hz-measured4Hz-predicted


80

obvious.

Figure 3.20 k0 dependent responses of the generalised strain-stiffening model: (a) force-

displacement loops; (b) force-velocity loops

Figure 3.21 c0 dependent responses of the generalised strain-stiffening model: (a) force-


-5 0 5-400

-300

-200

-100

0

100

200

300

400

Displacement (mm)

Shea

r for

ce (N

)

k

0=5

k0=23.1482

k0=40

k0=60

-60 -40 -20 0 20 40 60-400

-300

-200

-100

0

100

200

300

400

Velocity (mm/s)

Shea

r for

ce (N

)

(a) (b)

-5 0 5-200

-150

-100

-50

0

50

100

150

200

Displacement (mm)

Shea

r for

ce (N

)

c

0=0.5

c0=1

c0=1.42

c0=2

-60 -40 -20 0 20 40 60-200

-150

-100

-50

0

50

100

150

200

Velocity (mm/s)

Shea

r for

ce (N

)

(a) (b)

81

Table 3.2 Identified parameter values for strain-stiffening model under different excitation scenarios

Frequency 0.1Hz

Current 0A 1A 2A 3A

Amplitude 2mm 4mm 8mm 2mm 4mm 8mm 2mm 4mm 8mm 2mm 4mm 8mm

k0 4.58 3.83 3.10 19.56 12.87 8.78 35.82 23.01 15.19 53.79 36.15 23.12

c0 2.22 1.89 1.61 17.05 12.61 9.43 30.97 21.73 15.92 39.81 27.81 21.19

α 0.03 0.01 0.00 0.66 0.09 0.01 1.25 0.16 0.02 1.54 0.20 0.02

F0 1.61 1.47 1.22 -1.98 -2.65 -3.08 -4.79 -5.34 -5.66 -7.23 -6.82 -4.58

Frequency 1Hz

Current 0A 0A 0A 0A


k0 4.94 4.45 3.84 20.05 13.17 9.17 37.20 24.05 16.30 50.03 33.79 22.87

c0 0.37 0.35 0.32 2.27 1.63 1.23 3.90 2.68 2.01 4.48 3.14 2.37

α 0.02 0.00 0.00 0.95 0.13 0.02 1.74 0.22 0.03 1.69 0.22 0.03

F0 -0.04 0.48 -1.35 -0.06 -0.80 -1.47 0.95 -2.05 -2.97 -3.86 -4.28 -4.61

82

Table 3.2 Identified parameter values for strain-stiffening model under different excitation scenarios (cont’d)

Frequency 2Hz

Current 0A 0A 0A 0A


k0 5.81 5.19 4.39 20.43 13.34 9.08 36.22 23.15 15.30 47.62 31.71 21.49

c0 0.24 0.22 0.20 1.21 0.88 0.67 2.05 1.42 1.06 2.38 1.65 1.26

α 0.01 0.00 0.00 0.93 0.13 0.02 1.72 0.22 0.03 1.80 0.24 0.03

F0 1.67 1.59 1.34 0.34 -0.07 -0.98 -1.26 -1.36 -2.07 -3.31 -2.93 -3.16

Frequency 4Hz

Current 0A 0A 0A 0A


k0 7.07 6.27 5.31 21.29 13.37 8.81 36.58 22.82 14.45 47.89 30.71 20.06

c0 0.15 0.14 0.13 0.65 0.47 0.37 1.06 0.74 0.56 1.23 0.86 0.65

α 0.02 0.01 0.00 0.79 0.13 0.02 1.71 0.22 0.03 1.87 0.25 0.03

F0 1.58 1.55 1.28 0.86 0.50 -0.57 0.48 0.41 0.31 -1.09 -0.82 -1.10


83

Figure 3.22 α dependent responses of the generalised strain-stiffening model: (a) force-


Figure 3.23 F0 dependent responses of the generalised strain-stiffening model: (a) force-


So far, the parameter values are considered as function of applied current, excitation

amplitude and frequency since previous studies have pointed out that the performance of

the MRE base isolator is closely related to those three variables (Li, Li, Tian, et al. 2013;

Yang et al. 2013). However, as discovered in Figure 3.19, the changes in hysteresis loops

are negligible with different frequency values. Hence, to further simplify the generalised

model, the effect of excitation frequency on the model parameter is to be explored. Figure

3.24 illustrates the relationships between applied current and model parameters k0, c0, α

and F0 at different frequencies (from 0.1Hz to 4Hz) when excitation amplitude is 4mm.

-5 0 5-400

-300

-200

-100

0

100

200

300

400

Displacement (mm)

Shea

r for

ce (N

)

=0.05=0.22=0.6=1.0

-60 -40 -20 0 20 40 60-400

-300

-200

-100

0

100

200

300

400

Velocity (mm/s)

Shea

r for

ce (N

)

(a) (b)

-5 0 5-300

-200

-100

0

100

200

300

Displacement (mm)

Shea

r for

ce (N

)

F

0=-30

F0=-1.36

F0=30

F0=60

-60 -40 -20 0 20 40 60-300

-200

-100

0

100

200

300

Velocity (mm/s)

Shea

r for

ce (N

)

(a) (b)


84

As seen, the scatter lines of 1Hz, 2Hz and 4Hz are close to each other for all parameters.

It is safe to conclude that all the parameters are just related to the supplying current when

the amplitude is fixed when the frequency is above 0.1Hz. As the 0.1Hz test is conducted

as a quasi-static excitation, the change of parameter values from the 0.1Hz frequency case

can be neglected when building the generalized field-dependent model in this paper.

Figure 3.24 Correlations between parameter values and applied current with different excitation

frequencies

To further demonstrate the point, Figure 3.25 shows the effect of varied excitation

frequency on the model parameters for 4mm loading excitations at different applied

current levels from 0A to 3A. As can be seen from the figure, damping coefficient c0

presents a nearly exponential decline with the ascending frequency, but when the

frequency is larger than 1Hz, the differences between c0 with different frequencies are

negligible. The changes in parameters k0 and α, however, are fairly small with the

0 1 2 30

5

10

15

20

25

30

35

40

Current (A)

Para

met

er fo

r k0

0.1Hz1Hz2Hz4Hz

0 1 2 30

5

10

15

20

25

30

Current (A)

Para

met

er fo

r c0

0.1Hz1Hz2Hz4Hz

0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Current (A)

Para

met

er fo

r

0.1Hz1Hz2Hz4Hz

0 1 2 3-8

-6

-4

-2

0

2

Current (A)

Para

met

er fo

r F0

0.1Hz1Hz2Hz4Hz


85

enhanced frequency. Especially when the frequency is in the range between 1Hz and 4Hz,

there are very tiny differences among parameter values with different frequencies. The

effect of frequency changes on parameter F0, although is relatively more obvious than the

other three parameters, is still acceptable. Nevertheless, the difference between every line

in each graph shows the parameter values are closely related to current level.

Figure 3.25 Correlations between parameter values and excitation frequency with different

applied current

Next, Figure 3.26 further explores the correlations between model parameters and applied

currents as well as excitation amplitude when frequency is fixed at 2Hz. It can be seen

from the figure that in the case of no current applied to the device, all model parameters

for different loading amplitude conditions have the similar values, which is also

demonstrated in Figure 3.24. When the device gets energised, these parameters show a

rather linear change with the current and amplitude. Another obvious phenomenon is that

0 1 2 3 40

5

10

15

20

25

30

35

40

Frequency (Hz)

Para

met

er fo

r k0

0A1A2A3A

0 1 2 3 40

5

10

15

20

25

30

Frequency (Hz)

Para

met

er fo

r c0

0A1A2A3A

0 1 2 3 40

0.05

0.1

0.15

0.2

0.25

Frequency (Hz)

Para

met

er fo

r

0A1A2A3A

0 1 2 3 4-8

-6

-4

-2

0

2

Frequency (Hz)

Para

met

er fo

r F0

0A1A2A3A


86

the smaller the loading amplitude, the quicker the parameters vary with the increasing

current. These relationships will provide the useful information on the development of

the generalized model for the system identification and structural control based on this

device.

Figure 3.26 Correlations between parameter values and applied current with different excitation

amplitudes

According to the above analysis, it is concluded that the model parameters are mainly

dependent on the loading amplitude and applied current. The specific relationships of

each parameter regarding to the loading amplitude and applied current are depicted in

0 1 2 30

10

20

30

40

50

Current (A)

Para

met

er fo

r k0

2mm4mm8mm

0 1 2 30

2

4

6

8

10

12

Current (A)

Para

met

er fo

r c0

2mm4mm8mm

0 1 2 30

0.5

1

1.5

2

Current (A)

Para

met

er fo

r

2mm4mm8mm

0 1 2 3-4

-3

-2

-1

0

1

2

Current (A)

Para

met

er fo

r F0

2mm4mm8mm


87

Figure 3.27 and expressed by Eq. 3.8.

Eq. 3.8

where xmax denotes the maximal value of the displacement corresponding to the loading

amplitude. Hence, Eq. 3.4 can be re-written as in Eq 3.9 and LS method is used to identify

the parameters in these expressions, results of which are listed in Table 3.3.

Eq. 3.9

Figure 3.27 Relationships between model parameters and applied current as well as absolute

24

68

01

230

1

2

3

Max-displacement (mm)Current (A)

c 0

24

68

01

230

20

40

60


k 0

24

68

01

230

1

2

3


a

2

4

6

8

0

1

2

3-5

0

5

Max-displacemenCurrent (A)

F 0


88

maximal displacement

Table 3.3 Final identified parameter values of strain-stiffening model

Parameter Unit Value

N/mm 5.06

N / (mm·A) 24.41

N·s / mm 0.3212

N·s / (mm·A) 1.139

N / mm4 0.05346

N / (mm4·A) 6.905

N 1.446

N / A -1.358

a1 -- -0.7332

a2 -- -0.6053

a3 -- -3.354

a4 -- 0.08596

3.3.2.4 Validation of Strain-Stiffening Model

To demonstrate the effectiveness and accuracy of this generalized model, a series of

dynamic tests are executed based on the random inputs with the maximum amplitude of

5mm and excitation frequency between 1Hz and 20Hz. Meanwhile, two cases of applied

current, namely, 0A and 3A, are considered. The sampling time and frequency for all

dynamic tests is set as 2s and 256Hz, respectively. As can be seen from Eq. 3.8, all the

parameters used in the mathematical expression of the strain-stiffening model are

functions of two variables, namely, applied current and maximum displacement of the

input. Therefore, the maximal displacement of the random excitation, 3mm, is chosen as

the value of variable xmax in the numerical validation. It is worth pointing out that it is

unrealistic to acquire the maximum displacement of an unexpected displacement input.

Therefore, the performance of the proposed model can be compromised in practical

k01

k02

c01

c02


89

application.

Figure 3.28 Comparison between experimental force and predicted force by strain-stiffening

model with random displacement input (I = 0A)

Figure 3.28 (a) and Figure 3.29 (a) gives the sampled displacement and calculated

velocity of the device as well as the current level for two cases. Then these data are

regarded as the inputs and sent to the generalized strain-stiffening model to calculate the

outputs of shear force. Figure 3.28 (b) and Figure 3.29 (b) compares the force measured

0 0.5 1 1.5 2-40

-20

0

20

40

Time (s)

Shea

r for

ce/N

measured forcepredicted force

(a)

(b)

0 0.5 1 1.5 2-150

-100

-50

0

50

100

150

Time (s)

Vel

ocity

(mm

/s)

Random excitation (I = 0A)

0 0.5 1 1.5 2-3

-2

-1

0

1

2

3

Time (s)

Disp

lace

men

t (m

m)


90

by the load cell with output results from the model. It can be clearly observed that the

proposed strain-stiffening model offers predicted force of satisfactory agreements with

the experimental data for two random testing cases. And the fitting results verify the

feasibility and reliability of this model for its application in the vibration control of

building structures using MRE base isolator.

Figure 3.29 Comparison between experimental force and predicted force by strain-stiffening

0 0.5 1 1.5 2-300

-200

-100

0

100

200

300

Time (s)

Shea

r for

ce/N

measured forcepredicted force

(a)

(b)

0 0.5 1 1.5 2-150

-100

-50

0

50

100

150

Time (s)

Vel

ocity

(mm

/s)

Random excitation (I = 3A)

0 0.5 1 1.5 2-3

-2

-1

0

1

2

3

Time (s)

Disp

lace

men

t (m

m)


91

model with random displacement input (I = 3A)

3.3.3 Comparison of Bouc-Wen Model and Strain-Stiffening Model

The performances of Bouc-Wen model and strain-stiffening model have been compared

in this section to discuss their own strengths and disadvantages. Three aspects have been

compared, namely, involved parameters (complexity of the model), root mean square

(RMS) error between experimental data and predicted force, running time for model

identification. To construct an unbiased comparison, both the models are evaluated with

the same testing data (1Hz-4mm-2A). The comparison results are listed in Table 3.4.

Table 3.4 Comparison results between Bouc-Wen model and strain-stiffening model

Bouc-Wen model strain-stiffening model

Expression

Parameter k, c, α, A, β, γ k0, c0, α, F0

Dependent variable I I, xmax

RMS error 5.3194 5.4935

Running time (s) 168.4959 2.7367

As can be seen from the comparative results, the expression of Bouc-Wen model, which

involves six parameters and the evolutionary variable z(t), is apparently more complicated

than the strain-stiffening model. Hence, the identification of Bouc-Wen model is rather

time-consuming compared to that of the strain-stiffening model. Meanwhile, the RMS

error of Bouc-Wen model is slightly smaller than that of the strain-stiffening model,

which shows slight superiority in prediction accuracy to the strain-stiffening model.

However, the parameter values in Bouc-Wen model only depend on the input current I

while the strain-stiffening model is related to both current and maximum displacement of

excitation. In practical applications, especially earthquake attack situations, it is

impossible to predict or acquire the knowledge of input amplitude. Therefore, it is not

realistic to utilise the strain-stiffening model in practical applications or at least a

nn zxzzxxAzzxcxkF

100


92

compromise has to be made, which might degrade the performance of the model. To this

end, the generalised Bouc-Wen model is utilised in the following chapters for the control

synthesis and analysis of the MRE base isolation system.

3.4 INVERSE MODEL OF MRE BASE ISOLATOR

3.4.1 Introduction

To control a structure equipped with semi-active devices, such as MRF dampers and MRE

isolator, the design of controllers often requires two stage actions in order to generate the

required control: (i) determining the desired primary control action (such as actuation

force) based on the feedback responses; (ii) determining required control command (i.e.

the current/voltage) to drive the semi-active devices in order to generate primary control

action (Xia 2003). The forward models discussed in the previous sections of this chapter

both present the correlations between response feedback, applied current and the

generated control force of the MRE isolator. However, to realize the aforementioned

control procedure, another type of model is required to generate the desired current

applied on the isolator based on the calculated control force and real-time response

feedback. In other words, the control action required by the semi-active system relies on

not feedbacks of the system but the inversed dynamics of the semi-active devices under

a given status of the devices (i.e. instant displacements, velocities and accelerations).

When it comes to semi-active control approaches, a good demonstration is the clipped-

optimal control (COC) proposed by Dyke et al. (1996) for real-time control of structures

equipped with the MR dampers. In this control strategy, a simple clipped algorithm is

used to generate the control command (zero or maximum voltage) to drive MR dampers

based on the measured force feedback. The control strategy combines H2/LQG optimal

controller for calculating the desired control force and a voltage selecting algorithm for

driving MR damper. In another word, two feedback loops are required: one for


93

determining the desired control force from the system feedbacks and the other one for

determining control commend (voltage to drive the devices) from the measured force

feedback (Jansen & Dyke 2000). There are two major drawbacks in these kinds of control

strategies: firstly, the measurement of feedback actuation force might not be always

feasible, e.g. in the case of MRE base isolator and secondly, the control efficiency is

greatly compromised due to simple clipped control (zero or maximum). To this end,

utilising inverse models that describes inverse dynamics between command signals and

actuator force for determining control command to drive the device based on system

feedbacks becomes popular in recent semi-active control research (Bahar et al. 2010;

Chang & Zhou 2002; Weber 2015). However, due to inherent highly nonlinear and

hysteretic nature of semi-active devices, it is rather challenging to obtain explicit inverse

dynamic model of semi-active devices. Taking advantage of neural network (NN) models

in emulating arbitrary function at various accuracy levels (Cybenko 1989), several neural-

network based inverse models have been investigated for applications of MR dampers.

Chang & Zhou (2002) explored the possibility of utilising the recurrent NN models to

estimate the inverse dynamics of the MR dampers. Xia (2003) has developed an inverse

model for MR damper utilising optimal multi-layer NN and system identification. Weber,

Bhowmik & Høgsberg (2014) utilised a neural network-trained inverse model of MR

damper and applied the scheme on the vibration control of a five-storey shear model.

Askari et al. (2016) investigated an NN inverse model optimised by Takagi-Sugeno-Kang

fuzzy scheme and such inverse model can well recurrent the desired control force.

However, inverse models published so far are complicated and unsuitable for real-time

control applications. For example, they often require information not only at the present

moment but also in previous time history (Xia, 2002, 2 historical time instants tracked;

Weber et al., 2014, 4 historical time instants tracked; Askari, 2016, 5 variables with 3

historical time instants tracked each). The more retroactive information required, the

longer inevitable delay tolerance will be produced. Some require a wide range of system

inputs as training signal and extremely careful selection of regressor set. In addition, there


94

is neither inverse model nor current selecting strategy being reported for real-time control

of the MR elastomer base isolation systems.

To address the aforementioned challenges, an inverse model based on general regression

neural network (GRNN) is developed to determine the applied current to the MR

elastomer isolator so as to generate desired control force calculated by the designated

controller. The main superiority of the proposed GRNN-based inverse model is

summarised as following:

1) The model structure of GRNN-based inverse model is free of assumptions, which

avoids complicated model identification.

2) The proposed GRNN inverse model only requires inputs of displacement,

velocity, force at present and one previous time instant, which will result in much

less time delay in the control.

3) The GRNN adopts one-pass-learning algorithm which makes it much faster to

form the conditional mean regression surface than commonly used back

propagation (BP) algorithm, which is beneficial to online model training in the

practical application.

4) Different from other neural networks, the predictions of GRNN are always apt to

converge to the global optimal solution and will not fall into the local optimum.

5) The time interval from the calculation of optimal control force to the generation

of the desired applied current is less than 1 ms, satisfying the requirement of real-

time structural control.

3.4.2 Experimental Setup and Training Data

To acquire the training data for GRNN inverse model development, an experimental setup

similar as shown in Figure 3.1 is employed. Since the inverse model needs to generate

current at a wide range based on the input signals, constant current excitation is no longer


95

suitable for the training data selection. Hence, a random current input needs to be chosen

so as to cover the possible scope in real application. To this end, the testing frame

displayed in Figure 3.30 was designed and setup to acquire adequate MRE isolator’s

response data for the training. As shown, a dSPACE DS 1104 R&D controller board was

employed as data acquisition system as well as command current controller. The A/D

converter of dSPACE board consists of four 12-bit parallel channels and four 16-bit

multiplexed channels. Three parallel channels were used to acquire the current, force and

displacement signals, respectively. PWM output portal in slave DSP of dSPACE

generates duty cycle signal to drive the current source according to the current control

command. The PWM servo current drive was designed to minimise the response time of

MRE isolator, of which details can be seen in the reference (Gu, Li & Li 2016). As can

be seen in Figure 3.30, the top plate of the isolator was connected to the reference wall

via a Tedea Huntleigh C&T load cell (Part No. 0615-0200-G000-RS). The bottom plate

of MRE isolator was fixed to the shake table, which provides horizontal motion for

generating the deformation of the isolator. The displacement was measured by Baumer

laser distance sensor (Part No. OADM 20I4460/S14C). The current input to the isolator

was measured by a Hall Effect current transducer (Part No. CSLA2CD).

Figure 3.30 Experimental setup for MRE inverse model identification

Using experimental setup displayed in Figure 3.30, a series of tests has been conducted

to observe the MRE isolator’s dynamic response under various types of loadings. To

obtain high quality trained inverse model, the training and testing data has to be selected

carefully. In this study, the current signal was chosen to be a normally distributed random

process within the range between 0A and 5A while the displacement signal was a sine


96

sweep excitation with amplitude of 5mm and a frequency range from 0.1 to 4Hz. The

reason for choosing 5A as the upper limit of input current is to enlarge the stiffness

varying range of the isolator so it can provide better adjustability for the isolated structure

during practical application. The data was sampled at a rate of 1000Hz for 35 seconds,

which means 35,000 sets of data and the first 30,000 sets were utilised as the training data

and last 5000 sets were used as validation data. Loading signals of current and

displacement as well as force response of MRE isolator are shown in Figure 3.31.

Figure 3.31 Training data for GRNN inverse model

3.4.3 Inverse Modelling of MRE Base Isolator

This section presents the development of the optimal inverse model of MRE base isolator.

0 5 10 15 20 25 30-5

0

5

Time (s)

Dis

plac

emen

t (m

m)

0 5 10 15 20 25 300

2

4

6

Time (s)

Cur

rent

(A)

0 5 10 15 20 25 30

-20

0

20

Time (s)

Forc

e(N

)


97

The methodology of general regression neural network (GRNN) is firstly introduced,

followed by a fruit fly optimisation seeking for best smoothing factor σ in GRNN. In the

third part, an inverse model based on optimal GRNN is developed and the accuracy of

the proposed inverse model was testified by comparing the measured and predicted

currents for MRE isolator.

3.4.3.1 General Regression Neural Network (GRNN)

The general regression neural network (GRNN), proposed by Specht in 1991, is a radial

basis function (RBF) network, which is used to set up the complicated regression between

a group of independent variables X and the target output Y (Specht 1991). It was

developed based on nonlinear regression analysis. Suppose the joint probability density

function (PDF) of random variables x and y is f(x, y), if the observed value of x is X, the

regression of X relative to y, i.e. conditional mean value, can be expressed as:

Eq. 3.10

where X denotes the input and denotes the predicted output. If the PDF f(x, y) is

unknown, its non-parametric estimation can be obtained from the sample observations of

x and y, shown as:

Eq. 3.11

where Xi and Yi denote the sample observations of random variables x and y; σ is the

smooth parameter that represents the width of the kernel function; n denotes the number

of the samples; m denotes the dimension of random variable x. Substitute Eq. (2) for the

PDF in Eq. (1) and the expression of expected conditional mean value of y given X is


98

changed to the following equation

Eq. 3.12

Here, a Euclid distance-based parameter is defined as

Eq. 3.13

Due to the fact that , the expression of is simplified via the integral

operation, which can be shown as

Eq. 3.14

In GRNN, the smoothing factor σ is a key parameter, which directly affects the

generalisation capacity of the trained network. When σ is assigned by a high value,

approximates the mean value of dependent variables of all the samples. However, when

the value of σ tends to be 0, will be close to the training samples. On this occasion,

if the sample to be predicted is included in the training samples, the prediction is

extremely close to corresponding dependent variable in the samples; otherwise, poor

result will be obtained when the predicted sample is excluded from the training samples,

which indicates the poor capacity of the network. Consequently, only when σ is

appropriately set, the dependent variables of the training samples will all be considered

in the calculation of output . Therefore, optimisation of smoothing factor σ has to

be conducted for high quality GRNN. In this study, fruit fly optimisation algorithm (FOA)

ze z2

dz 0


99

is employed to seek for best σ, which is illustrated in the following sections.

3.4.3.2 Fruit Fly Optimization Algorithm (FOA)

FOA is a novel heuristic swarm optimisation algorithm with the benefits of few

parameters, simple code implementation and easy adjustment. Based on the food search

behaviour of fruit flies, the brief procedure of FOA can be summarised as the following

steps.

Step 1. Initialise the position of the fly swarm: X_axis and Y_axis.

Step 2. Randomly assign the direction and range of each fly to search for food using the

sense of smell

Eq. 3.15

Eq. 3.16

where RandomValue denotes the search range.

Step 3. Because the actual position of food is unknown, the distance Disti between the ith

fly and the original point (0, 0) is calculated first. Then its reciprocal Si, representing the

smell concentration decision value of ith fly, is obtained according to the following

expression

Eq. 3.17

Eq. 3.18

Step 4. Substitute the value of Si into the fitness function to get the smell concentration

Xi Xaxis RandomValue

Yi Yaxis RandomValue

Disti Xi2 Yi

2

Si 1Disti


100

value of ith fly

Eq. 3.19

Step 5. In the fruit fly swarm, find out the fly with minimum smell concentration value

(for minimization optimisation problem)

Eq. 3.20

where bestSmell denotes the optimal concentration value and bestIndex denotes the index

number of the fly with the optimal smell concentration.

Step 6. Preserve the coordinates of x and y as well as the best smell concentration

bestSmell. In the meantime, the whole swarm will fly to this location according to the

visual sense.

Eq. 3.21

Step 7. Iteratively repeat Step 2 to Step 5. Compare the current optimal smell

concentration with the previous one. If the current result is better than the previous one,

conduct Step 6.

3.4.4 MRE Base Isolator Inverse Model Based on FOA-Optimised GRNN

A GRNN-based inverse model is built to depict the nonlinear relationship between device

responses and applied currents. In this model, the input variables are displacement,

velocity and shear forces captured at time t - 1 and t while the output is the desirable

applied current at time t. The configuration of the proposed inverse model of MRE

isolator is shown in Figure 3.32, which consists of an input layer, a hidden layer, a

summation layer and an output layer. The neuron number of input layer corresponds to

the dimension of input variables and the function of input layer is to transmit these

Smelli function Si

bestSmell bestIndex min Smelli

Smellbest bestSmellXaxis X bestIndex Yaxis Y bestIndex


101

variables to next layer. In the hidden layer, each neuron corresponds to each training

sample and the transfer function in this layer can be obtained from the denominator part

in Eq. 3.14. Two sorts of neuron summations exist in the summation layer: one is the

arithmetic summation and the other one is weighted summation. The neuron in the output

layer corresponds to the current level that is supplied to the MRE isolator, which is equal

to the ratio between two summations.

As aforementioned, smoothing factor plays a significant role on the generalisation ability

of trained network. Hence, to obtain the best prediction ability of the network, FOA is

employed to select the best smoothing factor σ in GRNN. The detailed optimisation

procedure is provided as follows:

Figure 3.32 Schematic diagram of inverse model based on GRNN

i) Initialise the fruit fly swarm, including swarm size, maximum iteration number and

initial positions. Here, the swarm size and maximum iteration number are set to be 20 and

100, as suggested by Pan et al. (2012). Because the food source is not known, each fly

calculates the range between its position coordinate and original point according to Eq.

Input Layer

Pattern Layer

Summation Layer

Output Layer

(n)

x(n-1)

(n-1)

x(n)

F(n)

I(n)

1

1

1

1

Y1Y2

Yn

Y3

F(n-1)


102

(8), and then calculate the smell concentration according to Eq. 3.18.

ii) Replace the smoothing factor with the calculated smell concentration. Then, input the

training samples and get the outputs of the network. For each fly, estimate its best

individual fitness value and the best global fitness value of the whole swarm. Here, the

fitness function is defined as the root mean square error (RMSE) between practical

measured values and outputs of the GRNN, shown as

Eq. 3.22

where N denotes the number of training samples; IT and IO denote the practical measured

currents and predicted currents from GRNN, respectively. The smaller the fitness value

is, the better the obtained smoothing factor is. Store the fly with optimal fitness value and

corresponding smell concentration in the swarm.

iii) Conduct the iteration procedure and repeat Steps 2-5 in Section 3.4.3.2. If the result

at current iteration is superior to the previous best result, substitute the current best value

for the previous one. This procedure will be terminated if the iteration number arrives at

its maximum value.

The accuracy of the obtained inverse model is then demonstrated by comparing the

measured current and model-predicted current in Figure 3.33(a). It can be clearly

observed from Figure 4 that the optimal GRNN inverse model can precisely recurrent the

inverse dynamics of the MRE base isolator. Moreover, Figure 3.33(b) provides the

correlation coefficient R between experimental results and model outputs. The higher of

this value is, the better the match between two types of responses is. Apparently, the

optimal GRNN model can get the high value of R (0.9526), which satisfies the

requirement in the modelling study. Accordingly, the proposed GRNN-based inverse

model can be considered as a satisfactory solution to overcome the challenges in the semi-

active control caused by high nonlinearity of the MRE base isolator and thus realise the


103

vibration suppression control of isolated structures.

Figure 3.33 Performance of the GRNN inverse model (a) comparison between measured current and GRNN output; (b) regression analysis of results

3.5 SUMMARY

For the control analysis and synthesis, the forward and inverse model of MRE base

isolator are developed to describe its dynamic characteristics in practical loading and

excitation scenarios. As for the forward dynamics, a Bouc-Wen model and a novel strain-

stiffening model are proposed to capture the unique strain-stiffening feature as well as the

highly non-linear and hysteretic property of the isolator. In the identification of Bouc-

Wen model, a genetic algorithm is employed to acquire best fitting model parameters

(a)

(b)

0 1 2 3 4 51

2

3

4

5

Time(s)

Cur

rent

(A)

Measured currentPredictions of GRNN


104

while in identification of strain-stiffening model, the parameters are acquired by solving

the LS problem. Influences of parameter changes on the model’s dynamic responses are

then discussed in both models utilising the force-displacement and force-velocity

hysteresis loops. The performance of both forward models are evaluated under random

displacement excitations. Testing results show that both models can accurately predict

the shear force generated by MRE isolator but the Bouc-Wen model has slightly smaller

RMS error between numerically predicted and experimentally measured results. As for

identification complexity, the strain-stiffening model has a much smaller running time

than the Bouc-Wen model. Nevertheless, the parameters of strain-stiffening model

depend on both applied current and maximum displacement, which is unrealistic to

acquire during practical application in reality. To this end, the generalised Bouc-Wen

model is employed in the numerical study and control system design in the following

chapters in this thesis.

To realise semi-active control of a MRE base isolation system, the inverse dynamics of a

MRE base isolator has to be investigated to select current command properly according

to the optimal control force. To this end, a GRNN inverse model of MRE isolator is then

proposed and investigated. FOA is then adopted to optimise the proposed GRNN inverse

model, reason being the GRNN inverse network optimised by FOA is able to speed up

training procedure by employing one-pass-learning strategy. The performance of GRNN

inverse model is then evaluated by applying random current as well as random

displacement excitation to the MRE isolator. Testing results show an ideal agreement

between desired current and current generated by the inverse model based on same

excitations. The GRNN inverse model is going to be utilised in the LQR control discussed

in Chapter 5 to effectively avoid the influence of highly nonlinear hysteresis of the semi-

active device on the control system.

Investigation Of Response Time Of MRE Isolator For Real-Time Control

105

CHAPTER 4

INVESTIGATION OF RESPONSE TIME OF MRE

ISOLATOR FOR REAL-TIME CONTROL

4.1 CHAPTER OUTLINE

Real-time control of the MRE isolators holds the key to unlock MRE material’s unique

characteristics, i.e. instantly changeable shear modulus in continuous and reverse fashion.

However, one of the critical issues for the applications of real-time control is the response

time delay of MRE vibration isolators, which has not yet been fully addressed and studied.

In this chapter, the meaning and research gap of investigations on response time and its

effect on the control synthesis of MRE base isolation system has been discussed.

Secondly, a new testing method is proposed to determine the response time of stiffness-

variable MRE device for real-time control implementation. Using such setup, the

response time of the MRE base isolator introduced in Chapter 2 with large solenoid coil,

is evaluated experimentally. Analysis on the response time of the generated force

validates that the inductance of the coil and the electrical impedance have major

contribution to the overall response time of the device. Therefore, several approaches are

proposed and applied to reduce the impact of the coil inductance and electric impedance.

Next, the success in reducing overall response time of the MRE base isolator is reported

in both rise and fall edges. Finally, the feasibility of its implementation for real-time


106

control is validated through a case study.

4.2 BACKGROUND

For implementations of real-time control, a prompt response time of the control devices

is critically important as the control command needs to be transferred to a control action

instantly (Du & Zhang 2008; Karimi 2011). A degradation of the control performance

may be caused by applying unsynchronised control force due to time-delay in control

channel (Van de Beek, Sandell & Borjesson 1997). Moreover, time-delay may even

render instability of the control systems in some cases (Abdel-Rohman, John & Hassan

2010). Hence, time delay and its effect on the control system have to be identified clearly

before the design and application of control strategies. Normally, a time-delay

encountered by the control system can be divided into three parts: (i) time consumed for

online data acquisition by the sensors; (ii) time taken for data processing and control

command calculation; (iii) time used to output/display the control command by actuator

(Shin & Cui 1995). More generally, the delay process can be identified as two stages: (a)

data acquisition, processing and analysis and calculating and transmitting control

command (normally control force) from the computer interface to actuators, which can

be defined as the software time-delay β1; (b) time required for the actuator to realise the

output of desired control force, which can be defined as the hardware time-delay β2

(Agrawal & Yang 2000). As for β1, the time delay varies depending on the acquisition

system and control strategies employed and the methods to compensate such time delay

have been intensively studied (Richard 2003).

The hardware time-delay β2, on the other hand, mainly depends on the control device, i.e.

actuator, which apply desired actions on the structure under control. Therefore, to realise

the control of MRE base isolation system, it is necessary to investigate the response time

delay of MRE vibration isolators. Furthermore, approaches to minimise the response time

to achieve acceptable time delay β2 in control synthesis have to be explored as well. So


107

far, there have been handful researches on the response time of MR dampers, which is

hardware time-delay β2 in the control system utilising such devices (Choi & Wereley

2002; Koo, Goncalves & Ahmadian 2006; Strecker et al. 2015; Weiss et al. 1993). For

example, the typical response time of MR damper products from Lord Corporation, such

as RD-1005-3, is around 20ms (Koo, Goncalves & Ahmadian 2006). The well-known

180kN MR damper fabricated by Lord Corporation has response time of less than 60ms

(Koo, Goncalves & Ahmadian 2006), which is considered to be adequate for structural

control application in civil engineering structures (Yang et al. 2002). It is commonly

known that the main source causes time delay in MR dampers is not the response time of

MR fluids (usually less than 1 ms) but the inductance of the electromagnetics and the

output impedance of the driving electronics (Koo, Goncalves & Ahmadian 2006). It is

worthwhile to pointing out that current research on time delay of MRF dampers have

been focused on the control response (force) respect to the given current input rather than

the control response (force) respect to the command signal. However, the actual responses

time in a control system should be the physical response of a control device respect to the

command signal rather than the intermediate signal (such as current).

Same theory about response time can be applied in control system utilising MRE base

isolator, since most of the MRE isolator designs also adopt solenoid coils to provide

adjustable magnetic field to the MRE material, which may be the major source of system

time delay. However, main difference in MRF devices and MRE devices is that the design

of MRE devices usually adopts much larger electromagnetic coils, reason being in MR

damper, the magnetic field is only required to be applied on the small area of orifice to

change the status of MR fluid while in MRE isolator the magnetic filed is required across

all the MRE sheets to drive the isolator. As a result, much more complex design of driving

electronics is inevitably required for the MRE isolators. Furthermore, it is not surprising

that, when the MRE isolator features larger scale, especially in practical application in

civil structures, the inductance of solenoid can result in significant response lag and thus

jeopardises the whole control system. Looking at the existing publications on the real-


108

time control implementations of MRE device, critical issues such as the response time of

MRE device, has not yet been properly addressed. In addition, the response time effects

due to such design features of MRE devices and methods to mitigate time delay caused

by the device deserve comprehensive study.

4.3 RESPONSE TIME DEFINITION

As discussed in last section, the MRE material is able to respond to the change of applied

magnetic field rapidly and hence the response time of the current in the isolator’s solenoid

is representative in regarding to the time-delay of the isolator response. Neglecting eddy

currents in the steel components, the behaviour of the circuit can be modelled using a

resistor and an inductor in series connection. The circuit diagram of the solenoid is

illustrated when the coil is energised by current source or voltage source in Figure 4.1.

Figure 4.1 Circuit diagram of the solenoid with current and voltage sources

According to Figure 4.1, when the circuit is switched on, the equivalent excitation of the

coil is a step voltage signal with the value of VH (or step current signal of with the value

of IH). The current is governed by a first order differentiation equation Eq. 4.1. When the

applied voltage or current signal is switched to zero after the system is steady, the current

i(t) still flows in the circuit through the diode until the resistor R0 consumes all the energy.

Therefore, the governing equation for current in this case can be written as Eq. 4.2.

i(t)L0

R0

IH i(t)L0

R0

VH

+

_


109

Eq. 4.1

Eq. 4.2

in which, L0 and R0 are the inductance and resistance of the coil, respectively. Hence,

corresponding current flowing in the circuit when it is subjected to a step signal, as shown

in Figure 4.1, can be written as Eq. 4.3 and Eq. 4.4, respectively.

Eq. 4.3

Eq. 4.4

where is the time constant of this circuit. Meanwhile, the zero input response

when the power supply is switched off can be written as

Eq. 4.5

As can be calculated from Eq. 4.3 and Eq. 4.4, at the rise edge, when ,

; when , . Meanwhile, at

the fall edge, when , ; when ,

. In other words, the time required to accomplish 95% of

transition change at both rise and fall edges is three times of the time constant τ. Hench,

is then defined as the response time. The illustration of response time is displayed

in Figure 4.2. As can be seen from the formulae, the response time is only relevant to the

impedance parameters of the device itself. In other words, the response time is the

circuit’s (o MRE base isolator’s when there are no other electronic components in the

HViRdtdiL 0

00iRdtdiL

t

HRL

tH eIe

RVti 11 00

0

t

HRL

t

H eIeIti 11 00

00 RL

t

HRL

tH eIe

RVti 00

0

t

HH IRVti 631.0631.0)( 0 3t HH IRVti 95.095.0)( 0

t HH IRVti 368.0368.0)( 0 3t

HH IRVti 05.005.0)( 0

3t


110

circuit) inherent attribute.

Figure 4.2 Definition of response time at rise edge and fall edge

4.4 RESPONSE TIME CALIBRATION OF MRE BASE ISOLATOR

This section details the experimental set-up, describing the procedure used in searching

for the response time of MRE base isolator. It discusses the dynamics of the isolator used

in this study. The input signal is defined and the experimental setup measuring current

and force responses due to input excitations is illustrated. Finally, the original response

time of MRE base isolator is reported.

4.4.1 Input Excitations

In order to accurately evaluate the response time of the MRE isolator, an input signal has

to be chosen that would ensure constant displacement across the isolator. The importance

of maintaining a constant displacement becomes clear if we consider the force due to the

isolator. As mentioned earlier, different from MRF dampers, the MRE isolators are

considered as stiffness-variable devices in which the force generated are mainly

dependent on the deformation and current input. As for the deformation input, a signal

with three different constant values each lasting for seven seconds is adopted. The reason

for selecting constant displacement signal when the current is varying is obvious: since

0 0.5 1 1.5Time (s)

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5C

urre

nt (A

)Rise Time

0 0.5 1 1.5Time (s)

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Cur

rent

(A)

Fall Time

command signalresponse signal

τ, time constant

3τ,rise time

τ, time constant

3τ,fall time

F95%

F63.1%F5%

F36.8%


111

we are only concerned with the transient force response of the isolator subjected to step

change of the control command, the force change due to the deformation of isolator

complicates the analysis. For example, if a sine wave were chosen as the input, the isolator

force would vary continuously according to the changing displacement of the input.

Meanwhile, to explore the influence of displacement value on response time, the isolator

was tested under constant displacement excitations with three different values. For these

reasons, the displacement signal shown in Figure 4.3 with 2 mm, 4 mm and 6 mm is

selected in the test.

Figure 4.3 Illustration of input displacement and current excitations

To observe both the rise and fall edges of the response, a square-shape control signal with

a period of 10s was applied to the MRE isolator at each displacement stage. The peak

control signal corresponds to an applied current of 3A by amplification of the driving

electronics. Current excitation is also shown in Figure 4.3.

4.4.2 Experimental Setup

With the input signal defined, the experimental setup is shown in Figure 4.4. As discussed

in Section 4.2, there are two genres of responses in this procedure: the response of actual

current in the solenoid and the response of lateral shear force output by the isolator.

Therefore, both of the current response and force response of the isolator when subjected

to inputs should be measured, as illustrated in Figure 4.3. As shown in Figure 4.4, the

0 5 10 15Time (s)

0

1

2

3

4

5

6

7

Dis

plac

emen

t (m

m)

Displacement and current input

displacementinput current


112

MRE isolator is fixed on the shake table which undertakes designated motion during

testing. A load cell is installed in-between the MRE isolator and the reference wall for

shear force measurement. A dSPACE system is used here for dual-purposes: 1) to apply

step control signal which inputs to driving electronics and then the electromagnetic coil;

and 2) to synchronize the force and current transient responses. The detailed introduction

of dSPACE will be presented in Chapter 5. To achieve a fast response time of the current,

a PWM servo current source has been utilised by regulating an AMETEK programmable

power supplier with 1kHz PWM signal generated by dSPACE control board. The control

system will be presented in next section.

Figure 4.4 Experimental setup of current and force response testing

4.4.3 Measured Response Time

With the experimental setup, the original current and force responses of the MRE base

isolator have been measured. Table 4.1 and Figure 4.5 display the response time of rise

and fall edges when the isolator is subjected to a constant displacement of 4mm.

Table 4.1 Original current and force response time (4mm displacement)

Current response Force response

Rise edge Fall edge Rise edge Fall edge

308 296 421 402

As displayed in Table 4.1, the current response times of the rise and fall edges are 308

dSPACEcontroller board

Hall effect current transducer

Load cell

PWM servo current drive

Force response

Current response

Control commandShake table motion

MRE base isolator

Reference wall


113

ms and 296 ms while the force response times are 421 ms and 402 ms, respectively. As

observed, the majority of the response time, about 73%, is consumed during the

conversion from control command to the applied current. There is a relatively small time

lag (around 110 ms) between the current and force responses, which indicates the rapid

response of MRE material when subjected to the changing magnetic field.

Figure 4.5 Original current and force response of MRE isolator

4.5 APPROACHES TO MINIMISE RESPONSE TIME

4.5.1 Optimal Controlled PWM Servo Current Source

4.5.1.1 Briefing of PWM Servo Amplifier

To drive the solenoid of MRE base isolator, large current input is required, which,

unfortunately, cannot be provided directly by the controller board which usually outputs

low-energy control signals. A servo amplifier uses a low-energy signal to control a high-

energy power output in voltage or current sense. Servo amplifiers have been widely used

in servo systems. Schematic diagram of a typical motion control servo system is shown

0 0.5 1 1.5Time (s)

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Cur

rent

(A)

40

45

50

55

60

65

Forc

e (N

)

Rise Time

0 0.5 1 1.5Time (s)

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Cur

rent

(A)

40

45

50

55

60

65

Forc

e (N

)

Fall Time

command signalcurrent responseforce response

current rise time

force rise time

current fall time

force fall time


114

in Figure 4.6.

Figure 4.6 Schematics of a typical servo system

PWM (pulse width modulus) amplifier, as its name suggests, is an amplifier achieving

desired current/voltage level by modulating the pulse width of the output signal. At the

basis of a PWM amplifier is a current control circuit that controls the output by varying

the duty cycle of pulses at the power output stage. Duty cycle, denoted by DC, is defined

as Eq. 4.6 referring to Figure 4.7.

Figure 4.7 Definition of duty cycle

Eq. 4.6

where T is the pulse period, Ton is the on-time of the pulse and Toff is the off-time of the

pulse. In this experiment, the frequency of the PWM signal is fixed as 10kHz.

To derivate the current flow in the solenoid when the circuit is governed by the PWM

amplifier, the circuit diagram in Figure 4.1 and current formulae Eq. 4.3 and Eq. 4.5 when

the power source is switched on and off can be taken into consideration. Assume that the

solenoid is activated by a sequence of pulses with fixed duty cycle and i(0) = 0. During

Controller Servo Amplifier Actuator Load

Feedback

Feedback

CurrentReference

signal

Time

PWM

sign

al

Ton Toff

T

TTDC ON


115

the on-time of the first pulse, current i can be given by

Eq. 4.7

Where VH is the bus voltage and τ is the time constant of the circuit. Therefore, the

increment of current i during the on-time is

Eq. 4.8

At , the pulse switches to zero and according to Eq. 4.5 the current during off-time

is expressed by

Eq. 4.9

Hence, the current decrease during the off-time is

Eq. 4.10

Similarly, current changes (both increase and decrease) during the nth pulse can be derived

by

Eq. 4.11

Eq. 4.12

It can be observed from Eq. 4.11 and Eq. 4.12, with the increase of n, is becoming

smaller while grows larger, which indicates that the current will reach a steady

on

tH Tte

RVti 01

0

onTH

onon eRViTii 1)0()(

0

onTt

TtTeeRVti on

TtTH

onon

10

offon TTH

onoff eeRVTiTii 11)()(

0

onT

nTH

onon eiRVnTiTnTii 1)()(

0

offonon TT

nT

TH

onoff eeieRVTnTiTnTii 11)()(

0

oni

offi


116

state when . Notify the steady state current as Is and it can be expressed by

Eq. 4.13

As mentioned, the frequency for PWM signal is chosen as 1kHz in this study, which

makes . In that case, Eq. 4.13 can be simplified as

Eq. 4.14

which indicates that the steady state current is proportional to the duty cycle of the pulse.

4.5.1.2 PWM Servo Current Drive

Figure 4.8 PWM signal governed current source: (a) schematic diagram; (b) transfer function

block diagram

Normally, the open loop control of the PWM servo amplifier with fixed duty cycle is

considered as an ordinary constant voltage source. According to Eq. 4.14, the duty cycle

offon ii

T

TTH

s

e

eeRV

I

offon

1

10

T

DCRV

TT

RVI HonH

s00

Controller PWM switch logic

Load(Solenoid)

Feedback

Duty cycleα

Current sensor

errorIcommand

+

Imeasure=βI

Bus voltageVH

αVH I

Feedback

Duty cycleα

Current sensor

errorIcommand

+

Imeasure=βI

VH

αVH I

(a)

(b)


117

in this case should be set as

Eq. 4.15

Normally, a current driver can speed up the response of energised solenoid. Hence, as an

attempt to further reduce the response time of the MRE isolator’s magnetic circuit, a

current driver instead of the voltage source is utilised. The schematic diagram and

corresponding transfer function block diagram is shown in Figure 4.8. As can be seen in

Figure 4.8, a PI controller is employed in the feedback loop to regulate the duty cycle of

PWM signal. A current sensor is used to feedback the actual current in the solenoid. The

sensitivity factor of the sensor is assumed as β and relationship between measured current

and actual current is

Eq. 4.16

Hence, when the duty cycle is smaller than 1, i.e. the bus voltage is not saturated, the

voltage applied on the solenoid illustrated by Figure 4.8 can be written as

Eq. 4.17

where Kpi is the gain for both proportional and integral in the PI controller; Icommand is the

reference control current. Hence the steady state current is

Eq. 4.18

It is quite obvious from Eq. 4.18 that the steady state current is only affected by the

reference current as well as the sensitivity of the current sensor and hence neither the bus

voltage nor parameters of the load will affect Is.

The working principle behind the response time mitigation is simple. When the reference

current is increased, at the beginning of the response, the controller output is saturated

H

command

VRIDC 0

IImeasure

10

t

commandpiH dtIIKVtV

commands

II


118

(DC = 1) and hence apply full bus voltage on the load. During this process, the current is

governed by Eq. 4.3, where the current flow follows the same path as that of a current

increase with 100% duty cycle. The error signal decreases with the increase of the current

in the circuit, leading to the decrease of controller output. During this process, the current

is governed by Eq. 4.17 until the current is regulated to a steady state. With such operation

procedure, the current source can dramatically reduce the response time compared to a

voltage drive. Figure 4.9 illustrates the working principle and response time reduction

performance of a PWM servo current drive.

Figure 4.9 Working principle of a PWM servo current drive responding under a step command

As can be seen from Figure 4.9, the closed loop controlled current drive achieves

significant response time reduction when compared to an open loop voltage drive. As

defined in Section 4.3, the time required to reach 95% transient change is defined as

response time, which equals to three times of the time constant of the circuit. As can be

seen from Figure 4.9, regardless of the reference signal value, the response time of the

voltage source is the same, indicating that it is only affected by the nature of the load

Time

Cur

rent

Saturated response (100% duty cycle)

Closed loop control (Current drive)

Open loop control (Voltage drive)

95%Ismax

95%Is

3τ,rise time


119

itself.

4.5.1.3 Circuit Description to Implement PWM servo current source

Figure 4.10 Circuit description of isolated IGBT drive driven by PWM signal

Figure 4.11 Circuit description of power supplies used in IGBT switch system

To implement the PWM servo current source, a circuit featuring IGBT (insulated gate

bipolar transistor) electronic switches is designed and manufactured. IGBT is employed

in the current source driver to implement high frequency PWM signal. The circuit

description of isolated IGBT drive governed by PWM signal is shown in Figure 4.10. As

can be observed in Figure 4.10, two power supplies were used to power circuitry on either

side of the opto-isolator. The opto-isolator was used as a precautionary measure such that

in the event of an IGBT failure, excessive voltage would not find its way back into the

computer interface thus damaging the control equipment. The circuit description of power

supplies adopted in the IGBT current source drive is shown in Figure 4.11. The reason

for introducing the voltage regulator (LM7815) in the circuit is that regulated power

15V Power Supply 215V Power Supply 1

PWM signal

Optocoupler

TC45

22

IGBT drive

IGBT switch

0~400V

NGTB4DN120FLWG

KIK1010

D9

240V+

_

LM7815

Transformer


120

supplies were deemed necessary to maintain a healthy gate drive voltage. It can also be

observed that an IGBT driver (TC4552) is employed in Figure 4.10. IGBT driver is

necessary to enable fast switching of the IGBT to ensure low thermal dissipation. The

diode in parallel with the coil suppresses high voltage transience, which could destroy the

IGBT by providing a circulating path when the IGBT switch turns off.

4.5.2 Modification to The Solenoid Circuit

As can be seen from Figure 4.9, when the circuit is over driven by full bus voltage, the

current inside the solenoid can hit the reference value rapidly. As a matter of fact, the

higher applied voltage is, i.e. the larger instant current pulse applied on the solenoid, the

faster current response will be. However, the bus voltage cannot be increased infinitely.

Hence, it is worth considering reducing the resistance of the coil. Moreover, the magnetic

flux across the MRE core should not be affected by the change. Based on these thoughts,

it is proposed to split the original solenoid into several identical secondary coils to reduce

individual resistance and inductance. It has to be point out that, reducing the size of coil

will reduce both resistance and inductance at the same rate. So the change in response

time is not caused by changes in time constant of the circuit.

Assume that the solenoid was divided into n identical small coils sitting along the yoke

in sequence. To achieve same magnetic flux density, the coils are with the total number

of turns of N (each has m turns and N=m × n) and same winding arrangement. When each

coil is energised with the same current IH, the magnetic flux density can be calculated as

Eq. 4.19

When the n coils are connected in series configuration, the total resistance and inductance

are the same as R0 and L0. To this end, the series configuration is equivalent to the original

solenoid. On contrast, when the n coils are connected in series configuration, equivalent

HH mnINIB


121

resistance and inductance of the circuit can be now written as

Eq. 4.20

Eq. 4.21

When the coils are in parallel connection, the total current of the circuit is nIH.

Consequently, according to Eq. 4.3 and Eq. 4.4 the governing current of the parallel coils

circuit can be given as

Eq. 4.22

As can be seen from the equation, the time constant is not changed but the steady current

is n times of that with the original coil. Hence, based on equation, the time to reach Is

is

Eq. 4.23

Conducting Taylor Expansion in the term of 1 n on the formula, can be

approximated as

Eq. 4.24

When n is large enough, retaining only the first term in the series can provide a reasonably

accurate estimate for . For instance, when n=8, the second term of the function is about

6.9×10-4, which is negligible. Moreover, it is obvious that the time to reach a desired

current and the number of divided coils n are approximately in inverse proportion. In

other words, if the original is substituted by n paralleled coils whose total impedance

equals to the original one, the response time of the isolator can be reduced by n times.

Therefore, it is safe to draw the conclusion that the response time of MRE isolator can be

20

nRR

20

nLL

t

HRL

t

H enIenIti 11

1

0

01

011ln11lnnR

Ln

t

30

02

0

0

0

00

13

12

1nR

LnR

LnR

Lt


122

achieved by replacing the original coil by a sequence of smaller coils connected in parallel

configuration.

Figure 4.12 Schematic diagram of MRE isolator with multi coils

To realise the parallel configuration of coils, the solenoid of the MRE isolator was re-

designed and divided into eight identical smaller coils. The schematic of the isolator with

new set of coils is shown in Figure 4.12. The ‘pancake’ coils were winded on a circular

tube mandrel without side cheeks. Silicon rubber was smeared on the wire as winding

and each coil was left on the jig to allow the silicon rubber to cure. Flat insulation washers

were fitted between each coil when they were mounted in the isolator side by side. A row

of holes were drilled on the steel tube to allow the leads of each coil come out of the

isolator. Eventually, copper wire with the diameter of 1mm is adopted and the coils

maintain an inner diameter of 140mm and outer diameter of 160mm. The total number of

the wire turns is 2904 while the total height along with the insulation layers between the

coils is 145mm.

4.5.3 Field-Quenching Coil Configuration

Due to the effect of the residual magnetic field, the falling edge of the current response

cannot be shortened significantly. To this end, a mechanism has been proposed by

splitting the eight coils into two sections, namely, energising section and field quenching

section. The energising section consists of six coils connected in parallel configuration

while the field-quenching section possesses two coils and the current direction is field-


123

quenching section is opposite from the energising section so as to generate opposite

magnetic field polarity.

A new control law based on the control system in Figure 4.8 is then proposed. When the

duty cycle output from PI controller is greater or equal to zero, which means the command

signal is greater than feedback, only the energise section is charged and the current is

regulated by the PWM signal. When the duty cycle is negative, which in other words, the

command signal comes to a falling edge, the field-quenching section is energised by the

full bus voltage to generate a magnetic field opposite to the residual one. The energising

procedure of the field-quenching section is ended when the PI controller output is back

to zero. The electrification logic of the energising section and field-quenching section can

be written as

Eq. 4.25

in which, α is the duty cycle calculated by PI controller, αenergise is the duty cycle for the

PWM signal regulating the voltage applied to the energising section, αquench is the duty

cycle for the PWM signal regulating the voltage applied to the field-quenching section.

When it comes to the feedback control of the split section mechanism, a magnetic field

feedback control arrangement is also introduced to replace the original current feedback.

The most important reason for using magnetic field as the feedback signal is that the cross

coupling between the quench and energising coils can cause the current from one section

affect the other section, which corrupts the current feedback signal for the quench and

energise controller. Secondly, given that the magnetic field in the core is what determines

the force output of the MRE isolator, adopting magnetic field as the feedback signal is

more straightforward and can save the calibration between the current and force response.

To deliver the design, a Hall effect sensor is equipped on the MRE isolator and calibrated

such that it can be utilised to measure the current as a result of either the energise coil or

quench coil being energised. The circuit description of split coil configuration is shown

05.01,

5.000,

quenchenergise

quenchenergise


124

in Figure 4.13. In Figure 4.13, two identical PWM servo current sources described in

Figure 8 were employed to drive the energising section and field-quenching section

separately. The detailed circuit diagram is shown in Figure 4.14.

Figure 4.13 Circuit description of split coil system

Figure 4.14 Circuit diagram of split coil system

PWM energisingsystem

PWM field-quench system

Energisingcoil section

Field-quenchingcoil section


125

4.6 RESPONSE TIME UNDER DIFFERENT CONFIGURATIONS

4.6.1 On Current and Force Responses

To demonstrate effects of the proposed configurations, the same current input adopted in

the original response testing is applied to the MRE isolator with a constant displacement

of 4mm. Three different coil configurations were experimentally compared, including the

series, parallel and field-quenching configurations. The transient current responses under

different configurations are shown in Figure 4.15.

Figure 4.15 Current response curves under different coil configurations

It can be clearly observed that, at rise edge, the parallel configuration achieves a much

shorter response time than the series configuration. The response time of the parallel

configuration is approximately 132ms while that of series configuration requires 540ms.

It is noteworthy that due to the limitation of power supply’s maximal current output, in

actual experimental testing, the eight identical coils are divided into two groups, each of

which parallels four coils. Hence, the comparative result of response time in series and

parallel configuration convincingly demonstrates that the response time of the parallel

configuration can be reduced by n times compared to the series scenario. However, it can

also be observed that the parallel configuration still receives considerable response time

0 0.5 1 1.5Time (s)

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Cur

rent

(A)

Rise Time

0 0.5 1 1.5Time (s)

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Cur

rent

(A)

Fall Time

command signalseries configurationparallel configurationfield-quenching configuration

field-quenching

parallel

series

field-quenching

parallel

series


126

at fall edge, around 700ms, which is even slower than the series configuration, i.e. 580ms.

The reason underlies the phenomena is that changing the connection method cannot

cancel the effect of long decay time of the magnetic field due to magnetic residence. The

field-quenching configuration, however, attained excellent response time reduction effect

in both rising and falling edges. The rise time is approximately 44ms while the fall time

is about 40ms. The fluctuation of the current response in field-quenching configuration

is due to the interaction of the inductance and the inter-winding capacitance. In both

rising and falling periods, the current fluctuation is around 0.3 A which also dampens

down very quickly.

Figure 4.16 Current and force response time under different displacements

The force response under field-quenching arrangement was tested with the same control

command excitation under three constant displacements. The response times of current

and force responses under three displacements are revealed in Figure 4.16. As observed,

the influence of displacement on either current or force response is not significant.

Meanwhile, under any displacement, the current response has a smaller fall time than rise

time, which proves the effectiveness of the field-quenching configuration.

The current and force responses under 4 mm displacement are displayed in Figure 4.17

and Table 4.2. It can be clearly seen from Figure 4.17 that the force response is as rapid

2 4 620

25

30

35

40

45

50

55

60

Displacement (mm)

Res

pons

e tim

e (m

Sec)

current rise timecurrent fall timeforce rise timeforce fall time


127

as current response at rise edge which again indicates the fast response of the MRE

material. The final force rise time and fall time are 52ms and 48ms, respectively.

Compared to the original response time, both current rise and fall time have been reduced

by 87% and force rise and fall time have been reduced by 88%. Fluctuation of the current

does not create large variation in the force rising transient. In the falling transient, the

fluctuation of the force is caused by the mechanical connection due to sudden loss of the

system stiffness rather than the fluctuating current.

Figure 4.17 Final current and force responses with field-quenching coil configuration

Table 4.2 Final current and force response time (4mm displacement, field-quenching configuration)

Current response Force response

Rise edge Fall edge Rise edge Fall edge

44 40 52 48

4.6.2 Performance evaluation for real-time control implementation

Further evaluation was conducted to verify the feasibility of MRE isolators for real-time

control implementation from structural control point of view. Seismic test of a smart base

isolation system comprising a 3-storey building model and MRE base isolators is used

with a simple on-off control algorithm for such purpose. The control method will be

0 0.5 1 1.5Time (s)

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Cur

rent

(A

)

40

45

50

55

60

65

Forc

e (N

)

Rise Time

0 0.5 1 1.5Time (s)

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

Cur

rent

(A

)

40

45

50

55

60

65

Forc

e (N

)

Fall Time

command signalcurrent responseforce response

current rise time

force rise time

current fall time

force fall time


128

introduced in detail in Chapter 5. Since the shear force generated by the MRE isolator

cannot be directly measured, the current responses under control command are used with

comparison between responses with original coil configuration and responses with all

proposed approaches to mitigate response time. The test was conducted under four

different earthquakes and results are illustrated in Figure 4.18 to Figure 4.21. As can be

observed in the four graphs, with the response time mitigation approaches, the MRE

isolator is able to simultaneously follow the control signal in both rise and fall transients.

An overshooting is observed at each edge. MRE isolator with original configuration, on

the contrary, struggles to maintain trace the control current command with considerable

time delay observed, which inevitably downgrades the control performance.

It is discovered that the control performance is significantly deteriorated when the ratio

between real time delay and critical time delay is greater than 0.6, in which critical time

delay represents the time delay rendering the controlled structure to be unstable (Agrawal,

Fujino & Bhartia 1993). For a SDOF system, the critical time delay is approximately 0.25

of the natural period of uncontrolled system. Although critical time delay of MDOF

system is much more complicated than that of a SDOF system, the aforementioned

approximation is still instructive when evaluating the effect of time delay to the controlled

structure. Hence, the critical time delay and thus allowable time delay of the control

system can be even smaller if higher modes of the MDOF system are also controlled

(Agrawal & Yang 1997). In the test, the fundamental period of the 3-storey building

model is 0.53s. Therefore, the critical time delay of the system should be less than 132ms

and allowable time delay of the system should be less than 79ms to avoid jeopardising

the stability and performance of the system. With a fast response time, i.e. 52ms and 48ms

in rise and fall time, the proposed MRE isolator has convincing capability for real-time

control implementation.


129

Figure 4.18 Response time comparison under El-centro earthquake

Figure 4.19 Response time comparison under Kobe earthquake

0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

Time(s)

Cur

rent

resp

onse

(A)

Current response with original configuration under El-centro earthquake

control command current response

0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

Time(s)

Cur

rent

resp

onse

(A)

Current response with time delay reducing approaches under El-centro earthquake

0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

time(s)

Cur

rent

resp

onse

(A)

Current response withoriginal configuration under Kobe earthquake


0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

time(s)

Cur

rent

resp

onse

(A)

Current response with time delay reducing approaches under Kobe earthquake


130

Figure 4.20 Response time comparison under Hachinohe earthquake

Figure 4.21 Response time comparison under Northridge earthquake

0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

time(s)

Cur

rent

resp

onse

(A)

Current response with original configuration under Hachinohe earthquake


0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

time(s)

Cur

rent

resp

onse

(A)

Current response with time delay reducing approaches under Hachinohe earthquake

0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

time(s)

Cur

rent

resp

onse

(A)

Current response with original configuration under Northridge earthquake


0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

time(s)

Cur

rent

resp

onse

(A)

Current response with time delay reducing approaches under Northridge earthquake


131

4.7 SUMMARY

This chapter reported an investigation for improving response time of a MRE isolator for

real-time control implementation. A testing method is firstly introduced to examine the

response time of MRE isolators. Due to inherent large coil design in the MRE devices,

there is significant delay in response time resulted from the inductance of the coil and the

electrical impedance which needs to be resolved in order to achieve real-time control.

From the experiment it was observed that the delay in response time is mainly due to the

delay of the coil current response. To resolve this issue, three approached were introduced

to reduce the response time of MRE isolator. The first approach is to design a PWM servo

current drive controlled by PI controller instead of utilising open-loop constant voltage

source. The second approach is to arrange the large coil with several identical coils (for

example, n parallel coil). With the proposed design, the response time can be reduced to

be 1/n of the original response time. To eliminate the influence of the residual magnetic

field, a field quenching configuration was design by driving top and bottom coil with

opposite current during falling time. It was found out that the modified design can reduce

the force response time from 421 ms to 52 ms in the rising and from 402 ms to 48 ms in

the falling, respectively. An experimental evaluation of real-time control of a MRE

isolator with the proposed time response reduction approaches confirmed that this isolator

is adequate for real-time control implementation for seismic protection.

The highlights of this chapter can be summarised as following:

1) Real-time control of MRE vibration isolator is able to maximise the strength of MRE

material and thus enlighten the MRE based semi-active control.

2) Time-delay is a critical issue encountered in any practical control. There is a gap of

recognition of response time delay caused by the MRE isolator device itself in

existing research.


132

3) This investigation explores the inherent response time delay of MRE isolator and

feasible approaches to reduce the response time so as to provide the possibility for the

realisation

Semi-Active Control Of MRE Base Isolation System

133

CHAPTER 5

SEMI-ACTIVE CONTROL OF MRE BASE ISOLATION

SYSTEM

5.1 CHAPTER OUTLINE

In this chapter, the experimental realisation of the real-time controlled smart MRE

seismic isolation system with shake table will be presented. First of all, a three-storey

building model is designed and manufactured. The frame structure is designated as a pure

shear building model to avoid motion coupling in different directions and thus assure the

accuracy of modelling. Next the modal analysis of the bare building and integrated

structure with two MRE base isolations are conducted by hammer testing. The system

identification is completed with assistance of DIAMOND (Damage Identification and

Modal Analysis for Dummies) (Doebling, Farrar & Cornwell 1997). The experimental

setup and instruments adopted in this test are then introduced. Next, five control

algorithms, namely, LQR control with GRNN inverse model, non-dominated sorting

genetic algorithm optimised neuro-fuzzy logic controller (NSGA-NFLC), Bang-Bang

control, Lyapunov-based current selection control and frequency control, are proposed

and derived in detail. The seismic protection performances of fixed base building,

passive-off isolation system (input current is 0A), passive-on isolation system (input

current is 3A), five controlled base isolation system with proposed control algorithms are

tested numerically and experimentally. Among all the controlled MRE base isolation

systems, the NFLC controller is set to generate continuous control current between 0 and


134

5A; the Bang-Bang controller, Lyapunov-based controller and frequency controller

switch current between 0 and 5A; the GRNN inverse model in LQR control strategy also

generates current between 0 and 5A due to the threshold setting in the training current

signal (as explained in Chapter 3). The reason for choosing 5A instead of 3A as the upper

limit of current is to allow larger adjustable range of MRE isolator’s stiffness. Meanwhile,

since the current changes during the entire control process, higher current doesn’t last for

a long time on the isolator, which will not bring about the hazard of damaging the isolator

as well as the electronic components in the circuit. The testing results are analysed

thoroughly with respects of peak floor responses, time histories of structural acceleration

and displacement responses, evaluative indices of structural responses and controller

requirements, control force and corresponding current, etc.

5.2 DESIGN AND IDENTIFICATION OF THE MRE BASE ISOLATION

SYSTEM

One of the challenges in control synthesis and analysis is the design of primary structure

and development of recurrent numerical model of the base isolated system. To this end,

a 3-storey building model is designed and manufactured as the testing bed. The isolation

system investigated consists of the 3-storey frame building model and two identical MRE

isolators connected and aligned symmetrically on the horizontal axis of the bottom plate.

In this section, detailed design and identification of the 3-storey building model are

presented, followed by the integration and identification of the isolation system.

5.2.1 Three-storey Building Model Design

The schematic diagram of the building model is shown in Figure 5.1. As can be seen from

Figure 5.1, the testing building is a three-storey frame structure with a height of 1200mm,

of which each floor is 400mm high. For computation efficiency, it is ideal that the system

can be simplified as a lumped mass model. Hence, this building model has been designed


135

and manufactured as a pure shear model. With such design, the likelihood of modal

coupling of two directions is minimised and thus avoid the distortion of modelling. To

achieve this objective, four identical steel strips, whose cross-section dimension is 34×4

mm, have been adopted as the columns of the structure so as to provide low stiffness at

the direction of the earthquake excitation and very high stiffness at the perpendicular

direction. Slab of each level consists of two aluminium plates with the dimension of

600×450×20mm bolted together with four countersunk head screws. At connections of

each floor, a steel clamp is bolted on the top of the strip with the mass plate, endowing

the connection with high rigidity to avoid the occurrence of torsional and rotational

modes.

Figure 5.1 Schematic diagram and dimensioning drawing of the three-storey shear building

model

Detailed structural design, dimension and material of each component are shown in Table

5.1. To represent low- to mid-rise buildings, the fundamental frequency of the structure

is designated as 1.934Hz, which also falls in the envelope of dominated frequency range

of majority of natural earthquakes. With such frequency arrangement, the three-storey

building is representative of the dynamic behaviour of real building model under

earthquake attacks and will experience resonance and hence highlight the contract

between seismic responses between bare and base-isolated building. The photos of the

frame structure and connecting joints are shown in Figure 5.2.


136

Figure 5.2 Photos of three-storey shear building model and connections in the structure

Table 5.1 Detailed designated parameters of each component

Component’s Name

Number Material Density

(kg/mm3) Length (mm)

Width (mm)

Height (mm)

Weight (kg)

Mass plate 6 Aluminum 2.70×10-6 600 450 20 14.58

Strip 4 Steel 7.85×10-6 34 4 1200 1.28

Clamp 6 Steel 7.85×10-6 450 5 40 0.57

Bottom plate 1 Steel 7.85×10-6 706 550 20 61

According to the structural parameters, if the three-storey building is simplified to a

lumped mass model, the mass at each level is 31.044kg while stiffness is 42866.94N/m.

Therefore, the mass matrix and stiffness matrix can be written as

Eq. 5.1

Eq. 5.2

Column-plate connection

Fixed base connection

Front view Left view

kgM44.3100

044.3100044.31

mNK5.214335.2143305.2143394.428665.21433

05.2143394.42866


137

Accordingly, the undamped frequencies of three modes are 1.934Hz, 5.419Hz, 7.831Hz,

respectively. According to references (Asoor & Pashaei 2010; Australia 2011), the

damping ratio of a steel frame structure with rigid connections can be chosen as 0.5%. In

case of Rayleigh damping, the damping matrix can be calculated as

Eq. 5.3

in which

Eq. 5.4

where and are the circular natural frequency and damping ratio of the ith mode.

Hence, , the damping matrix can be written as

Eq. 5.5

5.2.2 System Identification

Next, system identification of the MR elastomer smart base isolation system has been

conducted to obtain accurate mathematic model of the system for the synthesis and

analysis of control system. System identification, as the name suggests, directly employs

measured input/output data from the system to construct a mathematical model that

replicates the observed behaviour. The identification procedure of the MRE base isolation

system is divided into four steps: i) identification of the three-storey building model; ii)

characterisation and modelling of the MR elastomer base isolator, which has been

completed in Chapter 3; iii) integration of the MR elastomer and three-storey building

model; iv) validation of the integrated model of the system. Therefore, the identification,

integration and validation of the three-storey bare building as well as the base-isolated

KMC

21

22

1122

21

22

211221

2

2

i i

smNC /419.7639.40639.4058.12639.40639.4058.12


138

structure will be introduced.

5.2.2.1 Identification of the three-story building model

Figure 5.3 Modal testing experimental setups of fixed base building and base isolated structure

Impulse hammer testing was conducted for the modal testing of the three-storey building.

Figure 5.3 displays the experimental setup of modal testing. Since the building is

modelled as a three degree-of-freedom system, only the horizontal movement at each

floor is measured. As shown in Figure 5.3, two accelerometers (Series No.: ADXL193)

were installed at the corner of each floor. The average acceleration value of the two

accelerometers is taken as the floor acceleration of the corresponding level in order to

cancel out the effect of possible torsional movement. The hammer excitation locations

were chosen as the centre point of each floor to further reduce the likely torsional

movement. To ensure the accuracy and representativeness of the modal testing results, at

each excitation location, the test was repeated 50 times. A LabVIEW based data

MRE base isolator

Base isolated building modal testing

Fixed base building modal testing

Shake table

Data acquisition system

Accelerometer


139

acquisition system was utilised to acquire and record the data.

Figure 5.4 Flowchart of experimental modal analysis / statistical modal analysis module in

DIAMOND (Doebling, Farrar & Cornwell 1997)

The system identification normally consists of the following steps: i) collection of high-

quality input/output data, ii) computation of the best model within the class of system

considered, i.e. modal analysis, and iii) evaluation of the adequacy of the model’s

properties. After data collection from impulse hammer testing, the modal analysis is

accomplished by adopting a Matlab based graphical interface toolbox known as

DIAMOND (Damage Identification and Modal Analysis for Dummies) (Doebling, Farrar

& Cornwell 1997). DIAMOND is divided into four primary modules at the top level: i)

numerical vibration test simulator, ii) experimental modal curve fitting and statistical

Experimental and Statistical Modal Analysis Module

Import FRF, CPS, PSD, COH (from DAQ)

Analyse and View Imported Data

Define Sensor Locations and Trace Lines

Statistical Analysis Of Modal Parameters

Mode Indicator Functions CMIF, MIF, APS COH-Based Analysis of FRFs

Plot and Overlay Imported DataReal, Imag, Mag, Phase

Analysis of Variance on Identified Modal Parameters Using Monte

Carlo Simulation

Operating Shape

Eigen-system Realisation Algorithm

Complex Exponential

Nonlinear Least Squares

Damping Corrections(Hanning or Exponential Windows)

Modal Parameter Postprocessing

Screen Identified Modes

Plot Phase Collinearity

Plot MAC

Complex to Real Mode Conversion

Mass Normalisation of Real Modes

Rational Polynomial

Modal Parameter ID(Forced or ambient data)

List Modal Parameters Animate Mode Shapes


140

analysis, iii) damage identification, and iv) finite element model refinement, among

which the experimental modal curve fitting and statistical analysis module is employed

to conduct the modal analysis. In this research, the second module of DIAMOND,

namely, experimental and statistical modal analysis module is employed for modal

analysis. The most important feature of the module is the variety of modal parameter

identification algorithms available, which are shown in Figure 5.4.

By utilising DIAMOND, the natural frequency, damping ratio and mode shape of each

mode are identified. Comparison between numerically predicted modal parameters and

modal analysis results are displayed in Table 5.2 and Table 5.3. It is noteworthy that the

natural frequencies resulted from modal analysis in Table 5.2 are damped frequencies.

The typical mode shapes along dimension with lower stiffness are illustrated in Figure

5.5 (a) ~ (c).

Table 5.2 Comparison of natural frequency and damping ratio between numerically predicted and modal analysis results

Mode No. Natural frequency (Hz) Damping ratio (%)

Predicted Modal analysis Predicted Modal analysis

1 1.934 1.913 0.50 0.70

2 5.419 5.256 0.50 0.72

3 7.831 7.237 0.50 0.43

Table 5.3 Mode shape vectors from modal analysis results

Mode No. 1 2 3

Φ1 Φ2 Φ3

0.275 0.712 0.635

0.601 0.392 -0.699

0.750 -0.583 0.328


141

Figure 5.5 Experimental dynamic mode shapes (along softer direction): (a) first mode shape; (b)

second mode shape; (c) third mode shape

Given the modal parameters listed in Table 5.2 and Table 5.3. the modal frequency and

mode shape matrices can be written as

Eq. 5.6

Eq. 5.7

According to modal analysis theory (Maia & Silva 1997), the following relationships are

satisfied

Eq. 5.8

Eq. 5.9

Eq. 5.10

In which, [M], [K] and [C] are the structural mass, stiffness and damping matrices,

respectively, while [Mr], [Kr] and [Cr] are the modal or generalized mass, stiffness and

damping matrices. The relationships between [Kr] and [Mr] and [Cr] and [Mr] can be

(a) (b) (c)

2223

22

21

2 /647.206700

0612.1090000474.144

sraddiagd

328.0583.0750.0699.0392.0601.0

635.0712.0275.0

321diag

rrrrT MmmmdiagM 321

rrrrT KkkkdiagK 321

rrrrT CcccdiagC 321


142

described as

Eq. 5.11

Eq. 5.12

in which ζi is the damping ratio of the ith mode. Hence, given the mass matrix

, the stiffness and damping matrices calculated from

modal analysis results can be written as

Eq. 5.13

Eq. 5.14

Figure 5.6 Comparison between experimental and predicted top floor displacement in fixed base

building

As can be seen from the results, the modal analysis results of the three-storey building

are fairly close to the numerically predicted results. To further validate the accuracy of

the structural parameters identified by modal analysis, the numerically predicted and

experimental responses were compared under El-Centro earthquake. The numerical and

experimental relative displacements at the top level (first 10 seconds) are shown in Figure

5.6. As can be observed from the curves, there is adequate agreement between numerical

and experimental results, which indicates the satisfactory accuracy of the three-storey

rdr MK 2

ndnnidiidr mmmdiagC 222 111

kgdiagM 44.3144.3144.31

mNC6.204807.198420.1341.203048.383871.18259

9.1251.185455.44019

smNC /944.8613.5403.0613.5058.12518.4403.0518.4162.13

0 1 2 3 4 5 6 7 8 9 10

-20

-10

0

10

20

Time(s)

Disp

lace

men

t(mm

)

Predicted Experimental


143

building’s numerical model.

5.2.2.2 Integration and identification of the MRE base isolation system

With the three-storey structure and MR elastomer isolator models, the base isolation

system is then integrated in the form of state space function. As aforementioned, the MRE

base isolation system consists of the three-storey shear building model and two MRE base

isolators aligned symmetrically on the axis of the bottom plate of the structure. The

numerical model for MRE base isolator adopted is the Bouc-Wen model described in

Chapter 3. The force predicted by the model is governed by the following equations

Eq. 5.15

where z is the evolutionary variable indicating the result’s dependence on response

history. To simplify the identification, the power variable n was set to be 1. The

relationship between variables in the field-dependent model and the input current are

summarised by Eq. 5.16. The values of parameters in Eq. 5.16 are listed in

Eq. 5.16

Table 5.4 Parameter values of MRE base isolator’s Bouc-Wen model

Factor name

k c α

Value 11760 6053 272.5 232.9 -1900 14160 7106

β

Value 1.109 1.324 -0.4554 4.617 -0.2108 1.289

Assume an N-storey building model isolated by a MR elastomer base isolator, which can

nn zxzzxxAzzxckxF

1

01

01

01

012

01

01

bb

bb

bb

bbb

bb

bb

IIII

AIAIAIII

cIcIckIkIk

1bk 0bk 1bc 0bc 2b 1b 0b

A

1bA 0bA 1b 0b 1b 0b


144

be modelled by Eq. 5.16. The schematic diagram of the system can be illustrated as in

Figure 5.8. Since the base isolation level counts for one degree of freedom (DOF), the

integrated system becomes an N+1-DOF system. The motion equation of top level can

be written as

Eq. 5.17

in which xb and xi (i=1~n) represent the displacement of base isolation and the ith floor

relative to ground motion; mb and mi (i=1~n) represent the effective mass of base isolation

and the ith floor; represents the acceleration of earthquake excitation; ki and ci (i=1~n)

represent the stiffness and damping coefficients of the ith floor. The last motion equation

represents the movement of base isolation level, in which kb0 and cb0 corresponds to the

stiffness and damping coefficients when input current is zero whose values can be found

in Table 5.4. FBW is the control force provided by the MR elastomer isolator depending

on the control current, whose formula can be written as

Eq. 5.18

Therefore, using state vector , the state-space

function of the MRE base isolation system can be described as

Eq. 5.19

where [A] is the state-space matrix while [B] and [E] are the location matrices showing

the location of control force and external excitations. [A], [B] and [E] can be expressed

gbBWbbbbbbb

gbb

gjjjjjjjjjjjjjjj

gnnnnnnnn

xmFxkxcxxkxkkxccxmxmxxkxxcxxkxxcxm

xmxxkxxcxxkxxcxm

xmxxkxxcxm

1111111010

1122122111111

111111

11

tzIIxIcxIkF bbbbxbbbBW 01211

321321 xxxxxxxxz bb

gBW xEBFAzz


145

as

Eq. 5.20

where [M], [K] and [C] are the structural mass, stiffness and damping matrices, which

can be expressed by

Eq. 5.21

Based on the identification results in the previous two sections, the structural parameters

are listed in

Table 5.5.

Table 5.5 Identified structural parameters of the base isolated building model

Base isolation Level 1 Level 2 Level 3

Mass (kg) 110 31.044 31.044 31.044

Effective stiffness (Nm) 6053 25474.4 18545.1 20480.6

Damping coefficient (Nm/s) 232.9 8.644 6.415 5.613

To validate the integrated model, the base isolated structure was tested numerically and

experimentally with El Centro earthquake excitation when the input current is zero. The

numerically predicted and experimentally measured top floor displacements are

14

14

13

14

`114444 0

0

10

0I

Em

BCMKM

IA

b

33

3322

2211

110

33

3322

2211

110

3

2

1

000

000

000

000

000000000000

cccccc

ccccccc

C

kkkkkk

kkkkkkk

K

mm

mm

M

b

b

b


146

compared in Figure 5.7. It can be clearly observed that although the magnitudes of

numerical and experimental results are fairly close, the goodness of fit is not as good as

that of the bare building model shown in Figure 5.6. This maybe result from the high

nonlinearity and inherent hysteresis introduced to the isolated system by the MRE base

isolation system. In this case, the design of control method should take into consideration

of approaches to cancel out the hysteresis of the MRE isolator to avoid affecting the

control performance and even stability of the control system due to the influence of

nonlinearity.

Figure 5.7 Comparison between experimental and predicted top floor displacement in base

isolated building

5.3 EXPERIMENTAL SETUP AND SYSTEM DESCRIPTION

Figure 5.8 Experimental setup schematics of comparative testing of proposed MRE base

0 2 4 6 8 10 12 14 16 18 20-6

-4

-2

0

2

4

6

Time(s)

Disp

lace

men

t(mm

)

Predicted Experimental

m3

m2

m1

mb

c3

c2

cb

c1

kb

k1

k2

k3

m3

m2

m1

mb

c3

c2

cb(I)

c1

kb(I)

k1

k2

k3

m3

m2

m1

c3

c2

c1 k1

k2

k3

Smart base isolator

Passive base isolator

Fixed base building

Passive base isolated building

Semi-active controlled base isolated building

x3

x2

x1

xb

xg

Laser sensor reference wall

Shake table

A/D Converter

D/A Converter

Digital Controller

Data Acquisition

dSPACE

PWM servo current driver

Duty cycle

I, B


147

isolation system

Figure 5.8 illustrates the experimental setup of the comparative experimental testing of

the seismic protection performance of the three isolation scenarios, i.e. fixed base

building, passive base isolated structure and semi-active MRE base isolation system. As

mentioned in the previous section, the structure adopted in this experiment is a three-

storey pure shear building model with a total mass of 93.13kg (equivalent mass of

31.04kg on each floor) and a fundamental frequency of 1.91Hz. In isolation scenarios,

two MRE base isolators are symmetrically mounted under the three-storey frame

structure on the central axis of the structure’s bottom plate. Hence, the equivalent mass

of the isolation level is approximately 50kg. In the passive isolation scenario, zero current

is applied on the MRE isolator, which indicates the softest status of the isolator and thus

the lowest corresponding natural frequency of the system.

The photo of experimental setup is displayed in Figure 5.9. A number of sensors are

installed in this testing to measure the structure’s movement feedback as well as the real-

time current in the solenoid and magnetic field across the laminated MRE core of the

isolator. Five Baumer laser distance sensors (Part No. OADM 20I4460/S14C) provide

the measurements of shake table movement and relative displacement of each floor, ,

, , , (only four are used in the fixed base building case). As can be seen from

Figure 5.9, a sensor reference wall is built to hold the laser sensors precisely at the

elevation of each floor. Sensors measuring 2nd and 3rd floors haves a sensing span of

130mm while sensors measuring 1st and base floors as well as the table movement have

a sensing span of 50mm. Reason for this selection being the bottom two floors and shake

table features relatively small displacement. Therefore, distance sensors with smaller

measuring range can guarantee higher accuracy. Figure 5.10 shows the photos of

employed laser sensor and the adapter between sensing system and the data acquisition

system. A Hall Effect current transducer (Part No. CSLA2CD) is utilised to monitor the

real-time current I in the solenoid of MRE isolator. The magnetic flux B across the MRE

core is measured by a digital Hall Effect sensor IC (Part No. SS461A). Two wire

xg

xb x1 x2 x3


148

connectors are used for flexible configuration of small coils in MRE isolators.

Figure 5.9 Photo of experimental setup: (a) front view; (b) side view

Figure 5.10 Laser sensor and sensor adapter

One of the essential equipment utilised in the control system is dSPACE Real-time PPC

Controller Board (DS1104). This control board, based on MATLAB/Simulink

operational interface, is a software-hardware platform for semi-physical simulation and

can be installed in virtually any PC with a free PCI or PCIe slot. With dSPACE controller

board, the PC can be upgraded to a powerful development system for rapid control

MRE isolator

3-storey shear building model

Laser sensor reference wall

Laser sensor

Wire connector

(a) (b)

Sensor front view

Sensor back view

Wire plug of laser sensor

Wire plug of dSPACE DAQ

Sensor adapter


149

prototyping, which is crucial in the realisation of real-time control of the MRE base

isolation system. The photo of dSPACE DS 1104 board is shown in Figure 5.11.

In the experimental system, the role of controller board comes in functional variants. First,

it was employed as data acquisition system (DAQ). As shown in Figure 5.11, there are

eight A/D converters and eight D/A converters on the board. Secondly, it also functions

as a real-time controller based on Simulink software by generating the PWM control

signal governing MRE isolator at a switching frequency of 1000Hz. Seven out of eight

A/D converters have been utilised to acquire feedback signals of five laser sensors,

current transducer and Hall effect sensor. The control flow can be observed from Figure

5.8: the structural and shake table movement ( , , , , ) as well as current and

magnetic field (I and B) in MRE isolator are measured and transmitted to data acquisition

system of dSPACE board; the inbuilt digital controller calculates desired control current

and corresponding PWM signal; subsequently, the dSPACE board outputs command of

duty cycle through PWM servo portal; according to the duty cycle, iGBT electrical switch

aforementioned modulates the voltage applied on the MRE isolator. Two AMETEK

programmable power supplies (Sorensen SG Series, 400V/12A) in Figure 5.11 have been

employed to provide electricity.

Figure 5.11 Power supplies and data acquisition system with dSPACE

It is well-known that the mechanical properties of MRE material is typically sensitive to

xg xb x1 x2 x3

A/D converter

D/A converter

PWM servo portal

Functionality indicator

dSPACE R&D controller board

AMETEK programmable power supplies


150

temperature changes. However, the energised solenoid around the base isolator’s

laminated core as well as the MRE material activated by the magnetic field both generates

considerable heat, which brings raises environmental temperatures obviously. Hence, to

avoid the property change of isolator due to overheated MRE sheets, two actions have

been taken. Firstly, the testings are conducted in a well ventilated environment, with

which the air flow can effectively take away part of the heat. Secondly, the duration of

individual testing is strictly restrained under one minute, during which the temperature

rise is acceptable.

5.4 CONTROL ALGORITHMS

Figure 5.12 shows a block diagram of a general semi-active controlled structure. As can

be seen from the figure, the controller transmits optimal control command based on the

feedbacks from both semi-active controller and the primary structure. Normally, control

command input to the semi-active device is the governing current or voltage for it to

generate the actual control action. As discussed in Chapter 2, in civil engineering

applications, especially for seismic protections of structures, semi-active control is

considered to be superior to both passive control and active control as it enables high

authority control for high performance and flexibility as that of active control without

compromising reliability and energy requirement (Symans & Constantinou 1999;

Yoshioka, Ramallo & Spencer Jr 2002). However, the design of appropriate semi-active

controller to ensure control effectiveness and efficiency imposes a challenge due to the

nature of the semi-active control, i.e. the control action, which is also a function of the

system status, can only be indirectly achieved by adjusting mechanical properties of semi-

active devices such as stiffness or damping. On the other hand, most semi-active devices,

such as MRF dampers or MRE isolators are known to be highly nonlinear and hysteretic

by nature. Hence, proper control algorithms which are able to avoid or neutralise the

influence of hysteresis and nonlinearity introduced by incorporating MRE base isolator,


151

as well as exploit the uniqueness of MRE isolator have been developed and validated in

terms of seismic protection effectiveness.

Figure 5.12 Block diagram of a general semi-active structural control problem

5.4.1 LQR Control with GRNN Inverse Model

The first control algorithm introduced in this section is LQR control with GRNN inverse

model. As known, LQR control in civil engineering application normally calculates the

optimal control force based on full-state feedback of the controlled structure. To realise

a MRE base isolation system based on LQR control, an inverse model is essential to

describe the inverse dynamics of the isolator since the MRE isolator can only generate

control action required by LQR controller based on the excitation current. In other words,

to apply LQR control to a structure equipped with semi-active MRE base isolator, the

design of controllers often requires two stage actions in order to generate the required

control: (i) utilise LQR controller to determe the desired primary control force based on

the structural feedback responses; (ii) determining required current control command to

drive the semi-active MRE base isolator in order to generate primary control action.

Hence, an inverse model which can accurately describe the correlation between actual

control force generated by MRE isolator and the current applied on it is indispensable in

the LQR controlled MRE base isolation system. Based on the inverse model validation

results in Chapter 3, the GRNN inverse model is selected due to its ideal performance in

Semi-active device

Primary Structure

Controller

Ground motion

Control command V/I

Actual control action u

Device feedback

Structural feedback

Output y


152

fitness and calculation efficiency.

Figure 5.13 Semi-active control strategy of MRE base isolation system with GRNN inverse

model

The control system block diagram and flow chart of the LQR controlled MRE base

isolation system is shown in Figure 5.13. As shown in Figure 5.13, the LQR controller

calculates desired control force based on the system’s response and then transmitted the

force to the inverse model. Based on control force command, the inverse model generates

desired control current. Due to current limitation of the MR elastomer isolator, a

saturation link is required to restrain the current within the range of 0~5A. The classic

LQR control method is developed based on the state-space function expressed by Eq.

5.19 to Eq. 5.21. Matrices Q and R are obtained by minimising the LQ function

Eq. 5.22

The LQR gain matrix is then derived by

Eq. 5.23

in which P is the solution of the algebraic matrix Riccati equation

Eq. 5.24

Thus the control force can be calculated by

m3

m2

m1

c3

c2

c1 k1

k2

k3

LQR controller

GRNN Inverse model

MRE isolator

Earthquake

Sensors

, , ,

Measurement noise

Derivation

Desired control forceCurrent

Real control action

021, dtRFFQzzFzJ BW

TBW

TBW

PBRG T1

01 PBBRPQPAPA TT


153

Eq. 5.25

where z(t) is the state vector, A and B are the structural matrices in state-space function

Eq. 5.19.

Figure 5.14 Schematic diagram of inverse model based on GRNN

After the LQR controller calculates the desired control force, an inverse model of the MR

elastomer isolator is employed to obtain the desired control current input. The inverse

model is designed based on general regression neural network (GRNN), whose schematic

diagram is shown in Figure 5.14.

The relation between input vector X and output value can be written as

Eq. 5.26

in which , n is the number of sample observations; and

are the sample values; is the spread parameter. As can be observed in Figure 5.14, the

tGztu

Input Layer

Pattern Layer

Summation Layer

Output Layer

(n)

x(n-1)

(n-1)

x(n)

F(n)

I(n)

1

1

1

1

Y1Y2

Yn

Y3

F(n-1)

Y

n

ii

n

iii

D

DYY

1

22

1

22

2exp

2expˆ

)()(2i

Tii XXXXD iX iY


154

GRNN consists of four layers, namely, input layer, pattern layer, summation layer and

output layer. In the case of MR elastomer isolator, the input layer includes independent

features chosen as displacement and velocity of the isolator at present and previous time

instant and the force at the present time instant. The unit of pattern layer each represents

a training pattern. The summation layer includes two units: the first unit is evaluated by

the numerator of Eq. 5.26 while the second unit represents the denominator of Eq. 5.26.

The units in pattern layer are connected to both of the units in summation layer

individually. The weight of connection between units in pattern layer and first unit in

summation layer is while the weight for the second unit is unity. The output of

GRNN, which is the control current in this case, calculates the quotient of the two units

of the summation layer. More details about GRNN inverse model can be found in Chapter

3.

5.4.2 GA Optimised Fuzzy Logic Control

As mentioned previously, because of the high nonlinearity and uncertainty of MR

elastomer base isolated structure, the uncertain and imprecise of the isolation system is a

significant issue in real experimental applications. It is well-known that the fuzzy logic

control, which is not dependent on the synthesis and analysis of the mathematical control

system (Kim & Roschke 2006), is rather suitable for the control of MRE base isolation

system and thus allows considerable nonlinearity and uncertainty of the input excitation,

feedback signal and the controlled structure itself. The inputs and outputs of the fuzzy

controller are described in linguistic directions and then connected by the fuzzy inferences

of “IF-THEN” rules. In other words, the fuzzy logic control systems are capable of

transforming linguistic information and expert knowledge into control signals, which

endows the fuzzy control methods major advantages over traditional control approaches,

i.e. optimal and adaptive control techniques. Another advantage of fuzzy logic control is

that it doesn’t require full-state feedback, which possesses much more practical

iY


155

significance in real civil engineering applications.

However, despite the superiority of the distinguishable fuzzy logic controller (FLC),

some inherent drawbacks also attract researcher’s attentions in the design stages. This

includes: (i) the development of fuzzy logic rules depends on observation of the control

process, of which complexity increases along with the complexity of the system; (ii)

except for control rules, a number of parameters of FLCs need to be carefully selected in

prior, namely, the centre and width of membership functions, scaling factors, etc. Hence,

it is of significant meaning to develop a FLC which can be trained to obtain optimal

parameters automatically for best performance. A neuro-fuzzy controller (NFLC) is an

ideal candidate.

In this section, a self-tuning neuro-fuzzy logic controller (NFLC) is developed and tuned

by utilising genetic algorithm (GA) for optimisation process. To avoid extremely long

encoded strings, a radial basis function (RBF) neural network (Shimojima, Fukuda &

Hasegawa 1995) is implemented in the FLC. Next, the FLC based on RBF neural network

(RBF-NFLC) and its GA optimisation procedure will be introduced in details, followed

by the description of the training of RBF-FLC and its generated parameters.

5.4.2.1 RBF-Fuzzy Controller

This section introduces the establishment of the RBF neural network based fuzzy logic

controller (RBF-NFLC). The RBF-NFLC has been proposed and intensively investigated

since its superiority of computational efficiency and robustness to the conventional FLC

(Jang & Sun 1993; Pedrycz 1998; Yingwei, Sundararajan & Saratchandran 1997).

Traditionally, the backpropagation network doesn’t possess the mechanism in the

standard training scheme for identifying regions which don’t have any known

classification. Reason of such phenomenon lies in that the inherent nature of the sigmoid

transfer function, the definition of the training set, and the error function used for training

(Leonard & Kramer 1991). On the contrary, the RBF neural network, being the

abbreviation of radial basis function, uses a non-monotomic transfer function based on


156

the Gaussian density function to overcome the challenges of the backpropagation

networks generating non-intuitive, non-robust decision surfaces (Linkens & Nie 1993).

Thanks to the characteristics, the RBF neural network is usually used to approximate a

continuous linear or nonlinear function mapping. The schematic diagram of the RBF-

FLC with multi inputs and outputs can be found in Figure 5.15.

Figure 5.15 Schematic diagram of the RBF based NFLC

As can be seen from Figure 5.15, such neuro-FLC consists of three layers, including input

layer, hidden layer and output layer, of which the hidden layer processes the fuzzy

inference of the controller. The strength of the control action for each of the fuzzy rules

is given by the interconnected weights between the hidden and the output layers. Assume

that the system possesses N inputs (x1, x2, …, xn, …, xN) and M outputs (y1, y2, …, ym, …,

yM), of which the inputs are normally the feedback signals from the controlled system

while outputs are the control signals normalised by the output layer based on the radial

weight from hidden layer. The fuzzy control rules governed by the RBF structure can

hence written by

Eq. 5.27

where wim is the control action for the ith control rule of the mth output variable.

……

……

……

………

… ……

Input layer Hidden layer Output layer

Weights, wim

x1

x2

xN

y1

y2

yM

X Y

……

iMimii

iN

in

ii

wandwandwandwThenXandXandXandXIF

21

21


157

Figure 5.16 Fuzzy rule base matrix at hidden layer

Next, the NFLC is designated on the basis of the MRE base isolation control scheme.

Normally, a well-designed base isolation system should be able to achieve small base

drift and structural acceleration simultaneously(Kim & Roschke 2006). Thus the aim of

the fuzzy logic controller designed here is to minimise the structural acceleration and base

drift simultaneously. Top floor acceleration and base level displacement are then

chosen to be the inputs of controller whose output is the control current of the MR

elastomer isolator. Scilicet, the NFLC implemented in the MRE base isolation system has

two inputs variables and one output. For each inputs, five fuzzy membership functions

(MFs) have been chosen and labelled as positive big (PB), positive small (PS), zero (Z),

negative small (NS), negative big (NB). Meanwhile, Gaussian-type MFs are selected

here, of which each MF is characterised by only two parameters, i.e. centre and width of

the Gaussian function. With such arrangement, certain length of chromosome in Genetic

Algorithm can encode more fuzzy memberships. To this end, the proposed RBF-NFLC

structure features fewer parameters compared to conventional FLC (Mamdani & Assilian

1975) and Takagi-Sugeno type of FLC (Lee & Takagi 1993), resulting in higher

efficiency for optimal parameter searching by GA. To better visualise the NFLC

designated specifically in the MRE isolation case, the rule base matrix at hidden layer,

NB NS Z PS PB

Z

NS

NB

PS

PB

Fuzzy membership function at hidden layer

If is NS) and is PS)

3x bx


158

i.e. the interconnected weight element for output control rule, is shown in Figure 5.16.

Conventionally, a fuzzy logic control consists of three main stages: (i) fuzzification; (ii)

inferencing, and (iii) defuzzification. A approach proposed by (Seng, Khalid & Yusof

1999) has been adopted to further simplify the fuzzy inference mechanism. This approach

involves two major steps, i.e. pattern matching and weights averaging and hence gets rid

of the fuzzification and defuzzification procedures. The first operation of pattern

matching requires the determination of the matching degree of the input values to each of

the membership function. As mentioned before, each MF is featured as a Gaussian

function and hence only two parameters, namely centre Cx and width Dx, need to be

identified. The formula to for matching degree of the ith control rule can be written as

following.

Eq. 5.28

where and denote the centre and width of nth input variable’s MF assigned to

the ith control rule; The operator represents norm of the function. The value of hi,

which is between 0 and 1, indicates the matching level of nth input to the ith rule: a

matching degree of 1 means that a full match occurs to that rule, while a small hi indicates

poor matching between the input pattern and the particular rule pattern (Seng, Khalid &

Yusof 1999).

The control action of each output variable is then obtained by averaging the weights. For

the mth controller output, ym can be computed by normalising the weights using the

following formula

Eq. 5.29

in which, T is the total number of control rule while wim is the interconnected weight

between the ith control rule to the mth output. GA is then implemented as an optimization

inx

ni

nxi D

xCh

,

,exp

inxC ,

inxD ,

T

ii

p

iimim hwhy

11,


159

algorithm to tune all the parameters of this NFLC, which is discussed in the next section.

5.4.2.2 Design of the NFLC by GA

Genetic algorithm (GA) is a metaheuristic inspired by the process of natural evolution

with Darwinian survival of the fittest approach. The GA adopted in searching optimal

parameters of the FLC is named as Non-Dominated Sorting Genetic Algorithm II (NSGA

II), because NSGA II has been demonstrated to be one of the efficient algorithms for

solving multi-objective optimisation on a number of benchmark problems (Deb et al.

2002). Moreover, NSGA II is also recognised as a good candidate for assuring a good

Pareto optimal front convergence without losing solution diversity since it is able to

introduce elitism into a multi-objective optimisation procedure while guarantees a

diversity-preserving mechanism at the same time. On the basis of NSGA II, dynamic

crowding distance (DCD) is introduced into the standard NSGA-II as a novel evaluation

index to keep good diversity among the solutions.

Generally, GA consists of three basic operations: reproduction, crossover and mutation.

In reproduction process, members of the population reproduce next generation, judging

by the relative fitness of the individuals. In other words, the chromosomes with higher

fitness have higher possibility to have more offspring in the coming generation. The

tournament scheme is employed here for reproduction selection scheme (Goldberg &

Holland 1988). Crossover means the selected chromosomes exchange part of their

information. Mutation is occasionally diversification of information at a particular

position of the chromosome. When reproduction and crossover alone cannot provide a

global optimal solution, mutation serves as a safe mechanism which is able to recover

some specific information. More detailed information about GA can be found in

(Goldberg 1989).

As aforementioned, two inputs, and , as well as one output, control current I, are

included in the NFLC. Each input has been quantified into five Gaussian membership

functions, each of which features two characteristics: centre and width .

3x bx

inxC ,

inxD ,


160

Therefore, 20 parameters (5×2×2) need to be tuned. In the reference (Seng, Khalid &

Yusof 1999), the authors have demonstrated that the selection of five MF is a judicious

balance of control performance and GA searching complexity. With each input having

five MFs, 25 fuzzy radial units (5×5) have been generated at the hidden layer, resulting

in 25 weights connecting the hidden units and the output node. Hence, the NSGA II need

to search the optimal value for 45 parameters in total. The original form of Real-Coded

NSGAII, uses simulated binary crossover (SBX) operator and polynomial mutation and

is designed for optimisation of continues adjustable parameters (Askari 2014). To encode

the parameters, the Linear Mapping Method (Goldberg 1989) is used, which can be

expressed as

Eq. 5.30

where gq is the actual value of the qth parameter, Aq is the integer represented by a N-bit

string gene. Gqmax and Gqmin are the user-defined upper and lower boundary of the gene,

respectively.

Figure 5.17 Schematic diagram of one chromosome with encoded NFLC parameters

Next, all encoded gens are concatenated to form a complete chromosome. As each

parameter is encoded into 8-bit strings, the whole chromosome is 360 bits. The

arrangement of coded parameters of the NFLC is illustrated in Figure 5.17.

As can be seen from Figure 5.17, altogether 45 genes are in one chromosome, each

representing one encoded parameter. The first 10 genes are allocated to sub-chromosome

of the first input of top floor acceleration . The odd genes represent centres of the five

MFs while the even genes are the corresponding width of the Gaussian functions. Genes

11 to 20 are allocated to sub-chromosome of the first input of base displacement with

12/minmaxminN

qqqqq AGGGg

Sub-chromosome of X2

Base displacement 13

Sub-chromosome of X1

Top floor acceleration 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20

11xC 1

1xD 21xC 2

1xD 31xC 3

1xD 41xC 4

1xD 51xC 5

1xD 12xC 1

2xD 22xC 2

2xD 32xC 3

2xD 42xC 4

2xD 52xC 5

2xD

21 22 … 25 45

11w 12w 15w 55w

… …

1iw

… …

… … … … …

Sub-chromosome of weights

3x

bx


161

the same parameter arrangement as the first sub-chromosome.

Figure 5.18 Flow chart of NSGA-II with DCD

With the population of coded chromosomes, the NSGA II with DCD is then employed to

seek for the solution of parameters with best fitness results. The working process of the

NSGA II with DCD is illustrated by a flow chart in Figure 5.18. Detailed introduction

about NSGA II with DCD will be presented in Chapter 6.

To evaluate the fitness of the chromosomes of each generation, four evaluative indices

have been chosen, namely, peak top floor acceleration, RMS of top floor acceleration,

peak base displacement and RMS of base displacement. A fitness function to evaluate the

multi-objective optimisation is then developed based on the four indices. The

mathematical expressions of the evaluative indices are given by Table 5.6 and the fitness

Start

End

Determine the multi-objective optimisation problem

Set parameter values of NSGA-II: population=20; crossover probability=0.9; mutation probability=0.15; maximum iteration number=100

Initialise the population

Calculate the fitness values: peak top floor acceleration and base shift, RMS of top floor acceleration and base shift

Initialise iteration number n=0

Perform crossover and mutation operations to produce the offspring

Carry out non-dominated sorting for integrated parent and offspring population

Adopt DCD method to produce new population from integrated parent and offspring populations

Use tournament rule to choose the parent

n<Niter?

No

Set n=n+1

Yes


162

function is then expressed by Eq 5.31.

Eq. 5.31

Table 5.6 Evaluative indices for NSGA II

Description Expression Description Expression

Peak top floor acceleration

RMS top floor acceleration

Peak base drift

RMS base drift

In Table 5.6, and represent top floor acceleration and base displacement of the

evaluated structure; and represent peak and RMS of top floor acceleration of

fixed base building; and represent peak and RMS of base displacement of

fixed base building. Figure 5.19 and Table 5.7 shows the optimised NFLC tuned by the

NSGA II, of which Figure 5.19 shows the Gaussian type MFs of both inputs while Table

5.7 shows the tuned weights of all 25 fuzzy control rules.

Figure 5.19 NSGA-II optimised membership function for top acceleration and base displacement

BD

NorthridgeKobeHachinohe

CentroEl


CentroEl

FA


CentroEl


CentroEl

RMSobjPBDobj

RMSobjPFAobj

f max,max

max,max

minimise11

11

PBD maxt,ixb t xb

max

xb

xbmax xb

RMS

0.0

1.0

Membership function of top floor acceleration

0

A1 A2 A3 A4 A5

Label A1 A2 A3 A4 A5

Centre -0.898 -0.137 0.019 0.451 0.868

Width 0.773 0.702 0.143 0.580 0.337

0.0

1.0

Membership function of base displacement

0

D1 D2 D3 D4 D5

Label D1 D2 D3 D4 D5

Centre -0.859 -0.525 0.143 0.702 0.827

Width 0.294 0.843 1.072 0.675 0.255


163

Table 5.7 NSGA-II optimised weights for NFLC

Weight D1 D2 D3 D4 D5

A1 0.72549 0.51373 0.19216 0.96863 0.72549

A2 0.01961 0.74118 -0.92157 -0.12941 0.20784

A3 0.84314 -0.69412 -0.25490 -0.30980 -0.23137

A4 -0.41961 -0.46667 -0.97647 -0.85882 0.50588

A5 -0.56863 0.93725 0.76471 -0.04314 -0.79608

5.4.3 Lyapunov-Based Control

5.4.3.1 Brief of Lyapunov Stability

Stability is one of the most important properties of dynamic system. Civil infrastructures

have inherent asymptotic stability. Moreover, only when a structure features asymptotic

stability, the structure is stabilised. Consider a system with zero input, whose state

function can be written as

00,,0, ZZttZFtZ Eq. 5.32

The system is recognised to possess Lyapunov stability if, for any real number ,

there exists a number such that the system response caused by

satisfies

0, tttZ Eq. 5.33

when . In other words, the meaning of system stability lies in that the error

caused by minor disturbance in a stabilised system will be reduced gradually, while on

the contrary, an unstable system will amplifier the disturbance causing loss of the control

to the system. Hence, it is of great significance to ensure the system stability during the

design of the control system so as to guarantee the controllability of the system.

Lyapunov functions, also known as Lyapunov’s second method for stability, is named

0

0, 0t 00 ZZ

00 , tZ


164

after the Russian mathematician Alexsandr Mikhailovich Lyapunov (Lakshmikantham,

Matrosov & Sivasundaram 2013). Since the existence of Lyapunov function is a

necessary and sufficient condition for stability for certain classes of ODEs requiring no

knowledge of trajectories of the system, this method has been widely adopted in the

stability analysis of dynamical systems and control theory.

Lyapunov function analyses the system stability in the point view of energy. As shown

in Figure 5.20, a simple dynamic system has a mass block whose displacement and

velocity can be expressed by and . Hence the state space vector of the system is

. At the time instant t, the total energy of the system can be expressed

by

Figure 5.20 Schematics of the dynamic system

mk

P

tPZtZtkxtxmEEtE TPK

0021

21 22

Eq. 5.34

in which, txmEK221 and tkxEP

221 are the system kinetic energy and

potential energy, respectively.

Since P is known, the total energy E is a monotropic and continuous quadratic function

of the state variable Z(t). When , E > 0; only when , E = 0. Consider the

derivative of E(t), if , E(t) decreases along with the time and rounds towards zero

while E = 0 means . To this end, if , when t is large enough, ,

which means the system is asymptotically stable; if , E won’t increase with time

but also does not necessarily round towards zero, which is called Lyapunov stable; when

tx txTtxtxtZ

m

k

c

x

0tZ 0tZ

0tE

0tZ 0tE 0tE

0tE


165

, E will increase infinitely with time, which means Z(t) is increasing infinitely

with time and hence the system is unstable.

As seen from last paragraph, the stability of the system can be judged by analysing the

time-variation of the system’s total energy. However, due to the complexity and diversity

of dynamic systems, it is difficult to name a uniform energy function to describe the

energy relationship of the system. Therefore, Lyapunov function is defined as a positive

definite scalar function v(Z(t)), which features all the characteristics of the system energy

function. Then the stability of the system is assessed by the symbol feature of

dtZdvtZv . Now, consider a time invariant system (linear or nonlinear) whose

state space function is

Eq. 5.35

of which the equilibrium is state space’s coordinate origin, i.e. Ze=0 satisfies equation

. Lyapunov’s second method for stability can be induced by the following three

theorems:

Theorem 1. If there exists a Lyapunov function such that , the

system is Lyapunov-stable.

Theorem 2. If there exists a Lyapunov function such that , the

system is asymptotic stable.

Theorem 3. If there exists a Lyapunov function such that , and

when , , the system is asymptotic stable on the whole definitional

domain.

5.4.3.2 Lyapunov-Based Sliding Model Control (SMC)

Sliding Mode Control is also named as variable structure control. As the name suggests,

SMC is particular suitable for the semi-active stiffness control where the parameters of

the controlled system is variable in the control process. Different from LQR control, SMC

0tE

tZFtZ

0tF

tZv 0tZv

tZv 0tZv

tZv 0tZv

Z Zv


166

is suitable for the control of both linear and nonlinear structure. Thanks to those

advantages, SMC becomes a quite ideal candidate for the control of MRE base isolation

system. In the SMC, a controller needs to be designed to drive the structural motion

towards the sliding surface, where the structural movement is stable. Hence, SMC

consists of two aspects: (i) the determination of sliding surface and (ii) design of the

controller (Bartoszewicz & Patton 2007).

Next, the procedure to implement SMC based on Lyapunov method to the MRE base

isolation system is to be discussed. Still consider the state space function shown in Eq.

5.19 to Eq. 5.21. Assume that p controllers have been installed on the system. The sliding

surface in the p-dimensional space is

0tztS Eq. 5.36

in which z(t) is the state vector; is a 1x2N matrix. The system motion is stable on the

sliding surface and the design of sliding surface is actually the process determining .

When full state feedback is available, the sliding surface can be determined by both LQR

or pole assignment method; when only partial states can be observed, the sliding surface

can only be determined by pole assignment method. In recent years, many methods have

been proposed as well to design the sliding surface. The process of finding can be

found in references (Bartoszewicz & Patton 2007; Edwards & Spurgeon 1998; Tang &

Misawa 2002; Yang, Wu & Agrawal 1995).

Next, the sliding mode controller is designed based on Lyapunov’s second method. The

control action generated by this controller should be able to drive the system’s response

towards the sliding surface in Eq. 5.36. Assume that the Lyapunov function

zzSSv TTT 5.05.0 Eq. 5.37

, when , the necessary and sufficient condition for S = 0 is that the 00 ttv t


167

derivative of Eq. 5.37 is smaller than zero, i.e. being a monotonic decreasing function.

0SSv T Eq. 5.38

Substitute the state-space function Eq. 5.19 into Eq. 5.38,

sbb

TTT GFBFAZSZSSSv Eq. 5.39

in which, Fb is the control force provided by the MRE isolator and

AzBGBS s

T 1 Eq. 5.40

In order to make , the control force can be chosen as

Tsb GF Eq. 5.41

In this formula, is named as sliding margin and thus is always satisfied

during the whole control process. The civil engineering structures feature inherent

stability when there is no controller or actuators equipped on the structure and the

derivative of Lyapunov function is then

v Eq. 5.42

To drive the response of the system to sliding surface, the designated SM controller

should either reduce the derivative or keep it negative. Hence, the control force should be

confined as

mssm

mssb uGGu

uGGF

sgn Eq. 5.43

where is the upper and lower bounds of control force that can be provided by the

MRE base isolator.

5.4.3.3 Bang-Bang (ON/OFF) Control

Based on the SMC, researchers have proposed Bang-Bang (ON/OFF) control algorithm

that is simpler and more straightforward (Kamagata & Kobori 1994; Kobori & Kamagata

v

0v

0Tv

mu


168

1992; Yang, Kim & Agrawal 2000). The Bang-Bang control can also be implemented in

the MRE base isolation system. Since the control force of MRE base isolator Fb is on the

right side of Eq. 5.19, it has the opposite sign of the realised elastic force of the variable

stiffness device. Hence, the control force can be expressed as

txktgtututF

bvv

vb Eq. 5.44

where, is the elastic force (shear force) provided by the MRE isolator; is

switching function, i.e. when , the MRE isolator is at ON-state and when

, the MRE isolator is at OFF-state. Substitute the control force into Eq. 5.41, the

derivative of Lyapunov function is

sbv Gxgkv Eq. 5.45

To achieve minimum value of , the switching function should satisfy the following

condition

0100

b

b

xx

tg Eq. 5.46

It can be observed from Eq. 5.46 that, the switching principle of variable stiffness is

related to the structural response xb and variable . In this case, . The derivation

of is not discussed here. In the end, the Bang-Bang control law can be summarized

as following

0100

bb

bb

xxxx

tg Eq. 5.47

The Bang-Bang control in Eq. 5.47 has its own physical interpretation: when the

structure’s displacement and velocity are with the same sign, which means the

superstructure is moving away from the equilibrium position, the MRE base isolator

provide additional stiffness for the system; on contrast, when the displacement and

velocity are with the opposite signs, which means the superstructure is moving towards

tuv tg

g(t) 1g(t) 0

v

bx


169

the equilibrium position, the isolator maintains the softest situation. Such physical

meaning of Bang-Bang control can be well illustrated by Figure 5.21. The energy

dissipated by the control logic is the area of triangles in the figure.

Figure 5.21 Stiffness ON-OFF control (Liao et al. 2012)

5.4.3.4 An Innovative Lyapunov-Based Semi-Active Control of MRE Base Isolation

System

Despite being simple and straightforward, the Bang-Bang control also has its inherent

drawbacks. For instance, due to the output limitation of the MRE base isolator, the

inequality cannot always be realised. Therefore, the control strategy can only achieve the

minimum value of derivative of Lyapunopv function, leading to degradation of control

performance occasionally. To this end, an innovative Lyapunov-based semi-active

control strategy especially for the MRE base isolation system.

Rewrite the state-space function described by Eq. 5.20 and Eq. 5.21 as

EWIxbAxx Eq. 5.48

where

13

2111

14

0

10

tzxcxkm

xb bbbbbbb

Eq. 5.49

and


170

gE xI

W14

140

Eq. 5.50

Consider a Lyapunov function of this system with a positive-definite symmetric matrix

P

PxxV T Eq. 5.51

Hence, the derivative of the Lyapunov function can be expressed by

ETT

ETTT

ETT

ETTT

ETT

E

TT

WIxbPxPxWIxbxPAPAxWIxbAxPxPxWIxbAx

WIxbAxPxPxWIxbAx

xPxPxxV

Eq. 5.52

Note that is a scalar, whose transpose equals to itself, i.e.

E

TTTE

TTE

T WIxbPxPxWIxbPxWIxb Eq. 5.53

Therefore, Eq. 5.52 can be written as

ETT

ETTT

WIxbPxQxxWIxbPxxPAPAxV

2

2 Eq. 5.54

in which, PAPAQ T .

According to Rayleigh-Ritz theorem, Eq. 5.54 can be adjusted to an inequality

E

T WIxbPxxV 2min Eq. 5.55

where is the minimum eigenvalue of Q.

It is obvious that one of the sufficient conditions to ensure lies in that

02 ET WIxbPx Eq. 5.56

Hence,

E

TT PWxIxPbx Eq. 5.57

So far, the control problem has been evolved into the selection of current at each control

PxWIxb TE

T

min

0V


171

time instant, based on which the inequality in Eq. 5.57 is established.

5.4.4 Frequency Control

The essence of base isolation system is to shift the natural frequency of the superstructure

so as to avoid resonance caused by earthquake ground motion. However, it is impossible

for the passive isolation system to dodge all the frequency components of the seismic

input during the whole time history. Hence, another intuitive idea has been come up with

to alter the parameter of the base isolation layer and thus change the frequency of the

superstructure at every time instant so as to avoid the matching of structural frequency to

the dominant frequency of the input, i.e. resonance. To this end, a frequency control

method, inspired by the control strategy proposed by Kobori et al. (Kobori et al. 1993)

for AVS (active variable stiffness) system, has been developed. This method, developed

especially for better utilising the characteristics of MRE isolator, changes the structural

matrices in accordance with the changes of the stiffness and damping properties of the

isolator by adjusting the input current of the MRE isolator. More elaborately, the control

method is to generate the current that will alter the stiffness of the structure as far away

as possible from the predominant frequency of the earthquake so as to minimise the

probability of resonance. The proposed control system consists of four primary units.

Earthquake excitations will be measured by the accelerometers in the first unit and then

input to the motion anticipating analysers in the second unit. The response of each

stiffness scenario will be forecasted by the analysers and then forwarded to the control

decision processor. Judged by the control law, the best stiffness scenario will be chosen

and the control signal will be sent to the MRE isolators to change the structure’s state.

The control system endeavours to produce a non-stationary, non-resonant condition

changing continuously during the earthquake attack. By maintaining the non-resonant


172

condition, the method can isolate the seismic energy from transmitting into the building.

5.4.4.1 Control system working flow

The control system mainly consists of 4 parts: (1) earthquake measurement unit, (2)

motion anticipating unit, (3) control decision processor and (4) smart base isolation

system. Figure 5.22 displays the working flow chart of the control system.

Figure 5.22 Flow chart of the feed-forward frequency control system (Gu et al. 2016)

As can be seen from Figure 5.22, four steps will be executed during every control interval.

During an earthquake, the accelerometers in earthquake measurement unit capture the

ground motion acceleration and send the earthquake signal to the motion-anticipating

unit. The analysers in the motion-anticipating unit calculate the approximate

corresponding responses of each stiffness scenario (0A and 5A). Based on the anticipated

output, the control decision processor chooses the stiffness type which cause the smallest

structure responses according to the stiffness scenario selection algorithm discussed in

next section. Finally, the control signals (current adjusting command) generated by the

control decision processor will be forwarded to the MRE base isolator so that the

frequency of the structure can be alternated in real-time. In this method, each control

interval takes 0.005s.

5.4.4.2 Stiffness Scenario Selection Method

The motion anticipating analyser is to forecast the uncontrolled structural response of

each stiffness type i (i = 1, 2) based on the present state of the subject. In this control

strategy, acceleration, relative displacement and inter-storey drift are used as the

evaluative subjects. Therefore, j, the number of evaluative subjects varies from 1 to 3.

is the evaluation in terms of the evaluative subject j of the scenario i, which can

Earthquake Measurement Unit

Motion Anticipating Unit

Control Decision Processor

Smart Base Isolation System

Measuring:Ground motion acceleration

Evaluating response:Scenario 1 (3A) Scenario 2 (0A)

Scenario selection: Judge and adjust the input current

Change stiffness: Change the structural frequencies

tE ji,


173

be written as:

Eq. 5.58

where, is a coefficient for scenario i reflecting the maximum amplitude of the

subject j corresponding to the resonant frequency of the scenario; is the output of

the subject j from the motion anticipating analyser; ∆t is the control interval;

represents the number of control interval samplings during half of the

fundamental period of scenario i.

By calculating , one can obtain the uncontrolled response of each stiffness

scenario in terms of the proximity of the instant of interest. This index is robust because

includes the average output of the motion anticipating analyser during half

scenario i’s corresponding fundamental period and also times the average value with the

maximum resonant amplitude . Nevertheless, a delay tolerance of 1/2 fundamental

period of corresponding stiffness type i is inevitably required in the stiffness switching

time based on such method.

Next, the decision of which stiffness scenario is to be chosen has to be made based on the

calculation of the judgment index which can be formed as

Eq. 5.59

consists of two terms, of which the first item represents the ratio between the

evaluation of a certain subject in a certain scenario and the maximum evaluation of all

the subjects in every scenario while the second item reflects the increasing and decreasing

trend of the evaluation . The t’ in Eq. 5.49 is an abbreviated time to assess the

increase or decrease trend of evaluation, which is chosen as 5mSec in this study. In the

N

tnttRetE

N

nji

jiji1

2,

,,

jie ,

jiR ,

ttN i 2

tE ji,

tE ji,

jie ,

tJ i

2

1 ,,

,,

,

,

maxmax'maxmax'

maxmaxj jiijjii

jiiji

jiij

jii tEttE

tEttEtE

tEtJ

tJ i

tE ji,


174

end, the stiffness scenario with minimum value of index will be selected to operate

during the next control interval.

5.4.4.3 Control Law

Figure 5.23 Time histories of evaluative indices and corresponding control command

Since there are only two types of stiffness scenario corresponding to two current inputs, the control law for the current I(t) can be described as

tJ i

0 2 4 6 8 100

0.5

1

1.5

2

Time (s)

Eval

uativ

e in

dice

s val

ueEl-centro Earthquake

J1 J2 Control command

0 2 4 6 8 100

0.5

1

1.5

2

Time (s)

Eval

uativ

e in

dice

s val

ue

Kobe Earthquake

0 2 4 6 8 100

0.5

1

1.5

2

Time (s)

Eval

uativ

e in

dice

s val

ue

Hachinohe Earthquake

0 2 4 6 8 100

0.5

1

1.5

2

Time (s)

Eval

uativ

e in

dice

s val

ue

Northridge Earthquake




Cur

rent

(A)

Cur

rent

(A)

Cur

rent

(A)

Cur

rent

(A)

0

5

0

5

0

5

0

5


175

tJtJAtJtJA

tIAA

AA

05

05

05

Eq. 5.60

Therefore, the control force generated by the MRE isolator can be calculated by

substituting I(t) into the force formula Eq. 5.15.

5.4.4.4 Examples of current selecting utilise frequency control

To further elaborate the control law, a numerical case study has been conducted by

applying four benchmark earthquakes, i.e. El Centro, Kobe, Hachinohe and Northridge

earthquakes, on the MRE base isolated three-storey building. The values of evaluative

indices and corresponding control command under four benchmark earthquakes are

shown in Figure 5.23.

5.5 COMPARATIVE INVESTIGATION RESULTS AND DISCUSSION

In this section, a comprehensive report about the seismic protection performance of the

MRE base isolation system with different control algorithms will be presented. Four

benchmark earthquakes, namely, Imperial Valley (El-Centro) 1940, Kobe 1995, Tokachi-

Oki (Hachinohe) 1968, Northridge 1994, have been adopted as the ground excitation to

simulate real seismic environment. The reasons behind such choice are discussed in the

first part. Nine evaluative indices have been utilised to assess the structural responses and

control performance of different isolation and control scenarios. A comparison between

simulation and experimental results is then displayed to show the accuracy and fitness of

the numerical model of MRE isolator, primary three-storey structure and the integrated

base isolation system. Next, the comparative experimental results of different isolation

scenarios are reported in terms of peak responses of inter-storey drift ratio, acceleration,

relative displacement and inter-storey shear at each floor as well as the time histories of

top and base floor acceleration, base displacement and control force. In this process, eight

isolation scenarios are compared, i.e., fixed base building, passive-off base isolation


176

system (I = 0A), passive-on base isolation (I = 3A), isolation system with NSGA-NFC

algorithm, isolation system with Bang-Bang controller, isolation system with LQR

controller and inverse MRE isolator model, isolation system with frequency controller

and isolation system with Lyapunov-based current controller. As mentioned in Section

5.1, the control current in all the controlled isolation scenarios are set to vary between 0

and 5A to endow the isolated structure with larger adjustable range. Last but not least,

time histories of control force and corresponding control current signals are presented

with selected control algorithms.

5.5.1 Earthquake Records

To appraise the seismic protection performance of the smart base isolation system under

different control configurations, numerical and experimental testings are conducted under

four natural acceleration records of historical earthquake events, namely, Imperial Valley

1940, Kobe 1995, Tokachi-Oki 1968, Northridge 1994. Selected from the databases of

Pacific Earthquake Engineering Research Centre (PEERC) and National Geophysical

Data Centre (NOAA-NGDG) (K-Karamodin & H-Kazemi 2010), records of Imperial

Valley (station: El Centro Array) and Tokachi-Oki (station: Hachinohe) earthquakes are

categorised as far-fault earthquake, which features wider frequency range but longer

excitation time while Kobe (station: KJMA) and Northridge (station: Sylmar) are

classified as near-fault earthquakes which features waveforms containing large velocity

pulses with lower frequency. Details of the four accelerograms are summarised as

following and in Table 5.8.

El-Centro earthquake: The N-S component recorded at the Imperial Valley Irrigation

District substation in El-Centro, California, during the Imperial Valley, California

earthquake on May 19, 1940. The magnitude was 7.1 on the Richter scale.

Hachinohe earthquake: The N-S component recorded at Hachinohe City during the


177

Takochi-oki earthquake on May 16, 1968. The magnitude was 7.9 on the Richter scale.

Figure 5.24 Earthquake time histories and pseudo-acceleration spectra (damping ratio=5%)

Kobe earthquake: The N-S component recorded at the Kobe Japanese Meteorological

Agency (KJMA) during the Hyogo-ken Nanbu earthquake on January 16, 1995. The

0 10 20 30 40 50

-0.2

0

0.2

Time (s)

Acc

eler

atio

n (g

)El Centro Earthquake

0 1 2 3 40

0.1

0.2

0.3

0.4

Period (s)

Pseu

do-A

ccel

erat

ion

(g) El Centro Earthquake

0 10 20 30 40 50-1

-0.5

0

0.5

Time (s)

Acc

eler

atio

n (g

)

Kobe Earthquake

0 1 2 3 40

0.5

1

Period (s)

Pseu

do-A

ccel

erat

ion

(g) Kobe Earthquake

0 10 20 30

-0.1

0

0.1

0.2

Time (s)

Acc

eler

atio

n (g

)


0 1 2 3 40

0.05

0.1

0.15

0.2

Period (s)

Pseu

do-A

ccel

erat

ion

(g) Hachinohe Earthquake

0 10 20 30-0.5

0

0.5

1

Time (s)

Acc

eler

atio

n (g

)


0 1 2 3 40

0.2

0.4

0.6

0.8

Time (s)

Pseu

do-A

ccel

erat

ion

(g) Northridge Earthquake


178

magnitude was 7.2 on the Richter scale.

Northridge earthquake: The N-S component recorded at the Sylmar County Hospital

parking lot in Sylmar, California, during the Northridge, California earthquake on

January 17, 1994. The magnitude was 6.8 on the Richter scale.

Table 5.8 Benchmark earthquakes information

Record Earthquake Date Station Mag PGA (g)

PGV (cm/s)

Predominant freq. (Hz)

I-ELC180 Imperial Valley,

1940 19/05

El Centro Array

7.1 0.349 29.69 0.5~2.8

KJM000 Kobe, 1995 16/01 KJMA 7.2 0.834 40.65 0.6~2.7

Jap02.089 Tokachi-Oki,

1968 16/05

Hachinohe Harbor

7.9 0.229 22.71 0.2~3.2

SYL360 Northridge,

1994 17/01

Sylmar Olive View

6.8 0.843 64.68 0.5~2.5

Such selection consideration is capable of demonstrating the versatility of the proposed

MRE base isolation system. Normally, the traditional base isolation performs well in

coping with far-fault earthquake. However, near-fault ground motion may strongly

impact seismic isolation systems due to the presence of long-duration pulses. The ground

motions may have one or more displacement pulses, with peak velocities of the order of

0:5m/sec and durations in the range of 1 to 3 sec. That is to say, most conventional

structural systems tend to soften as damage progresses, and a stiff structure subjected to

strong-ground acceleration at short periods will be vulnerable to long-period pulses

(Jangid & Kelly 2001). It is feasible to design an optimal isolation system to perform well

under either near-fault or far-fault earthquake excitations, but can be rather challenging

for a conventional base isolation system to meet the requirement of both seismic types

with its passive nature. Hence, the four benchmark earthquakes are selected to validate

the capability and necessity of the adaptive MRE base isolation system.

The time history, pseudo acceleration spectrums (damping ratio is assumed to be 5%) of

the four earthquakes are shown in Figure 5.24. As can be seen in Figure 5.24, long-period


179

pulse-like waveforms can be clearly observed in Northridge earthquake. Meanwhile,

pseudo-acceleration spectrums show that Kobe and Northridge earthquakes possess

larger acceleration spectra when the structural period is larger than 1s. In contrast, the El

Centro and Hachinohe earthquakes have relatively small acceleration values and less low-

frequency components but longer excitation duration. In particular, the Hachinohe

earthquake brings about continuous vibration throughout the entire time history of 36

seconds. Meanwhile, it can be seen from Table 5.8 that the peak ground accelerations

(PGA) of El Centro, Kobe, Hachinohe and Northridge earthquakes are 0.349, 0.834,

0.229 and 0.843g, respectively. To guard against possible yielding of columns in the

isolated structure and restrict the base isolator’s deformation under critical level, the peak

building responses should be limited by scaling the earthquakes’ acceleration magnitudes.

As a result, four scaling factors, namely, 5%, 10%, 15%, and 20% have been adopted for

better observation and safety insurance.

5.5.2 Evaluative Indices

To systematically assess the performance, nine evaluative indices are adopted to show

the seismic response suppression effectiveness. The evaluative indices can be divided into

two groups: (i) building responses and (ii) control device performances. The first six

indices belongs to the first group, includes the peak and normed structural responses,

namely, peak inter-storey drift ratio (J1), level acceleration (J2), base shear (J3) and

normed inter-storey drift ratio (J4), level acceleration (J5), base shear (J6). The next three

indices belong to the second group, evaluating peak control force (J7), control device

stroke (J8) and power used for the control (J9). The formulation and meaning of

parameters are explained in Table 5.9.


180

Table 5.9 Evaluative indices description

Description Peak inter-storey drift Peak floor accel. Peak base shear

Formula

Description Normed inter-storey

drift Normed floor accel. Normed base shear

Formula

Description Peak control force Peak controller stroke Peak control power

Formula

As can be seen in Table 5.9, , , and are the acceleration, inter-storey drift

ratio and mass at the ith floor (i = base, 1, 2, 3); , , and are the peak

acceleration, inter-storey drift and base shear of the fixed base building. Inter-storey drift

ratio is a ratio between actual drift and the floor height. The norm is the same as

defined previously. As suggested by the reference, T is a sufficiently large time to allow

the response of the structure to attenuate. The third row of Table 5.9 shows the indices

regarding to required performance of control device, which is the MRE base isolator in

this study. In the formulae, is the force generated by the lth controller over time

history; W is the seismic weight of the structure based on the above ground mass of the

structure; is the displacement across the lth controller during the earthquake; xmax is

the maximum uncontrolled displacement of the levels relative to the ground; is a

measure of the instantaneous power required by the lth controller and is the

maximum uncontrolled relative velocity of the levels. Here, uncontrolled responses refer

to the responses in passive-off (I = 0A) base isolation scenario.

Each value shows the comparison between the indices of interest of the evaluated

isolation scenario with that of the fixed base building. Hence, the value smaller than 100%

max,

1

max

i

iit

d

tdJ max

,2

max

a

aiit

x

txJ

max1,

2

max

b

n

iaiiit

F

txmJ

max,

4

max

i

iit

d

tdJ

max,

5

max

a

aiit

x

txJ

max1,

6

max

b

n

iaiiit

F

txmJ

W

tfJ

llt ,7

maxmax

,8

max

x

tyJ

allt

Wx

tPJ l

llt

max

,

8

max

txai tdi immaxax max

id maxbF

lf

aly

lPmaxx


181

shows a reduction while value larger than one implies amplification in the corresponding

index and small index value is generally more desirable.

5.5.3 Comparison between Numerical and Experimental Results

Figure 5.25 Experimental and numerical relative displacement responses of Passive-on system

(0.15 Hachinohe)

The experimental and analytical results are compared in this section under four

benchmark earthquakes with a magnitude scaling factor of 15%. Figure 5.25 and Figure

5.26 display the comparative relative displacement and absolute acceleration at each floor

of the structure under 0.15 Hachinohe earthquake. For better observability, the responses

during first 15 seconds are illustrated in the graphs. As can be seen from Figure 5.25, the

ideal fitness is achieved between numerical and experimental floor displacement at each

0 5 10 15

-2

0

2

Dis

plac

emen

t (m

m)

1st Floor Displacement

Numerical Experimental

0 5 10 15-5

0

5

Dis

plac

emen

t (m

m)

2nd Floor Displacement


0 5 10 15

-5

0

5

Time (s)

Dis

plac

emen

t (m

m)

3rd Floor Displacement



182

level. The experimental displacement results are slightly larger than the numerical ones

around the local peaks with large values. Meanwhile, the experimental results have more

fluctuation than the numerical displacement. Regarding to the acceleration responses, the

experimental results share the same curve trend and profile as the numerical one. It can

be observed from Figure 5.26 that, compared to the displacement response, the

acceleration responses have more components with higher frequency. Meanwhile, the

distortion in acceleration response seems to be slightly more severe than that in

displacement responses. The distortion decreases with the increase of floor number, i.e.

when floor height increase, the difference between experimental acceleration response

and numerical acceleration response declines. Moreover, it can be observed from the time

history of acceleration responses that there is a small phase shift in the numerical

acceleration when compared with the measure acceleration, which is caused by the

differential process in numerical analysis.

To further validate the numerical model, the numerical and experimental peak inter-

storey drift, floor acceleration, relative displacement as well as floor shear are compared

in Table 5.10 to Table 5.13 under four earthquakes scaled by 15%. Furthermore, the peak

responses of the seven isolation scenarios (passive-off, passive-on, NSGA-NFLC, Bang-

Bang controlled, LQR controlled, frequency controlled and Lyapunov controlled) are also

compared to the responses of fixed base building. The percentage reductions by each

isolation system are listed in the second row of the corresponding controller. The peak

responses of numerical and experimental results are fairly close with numerical slightly

smaller than experimental under all conditions, which is consistent to the observation in

Figure 5.25 and Figure 5.26. As for the reduction performance, the passive-off system

ends up in amplifying the inter-storey drift under all earthquakes but Northridge

earthquake and relative displacement under Kobe and Hachinohe earthquakes. All the

controlled base isolation systems can reduce all four peak responses to some extent. The

passive-on system, however, is a bit reluctant in suppressing the displacement responses


183

Figure 5.26 Experimental and numerical absolute acceleration responses of Passive-on system

(0.15 Hachinohe)

under El Centro and Hachinohe earthquakes but performed well in terms of acceleration

and floor shear reduction under all earthquakes. Moreover, it can be observed from Table

5.10 ~ 5.13 that there is a slight performance degradation of experimental results in

comparison with the numerical results in most isolation scenarios. Two factors may have

contributed to the degradation: the model is not able to fully track the nonlinearity of the

MRE base isolation system; ii) the time delay in the control system is inevitably affecting

the control performance. However, the degree of deterioration varies with different

control strategies. The passive-off system experiences the most obvious degradation since

the nonlinearity of MRE base isolation is more significant than that in a passive-on system

and there is no action taken to attempt to neutralise the nonlinearity in a passive-off

system. Among all the control strategies, the LQR control, NFLC and Lyaounov control

0 5 10 15-0.04

-0.02

0

0.02

0.04

Acc

eler

atio

n (g

)

1st Floor Acceleration


0 5 10 15-0.06

-0.04

-0.02

0

0.02

0.04

Acc

eler

atio

n (g

)

2nd Floor Acceleration


0 5 10 15-0.1

-0.05

0

0.05

0.1

Time (s)

Acc

eler

atio

n (g

)

3rd Floor Acceleration



184

Table 5.10 Comparative peak responses of experimental and numerical results (0.15 El Centro)

Peak inter-storey

drift ratio Peak floor

acceleration Peak relative displacement

Peak floor shear

Exp. Num. Exp. Num. Exp. Num. Exp. Num.

Fixed base 11.32 10.48 0.28 0.22 28.90 26.91 0.19 0.18

15.85 15.08 0.12 0.10 25.31 23.00 0.09 0.09 -40.1% -34.9% 58.1% 59.3% 12.4% -44.2% 50.5% 53.9%

5.61 5.33 0.15 0.11 18.53 18.42 0.08 0.08 50.4% 51.9% 46.9% 51.5% 35.9% -6.7% 57.1% 58.7% 1.47 1.47 0.02 0.02 3.14 2.87 0.01 0.01

87.0% 86.7% 92.7% 93.3% 89.1% 89.2% 93.8% 93.8% 3.03 2.81 0.08 0.08 3.78 2.82 0.04 0.04

73.3% 74.0% 69.3% 71.3% 86.9% 87.8% 80.2% 81.6% 4.94 4.66 0.13 0.11 15.69 8.95 0.07 0.07

56.3% 56.0% 53.6% 49.0% 45.7% 19.3% 63.0% 65.4% 6.74 6.63 0.07 0.07 10.76 5.96 0.05 0.05

40.5% 44.5% 73.4% 73.7% 62.8% 43.2% 72.6% 73.1% 1.04 1.04 0.04 0.04 3.13 2.96 0.03 0.03

90.8% 90.7% 84.7% 83.1% 89.2% 87.3% 85.8% 86.8%

Table 5.11 Comparative peak responses of experimental and numerical results (0.15 Kobe)

Peak inter-storey



Peak floor shear

Exp. Num. Exp. Num. Exp. Num. Exp. Num. Fixed base 31.95 31.43 0.73 0.52 76.65 62.10 0.52 0.49

60.77 58.33 0.45 0.41 95.94 60.88 0.36 0.34 -90.2% -85.6% 38.5% 20.6% -25.2% 2.0% 31.8% 30.6% 15.15 14.45 0.41 0.34 49.71 31.75 0.23 0.21 52.6% 54.0% 43.7% 34.3% 35.1% 48.9% 55.5% 57.5% 5.18 4.81 0.05 0.04 9.76 6.24 0.04 0.04

83.8% 84.7% 92.9% 92.2% 87.3% 90.0% 92.9% 92.7% 6.91 6.68 0.28 0.25 12.92 9.21 0.14 0.14

78.4% 78.7% 62.0% 52.3% 83.2% 85.2% 72.5% 72.1% 8.62 7.89 0.23 0.21 27.88 16.18 0.13 0.13

73.0% 74.9% 67.9% 59.7% 63.6% 74.0% 74.6% 74.1% 25.83 25.49 0.22 0.21 40.77 29.75 0.17 0.16 19.2% 18.9% 69.6% 60.2% 46.8% 52.1% 67.7% 67.1% 2.13 1.94 0.08 0.07 6.51 3.97 0.07 0.06

93.3% 93.8% 88.8% 85.6% 91.5% 93.6% 87.0% 87.7%


185

Table 5.12 Comparative peak responses of experimental and numerical results (0.15 Hachinohe)

Peak inter-storey



Peak floor shear


13.25 12.94 0.11 0.09 21.42 19.92 0.07 0.07 -178.0% -192.6% 11.4% 5.7% -80.1% -112.4% 7.0% 6.5%

4.62 4.22 0.09 0.07 11.12 9.71 0.05 0.05 3.0% 4.6% 23.5% 30.8% 6.5% -3.5% 33.4% 31.3% 1.20 1.15 0.01 0.01 2.10 1.17 0.01 0.01

74.8% 73.9% 90.5% 88.6% 82.3% 87.6% 90.7% 90.2% 2.90 2.86 0.07 0.06 3.21 2.85 0.03 0.03

39.1% 35.4% 42.9% 38.2% 73.0% 69.6% 58.3% 56.7% 2.18 2.14 0.05 0.04 6.76 6.47 0.03 0.03

54.3% 51.6% 58.8% 54.4% 43.2% 31.1% 63.9% 63.7% 5.62 5.30 0.06 0.05 9.10 5.99 0.04 0.04

-18.0% -19.8% 53.9% 48.7% 23.5% 36.1% 52.7% 51.7% 0.56 0.55 0.02 0.01 1.27 1.07 0.02 0.01

88.3% 87.6% 87.1% 86.9% 89.4% 88.6% 80.9% 80.9%

Table 5.13 Comparative peak responses of experimental and numerical results (0.15 Northridge)

Peak inter-storey



Peak floor shear


31.42 29.00 0.30 0.27 53.23 45.22 0.22 0.22 7.8% 6.2% 63.8% 62.3% 38.4% 28.1% 63.3% 62.2% 14.70 13.54 0.42 0.39 49.36 31.72 0.24 0.22 56.9% 56.2% 49.6% 46.1% 42.8% 49.6% 60.0% 62.5% 3.15 3.02 0.05 0.04 6.94 5.63 0.03 0.03

90.7% 90.2% 94.3% 94.4% 92.0% 91.1% 95.0% 95.4% 6.40 6.13 0.19 0.17 9.98 9.51 0.09 0.09

81.2% 80.2% 76.6% 76.9% 88.4% 84.9% 84.0% 84.0% 8.17 7.53 0.23 0.18 26.48 19.21 0.13 0.13

76.0% 75.6% 72.1% 74.4% 69.3% 69.5% 78.3% 78.2% 13.34 12.63 0.19 0.18 22.62 20.19 0.13 0.12 60.9% 59.1% 77.1% 74.7% 73.8% 67.9% 77.8% 78.3% 1.74 1.68 0.08 0.08 5.71 3.99 0.06 0.06

94.9% 94.6% 89.9% 89.4% 93.4% 93.7% 89.6% 89.5%


186

resulted in relatively small performance degradation, which indicates that those control

strategies can well accommodate the hysteretic dynamics of the MRE base isolation

system.

5.5.4 Peak Responses

The peak responses at each floor unit are of great interest because when depicted over the

floor number, the peak responses at each floor are able to illustrate the monitored

structure’s profile along the structural height. Meanwhile, it is significant to control and

suppress the peak responses under threshold limit values for the safety concern. Four peak

responses are investigated in this section including peak inter-storey drift ratio, floor

acceleration, relative displacement and inter-storey shear force.

5.5.4.1 Peak responses under different earthquakes and different magnitudes

As mentioned, the base isolation systems are tested under four benchmark earthquakes,

each with different scaling magnitudes of 5%, 10%, 15% and 20%. When the isolated

structure is subjected to each of the four earthquakes, the peak responses are compared

as functions of the magnitude scaling factor. Figure 5.27 and Figure 5.28 illustrate the

correlation between four peak responses and the scaling factor under El Centro

earthquake and Kobe earthquake, respectively. It is obvious that with the increase of

earthquake intensity, all of the peak response items increase under both earthquakes.

Especially for NSGA-NFLC and Lyapunov-based current controller, the controlled base

isolation systems show superiority of low sensitivity to the magnitude change of both

types of the earthquakes. However, unlike the passive base isolation systems (both

passive-on and -off), the controlled base isolation system have rather similar changing

trend under both earthquakes. The passive systems, on contrast, express a great

dependence on the input signals’ magnitude and characteristic. Under El Centro

earthquake, the passive-on system has larger peak responses expect for inter-storey drift,

reason being when the isolator is energised, the isolated system is stiffer than the passive-


187

off system, leading to bigger acceleration and shear force responses and smaller structural

deformation under moderate far-fault earthquakes. Under near-fault earthquake, however,

the stiffer structure has better performance to resist the deformation while the passive-off

system receive poor performance because of resonance caused by overlapping natural

frequency to the predominant frequency range of earthquake.

Figure 5.27 Peak responses with four different earthquake magnitudes of El-Centro earthquake

After the trend of peak responses’ change along with input magnitude, the peak responses

for each storey unit due to four earthquake records are also displayed in Figure 5.29 where

the scaling factor is 15%. To ensure the consistency of presentation and avoid confusion,

5% 10% 15% 20%0

0.02

0.04

0.06

Drif

t rat

io

Peak drift ratio with different maginitudes

Passive-offPassive-onNSGA-NFLCBang-BangLQRFrequencyLyapunov

5% 10% 15% 20%0

1

2

3

Acc

eler

atio

n (g

)

Peak acceleration with different maginitudes


5% 10% 15% 20%0

0.01

0.02

0.03

0.04

Rel

ativ

e di

spla

cem

ent (

mm

) Peak displacement with different maginitudes


5% 10% 15% 20%0

0.05

0.1

0.15

0.2

Peak

shea

r/W

Peak shear with different maginitudes



188

all the results presented following are recorded when the input earthquake is scaled by

15%. The results measured under earthquake with other magnitudes are shown in

Appendix.

Figure 5.28 Peak responses with four different earthquake magnitudes of Kobe earthquake

As can be seen from Figure 5.29, the passive systems result in larger peak responses

except for inter-storey drift, where the response of frequency controlled isolation system

surpasses that of passive-on system. On general, the near-fault earthquakes (Kobe and

Northridge) lead to larger responses than far-fault earthquakes. All controlled base

isolation systems, except for frequency controller, have significantly reduced the values

5% 10% 15% 20%0

0.05

0.1

0.15

0.2

0.25D

rift r

atio

Peak drift ratio with different maginitudes


5% 10% 15% 20%0

2

4

6

Acc

eler

atio

n (g

)

Peak acceleration with different maginitudes


5% 10% 15% 20%0

0.05

0.1

0.15

0.2

Rel

ativ

e di

spla

cem

ent (

mm

) Peak displacement with different maginitudes


5% 10% 15% 20%0

0.1

0.2

0.3

0.4

0.5

Peak

shea

r/W

Peak shear with different maginitudes



189

of all four indices. The type of earthquake shows litter influence on NSGA-NFLC and

Lyapunov controller, particularly.

Figure 5.29 Peak responses under four earthquakes (scaling factor = 15%)

5.5.4.2 Peak Floor Responses under Four Earthquakes

Figure 5.30 to Figure 5.33 illustrates, from top to bottom, the variations of peak value of

inter-storey drift ratio, acceleration, displacement and floor shear over the elevation of

the testing structure, in fixed base, passive-off isolation, passive-on isolation, NFLC

El-centro Kobe Hachinohe Northridge0

0.05

0.1

0.15

0.2D

rift r

atio

Peak drift ratio under four earthquakes



1

2

3

4

5

Acc

eler

atio

n (g

)

Peak acceleration under four earthquakes



0.02

0.04

0.06

0.08

0.1

Rel

ativ

e di

spla

cem

ent (

mm

) Displacement under four earthquakes



0.1

0.2

0.3

0.4

Peak

shea

r/W

Peak shear under four earthquakes



190

controlled isolation, Bang-Bang controlled isolation, LQR controlled isolation, frequency

controlled isolation and Lyapunov current controlled isolation scenarios and under four

earthquake accelerograms. As aforementioned, inter-storey drift ratios are obtained by

dividing peak inter-storey drift with an inter-storey height of 400mm; floor accelerations

are the peak acceleration at each level throughout the whole time history expressed in the

term of gravitational acceleration g; the last graph shows the ratio between floor shear

force and the structural weight (912.57N for fixed base building; 1402.58N for base-

isolated building). The peak floor response of fixed base building is employed as the

benchmark for protection effectiveness evaluation. The percentage reductions of

evaluative indices in different isolation scenarios compared to the fixed base building are

listed in Table 5.14. When the listed value is greater than zero, it indicates a reduction in

the corresponding index. On contrast, a value smaller than zero implies an amplification

of the response. In Table 5.14, the percentage reduction values smaller than zero are all

underlined.

Broadly, the reduction of peak floor responses achieved by controlled semi-active MRE

base isolation system is rather pronounced, of which the NFLC and Lyapunov controlled

isolation system attains the smallest monitored responses among all the isolation

scenarios under any earthquake accelerograms. On contrast, the passive isolation system

shows a great dependence on the characteristics of external excitations according to the

responses, especially in terms of peak relative displacement. The LQR controlled

isolation system is able to achieve smaller evaluative indices values than the fixed base

building. However, it doesn’t show much superiority to the passive isolation system and

in some cases, its responses may even surpass those of passive isolation system. For

instance, its inter-storey drift ratio and floor acceleration are larger than passive-off

system under El Centro earthquake.


191

Figure 5.30 Peak inter-storey drift ratio under four earthquakes (inter-storey drift ratio = inter-

storey drift/floor height (0.04m); earthquake scaling factor= 15%)

As can be seen from Figure 5.30, in the fixed building, the inter-storey drift ratio

decreases as the structural height increases under all four earthquakes. Additionally, the

inter-storey drifts of all seven isolation scenarios are reduced, with respect to the fixed

base building, on all levels except for the base level. The base inter-storey drift is actually

0 0.01 0.02 0.03 0.04base

1

2

3

Leve

l

El Centro Earthquake

Fix basePassive-offPassive-onNSGA-NFLCBang-BangLQRFrequencyLyapunov

0 0.05 0.1 0.15 0.2base

1

2

3

Leve

l

Kobe Earthquake


0 0.01 0.02 0.03 0.04base

1

2

3

Leve

l



0 0.02 0.04 0.06 0.08 0.1base

1

2

3

Peak inter-storey drift ratio

Leve

l




192

equal to the base displacement and hence is not representative in the comparison of inter-

storey drift. Except for the base level, the NFLC, Bang-Bang controller, Frequency

controller and Lyapunov-based current controller all achieves smaller inter-storey drift

ratio than both passive isolation systems. Moreover, the differences between inter-storey

drift ratios of level 1~3 are not remarkable with the four controllers, which indicates that

the superstructure of isolated building approaches rigid body motion through

concentrating structural flexibility in the base isolation level. The LQR controller,

however, shows very similar trend of inter-storey drift along the height of building as the

passive-on isolation system and the suppression performance is not very ideal under all

earthquakes. It is also noteworthy that the passive-off base isolation system presents a

much larger base displacement than passive-on system regardless of the earthquake type.

Such phenomenon offers another perspective on the hardening effect when the isolator is

energised by current input. For instance, since the hardening of MRE isolator can

effectively restrain the base displacement, good control performance can be achieved by

maintain the stiffness at a high level during most of the service time and lower it when

the acceleration is excessive or reaches designated threshold. For better observability and

comparability, the base inter-storey drift ratio is excluded when comparing the peak inter-

storey drift under all isolation scenarios in Table 5.14. According to Table 5.14, all the

isolation scenarios achieve reduction of more than 24% in inter-storey drift ratio at each

floor under four earthquakes. The NSGA-NFLC, Bang-Bang controller, and Lyapunov

controller each realised dramatical reduction of 92% to 95%, 80% to 92%, 91% to 95%,

respectively (Table 5.14). The frequency controller shows the second-best drift reduction

performance under all earthquakes, which ranges from 68% to 89% (see Table 5.14). The

LQR controller achieves highest reduction at 2nd floor under all earthquakes but El Centro

earthquake, where the reduction is fairly close to the biggest one.

Both peak floor acceleration and relative displacement increase along the elevation of

testing structure in all isolation scenarios and under all earthquake accelerograms, except

for Bang-Bang controller under which the correlation between peak acceleration and floor


193

height doesn’t seem to have a certain pattern. The increase of acceleration and

displacement along floor height side-proves that the first mode (1.91Hz) is the major

vibrational mode participating throughout all four seismic events. Meanwhile, it is

observed from Figure 5.31 that the Bang-Bang controlled isolation system tends to exhibit

high level of base acceleration under all earthquakes, especially under Hachinohe

earthquake, where the base acceleration even exceeds both passive-on and passive-off

system. Its peak acceleration even outweighs that of the fixed base building by 14% under

Hachinohe earthquake. This may be caused by the sudden current and therefore stiffness

status changes made by switching law causing excessive acceleration response at the base

level. Regarding to the passive isolation systems, it is obvious that the passive-on system

outperforms the passive-off system in general, particularly at the lower levels. The

NSGA-NFLC, LQR and Lyapunov controlled isolation scenarios managed to

significantly reduce the peak floor acceleration under different earthquakes at every

storey unit. The frequency controller, however, although beats the passive isolation

systems at 1st to 3rd floors, has larger peak acceleration at the base level than the passive-

on system under all earthquakes. Since the frequency controller law also involves

frequently switched control current between maximum and minimum values, it may share

similar reason with the Bang-Bang controller leading to the high base isolation level.

Regarding to the exact value of peak floor acceleration reduction, generally, all the

isolation scenarios brings about significant reductions at all levels under El Centro, Kobe

and Northridge earthquakes, except for the passive-off system which increases the peak

acceleration by 19% at the 1st floor under Kobe earthquake. Under Hachinohe earthquake,

the passive-off system has a larger acceleration response at 1st and 2nd floors than the

fixed base building. As listed in Table 5.14, the NSGA-NFLC, LQR, frequency and

Lyapunov controller all reduce the floor acceleration dramatically by up to 94%, 72%,

77%, and 91%, respectively. The passive isolation systems both perform well under all

earthquakes except for Hachinohe earthquake, where the passive-off system’s peak

acceleration response outpaces the fixed base building by 44% at the 1st floor and 5% at


194

the 2nd floor while the passive-on system also surpass the bare building at the 1st level by

2% (see Table 5.14).

Figure 5.31 Peak floor acceleration under four earthquakes (earthquake scaling factor = 15%)

As for relative displacement, the passive isolation system shows a great reliance on the

earthquake type in terms of suppression performance, i.e. under Kobe and Hachinohe

earthquake, the passive-off isolation system’s peak acceleration value is way larger than

0 0.1 0.2 0.3 0.4base

1

2

3Le

vel



0 0.2 0.4 0.6 0.8base

1

2

3

Leve

l

Kobe Earthquake


0 0.02 0.04 0.06 0.08 0.1 0.12base

1

2

3

Leve

l



0 0.2 0.4 0.6 0.8 1base

1

2

3

Peak acceleration (g)

Leve

l




195

the fixed base building at all levels; under El Centro earthquake, the passive-off isolation

system only realised reduction of 12% at the top value while under Northridge

earthquake, the reduction is 29% at the 2nd floor and 38% at the top floor, respectively.

The passive-on isolation system has a better performance but still enlarges the peak

displacement by 57% under Hachinohe earthquake. Nevertheless, it needs to be pointed

out that although the relative displacement of passive isolation is rather large, the major

deformation is concentrated in the base level, leaving the superstructure unbothered by

excessive structural deformation. The NSGA-NFLC, Bang-Bang, LQR and Lyapunov

controllers achieve better displacement reduction performance compared to the passive

isolation systems, i.e. reductions ranging from 66% to 92%, 34% to 88%, 18% to 69%

and 82% to 93%, respectively (see Table 5.14). It is interesting that the Bang-Bang

controller achieves great relative displacement suppression performance considering the

flawed performance regarding to floor acceleration. The NFLC, LQR and Lyapunov

controlled base isolation system receive fairly close peak base displacement under all

accelerograms: 1.3mm, 3.2mm and 1.1mm under El Centro earthquake; 5.7mm, 6.3mm

and 3.5mm under Kobe earthquake; 1.4mm 3.7mm and 0.8mm under Hachinohe

earthquake; 4.3mm, 6.9mm and 3.6mm under Northridge earthquake; which are all far

less than the base displacement of passive isolation system. Considering both inter-storey

drift and base displacement graphs, although the LQR controller doesn’t outperform the

passive isolation system in terms of reducing inter-storey drift ratio in the superstructure,

the base displacement is well restrained by the LQR control, which shows one of the

superiority of the controlled isolation system to the passive ones. The frequency

controller, on contrast, doesn’t have a consistent performance in acceleration suppression

under different accelerograms and at each storey unit. For instance, the largest reduction

accomplished by the frequency controller is 74% at the top floor under Northridge

earthquake, However, under Kobe and Hachinohe earthquake, the response exceeds both

passive-on and fixed base building. Another aspect drawing attention is that, regardless

to the earthquake type, all the isolation scenarios’ displacement suppression capability is


196

increasing along with the floor height (see Table 5.14).

Figure 5.32 Peak relative displacement under four earthquakes (earthquake scaling factor = 15%)

Figure 5.33 illustrates the variation trend of inter-storey shear force with regarding to the

floor height. The floor shear force indicates the vibration influence applied on each level

0 5 10 15 20 25 30base

1

2

3

Leve

l



0 20 40 60 80 100base

1

2

3

Leve

l

Kobe Earthquake


0 5 10 15 20 25base

1

2

3

Leve

l



0 20 40 60 80 100base

1

2

3

Peak relative displacement (mm)

Leve

l




197

and hence the smaller floor shear force is, the less possible vibrational energy is

transmitted into the superstructure. As can be seen from Figure 5.33 and Table 5.14, the

floor shear is reduced at each storey unit by all types of isolation systems, especially under

Northridge earthquake, where the reduction ranges from 65% to 96%.

Regarding to the controlled isolation systems, all the controllers have smaller floor shear

at each storey unit when compared to the passive-off and passive-on systems. Meanwhile,

the inter-level shear force decreases with the elevation of structure except in the

Lyapunov controlled scenario, where the force between level 1 and level 2 is larger than

both base shear and the shear force between level 2 and level 3. The NSGA-NFLC

controlled isolation system receives the most promising performance under all four

accelerograms, with a reduction ranging between 93% and 96%. Moreover, in each

controlled isolation scenario, the dependence of shear force reduction on the structural

elevation is rather unpronounced under El Centro, Kobe and Northridge earthquakes. The

NFLC, Bang-Bang controller, LQR, frequency and Lyapunov current controlled isolation

system brought about shear force reduction ranging from 95% to 95%, 80% to 88%, 67%

to 70%, 79% to 83%, 86% to 91% under El Centro earthquake; 95% to 95%, 79% to 85%,

78% to 79%, 76% to 80%, 87% to 94% under Kobe earthquake; 96% to 96%, 85% to

86%, 81% to 82%, 83% to 85%, 90% to 94% under Northridge earthquake. Nevertheless,

the dependence is more pronounced under Hachinohe earthquake with a reduction

ranging from 70% to 81% with Bang-Bang controlled system, 68% to 73% with LQR

controlled system, 64% to 70% with frequency controlled system and 81% to 92% with


198

Lyapunov controlled system.

Figure 5.33 Peak floor shear/Seismic weight W under four earthquakes (W = 912.57N (fixed base building)/1402.58N (base-isolated building) ; earthquake scaling factor = 15%)

0 0.05 0.1 0.15 0.2base

1

2

3

Leve

l



0 0.2 0.4 0.6 0.8base

1

2

3

Leve

l

Kobe Earthquake


0 0.02 0.04 0.06 0.08 0.1base

1

2

3

Leve

l



0 0.2 0.4 0.6 0.8base

1

2

3

Peak floorshear/Seismic weight

Leve

l



199

Table 5.14 Reduction of peak floor responses of different isolation scenarios

El Centro Kobe Hachinohe Northridge

Floor No. 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd

Passive-off 61% 69% 65% 48% 62% 49% 24% 43% 28% 70% 74% 70%

Passive-on 50% 56% 59% 54% 55% 51% 31% 35% 27% 57% 60% 59%

NSGA-NFLC 94% 94% 94% 93% 95% 94% 92% 93% 92% 95% 96% 95%

Bang-Bang 91% 92% 88% 90% 89% 85% 89% 87% 80% 91% 92% 91%

LQR 56% 61% 64% 73% 74% 73% 56% 60% 57% 76% 78% 77%

Frequency 83% 87% 85% 78% 84% 78% 68% 76% 70% 87% 89% 87%

Lyapunov 91% 92% 91% 93% 94% 92% 92% 93% 92% 95% 95% 94%

Passive-off 16% 48% 58% -19% 27% 39% -44% -5% 11% 34% 60% 64%

Passive-on 36% 44% 47% 28% 43% 44% -2% 13% 24% 37% 46% 50%

NSGA-NFLC 90% 93% 93% 88% 92% 93% 85% 89% 90% 92% 94% 94%

Bang-Bang 27% 67% 69% 44% 51% 67% -14% 46% 54% 62% 70% 77%

LQR 44% 51% 54% 61% 67% 68% 44% 53% 59% 65% 70% 72%

Frequency 47% 69% 73% 45% 66% 70% 22% 47% 54% 59% 74% 77%

Lyapunov 80% 85% 85% 82% 89% 89% 76% 85% 87% 88% 91% 90%

200

Table 5.14 Reduction of peak floor responses of different isolation scenarios (cont’d)


Floor No. 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd

Passive-off -78% -4% 12% -140% -43% -25% -254% -110% -80% -17% 29% 38%

Passive-on 4% 30% 36% 10% 32% 35% -57% -2% 7% 18% 39% 43%

NSGA-NFLC 82% 88% 89% 77% 86% 87% 66% 80% 82% 86% 91% 92%

Bang-Bang 68% 84% 87% 71% 81% 83% 34% 67% 73% 77% 87% 88%

LQR 21% 41% 46% 50% 62% 64% 18% 38% 43% 57% 67% 69%

Frequency 24% 56% 63% -2% 39% 47% -50% 11% 24% 50% 70% 74%

Lyapunov 83% 88% 89% 87% 91% 92% 82% 88% 89% 90% 93% 93%

Passive-off 64% 70% 73% 50% 57% 60% 28% 37% 42% 73% 76% 76%

Passive-on 63% 64% 65% 62% 63% 63% 42% 46% 50% 65% 66% 67%

NSGA-NFLC 95% 95% 95% 95% 95% 95% 93% 93% 94% 96% 96% 96%

Bang-Bang 87% 88% 80% 85% 82% 79% 79% 81% 70% 85% 86% 85%

LQR 67% 69% 70% 78% 79% 79% 69% 71% 73% 81% 81% 82%

Frequency 79% 81% 83% 76% 79% 80% 64% 68% 70% 83% 84% 85%

Lyapunov 86% 91% 90% 87% 94% 93% 81% 91% 92% 90% 94% 93%


201

5.5.5 Evaluative indices comparison

There are nine evaluative indices adopted in this project to assess the seismic response

suppression performance of each controller. Among the nine indices, the first six indices

are related to the structural responses, including peak and normed values of inter-storey

drift ratio, acceleration and base shear. The last three indices are to appraise the

requirements of the controllers. The specific definitions of the evaluative criteria are

detailed in Section 5.5.2. Any index value greater than 100% indicates an amplification

of the corresponding index by the controller and the smaller index value is, the more

promising control performance it suggests.

Since the experimental testings were carried out under four earthquake accelerograms

with magnitude scaling factors of 5%, 10%, 15% and 20%, respectively, the results of

evaluative indices under different magnitudes of eight isolation scenarios are summarised

and compared in Table 5.15. For the six indices about structural responses, it can be easily

observed that all the isolation scenarios manage to bring the six indices values under

100% except for the passive-off isolation system, which results in a large value of J3 at

the value of 105% under Kobe earthquake and 143% under Hachinohe earthquake; and

the passive-on system, which results in J3 value of 102% under Hachinohe earthquake.

Generally, regarding to the reduction of peak structural responses, the passive-on system

has a better performance than passive-off system under Kobe and Hachinohe earthquakes

but a much poorer performance under El Centro and Northridge earthquakes. The NFLC

achieves best structural vibration elimination response in peak and normed value of the

responses among all the controllers, with a maximum value of 8.5% of J1, 8.5% of J1,

9.5% of J2, 14.3% of J3, 5.0% of J4, 5.5% of J5 and 8.6% of J6. Meanwhile, it is

noteworthy that the index values of all the isolation cases but Bang-Bang controller show

little sensitivity to the magnitudes of earthquake. In other words, the values of the

evaluative criteria barely display changes with the earthquake scaling factor. Since the

percentage number listed in Table 5.15 possesses 2 decimal places, most index values


202

have a difference of less than 0.005% from other values from the same earthquake with

different magnitudes. However, the Bang-Bang controller shows a variation of J1 ~ J6

with the change of earthquake magnitude.

Figure 5.34 Evaluative indices J1 ~ J6 under four earthquakes (earthquake scaling factor = 15%)

Indices J7 to J9 represent the characteristics related to the controller, i.e. peak control

force, controller stroke and control power. Since the passive-off controller is considered

J1 J2 J3 J4 J5 J60

20

40

60

80

Inde

x va

lue/

%El Centro Earthquake


J1 J2 J3 J4 J5 J60

50

100

150

Inde

x va

lue/

%

Kobe Earthquake


J1 J2 J3 J4 J5 J60

50

100

150

Inde

x va

lue/

%



J1 J2 J3 J4 J5 J60

20

40

60

80

Inde

x va

lue/

%




203

as the uncontrolled base isolation system, the corresponding rows in Table 5.15 are left

blank. As can be seen from Table 5.15, the magnitude of earthquake has a considerable

impact on the values of J7 and J9. Generally, the indices of control force and control power

increases with the increase of earthquake intensity with all isolation systems. Among all

the controllers, the Lyapunov controller has highest control force but its control power is

rather small. Such comparison reveals that fact that the Lyapunov controller is capable of

effectively restrain the base response, especially velocity, by applying high control force.

Since the control force is determined by both base response and control current, it also

indicate that during majority of the earthquake excitation, Lyapunov controller keeps the

current applied to MRE isolator at high value.

The values of J1 ~ J6 under four earthquakes when the scaling factor is 0.15 is shown in

a bar chart in Figure 5.34. As shown, the NSGA-NFLC and Lyapunov controller have

consistently good performance in reducing the peak and normed structural response. The

LQR, frequency and Bang-Bang controller, however, exhibit higher dependence on the

earthquake type. Fortunately, all the controllers achieve smaller evaluative criteria values

compared to both passive-off and passive-on systems. Figure 5.35 shows the maximum

value of J7 ~ J9 under four earthquake inputs. This is called the worst case scenario as

defined in the benchmark problem. As observed, the frequency controller has large values

of all three indices, which even surpass those of the passive-on system. It is not a desirable

performance since it indicates failing to reduce controller response even applying high

control force.

Figure 5.35 Evaluative indices J7 ~ J9 at worst case scenario (earthquake scaling factor = 15%)

0 50 100

Lyapunov

Frequency

LQR

Bang-Bang

NSGA-NFLC

Passive-on

Value of J7 (%)0 2 4 6 8

Value of J8 (%)0 5 10 15

Value of J9 (%)

204

Table 5.15 Evaluative indices value


Controller 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2

Passive-off 39.1% 39.1% 39.1% 39.1% 51.9% 51.9% 51.9% 51.9% 76.4% 76.4% 76.4% 76.4% 30.4% 30.4% 30.4% 30.4%

Passive-on 74.3% 74.3% 49.6% 74.3% 46.2% 46.2% 46.2% 46.2% 69.4% 69.4% 69.4% 69.4% 43.1% 43.1% 43.1% 43.1%

NFLC 6.3% 6.3% 6.4% 6.4% 6.6% 6.6% 6.6% 6.6% 8.5% 8.5% 8.5% 8.5% 4.8% 4.8% 4.8% 4.8%

Bang-Bang 6.0% 13.1% 8.7% 8.0% 10.9% 10.6% 10.2% 9.6% 10.5% 12.5% 12.0% 15.3% 7.3% 7.4% 8.8% 9.5%

LQR 43.6% 43.7% 43.7% 43.7% 27.0% 27.0% 27.0% 27.5% 43.7% 43.7% 43.7% 43.7% 24.0% 24.0% 24.0% 24.0%

Frequency 16.6% 16.6% 16.6% 16.6% 22.0% 22.0% 22.0% 22.0% 32.4% 32.4% 32.4% 32.4% 12.9% 12.9% 12.9% 12.9%

Lyapunov 9.2% 9.2% 9.2% 6.9% 6.6% 6.6% 6.6% 6.6% 8.5% 8.5% 8.5% 8.5% 5.1% 5.1% 5.1% 5.1%

Passive-off 41.9% 41.9% 41.9% 41.9% 61.5% 61.5% 61.5% 61.5% 88.6% 88.6% 88.6% 88.6% 36.2% 36.2% 36.2% 36.2%

Passive-on 79.7% 79.7% 53.1% 79.7% 56.3% 56.3% 56.3% 56.3% 76.5% 76.5% 76.5% 76.5% 50.4% 50.4% 50.4% 50.4%

NFLC 7.2% 7.2% 7.3% 7.3% 7.1% 7.1% 7.1% 7.1% 9.5% 9.5% 9.5% 9.5% 5.8% 5.7% 5.7% 5.7%

Bang-Bang 22.0% 53.5% 30.7% 32.0% 39.1% 40.5% 38.0% 33.7% 26.0% 48.6% 57.1% 65.9% 30.1% 17.6% 23.4% 25.1%

LQR 46.3% 46.3% 46.4% 46.4% 32.1% 32.1% 32.1% 33.1% 41.2% 41.2% 41.2% 41.1% 27.9% 27.9% 27.9% 27.9%

Frequency 26.6% 26.6% 26.6% 26.6% 30.4% 30.4% 30.4% 30.4% 46.1% 46.1% 46.1% 46.1% 22.9% 22.9% 22.9% 22.9%

Lyapunov 15.3% 15.3% 15.3% 11.5% 11.2% 11.2% 11.2% 11.2% 12.9% 12.9% 12.9% 12.9% 10.1% 10.1% 10.1% 10.1%

205

Table 5.15 Evaluative indices value (Cont’d)


Controller 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2

Passive-off 76.1% 76.1% 76.1% 76.1% 105% 105% 105% 105% 143% 143% 143% 143% 56.5% 56.5% 56.5% 56.5%

Passive-on 98.8% 98.8% 65.9% 98.8% 68.4% 68.4% 68.4% 68.4% 102% 102% 102% 102% 61.5% 61.5% 61.5% 61.5%

NFLC 9.5% 9.5% 9.5% 9.5% 10.9% 10.9% 10.9% 10.9% 14.3% 14.3% 14.2% 14.2% 7.6% 7.6% 7.7% 7.6%

Bang-Bang 24.3% 45.9% 30.4% 39.1% 36.3% 45.6% 42.2% 35.4% 39.8% 51.8% 64.0% 65.8% 24.0% 25.9% 24.5% 26.9%

LQR 56.9% 56.8% 56.8% 56.9% 39.1% 39.1% 39.1% 38.7% 55.5% 55.5% 55.5% 55.4% 33.4% 33.4% 33.4% 33.4%

Frequency 42.1% 42.1% 42.1% 42.1% 49.6% 49.6% 49.6% 49.6% 72.6% 72.6% 72.6% 72.6% 34.1% 34.1% 34.1% 34.1%

Lyapunov 16.2% 16.2% 16.2% 12.2% 11.9% 11.9% 11.9% 11.9% 16.9% 16.9% 16.9% 16.9% 10.2% 10.2% 10.2% 10.2%

Passive-off 19.2% 19.2% 19.2% 19.2% 36.0% 36.0% 36.0% 36.0% 39.6% 39.6% 39.6% 39.6% 8.9% 8.9% 8.9% 8.9%

Passive-on 25.8% 25.8% 17.2% 25.8% 44.9% 44.9% 44.9% 44.9% 46.0% 46.0% 46.0% 46.0% 12.5% 12.5% 12.5% 12.5%

NFLC 2.5% 2.5% 2.5% 2.5% 5.0% 5.0% 5.0% 5.0% 4.7% 4.7% 4.7% 4.7% 1.2% 1.2% 1.2% 1.2%

Bang-Bang 2.8% 3.8% 3.2% 3.3% 5.9% 6.1% 6.6% 6.6% 6.5% 6.8% 6.7% 7.0% 1.6% 1.5% 1.8% 1.9%

LQR 15.4% 15.4% 15.4% 15.4% 25.0% 25.0% 25.0% 24.9% 28.7% 28.7% 28.7% 28.7% 7.6% 7.6% 7.6% 7.6%

Frequency 8.1% 8.1% 8.1% 8.1% 15.3% 15.3% 15.3% 15.3% 16.8% 16.8% 16.8% 16.8% 3.8% 3.8% 3.8% 3.8%

Lyapunov 2.6% 2.6% 2.6% 2.0% 4.9% 4.9% 4.9% 4.9% 4.7% 4.7% 4.7% 4.7% 1.3% 1.3% 1.3% 1.3%

206



Controller 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2

Passive-off 22.0% 22.0% 22.0% 22.0% 42.3% 42.3% 42.3% 42.3% 41.6% 41.6% 41.6% 41.6% 10.3% 10.3% 10.3% 10.3%

Passive-on 26.3% 26.3% 17.5% 26.3% 44.3% 44.3% 44.3% 44.3% 47.2% 47.2% 47.2% 47.2% 13.8% 13.8% 13.8% 13.8%

NFLC 2.8% 2.8% 2.8% 2.8% 5.5% 5.5% 5.5% 5.5% 4.8% 4.8% 4.8% 4.8% 1.4% 1.4% 1.4% 1.4%

Bang-Bang 5.0% 9.9% 7.9% 9.2% 14.7% 13.9% 13.1% 12.9% 10.0% 13.8% 14.3% 16.8% 4.4% 3.2% 3.1% 2.9%

LQR 15.7% 15.7% 15.7% 15.7% 24.6% 24.6% 24.6% 24.6% 29.3% 29.3% 29.3% 29.3% 8.4% 8.4% 8.4% 8.4%

Frequency 2.8% 2.8% 2.8% 2.8% 5.5% 5.5% 5.5% 5.5% 4.8% 4.8% 4.8% 4.8% 1.4% 1.4% 1.4% 1.4%

Lyapunov 4.2% 4.2% 4.2% 3.2% 7.6% 7.6% 7.6% 7.6% 7.3% 7.3% 7.3% 7.3% 2.2% 2.2% 2.2% 2.2%

Passive-off 37.3% 37.3% 37.3% 37.3% 71.2% 71.2% 71.2% 71.2% 69.7% 69.7% 69.7% 69.7% 16.2% 16.2% 16.2% 16.2%

Passive-on 34.9% 34.9% 23.2% 34.9% 58.8% 58.8% 58.8% 58.8% 61.8% 61.8% 61.8% 61.8% 17.5% 17.5% 17.5% 17.5%

NFLC 4.3% 4.3% 4.3% 4.3% 8.6% 8.6% 8.6% 8.6% 7.3% 7.3% 7.3% 7.3% 2.0% 2.0% 2.0% 2.0%

Bang-Bang 10.9% 13.7% 11.5% 11.7% 21.2% 20.6% 21.8% 21.1% 22.8% 22.9% 22.4% 23.6% 5.6% 5.4% 6.1% 6.4%

LQR 20.3% 20.3% 20.3% 20.3% 31.7% 31.7% 31.7% 31.7% 37.6% 37.6% 37.6% 37.6% 10.4% 10.4% 10.4% 10.4%

Frequency 19.2% 19.2% 19.2% 19.2% 35.4% 35.4% 35.4% 35.4% 35.2% 35.2% 35.2% 35.2% 9.0% 9.0% 9.0% 9.0%

Lyapunov 5.6% 5.6% 5.6% 4.2% 10.0% 10.0% 10.0% 10.0% 9.5% 9.5% 9.5% 9.5% 2.8% 2.8% 2.8% 2.8%

207



Controller 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2

Passive-off ---

Passive-on 11.3% 22.6% 22.6% 45.2% 19.7% 39.4% 59.1% 78.9% 6.0% 11.9% 17.9% 23.9% 19.0% 38.1% 57.1% 76.1%

NFLC 1.9% 3.8% 5.6% 7.5% 5.4% 10.9% 16.4% 21.8% 1.5% 3.1% 4.6% 6.1% 4.0% 8.0% 12.0% 16.0%

Bang-Bang 6.4% 10.3% 16.1% 19.1% 15.5% 22.9% 28.3% 36.5% 2.9% 12.9% 12.3% 16.2% 13.0% 22.7% 28.8% 29.4%

LQR 5.3% 14.6% 16.5% 25.1% 22.7% 42.6% 60.2% 70.0% 4.8% 9.2% 13.9% 18.3% 14.1% 25.0% 42.7% 58.4%

Frequency 12.6% 25.2% 37.8% 50.4% 21.3% 42.6% 64.0% 84.6% 4.6% 9.2% 13.8% 18.4% 13.2% 26.5% 39.7% 53.0%

Lyapunov 7.8% 15.6% 23.4% 31.2% 32.2% 64.4% 96.7% 129% 7.0% 14.0% 21.0% 28.1% 16.5% 33.0% 49.5% 66.0%

Passive-off ---

Passive-on 6.2% 6.2% 4.1% 6.2% 3.4% 3.4% 3.4% 3.4% 5.5% 5.5% 5.5% 5.5% 4.5% 4.5% 4.5% 4.5%

NFLC 1.1% 1.1% 1.1% 1.1% 1.2% 1.2% 1.2% 1.2% 1.4% 1.4% 1.4% 1.4% 1.0% 1.0% 1.1% 1.1%

Bang-Bang 2.1% 3.2% 2.3% 2.3% 1.7% 1.8% 1.6% 1.3% 2.7% 3.4% 3.4% 2.8% 2.8% 1.5% 2.1% 1.9%

LQR 3.1% 3.1% 3.1% 3.1% 1.7% 1.7% 1.7% 1.6% 2.6% 2.6% 2.6% 2.6% 2.1% 2.1% 2.1% 2.1%

Frequency 5.2% 5.2% 5.2% 5.2% 5.9% 5.9% 5.9% 5.9% 6.6% 6.6% 6.6% 6.6% 4.5% 4.5% 4.5% 4.5%

Lyapunov 0.8% 0.8% 0.8% 0.6% 0.5% 0.5% 0.5% 0.5% 0.7% 0.7% 0.7% 0.7% 0.6% 0.6% 0.6% 0.6%

208



Controller 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2 0.05 0.1 0.15 0.2

Passive-off ---

Passive-on 3.7% 7.5% 5.0% 15.0% 3.4% 6.8% 10.2% 13.5% 0.8% 1.7% 2.5% 3.4% 3.6% 7.3% 10.9% 14.6%

NFLC 0.1% 0.2% 0.3% 0.4% 0.2% 0.5% 0.7% 1.0% 0.1% 0.1% 0.2% 0.2% 0.2% 0.4% 0.6% 0.8%

Bang-Bang 0.5% 1.1% 1.4% 1.7% 2.0% 2.1% 2.9% 3.3% 0.2% 0.7% 0.8% 1.2% 1.3% 2.1% 2.0% 1.8%

LQR 0.7% 1.9% 2.5% 2.2% 1.3% 1.7% 2.4% 3.6% 0.4% 0.9% 1.2% 1.6% 1.3% 1.5% 3.1% 3.5%

Frequency 3.2% 6.4% 9.6% 12.8% 4.9% 9.8% 14.6% 19.5% 1.0% 1.9% 2.9% 3.8% 0.8% 1.6% 2.4% 3.2%

Lyapunov 0.2% 0.5% 0.7% 0.7% 0.8% 1.5% 2.3% 3.0% 0.1% 0.2% 0.4% 0.5% 0.4% 0.7% 1.1% 1.5%


209

5.5.6 Time Histories

It is of great significance to conduct the time history analysis in structural dynamics.

Reason being a full time history will give the response of a structure over time during and

after the application of a load. Hence, the graphs presented in this section provide not

only the performance of peak response suppression but also the capability to maintain the

response at a low level during the entire time history. According to the discussion

previously, it is essential to reduce the structural acceleration and displacement

simultaneously and excessive base displacement is an unresolved issue in conventional

base isolation system. To this end, in this section, the time histories of top floor

acceleration, base displacement and base acceleration of base isolation system with

different controllers are presented. Since it is obvious that in most scenarios, the

controlled system can achieve a much lower response than the fixed building, the

performance is compared with that of the passive-off system, which is recognised as an

uncontrolled base isolation system.

5.5.6.1 Time History of Top Floor Acceleration

Figure 5.36 to Figure 5.39 displays the comparative time histories of top floor

acceleration in the isolation scenarios of NSGA-NFLC, Bang-Bang controlled, LQR

controlled, frequency controlled and Lyapunov controlled MRE isolation system under

four earthquakes. As observed, under El Centro earthquake, there are three local excited

acceleration peaks in the curve of passive isolation system. Comparatively, all control

system except for LQR controller can effectively suppress the top floor acceleration over

the entire time history. The LQR controller, however, not only surpasses the peak

acceleration of the passive system but also almost reaches the second and third local

peaks. Under Kobe earthquake, the passive isolation system is intensively excited

between 7 to 17 seconds and the peak acceleration occurs between 8 and 9 seconds. All

controllers can reduce the acceleration response, among which the Bang-Bang controller,


210

LQR controller and frequency controller share similar suppression performances. Under

Hachinohe earthquake, the passive isolation system long with Bang-Bang controlled,

LQR controlled and frequency controlled system experienced a re-excitation from the

12th second. It might be because, unlike other earthquakes, Hachinohe earthquake

maintains a relatively high volatility until the end of the seismic event as shown in Figure

5.24. Hence, the disturbance continues in the Hachinohe earthquake. Under Northridge

earthquake, a wave-like acceleration pulse is observed in all isolation scenarios at around

3.5 to 4.5 seconds, which is caused by the near-fault feature of the seismic accelerogram.

Meanwhile, it is interesting that the Bang-Bang controller seems to have an opposition

acceleration response to the passive isolation. In other words, the response is delayed by

one π by the Bang-Bang controller.

Figure 5.40 to Figure 5.43 displays the comparative time histories of top floor

acceleration in the isolation scenarios of NSGA-NFLC, Bang-Bang controlled, LQR

controlled, frequency controlled and Lyapunov controlled MRE isolation system under

four earthquakes. Regarding to the passive system, the base displacement response

exhibits a second excitation at around 13 second under El Centro earthquake. Under Kobe

earthquake, the passive base isolator experience intensive vibration between 7 second to

17 second. The displacement response maintains a relatively constant level under

Hachinohe earthquake, whose reason is explained in last section. The wave-like impulse

is more pronounce in the form of displacement under Northridge earthquake beginning

at around 4 second. Compared to the passive isolation system, all controlled isolation

system achieves considerable reduction in base isolation system, which means the

controlled MRE base isolation system is an effective resolution to the issue of

disproportionate base displacement happened in passive base isolation approaches. The

NSGA-NFLC and Lyapunov controlled isolation system are able to achieve smallest base

isolation responses along the whole time history under all earthquakes. Considering the

performance in acceleration reduction, the LQR controller achieves outstanding base

isolation reduction performance. This phenomenon, on the other hand, illustrates the fact


211

that by adding control force in both stiffness and damping form may effectively restrain

the base displacement but the side effect may be amplification of floor accelerations,

especially in the higher levels. Furthermore, the frequency controller results in the biggest

base displacement among all the control algorithms so this control method can be

recognised as holding a middle ground of seismic protection performance.

Figure 5.44 to Figure 5.47 illustrates the comparative base acceleration response with

different control algorithms under four earthquakes. The passive base isolation’s base

acceleration shows a similar profile to that of the top floor accelration time history, only

the absolute value of base displacement is much smaller than the top one. Such

observation side-proves that the participation factor of first mode is large in the passive

isolation system and the structure acts as an amplifier of acceleration with the structural

elevation. The NSGA-NFLC and Lyapunov system, once again, attained the best control

performance in the base acceleration responses. The LQR controller shows better base

acceleration suppression performance under Kobe and Northridge earthquakes, which are

categorised as near-fault eathquake but more moderate performance under El Centro and

Hachinohe earthquakes belonging to far-fault earthquakes. This can be a forte for the

LQR controller in that normally it is harder to control the seismic responses under near-

fault eartquakes. It can be seen from Figure 5.44 to Figure 5.47 that the Bang-Bang

controller and frequency controller don’t possess ideal base acceleration suppression

performance at all and the acceleration response of Bang-Bang controller even surpasses

that of the passive system at some time instantaneous under Kobe, Hachinohe and

Northridge earthquakes. The reason for poor base displacement responses lies in that both

controller adjust the status of MRE isolator with a ON-OFF law which leads to fequency

switching current between maximum and minimum values. The fast changes between

upper and lower threshold may be the origin of large base acceleration.


212

Figure 5.36 Time history of top floor acceleration with different control algorithms (0.15 El-

Centro)

0 10 20 30 40 50

-0.1

-0.050

0.05

0.1

Acc

eler

atio

n (g

)

Passive-offNSGA-NFLC

0 10 20 30 40 50

-0.1

-0.050

0.050.1

Acc

eler

atio

n (g

)

Passive-offBang-Bang

0 10 20 30 40 50

-0.1

-0.050

0.050.1

Acc

eler

atio

n (g

)

Passive-offLQR

0 10 20 30 40 50

-0.1

-0.050

0.050.1

Acc

eler

atio

n (g

)

Passive-offFrequency

0 10 20 30 40 50

-0.1

-0.050

0.050.1

Time (s)

Acc

eler

atio

n (g

)

Passive-offLyapunov


213

Figure 5.37 Time history of top floor acceleration with different control algorithms (0.15 Kobe)

0 10 20 30 40 50-0.5

0

0.5

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.5

0

0.5

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.5

0

0.5

Acc

eler

atio

n (g

)

Passive-offLQR

0 10 20 30 40 50-0.5

0

0.5

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.5

0

0.5

Time (s)

Acc

eler

atio

n (g

)

Passive-offLyapunov


214

Figure 5.38 Time history of top floor acceleration with different control algorithms (0.15

Hachinohe)

0 5 10 15 20 25 30 35

-0.1

-0.05

0

0.05

0.1

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30 35

-0.1

-0.05

0

0.05

0.1

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30 35-0.1

-0.05

0

0.05

0.1

Acc

eler

atio

n (g

)

Passive-offLQR

0 5 10 15 20 25 30 35-0.1

-0.05

0

0.05

0.1

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30 35

-0.1

-0.05

0

0.05

0.1

Time (s)

Acc

eler

atio

n (g

)

Passive-offLyapunov


215

Figure 5.39 Time history of top floor acceleration with different control algorithms (0.15

Northridge)

0 5 10 15 20 25 30-0.4

-0.2

0

0.2

0.4

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30-0.4

-0.2

0

0.2

0.4

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30-0.4

-0.2

0

0.2

0.4

Acc

eler

atio

n (g

)

Passive-offLQR

0 5 10 15 20 25 30-0.4

-0.2

0

0.2

0.4

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30-0.4

-0.2

0

0.2

0.4

Time (s)

Acc

eler

atio

n (g

)

Passive-offLyapunov


216

Figure 5.40 Time history of base displacement with different control algorithms (0.15 El-

Centro)

0 10 20 30 40 50-20

-10

0

10

20

Dis

plac

emen

t (m

m)


0 10 20 30 40 50-20

-10

0

10

20

Dis

plac

emen

t (m

m)


0 10 20 30 40 50-20

-10

0

10

20

Dis

plac

emen

t (m

m)

Passive-offLQR

0 10 20 30 40 50-20

-10

0

10

20

Dis

plac

emen

t (m

m)


0 10 20 30 40 50-20

-10

0

10

20

Time (s)

Dis

plac

emen

t (m

m)

Passive-offLyapunov


217

Figure 5.41 Time history of base displacement with different control algorithms (0.15 Kobe)

0 10 20 30 40 50

-50

0

50

Dis

plac

emen

t (m

m)


0 10 20 30 40 50

-50

0

50

Dis

plac

emen

t (m

m)


0 10 20 30 40 50-50

0

50

Dis

plac

emen

t (m

m)

Passive-offLQR

0 10 20 30 40 50-50

0

50

Dis

plac

emen

t (m

m)


0 10 20 30 40 50

-50

0

50

Time (s)

Dis

plac

emen

t (m

m)

Passive-offLyapunov


218

Figure 5.42 Time history of base displacement with different control algorithms (0.15 Hachinohe)

0 5 10 15 20 25 30 35

-10

-5

0

5

10

Dis

plac

emen

t (m

m)


0 5 10 15 20 25 30 35

-10

-5

0

5

10

Dis

plac

emen

t (m

m)


0 5 10 15 20 25 30 35-10

-5

0

5

10

Dis

plac

emen

t (m

m)

Passive-offLQR

0 5 10 15 20 25 30 35-20

-10

0

10

Dis

plac

emen

t (m

m)


0 5 10 15 20 25 30 35

-10

-5

0

5

10

Time (s)

Dis

plac

emen

t (m

m)

Passive-offLyapunov


219

Figure 5.43 Time history of base displacement with different control algorithms (0.15 Northridge)

0 5 10 15 20 25 30-40

-20

0

20

40

Dis

plac

emen

t (m

m)


0 5 10 15 20 25 30-40

-20

0

20

40

Dis

plac

emen

t (m

m)


0 5 10 15 20 25 30-40

-20

0

20

40

Dis

plac

emen

t (m

m)

Passive-offLQR

0 5 10 15 20 25 30-40

-20

0

20

40

Dis

plac

emen

t (m

m)


0 5 10 15 20 25 30-40

-20

0

20

40

Time (s)

Dis

plac

emen

t (m

m)

Passive-offLyapunov


220

Figure 5.44 Time history of base acceleration with different control algorithms (0.15 El-Centro)

0 10 20 30 40 50-0.1

-0.05

0

0.05

0.1

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.1

-0.05

0

0.05

0.1

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.1

-0.05

0

0.05

0.1

Acc

eler

atio

n (g

)

Passive-offLQR

0 10 20 30 40 50-0.1

-0.05

0

0.05

0.1

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.1

-0.05

0

0.05

0.1

Time (s)

Acc

eler

atio

n (g

)

Passive-offLyapunov


221

Figure 5.45 Time history of base acceleration with different control algorithms (0.15 Kobe)

0 10 20 30 40 50

-0.2

-0.10

0.1

0.2

Acc

eler

atio

n (g

)


0 10 20 30 40 50

-0.2

-0.10

0.10.2

Acc

eler

atio

n (g

)


0 10 20 30 40 50

-0.2

-0.10

0.10.2

Acc

eler

atio

n (g

)

Passive-offLQR

0 10 20 30 40 50

-0.2

-0.10

0.10.2

Acc

eler

atio

n (g

)


0 10 20 30 40 50

-0.2

-0.10

0.10.2

Time (s)

Acc

eler

atio

n (g

)

Passive-offLyapunov


222

Figure 5.46 Time history of base acceleration with different control algorithms (0.15 Hachinohe)

0 5 10 15 20 25 30 35-0.05

0

0.05

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30 35-0.1

-0.05

0

0.05

0.1

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30 35-0.05

0

0.05

Acc

eler

atio

n (g

)

Passive-offLQR

0 5 10 15 20 25 30 35-0.05

0

0.05

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30 35-0.05

0

0.05

Time (s)

Acc

eler

atio

n (g

)

Passive-offLyapunov


223

Figure 5.47 Time history of base acceleration with different control algorithms (0.15 Northridge)

0 5 10 15 20 25 30

-0.1

0

0.1

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30

-0.1

0

0.1

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30

-0.1

0

0.1

Acc

eler

atio

n (g

)

Passive-offLQR

0 5 10 15 20 25 30

-0.1

0

0.1

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30

-0.1

0

0.1

Time (s)

Acc

eler

atio

n (g

)

Passive-offLyapunov


224

5.5.7 Control Force and Current Comparisons

The time histories of control forces of NSGA-NFLC, Bang-Bang, LQR, frequency and

Lyapunov controllers are shown in Figure 5.48 to Figure 5.51. Since the passive-off

system is considered as an uncontrolled base isolation system, all the control forces are

compared with that of the passive-on system. It is difficult to directly measure the control

force generated by the MRE isolator during real experiment. Hence, the control forces

here are all calculated by Eq. 5.15 and Eq. 5.16 using the measurement of current,

displacement and velocity at sampling point. The current for passive-on system was

maintained at 3A during all experiments. As can be observed from Figure 5.48 to Figure

5.51, the Bang-Bang controller generates the smallest control force under all earthquakes,

which might be the reason for reluctance in restraining base acceleration. The control

force of NSGA-NFLC and LQR controllers shows a rather continuous pattern resulting

from the continuous current changes with the two controllers. The frequency and

Lyapunov controllers, on the other hand, exhibit a pattern of control force with evident

trace of the switching history of the current. Even for the Bang-Bang controller, the

indication of switching current can be observed from the time history of control force.

Among all the control algorithms, the Lyapunov controller has largest control force

during the entire time history. Considering the small base displacement and velocity

responses of the Lyapunov controller, the high level of control force values indicates large

current inputs during earthquake excitations. Also, the red curve of the control force by

Lyapunov controller is denser than that of any other controllers. Such observation

indicates more intensively concentrated switching between upper and lower thresholds of

the current inputs.

To illustrates the correlation between control force and corresponding control current, a

time history of 10-second comparative control force between controlled base isolation

and passive-on scenario is presented with corresponding control current command on the

background. Three representative controllers are selected, namely, NSGA-NFLC,


225

Lyapunov controller and frequency controller. As can be seen from Figure 5.52, the

current of NSGA-NFLC is rathe continuous as predicted by the profile of the control

force. It can be clearly observed that, the control current is mainly resting at an average

value and increases or decreases according to the controller’s requirement. Discrete

changes on the control force signal is observed where the current has a big jump within

one or two sampling point. In Figure 5.53 and Figure 5.54, it can be observed that the

fluctuation of control force of both controllers follows the switching of current. The

changes between maximum and minimum current values of the Lyapunov controller is

much more frequent than that of the frequency controller, which means the MRE base

isolator has more opportunity to be energised by maximum current with Lyapunov

controller. Such observation is consistent with the conclusion draw from the large value

of control force that the switching of current in Lyapunov controller is denser than other

controllers.

Moreover, as can be seen in Figure 5.48 to Figure 5.51, although the RMS of control

force generated by frequency controller is relatively small, the fast switching control law

brings about big peak control force. Compared to frequency controller, the Lyapunov

controller requires even larger control force and more frequent sudden changes in the

time history. As known, such phenomenon is caused by the incessant switching of the

applied current, which might produce higher pressure on the electronic components in the

driving circuits and hence increase potential risks of device damage. Furthermore, the

control force of NFLC is much smaller than that of the Lyapunov control. Since those

two controllers both managed to realise great reduction of structural responses, this fact

indicates that it can achieve equivalent or even better performance than Lyapunov

controller with smaller requirement in control force.


226

Figure 5.48 Time history of control force with different control algorithms (0.15 El Centro)

0 10 20 30 40 50-400

-200

0

200

400

Forc

e (N

)

Passive-onNSGA-NFLC

0 10 20 30 40 50-400

-200

0

200

400

Forc

e (N

)

Passive-onBang-Bang

0 10 20 30 40 50-400

-200

0

200

400

Forc

e (N

)

Passive-onLQR

0 10 20 30 40 50-400

-200

0

200

400

Forc

e (N

)

Passive-onFrequency

0 10 20 30 40 50-400

-200

0

200

400

Time (s)

Forc

e (N

)

Passive-onLyapunov


227

Figure 5.49 Time history of control force with different control algorithms (0.15 Kobe)

0 10 20 30 40 50-1000

-500

0

500

1000

Forc

e (N

)

Passive-onNSGA-NFLC

0 10 20 30 40 50-1000

-500

0

500

1000

Forc

e (N

)

Passive-onBang-Bang

0 10 20 30 40 50-1000

-500

0

500

1000

Forc

e (N

)

Passive-onLQR

0 10 20 30 40 50-1000

-500

0

500

1000

Forc

e (N

)

Passive-onFrequency

0 10 20 30 40 50-1000

0

1000

2000

Time (s)

Forc

e (N

)

Passive-onLyapunov


228

Figure 5.50 Time history of control force with different control algorithms (0.15 Hachinohe)

0 5 10 15 20 25 30 35

-200

-100

0

100

200

Forc

e (N

)

Passive-onNSGA-NFLC

0 5 10 15 20 25 30 35

-200

-100

0

100

200

Forc

e (N

)

Passive-onBang-Bang

0 5 10 15 20 25 30 35

-200

-100

0

100

200

Forc

e (N

)

Passive-onLQR

0 5 10 15 20 25 30 35

-200

-100

0

100

200

Forc

e (N

)

Passive-onFrequency

0 5 10 15 20 25 30 35

-200

-100

0

100

200

Time (s)

Forc

e (N

)

Passive-onLyapunov


229

Figure 5.51 Time history of control force with different control algorithms (0.15 Northridge)

0 5 10 15 20 25 30-1000

-500

0

500

1000

Forc

e (N

)

Passive-onNSGA-NFLC

0 5 10 15 20 25 30-1000

-500

0

500

1000

Forc

e (N

)

Passive-onBang-Bang

0 5 10 15 20 25 30-1000

-500

0

500

1000

Forc

e (N

)

Passive-onLQR

0 5 10 15 20 25 30-1000

-500

0

500

1000

Forc

e (N

)

Passive-onFrequency

0 5 10 15 20 25 30-1000

-500

0

500

1000

Time (s)

Forc

e (N

)

Passive-onLyapunov


230

Figure 5.52 Control force and corresponding control current with NSGA-NFLC (Earthquake

scaling factor = 15%)

0 2 4 6 8 10-300

-150

0

150

300

Time (s)

Con

trol f

orce

(N)

El-centro Earthquake

Current Passive-on NSGA-NFLC

0 2 4 6 8 10-1000

-500

0

500

1000

Time (s)

Con

trol f

orce

(N)

Kobe Earthquake


0 2 4 6 8 10-400

-200

0

200

400

Time (s)

Con

trol f

orce

(N)



0 2 4 6 8 10-1000

-500

0

500

1000

Time (s)

Con

trol f

orce

(N)



Cur

rent

(A)

Cur

rent

(A)

Cur

rent

(A)

Cur

rent

(A)

0

5

0

5

0

5

0

5


231

Figure 5.53 Control force and corresponding control current with Lyapunov control (Earthquake


Cur

rent

(A)

Cur

rent

(A)

Cur

rent

(A)

Cur

rent

(A)

0

5

0

5

0

5

0

5

0 2 4 6 8 10-600

-300

0

300

600

Time (s)

Con

trol f

orce

(N)


Current Passive-on Lyapunov

0 2 4 6 8 10-1600

-800

0

800

1600

Time (s)

Con

trol f

orce

(N)

Kobe Earthquake


0 2 4 6 8 10-300

-150

0

150

300

Time (s)

Con

trol f

orce

(N)



0 2 4 6 8 10-1000

-500

0

500

1000

Time (s)

Con

trol f

orce

(N)




232

Figure 5.54 Control force and corresponding control current with frequency control (Earthquake


Cur

rent

(A)

Cur

rent

(A)

Cur

rent

(A)

Cur

rent

(A)

0

5

0

5

0

5

0

5

0 2 4 6 8 10-600

-300

0

300

600

Con

trol f

orce

(N)


Current Passive-on Frequency

0 2 4 6 8 10-1600

-800

0

800

1600

Con

trol f

orce

(N)

Kobe Earthquake


0 2 4 6 8 10-300

-150

0

150

300

Con

trol f

orce

(N)



0 2 4 6 8 10-1,000

-500

0

500

1000

Time (s)

Con

trol f

orce

(N)




233

5.5.8 Comparative Evaluation between Different Control Methods

Table 5.16 Comparison of five controllers

Evaluative criteria NFLC Bang-Bang LQR Frequency Lyapunov

Acceleration Best Good Poor Medium Good

Inter-storey drift Best Medium Medium Poor Good

Base displacement Good Good Good Poor Best

Control force Medium Small Large Large Largest

Acceleration Best Medium Medium Medium Good

Inter-storey drift Good Good Poor Medium Best

Base displacement Good Good Good Medium Best

Control force Medium Small Large Medium Large

Dependence on earthquakes Least Medium Medium Strong Little

To complete the comprehensive evaluation of the five controllers studied in this research,

the comparison of controllers is in terms of peak and RMS values of significant

parameters are summarised in Table 5.16. As discussed, the major dilemma in

conventional base isolation study is to balance the reduction performance of floor

acceleration and inter-storey drift, of which the inter-storey drift is essential in evaluating

the potential damage of structural elements. Meanwhile, excessive base displacement is

also concerned in the base isolation system design. Hence, the performance in suppressing

acceleration, inter-storey drift and base displacement of all controllers are compared.

Furthermore, the control force required by each controller is also listed to compare the

efficiency of controller to achieve decent control performance. As can be seen from Table


234

5.16, the NFLC and Lyapunov achieve ideal reduction of both peak and RMS values of

acceleration, inter-storey drift and base displacement, with NFLC slightly better in

reducing peak value while Lyapunov controller slightly superior in RMS control of

structural response. Comparatively, the LQR controller is not as good as other controllers

in mitigating acceleration and inter-storey drift but performs well in base displacement

restriction. In terms of control force, the NFLC is able to achieve equal or even better

performance compared with Lyapunov controller with smaller requirement on control

force, which shows a superiority in control-efficiency and leads to better serviceability of

the MRE controller. In the end, the performance of NFLC shows the least dependence on

the earthquake’s characteristics, which indicates the best versatility of the MRE isolation

system utilising such a controller. Therefore, from a comprehensive perspective, all the

controllers proposed and applied in this study achieve good seismic protection

performance compared to passive base isolation system and NFLC can be considered as

the best one based on the presented evaluation.

5.6 SUMMARY

This chapter focuses on the experimental realisation of shake table testing of a semi-active

control base isolation system employing MRE base isolator. Several issues have been

addressed in this chapter: i) the design and manufacture of a three-storey pure shear

building model as the testing bed; ii) identification and modelling of the testing structure

and MRE base isolator and the integration of isolation system; iii) development of

multiple control algorithms: NSGA-II with DCD optimised NFLC, Bang-Bang control,

LQR control with GRNN inverse model, frequency control, Lyapunov-based current

selection control; iv) experimental implementation of the semi-active controlled MRE

base isolation system.

Comparative numerical experimental investigation has been conducted with fixed base

building, passive-off base isolated building, passive-on base isolated building and base


235

isolation controlled by the aforementioned five controllers. The three-storey frame

structure is designed closed to a pure shear building model since only the horizontal

movement is of interest in analysis of seismic influence on the structure and thus it was

modelled as a three-DOF system. Testing results were discussed in five categories: peak

floor responses of inter-storey drift ratio, acceleration, relative displacement and floor

shear force; time histories of top floor acceleration, base acceleration and base

displacement; evaluative indices of peak and normed acceleration, inter-storey drift and

base shear and controller related parameters; time history of control force with different

controllers and comparison between control force and corresponding control current

command. Test results show that the performances of passive systems, no matter on what

current stage, have a strong dependence on the input signals. Two controllers which

receive best control performance are NSGA-NFLC and Lyapunov current controller. The

NFLC tends to have more continuous current input while Lyapunov controller achieves

good control performance via frequently switching current between maximum and

minimum thresholds and thus leads to large control force.

Innovative Storey Isolation Utilising Smart MRE Isolation System

236

CHAPTER 6

INNOVATIVE STOREY ISOLATION UTILISING SMART

MRE ISOLATION SYSTEM

6.1 CHAPTER OUTLINE

As the base isolation techniques mature, it has been recognised that, the biggest issue

faced in base isolation technique is the challenge of great base displacement demand,

which leads to the potential of overturning of the structure, instability and permanent

damage of the isolators. Meanwhile, drain, ventilation and regular maintenances at the

base isolation level are quite difficult and rather time- and economical- consuming,

especially at the high-populated area. To address these issues and enlarge the application

scope of base isolation technique (especially on high-rise buildings), a novel idea of

segmental building, i.e. mid-storey isolation system, has been proposed and investigated

by various researchers. However, such techniques have their own flaws, among which

whipping effect is the most obvious one. Moreover, due to their inherent passive nature,

all these techniques, including traditional base isolation system, show defects in

incapability to cope with the unpredictable and diverse nature of earthquakes. The

solution for the aforementioned challenge is to develop an innovative storey isolation

system to realise variable structural stiffness to maximise the adaptability and

controllability of the system, which is comprehensively explored in this chapter.

In this chapter, an elaborate literature review is firstly presented to reveal the advantages

and drawbacks of the current mid-storey isolation systems and the research gap to be


237

filled by MRE storey isolation system, followed by a brief description of the storey-

isolation system. Next, the NSGA II with DCD optimisation introduced in last chapter is

employed to explore the optimal current input and placement location of each MRE

isolator. A NFLC is then utilised to control the seismic protection performance of the

storey-isolation system. A comparative numerical investigation has been conducted using

a 5-storey benchmark model to evaluate the performance of the proposed isolation system

under different earthquake excitations. Tests compare the seismic responses of bare

building, building with passive controlled MRE base isolation system, building with

optimised storey isolation system and building with FLC controlled storey isolation

system.

6.2 BACKGROUND AND INTRODUCTION

As discussed in Chapter 2, although proven to be effective in numerous practical

applications worldwide (Kelly 1993), base isolation technique has its own flaws, among

which large base displacement is the most concerned issue (Stewart, Conte & Aiken

1999). During earthquake excitation, if the base isolation system is designed properly, the

superstructure decoupled from ground motion behaves a rigid body motion, which

ensures great reduction of inter-storey drift but leads to enormous displacement across

the base isolation level (Pan & Cui 1998). Therefore, the foundation level of conventional

base-isolated structure is demanded to provide adequate lateral flexibility to satisfy the

massive base displacement requirement of the base isolation system, which is more time-

consuming and less economical efficient in terms of implementation and construction

(Jangid & Datta 1995). Meanwhile, even the structural element can meet base

displacement prerequisite, large deformation of the base isolators also lead to buckling

phenomenon and thus raise issues of instability, etc. (Forcellini & Kelly 2013). Secondly,

the natural frequencies of the structure are inversely proportional to its flexibility, which

increases with the height and slenderness of the building. Hence, the capability of shifting


238

structural frequency of the base isolation system reduces when structure becomes more

flexible and slender, which restrains the range of applicable structure to only low- to mid-

rise buildings (Skinner, Robinson & McVerry 1993).

Besides “smart” base isolation system, the motivation to mitigate problems above has

also driven researchers to come up with various resolutions and alternations of the

conventional base isolation systems. One of the resolutions is categorised as mid-storey

structure or segmental structure, which is especially targeting on the isolation system

which can be applied on high-rise structures. In 1993, Pan et al. proposed a concept of

segmental buildings to divide the superstructure into several segments and each of two

segments are interconnected by additional isolation systems (Pan, Ling & Cui 1993).

Numerical studies of the proposed concept are conducted and it is proved that the

segmental building can effectively reduce base displacement but the displacements of

higher levels are amplified to some extent when compared to base-isolated structure (Pan,

Ling & Cui 1995). Additional storey isolation (ASI) strategy was proposed by Chey et al.

(Chey et al. 2013) to behave as a tuned mass damper (TMD) system for seismic retrofit

of existing building. Isolation level is inserted between the added level and original

building to dissipate seismic energy via isolation level to reduce the seismic force

experienced by the structure. Such approach achieves good seismic retrofitting

performance but the large displacement in isolation level becomes a major hidden danger.

Mid-storey isolation is also an alternative strategy gaining popularity to replace base

isolation system. Many residential-commercial buildings with mid-storey isolation

system have been put into service around the world, especially in China, Korea and Japan

(Kawamura et al. 2000; Sueoka, Torii & Tsuneki 2004; Torunbalci & Ozpalanlar 2008;

Wang et al. 2012; Xu, Hu & Zhou 2004). At the moment, the mid-storey isolation system

is mainly equipped in the high-rise buildings where overturning is one of the significant

concerns with the isolation system (Chey et al. 2009). However, despite high popularity,


239

the mid-storey isolation system is still a weak link in the building.

In this chapter, a novel semi-active multi-storey isolation system has been proposed,

which can be recognised as a combination and extension of segmental building and mid-

storey isolation system. The MRE base isolator is again adopted as the inter-storey

bearing. Therefore, the storey isolation system acquires changeable lateral stiffness at the

MRE isolator’s installation location, which allows it to change the structural properties

and thus adapt to various disturbances. By interpolating the isolation system into different

levels of the structure, the storey isolation system distributes the flexibility along the

entire building which was concentrated at base level in base isolation case. During

earthquake excitation, all storey isolation levels collaboratively absorb and dissipate

energy instead of only by one isolation system. As a result, the displacement demand at

each isolation level will be much smaller than that of a solely base-isolated structure.

Moreover, it is revealed by literatures (Jin et al. 2012; Murakami et al. 2000; Ryan & Earl

2010) that in the mid-storey isolations system, the building has different seismic

protection performance in the structure upper and lower than the isolation level. In

contrast, the storey isolation is capable of reducing seismic response to the greatest degree

in every storey. Another common problem often encountered by the mid-storey isolation

or additional storey isolation system is whipping effect, which will significantly amplify

the velocity and displacement of the upper structure if resonance occurs. The major reason

causing whipping effect is the sudden change of lateral stiffness between structural

segments. Attribute to the adaptability of the proposed storey isolation system provided

by the smart MRE isolators, the structural component stiffness and thus frequency can be

simply adjusted according to the excitation property, which allows the system great

adaptability and controllability. In the end, drain, ventilation and regular maintenances at

the storey-isolation layer are much easier and time- and economical efficient than

underground isolation layer (Tasaka et al. 2008).


240

6.3 SYSTEM DESCRIPTION

Figure 6.1Sketches of: (a) fixed base building; (b) base-isolated building; (c) storey isolated

building

The storey isolation system proposed in this paper is a novel isolation approach to

incorporate the isolation system not only under the superstructure, but also in between

adjacent floors. The schematic diagram of the storey isolation system is shown in Figure

6.1. In this design, the isolation system can distribute flexibility alongside the height of

the building to significantly reduce the displacement demand on the base isolation level.

Meanwhile, the storey isolation system will not sacrifice but in contrast possibly enhance

the effectiveness of seismic protection in that it can interrupt the seismic energy flux level

by level to decouple every single level from the structure beneath it. The MRE isolators

are installed into the storey isolation system and its adaptable stiffness characteristic

allows changeable and controllable stiffness at each degree of freedom (DOF) of the

entire building.

Consider a civil infrastructure with N storeys. Since the movement along the direction of

ground motion is of interest, the building can be simplified as an N-DOF lumped mass

model. The mass, stiffness and damping coefficient at the ith storey are noted as mi, ki and

ci. When the isolators are installed at the ith floor, the MRE isolators at the corresponding

floor are considered to be connected with the original structural elements in series. The

model of storey isolation system can be seen in Figure 6.2. Hence, the equivalent stiffness

MRE isolators

Storey N

Storey N-1

Storey 2

Storey 1

(a) (b) (c)


241

kie and damping coefficient cie of the ith level can be written as

Eq. 6.1

Eq. 6.2

where kMRE and cMRE are the stiffness and damping coefficient of the MRE isolator

and m is the number of MRE base isolator installed at this level. To reduce the

computational complexity, a simplified forward model describing the correlation between

applied current and the MRE base isolator’s stiffness and damping, respectively, has been

developed. Functions of kMRE and cMRE regarding to current I can be written as

Eq. 6.3

Eq. 6.4

The values of parameters in Eq. 6.3 and Eq. 6.4 are listed in Table 6.1.

Table 6.1 Parameter values of MRE isolator model

Parameter Value

kb1 (kN/m·A) 11.76

kb0 (kN/m) 6.053

cb1 (kN·s/m·A) 0.02725

cb0 (kN·s/m) 0.02329

Hence, the stiffness and damping coefficient of ith storey can be expressed by

Eq. 6.5

Eq. 6.6

The motion equation of the storey isolation system is then

MREi

MREiie mkk

mkkk

MREi

MREiie mcc

mccc

01 bibiMRE kIkIk

01 bibiMRE cIcIc

01

01

bibi

bibiie kIkmk

kIkmkk

01

01

bibi

bibiie cIcmc

cIcmcc


242

Eq. 6.7

where MS, CS and KS are the mass, damping and stiffness matrices of the storey isolation

system, whose formulation can be expressed as following

Eq. 6.8

Eq. 6.9

Eq. 6.10

Figure 6.2 Schematic diagrams of: (a) fixed base building model; (b) storey-isolated building

model

gSSSS xMxKxCxM

NiS mmmmdiagM 21

NN

N

eee

eee

S

ccc

cccccc

C

0

0

322

221

NN

N

eee

eee

S

kkk

kkkkkk

K

0

0

322

221

mN

mN-1

m2

m1

cN

c2

c1 k1

k2

kN

mN

mN - 1

m2

m1

c(IN)

c2

c1 k1

k2

kNcN

k(IN)

c(I2) k(I2)

k(I1)c(I1)

(a) (b)


243

6.4 OPTIMAL CURRENT SELECTION OF THE MRE ISOLATOR

6.4.1 Five-Storey Benchmark Building Model

To investigate the performance of storey isolation system, a five-storey benchmark

building model created by Samali et al. is utilised as the testing bed(Samali et al. 1999).

The five-storey benchmark building model is recognised to be one of the International

Association of Structural Control and Monitoring (IASC) experimental building models.

The photo and floor plan of the 5-storey building model are shown in Figure 6.3 while

the structural parameters of the model, including mass, effective stiffness and damping

coefficients of each floor, are listed in Table 6.2.

Figure 6.3 Photo and typical floor plan of the 5-storey benchmark building model (Wu & Samali 2002)

Table 6.2 Structural parameters of the 5-storey model

Storey No. 1 2 3 4 5

Mass (kg) 214 207 207 207 207

Stiffness (kN/m) 1146 3124 3156 3156 2978

Damping (kN∙s/m) 0.0584 0.1117 0.1128 0.1100 0.1233

As can be seen in Table 6.2 and Figure 6.3, the self-weight of the 5-storey building model


244

is approximately 1 ton and there are 2 bays W-E and 1 bay N-S. Considering the vertical

loading capacity of individual MRE base isolator under limited displacement (Li, Li, Tian,

et al. 2013), 6 MRE isolators were adopted at each isolation level in both base- and storey-

isolation systems. In other words, m = 6 at each floor in Eq. 6.5 and Eq. 6.6.

6.4.2 Optimisation Problem Statement

The task of optimisation here is to explore the optimal current applied at the isolation

level on each storey. To find out the optimal current values applied to the proposed system

is of great significance in generating the guideline for system design, which is also

considered as solving the multi-objective optimisation problem. To optimise the current

related parameters of the system, primary objective is to set up the suitable fitness

functions. Since the major task of seismic isolation system is to minimise the floor

acceleration and inter-storey drift simultaneously, four important indices, i.e. peak floor

acceleration, peak inter-storey drift, root mean squared (RMS) floor acceleration and

RMS inter-storey drift, are selected to construct the fitness functions in this study.

Mathematical expressions of those functions are given as following:

(1) Peak floor acceleration (PFA)

Eq. 6.11

where i denotes the storey number and denotes the floor acceleration.

(2) Peak inter-storey drift (PISD)

Eq. 6.12

where denotes the inter-storey drift.

(3) Root mean squared floor acceleration (RMSFA)

Eq. 6.13

txPFA iti,max

x

tdPISD iti,max

id


245

where T denotes the sampling period and Δt represents the sampling interval.

(4) Root mean squared inter-storey drift (RMSISD)

Eq. 6.14

The fitness functions are then defined as the maximal values of the evaluative indices

shown in Eq. 6.11 to Eq. 6.14 when the storey isolation system is subjected to four

benchmark earthquakes, i.e. El Centro earthquake, Kobe earthquake, Hachinohe

earthquake and Northridge earthquake. Furthermore, the optimisation task is to minimise

all four objectives described by the fitness functions. The minimisation optimisation

problem for optimal applied currents can be written as below

Eq. 6.15

Same as aforementioned, Ii is the current values applied to the MRE base isolator at ith

storey and Imax denotes the extreme value of applied current to the device. It is worth

noticing that Imax is set as 5A to maximise the range of adjustability within the capability

limit of MRE isolator.

6.4.3 Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) with DCD

As explained in last section, the seeking for optimal control currents in storey isolation

system, in principle, gives rise to a set of optimal solutions (largely known as Pareto-

optimal solutions) rather than a single optimal solution due to the presence of multiple

objectives. To identify the best Pareto-optimal solution, further information is needed and

hence multi-objective evolutionary algorithms (MOEAs) have been utilised. The reason

why evolutionary algorithms (EAs) are suitable for multi-objective optimisation

tdtT

RMS iISD21

NiIIts

RMSobjRMSobj

PISDobjPFAobj

i

ISD

NorthridgeHachinoheKobe

CentroElFA


CentroEl


CentroEl


CentroEl

,,2,1,0..

maxmax

maxmax

min

max

43

21


246

problems is that they work with a population of solutions so a simple EA can be extended

to maintain a diverse set of solutions. With an emphasis for moving toward the true

Pareto-optimal region, an EA can be used to find multiple Pareto-optimal solutions in one

single simulation run. The nondominated sorting genetic algorithm (NSGA) proposed by

Deb et al. (2001) was one of the first such EAs. It is a very effective algorithm but has

been generally criticized for its computational complexity, lack of elitism and for

choosing the optimal parameter value for sharing parameter.

Figure 6.4 Illustration of Pareto frontier (Barraza et al. 2017)

To this end, the same group of researchers have developed a modified version, NSGA-II

(Deb et al. 2002). As explained previously, the main idea of the NSGA-II approach is to

find non-dominated solutions that represent a Pareto frontier. To understand Pareto

frontier, the definition of nondomination should be elaborated firstly. Consider two

solution vectors in a minimisation problem, x(1) and x(2), of which x(1) is partially less than

x(2). That is to say, no element of x(2) is smaller than x(1) and at least one element of x(2) is

strictly greater than x(1). In this case, we say that x(1) dominates x(2) or x(1) is inferior to

x(1) (Tamura & Miura 1979). Hence, any member of such vectors which is not dominated

by any other member is said to be nondominated. The definition of Pareto frontier can be

more vividly illustrated by the graph shown in Figure 6.4. As can be seen in Figure 6.4,

consider a multi-objective problem whose task is to minimise two objective functions, all

the points corresponding to feasible optimisation results are marked as hollow circles

Objective Function 1

Obj

ectiv

e Fu

nctio

n 2


247

while the non-dominated solutions are marked by black circles. It can be observed that

the non-dominated solutions correspond to the solutions which have better results in at

least one objective function. All the non-dominated solutions form the Pareto frontier.

As a type of EA, the typical steps of NSGA-II include random population initialisation,

uses an evolutionary process with surrogates for evolutionary operators including

selection, genetic crossover, and genetic mutation. In general, NSGA-II varies from

simple genetic algorithm (GA) only in the way how the selection operator works while

the crossover and mutation operators remain as usual GA. In every generation, the

population is sorted into a hierarchy of fronts based on the ordering of Pareto dominance.

More elaborately, once the population in the initial population is sorted based on non-

domination into each front. The first front being completely non-dominant set in the

current population and the second front being dominated by the individuals in the first

front only and the rest of the fronts go so on. Individuals in each front are then assigned

rank (fitness) values. Individuals in first front are given a fitness value of 1 and individuals

in second are assigned fitness value as 2 and so on. Similarity between members of each

sub-group is evaluated on the Pareto frontier, and the resulting groups and similarity

measures are used to promote a diverse front of non-dominated solutions. To summarise,

the NSGA-II is implemented with an effective sorting method based on individual

ranking by non-dominated sorting and a crowded distance sorting which evaluates the

population density of solutions in the same rank.

6.4.4 Parameter Identification Based on NSGA-II with DCD

In this study, an improved NSGA-II is proposed by introducing dynamic crowding

distance (DCD) into the standard NSGA-II as a novel evaluation index to ensure good

diversity level among the solutions. The detailed optimisation procedure of improved

NSGA-II with DCD is described as following

a. Determine the multi-objective problem. In this work, the fitness function are Eq.


248

6.11 to Eq. 6.14. The parameters to be identified are current levels applied to each

MRE base isolator.

b. Set the parameter values of NSGA-II with DCD. Here, the population number is

20, crossover probability is 0.9, mutation probability is 0.15 and maximum

iteration number is 100.

c. Initialise the population (generate random initial population).

d. Calculate the fitness values.

e. Initialize the iteration number n=0.

f. Carry out the crossover and mutation operations for the individual group.

g. Systematise the population based on the every fitness value in an increasing order.

h. Compute the dynamic crowding distances (DCD) among solutions.

i. Select parent using tournament rule: the individual, on the bare population area of

the front, is assigned with the higher fitness value.

j. Increase the iteration number and check the stop criterion. If the current iteration

arrives at its maximum value, the algorithm is terminated. Or else, repeat Step b

to Step i.

Apply NSGA-II with DCD to the 5-storey benchmark building model with adaptive

storey isolation system and the optimisation results are displayed in Table 6.3. As seen,

there is not much difference in objectives related to inter-storey drift when applied

different sets of optimised currents. Therefore, objectives associated with acceleration are

of more interest for the decision of optimised current selection. Hence, the current set that

leads to minimal acceleration response (i.e. obj1 and obj3) is selected for storey isolation

current inputs in the following numerical expectation of seismic proofing effectiveness

of the adaptive system. The chosen current set is underlined in Table 6.3.


249

Table 6.3 Optimisation current solutions and corresponding objective values

Current at each level (A) Obj1

(m/s2) Obj2 (mm)

Obj3 (m/s2)

Obj4 (mm)

Storey 1

Storey 2

Storey 3

Storey 4

Storey 5

0.061 3.076 2.569 4.253 1.120 158.033 1.159 71.782 0.376

0.061 3.394 2.569 3.902 1.120 160.099 1.137 69.959 0.367

0.000 3.059 2.561 3.729 3.300 142.672 1.231 60.499 0.268

2.544 1.693 1.672 3.740 3.187 41.998 2.834 12.658 0.428

0.480 3.131 2.675 3.982 1.556 95.435 1.327 48.169 0.464

2.534 1.784 1.564 3.740 3.144 43.848 2.745 12.131 0.422

2.308 1.951 1.866 3.112 2.847 37.348 2.522 14.466 0.478

0.438 3.114 2.561 3.759 3.098 105.291 1.268 36.917 0.336

0.000 2.870 2.569 4.198 0.889 140.626 1.416 69.845 0.316

0.965 2.360 1.503 4.595 2.859 63.919 1.550 25.097 0.384

0.715 3.114 3.126 3.759 2.693 84.389 1.432 31.223 0.387

0.132 3.537 2.675 4.241 1.496 151.190 1.374 55.923 0.333

1.216 1.315 1.570 3.516 3.046 53.103 1.542 21.249 0.391

0.612 3.537 2.800 3.765 1.496 85.477 1.425 28.184 0.332

0.000 3.059 2.561 3.729 2.975 143.089 1.214 60.436 0.269

0.529 3.114 2.561 3.729 2.975 99.825 1.285 44.385 0.439

0.536 3.142 2.675 3.982 1.556 97.220 1.386 43.999 0.454

1.434 1.605 1.430 3.835 2.872 48.869 1.679 14.861 0.323

0.000 3.059 2.561 4.058 3.254 142.354 1.244 60.834 0.268

2.039 2.125 1.859 3.112 2.755 43.449 2.232 14.951 0.442

2.231 2.125 1.859 3.112 2.755 39.413 2.066 17.623 0.545

2.231 2.125 1.859 3.112 2.755 39.413 2.066 17.623 0.545

2.231 2.125 1.859 3.112 2.755 39.413 2.066 17.623 0.545

2.231 2.125 1.859 3.112 2.755 39.413 2.066 17.623 0.545

2.231 2.125 1.135 3.278 2.755 51.203 1.938 15.750 0.426

2.231 2.125 2.172 3.112 2.755 47.703 2.240 25.841 0.748

2.977 2.125 1.859 3.112 2.755 43.299 3.308 18.103 0.658


250

6.5 CONTROL METHOD

In last section, a set of optimal currents is selected based on NSGA-II with DCD taking

four benchmark earthquakes into consideration. However, the corresponding optimal

storey isolation system is still, judging by its nature, a passive controlled isolation system.

Due to the unpredictability and diversity of earthquakes, it is impossible for the four

earthquakes to cover all types of seismic excitation, which leaves the optimal storey

isolation vulnerable facing undesignated seismic attacks. To further improve the

performance of the storey isolation system, a simple control system is proposed based on

the Bang-Bang control method. In last chapter, when dealing with the base isolation

system, the Bang-Bang controller didn’t achieve promising performance. The major

reason is that, although MRE base isolator is utilised as a semi-active device rather than

an actuator, the MRE base isolation system is categorised as an under-actuated system in

control engineering discipline since the control action is only applied at one degree-of-

freedom of the entire system by the device. Hence, it is not favourable to use Bang-Bang

control in the MRE base isolation system, which employs the displacement and velocity

of base level as input of the controller. The storey isolation system, in contrast, has MRE

isolator installed at each level, which makes it a fully actuated system and hence applying

Bang-Bang control on each isolator is reasonable.

The control law of the system can be written as

Eq. 6.16

The control law in Eq. 6.16 states the following procedure: when the mass block of the

ith storey is moving away from the equilibrium, the current applied on the isolator at the

corresponding floor is tuned to maximal value and hence attach stiffness to the ith storey

to prevent the movement; vice versa, when the mass block of the ith storey is moving

towards the equilibrium, the current applied on the isolator at the corresponding floor is

000max

iii

iii

xxIxxII


251

tuned to be zero and hence assure minimum stiffness.

6.6 NUMERICAL INVESTIGATION

To evaluate the performance of storey isolation system, a comparative numerical

investigation is conducted based on the five-storey benchmark building. Six isolation

scenarios are compared, namely, fixed base building, passive-on (applied current is 5A)

base isolation (BI), passive-off (no current applied) BI, passive-off storey isolation (SI),

optimal SI, controlled SI. Same as in Chapter 5, the structures in the six isolation scenarios

are subjected to four seismic ground accelerations defined in the benchmark problems

(El-Centro 1940, Hachinohe 1968, Kobe 1995 and Northridge 1994), among which El

Centro and Hachinohe earthquakes represent far-field, moderate seismic events while

Kobe and Northridge earthquakes are representative for near-field, more severe ground

movements. All the excitations are applied with the full intensity for the evaluation of the

proposed system’s performance.

The numerical results are firstly analysed in terms of peak floor responses, which includes

floor acceleration, inter-storey drift ratio and relative displacement. Next, time histories

of top floor acceleration between the five isolation scenarios and fixed base building are

compared. Furthermore, control currents at different floor under four earthquakes are also

presented.

Among all types of responses, floor acceleration is one of the most significant parameters

to indicate the seismic-proof performance of the isolation system. For low- to mid-rise

buildings, normally, the first mode is dominantly excited during an earthquake attack.

Therefore, the floor acceleration increases with the height of the building. Hence, the time

histories of the top floor accelerations of the five isolation cases are plotted in Figure 6.5

to Figure 6.8 with comparison to that of the fixed base building. It can be observed that

all the isolation systems, either BI or SI, can reduce the top floor acceleration in varying

degrees. However, the optimised SI and controlled SI achieve outstanding performance


252

in acceleration reduction. Moreover, they are able to maintain the response to a rather low

level on the entire time domain.

Figure 6.5 Time history of top floor acceleration under El Centro earthquake

0 10 20 30 40 50-2

-1

0

1

2A

ccel

erat

ion

(g)

Fixed basePassive-on BI

0 10 20 30 40 50-2

-1

0

1

2

Acc

eler

atio

n (g

)

Fixed basePassive-off BI

0 10 20 30 40 50-2

-1

0

1

2

Acc

eler

atio

n (g

)

Fixed baseOptimised SI

0 10 20 30 40 50-2

-1

0

1

2

Acc

eler

atio

n (g

)

Fixed basePassive SI

0 10 20 30 40 50-2

-1

0

1

2

Time (s)

Acc

eler

atio

n (g

)

Fixed baseControlled SI


253

Figure 6.6 Time history of top floor acceleration under Kobe earthquake

0 10 20 30 40 50-4

-2

0

2

4

Acc

eler

atio

n (g

)


0 10 20 30 40 50-4

-2

0

2

4

Acc

eler

atio

n (g

)


0 10 20 30 40 50-4

-2

0

2

4

Acc

eler

atio

n (g

)


0 10 20 30 40 50-4

-2

0

2

4

Acc

eler

atio

n (g

)


0 10 20 30 40 50-4

-2

0

2

4

Time (s)

Acc

eler

atio

n (g

)



254

Figure 6.7 Time history of top floor acceleration under Hachinohe earthquake

As for the passive controlled isolation systems, no matter BI or SI, the performance shows

a great dependence on the type of earthquake excitation. The passive SI, in particular,

obtains acceptable acceleration reduction under El Centro, Kobe and Hachinohe

earthquake, but results in the worst acceleration performance under Northridge

0 5 10 15 20 25 30 35-2

-1

0

1

2

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30 35-2

-1

0

1

2

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30 35-2

-1

0

1

2

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30 35-2

-1

0

1

2

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30 35-2

-1

0

1

2

Time (s)

Acc

eler

atio

n (g

)



255

earthquake among all five isolation systems.

Figure 6.8 Time history of top floor acceleration under Northridge earthquake

Another noteworthy fact is that the acceleration response of the passive SI system shows

more lower frequency components than those of the two BI systems, which indicate a

lower natural frequency of SI than BI. Such phenomenon indicates that the SI system can

endow the structure larger adjustable range of frequency to better avoid resonance of

0 5 10 15 20 25 30-2

-1

0

1

2

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30-2

-1

0

1

2

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30-2

-1

0

1

2

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30-2

-1

0

1

2

Acc

eler

atio

n (g

)


0 5 10 15 20 25 30-2

-1

0

1

2

Time (s)

Acc

eler

atio

n (g

)



256

external excitations.

Figure 6.9 Comparison of top floor acceleration between optimised SI and controlled SI

For better observability, the time histories of top floor acceleration are compared between

optimised SI and controlled SI in Figure 6.9. As can be seen in Figure 6.9, the acceleration

of controlled SI is slightly smaller than that of optimised SI under all earthquakes except

for Hachinohe earthquake, where the SI’s acceleration response surpasses that of BI

0 10 20 30 40 50-0.4

-0.2

0

0.2

0.4

Time (s)

Acc

eler

atio

n (g

)


Optimised SIControlled SI

0 10 20 30 40 50-1

-0.5

0

0.5

1

Time (s)

Acc

eler

atio

n (g

)

Kobe Earthquake


0 5 10 15 20 25 30 35-0.4

-0.2

0

0.2

0.4

Time (s)

Acc

eler

atio

n (g

)



0 5 10 15 20 25 30-1

-0.5

0

0.5

1

Time (s)

Acc

eler

atio

n (g

)




257

occasionally at some time instants. The sudden changes of acceleration caused by fast

switching by Bang-Bang controller can also be seen from SI’s acceleration curve

subjected to Hachinohe earthquake, which once again proves that the fast switching of

current signal may introduce high acceleration responses to the system.

Figure 6.10 Peak floor acceleration response under four earthquakes

0 0.5 1 1.51

2

3

4

5

Stor

ey N

o.El Centro Earthquake

Fix basePassive-on BIPassive-off BIOptimised SIPassive SIControlled SI

0 1 2 3 41

2

3

4

5

Stor

ey N

o.

Kobe Earthquake


0 0.5 1 1.51

2

3

4

5

Stor

ey N

o.



0.5 1 1.5 21

2

3

4

5

Peak floor acceleration (g)

Stor

ey N

o.




258

Furthermore, the controlled SI outperforms optimised SI under all earthquakes at later

stages of the earthquake strikes, which indicates that the control command can speed up

the structural response decay process when the external excitation reduces or vanishes

while the passive optimal SI experiences a free body like motion.

Figure 6.11 Peak inter-storey drift ratio response under four earthquakes (drift ratio = inter-

storey drift/floor height; floor height = 600mm)

0 0.01 0.02 0.03 0.04 0.051

2

3

4

5

Stor

ey N

o.El Centro Earthquake


0 0.02 0.04 0.06 0.081

2

3

4

5

Stor

ey N

o.

Kobe Earthquake


0 0.01 0.02 0.03 0.041

2

3

4

5

Stor

ey N

o.



0 0.01 0.02 0.03 0.04 0.05 0.061

2

3

4

5

Peak inter-storey drift ratio

Stor

ey N

o.




259

Figure 6.12 Peak relative displacement response under four earthquakes

Besides time histories of the top floor acceleration, the peak acceleration and inter-storey

drift are also of great interest. Meanwhile, the peak displacement versus floor height can

also provide an approximate building profile when the movement is at greatest intensity.

Therefore, Figure 6.10, Figure 6.11 and Figure 6.12 illustrate the peak acceleration, inter-

storey drift ratio, relative displacement, respectively. It is clearly shown in Figure 6.10

0 10 20 30 401

2

3

4

5

Stor

ey N

o.



0 10 20 30 40 501

2

3

4

5

Stor

ey N

o.

Kobe Earthquake


0 10 20 30 40 501

2

3

4

5

Stor

ey N

o.



0 20 40 60 80 1001

2

3

4

5

Peak relative displacement (mm)

Stor

ey N

o.




260

that the acceleration of the fixed base building increases with the floor number, which

proves that the first mode is the principle mode excited. The controlled SI system shows

the greatest peak acceleration reduction under El Centro, Kobe and Northridge

earthquakes. Under Hachinohe earthquake, the peak acceleration of controlled SI is larger

than optimised SI at top two floors. Considering the optimization performance of NSGA

II, although there is only a narrow lead over optimised SI, the superiority of controlled SI

is revealed by the results. Both passive-on and -off BI systems can also effectively

mitigate the acceleration at each floor. However, both passive controlled base isolation

system and the passive storey isolation system show great reliance on the earthquake,

which reveals the natural defect of the passive isolation system. Finally, the passive SI

system shows extremely large acceleration at some levels under certain earthquake,

which may be attributed to the existence of whipping effect. For instance, under El Centro

and Northridge earthquake, an extreme acceleration is witnessed by the top floor, which

indicates a significant amplification of acceleration at the upper structure beyond Storey

4. In contrast, the controlled and optimised SI system doesn’t suffer from such effect,

meaning the smart MRE isolators’ adjustable characteristics receive good influence when

proper control method applied.

As mentioned in Introduction section, the most concerned issue of a base isolation system

is the large demand in base displacement tolerance. The storey isolation system was

proposed to distribute flexibility along the structure to effectively relieve the base

displacement burden. The displacement distribution effect can be revealed in the peak

inter-storey drift response, which is shown in Figure 6.11. Peak inter-storey drift at each

floor represents the relative movement between the adjacent floors, which implies the

potential damage to the structural elements of the building. Moreover, values in the graph

represent ratio between inter-storey drift and floor height (600mm). As seen, the base

isolation systems show great potential in cutting down the inter-storey drift of the

structure from level 2 to 5. Although the controlled SI has larger drift at upper floors, it

achieves smallest base displacement among all the structures, which indicates that the of


261

structure instead of concentrating at the base level.

Figure 6.13 Control current of different storey under El Centro earthquake

0 10 20 30 40 50

0

5

Storey 5

Curr

ent (

A)

0 10 20 30 40 50

0

5

Storey 4

Curr

ent (

A)

0 10 20 30 40 50

0

5

Storey 3

Curr

ent (

A)

0 10 20 30 40 50

0

5

Storey 2

Curr

ent (

A)

0 10 20 30 40 50

0

5

Storey 1

Curr

ent (

A)

Time (s)


262

Figure 6.14 Control current of different storey under Kobe earthquake

0 10 20 30 40 50

0

5

Storey 5

Curr

ent (

A)

0 10 20 30 40 50

0

5

Storey 4Cu

rren

t (A

)

0 10 20 30 40 50

0

5

Storey 3

Curr

ent (

A)

0 10 20 30 40 50

0

5

Storey 2

Curr

ent (

A)

0 10 20 30 40 50

0

5

Storey 1

Curr

ent (

A)

Time (s)


263

Figure 6.15 Control current of different storey under Hachinohe earthquake

0 5 10 15 20 25 30 35

0

5

Storey 5

Curr

ent (

A)

0 5 10 15 20 25 30 35

0

5

Storey 4Cu

rren

t (A

)

0 5 10 15 20 25 30 35

0

5

Storey 3

Curr

ent (

A)

0 5 10 15 20 25 30 35

0

5

Storey 2

Curr

ent (

A)

0 5 10 15 20 25 30 35

0

5

Storey 1

Curr

ent (

A)

Time (s)


264

Figure 6.16 Control current of different storey under Northridge earthquake

controlled SI can deliver the design intent to distribute deformation along the elevation

0 5 10 15 20 25 30

0

5

Storey 5

Curr

ent (

A)

0 5 10 15 20 25 30

0

5

Storey 4Cu

rren

t (A

)

0 5 10 15 20 25 30

0

5

Storey 3

Curr

ent (

A)

0 5 10 15 20 25 30

0

5

Storey 2

Curr

ent (

A)

0 5 10 15 20 25 30

0

5

Storey 1

Curr

ent (

A)

Time (s)


265

As shown in Figure 6.12, the relative displacement raises as the floor height develops.

Once again, the controlled SI system shows smallest base displacement in all five

isolation mechanisms. The optimised SI can also reduce base displacement on the basis

of passive BI and SI but the displacements of both controlled and optimised SI exceeds

the BI systems’ as the level becomes higher. Such phenomenon makes sense in that the

storey isolation system is much more flexible in the structure above ground while the base

isolation system is only flexible at the base level. It is worth paying attention that the

acceleration and displacement profiles of the BI systems are close to vertical lines under

all earthquakes, which indicates that the movement of superstructure in these cases can

be approximately regarded to a rigid body motion. The essence of the rigid body motion

lies in effects of protecting structural elements of the superstructure.

The control currents at different floors are shown in Figure 6.13 to Figure 6.16 when the

controlled SI is subjected to four earthquakes. It can be observed that, at all the floors, the

control currents are at high level at the beginning of the earthquake strike. The reason

behind such arrangement lies in that during normal situation, the structure should stay

relatively stiff to resist minor external disturbance such as wind load and only when

earthquake strikes, the isolators will start working according to the designated control law.

Another interesting discovery is that under all earthquakes, the switching frequency of

current is much higher in lower levels than upper levels, which indicates a decrease of

relative movement with the increase of structure elevation.

Table 6.4 Evaluative indices description Description Peak floor accel. Peak inter-storey drift Peak base shear

Formula

Description Peak base displacement RMS inter-storey drift RMS floor accel.

Formula

J2 maxt ,idi t

dimax

J4 maxtxb t xb

max


266

Table 6.5 Values of evaluative indices J1~J6 under four earthquakes with different isolation scenarios

El Centro earthquake

Passive-on BI Passive-off BI Optimised SI Passive SI Controlled SI

J1 50.26% 63.31% 25.27% 60.46% 23.48%

J2 193.00% 149.51% 320.25% 126.45% 88.16%

J3 65.82% 80.85% 33.55% 35.94% 26.84%

J4 98.25% 84.52% 238.39% 200.04% 73.41%

J5 206.69% 151.27% 276.96% 102.26% 34.98%

J6 58.62% 0.05% 7.74% 30.22% 6.55%

Kobe earthquake


J1 98.25% 84.52% 238.39% 200.04% 73.41%

J2 46.16% 46.04% 22.02% 44.37% 19.77%

J3 168.77% 114.67% 61.00% 68.51% 37.04%

J4 84.02% 63.82% 36.26% 82.11% 28.07%

J5 184.97% 58.15% 23.35% 46.67% 14.35%

J6 53.05% 0.11% 6.35% 29.75% 5.66%

Hachinohe earthquake


J1 31.58% 47.46% 16.07% 42.34% 22.45%

J2 113.52% 128.14% 231.58% 152.95% 112.62%

J3 41.14% 63.01% 21.78% 36.01% 17.04%

J4 57.72% 70.84% 159.83% 263.16% 67.11%

J5 95.06% 108.90% 197.95% 159.07% 50.90%

J6 28.41% 0.26% 7.41% 38.52% 6.61%

Northridge earthquake


J1 76.64% 81.24% 51.85% 92.33% 45.01%

J2 280.61% 228.41% 250.74% 333.44% 210.81%


267

Table 6.6 Values of evaluative indices J1~J6 under four earthquakes with different isolation scenarios (Cont’d)

Northridge earthquake


J3 101.88% 103.55% 67.52% 77.24% 53.40%

J4 170.84% 156.32% 176.05% 580.01% 167.85%

J5 245.95% 282.29% 193.02% 406.36% 89.90%

J6 62.20% 0.44% 15.41% 88.34% 14.62%

P.S. All the values listed in this table are obtained by comparing with corresponding

parameter of fixed base building

Six evaluative indices, i.e. peak and RMS of acceleration, inter-storey drift and base shear, are

adopted to further evaluate the performance of isolation systems (Table 6.4). Table 6.5 lists the

values of J1 to J6 of different isolation scenarios under four earthquakes. Since all the evaluative

indices are defined as a ratio between parameter of interest of an isolation scenario and that of the

fixed base building, a reduction is indicated when the value is smaller than 100% while am

amplification of the corresponding parameter is suggested with the criteria value greater than

100%. As summarised in Table 6.5, the controlled SI has smallest value in all evaluative indices

among the five isolation scenarios. The optimal SI achieves the second-best performance in

regards of the criteria, particularly in reducing floor acceleration and base shear. Nevertheless,

the passive-off BI has better performance than optimal SI in inter-storey drift suppression.

Moreover, all the isolation scenarios have a J2 greater than 100%, which is caused by the

amplification of base displacement (also counted as inter-storey drift at first level). As a result,

the fact that controlled SI has smallest J2 demonstrates that the controlled SI can effectively

resolve the excessive base displacement issue.


268

6.7 SUMMARY

In this chapter, an innovative storey isolation system utilising MRE isolators was

proposed. The proposed isolation system aims to address the issue of excessive base

displacement demand of a base isolation system by distributing the isolation efforts at

strategic locations alongside the superstructure instead of concentrating it at the base

level. Meanwhile, the storey isolation system is also able to cope with the situation where

the structure has different seismic requirements at specific levels. The adjustable shear

stiffness of the MRE isolators endows the storey isolation system large adaptability and

controllability to better suppress the seismic responses of the protected structure. NSGA-

II with DCD has been adopted to acquire optimisation of the storey isolation parameters.

To further improve the performance of storey isolation system, a Bang-Bang control law

is employed to determine the control current applied on the MRE isolator at each storey.

Comprehensive simulation studies have been conducted to compare the seismic

protection performances of the bare building, passive-on BI building, passive-off BI

building, passive-off controlled SI building, optimised SI building and Bang-Bang

controlled SI building. Simulation results indicate that the controlled and optimised storey

isolation system is capable of significantly mitigating the floor acceleration and base

displacement. Moreover, they effectively resolved the whipping effect problem in passive

SI systems.

Conclusions And Future Research

269

CHAPTER 7

CONCLUSIONS AND FUTURE RESEARCH

This research project was aimed at exploring a new frontier in the field of structural

control, intelligent structures and earthquake engineering by developing and concept-

proofing innovative approaches and techniques, namely MRE-based smart base isolation

system for real-time earthquake hazard mitigation of civil infrastructures. In particular,

the thesis addressed the pressing issues in experimental realisation of the real-time

controlled MRE base isolation system targeting the challenges and research gap identified

in based on the literature review. The major achievements of this study are summarised

in the following sections.

7.1 MRE BASE ISOLATOR MODELLING

This thesis proposed two forward models in Chapter 3, namely, Bouc-Wen model and

strain-stiffening model, which are capable of predicting the response of MRE base

isolator over a wide range of loading conditions and command current. The major task of

forward model is to capture the isolator’s nonlinear hysteresis for its implementation in

structural vibration control, which is perfectly accomplished by both models. The

parameters in Bouc-Wen model are identified by a genetic algorithm while the strain-

stiffening model is identified by solving a related linear least square (LS) problem. The

resemblance between the numerically predicted and experimentally measured responses

verifies that both developed parametric models can identify and grasp the nonlinear

dynamics, especially the strain-stiffening feature of the MRE isolator. The accuracy of

the two models is tested and Bouc-Wen model achieves an RMS error of 5.3194 while


270

the RMS error of the strain-stiffening model is 5.4935. The identification running time of

strain-stiffening model is considerably less than that of the Bouc-Wen model, which

indicates the computational efficiency in control application. Moreover, the study on the

dependence of the models to each parameter further improves the models, which provides

a comprehensive guidance on easier controlling and adjusting the proposed models. In

the study of parameters in each model, it is discovered that the parameters in Bouc-Wen

model only depend on the applied current (or magnetic field) while the parameters in

strain-stiffening model depend on not only current but also maximum displacement of

input excitation. Hence, it is worth pointing out that, although the precision of hysteresis

and Bouc-Wen models are fairly close, the application of strain-stiffening model in reality

is rather challenging since it is impossible to acquire knowledge of the maximal input

displacement. Such problem can be partially solved by taking an approximation of the

maximal displacement variable, but the precision of the model will be deteriorated.

An inverse model of MRE base isolator is also proposed in Chapter 3 to counteract the

nonlinearity and hysteresis brought into control system by the device. Due to the inherent

nonlinearity and hysteresis of the devices, it is challenging to obtain a reasonably

complicated mathematical model to describe the inverse dynamics of MRE base isolators

and hence to realise control synthesis of the MRE base isolation system. To this end, an

inverse model based on GA optimised GRNN is developed and evaluated. The superiority

of GRNN inverse model lies in fewer input variables requirement, faster training process

and prompt calculation response, which makes it suitable for online training and real-time

control. Testing results show that the proposed GRNN inverse model can accurately

predict the control current which is required to be applied on the isolator to generate

desired control force. Moreover, the GRNN inverse model is utilised to develop a control

strategy employing LQR controller for optimal control force calculation is conducted in

Chapter 5. Due to the inverse model’s prompt and precise prediction of required control

current to be applied on the MRE isolator, it is feasible to conduct the control of MRE


271

base isolation system in real time.

7.2 RESPONSE TIME OF MRE BASE ISOLATOR INVESTIGATION

Real-time control of the MRE isolators holds the key to unlock MRE material’s unique

characteristics, i.e. instantly changeable shear modulus in continuous and reverse fashion.

However, one of the critical issues for the applications of real-time control is the response

time delay of MRE vibration isolators, which may lead to degradation of control

performance and even instability of the control system.

In Chapter 4, inherent response time of the MRE isolator was defined and then identified

experimentally. Three approached were introduced to reduce the response time of the

MRE isolator, i.e. i) design and utilise a PWM servo current drive controlled by PI

controller instead of utilising open-loop constant voltage source; ii) arrange the large coil

with several identical coils and change the connection style of the small coils in the

electrical circuit; iii) propose an innovative field-quenching configuration of the identical

coils to drive adjacent coils with opposite current during falling time to eliminate the

influence of the residual magnetic field. The results show that the proposed approaches

are effective and promising. For example, the proposed approach is able to reduce the

force response time from 421ms to 52ms at rising and from 400ms to 75ms falling edges

respectively. Such a level of short response time of the MRE isolators demonstrates the

feasibility of application of real-time control and hence is the essential step on the

realisation of real-time control of the vibration suppression system based on the MRE

isolator.

7.3 CONTROL ALGORITHM FOR MRE BASE ISOLATION SYSTEM

To make full use of the innovative MRE base isolator in the design of smart base isolation

system, five control strategies have been proposed in Chapter 5, including LQR control


272

with GRNN inverse model, NSGA II optimised NFLC, Bang-Bang controller, frequency

controller and Lyapunov-based current selecting controller.

As discussed previously, the classic optimal control algorithms like LQR control may not

be suitable for the control of the MRE smart base isolation system unless a method to

avoid the influence of nonlinearity of the MRE isolator is applied. To this end, a control

strategy is proposed by combining the LQR controller with the GRNN inverse model.

A RBF neural network based fuzzy logic controller (RBF-NFLC) is also proposed in

Chapter 5. The RBF-NFLC has been proposed and intensively investigated due to its

superiority of calculation efficiency and robustness to the conventional FLC. To train the

NFLC, a NSGA-II with DCD is adopted as the optimisation method and the optimal

parameters of the NFLC, i.e. centre and width of each membership function of input

variables, output weight of each fuzzy rule.

Bang-Bang controller evolved from sliding mode control is then proposed to control the

MRE base isolator since it is suitable for a variable stiffness/damping control scenario.

The sliding surface is determined based on Lyapunov stability of the control system.

Moreover, also based on the Lyapunov function, an innovative current selection

algorithm is developed by sustaining the derivative of the Lyapunov function to be

smaller than zero.

In the end, a novel frequency control algorithm is developed to shift the fundamental

frequency of the structure away from the dominant frequency range of earthquakes. Such

design enables the building to avoid a resonant state in real-time according to the on-

coming spectrum of the earthquakes.

7.4 EXPERIMENTAL REALISATION OF MRE BASE ISOLATION

SYSTEM

With the proposed control strategies, the experimental realisation of MRE base isolation


273

system is then presented in Chapter 5, which includes: i) design of a three-storey shear

building model as testing bed; ii) system identification with software DIAMOND of the

three-storey building model and integrated MRE base isolation system which combines

the building with two MRE isolators; iii) experimental setup; iv) shake table testing of

the structure under different isolation scenarios.

The seismic protection performance of the proposed MRE base isolation system is then

demonstrated by an experimental testing comparing the responses of fixed base building,

passive-on and passive-off base isolated system and base isolated building controlled with

five controllers mentioned in last section. The numerical and experimental results are

firstly compared and a good agreement between them shows satisfactory accuracy of the

building’s and integrated structure’s models generated from system identification. The

results are analysed in terms of time histories of top floor acceleration, base displacement

and base acceleration; peak responses of floor acceleration, relative displacement, inter-

storey drift and floor shear; evaluative indices assessing the structural responses and

control requirements of the MRE isolator.

Generally, all the isolation systems can, to varying degrees, reduce the structural

responses of floor acceleration and inter-storey drift compared to the fixed base building.

However, the passive-on and passive-off isolation systems suffer from excessive base

displacement, which is hazardous to the device and may cause the overturning of

superstructure. The five controlled systems, in contrast, effectively resolved the issue of

exaggerated base displacement. Furthermore, the controlled MRE isolation systems can

further reduce the structural responses on the basis of passive systems and the one with

best performance can achieve more than 76% reduction in all evaluation criteria.

The evaluation of the five controllers is conducted by comparing the peak and RMS

values of significant parameters. The first criterion is the capability of reducing the floor

acceleration and inter-storey drift simultaneously since balancing these two parameters is

the major dilemma facing conventional base isolation system. Meanwhile, capability of


274

reducing base displacement is also of great interest. According to the test results, the

NFLC and Lyapunov achieve ideal suppression performance of both peak and RMS

values of acceleration, inter-storey drift and base displacement. The NFLC is able to

reduce the peak value to the most extent while the Lyapunov controller is slightly superior

to NFLC in RMS suppression. Compared to the previous two controllers, the Bang-Bang

and frequency controllers attained middle-ground performances while the LQR controller

achieved least reduction in responses of acceleration and inter-storey drift but presented

favourable base displacement control capability. Furthermore, the control force required

by each controller is also compared to demonstrate the efficiency of controller to achieve

ideal control performance. Comparing the two controllers obtaining best control

performance, it is discovered that the NFLC requires much smaller control force than

Lyapunov controller, which indicates a better serviceability of the MRE controller when

using the NFLC because smaller control force means more modest applied current on the

isolator. Finally, the performance of NFLC exhibits the least dependence on the external

excitation, which shows the best adaptability of the system to diverse and unpredictable

earthquakes.

7.5 STOREY MRE ISOLATION SYSTEM

In the attempt to resolve the base isolation’s inherent issues, several other isolation

techniques have been proposed, including segmental building, additional storey isolation

(ASI) and mid-storey isolation system, etc. However, such techniques have their own

flaws, among which whipping effect is the most obvious one. Moreover, due to their

inherent passive nature, all these techniques, including traditional base isolation system,

show their defects in incapability to adjust their isolation frequency to cope with the

unpredictable and diverse nature of earthquakes.

To this end, a storey isolation system utilising the MRE base isolator is proposed in

Chapter 6 by inserting the MRE isolator between adjacent floors, which can be recognised


275

as a combination and extension of segmental building and mid-storey isolation system.

Therefore, the storey isolation system acquires changeable lateral stiffness, which allows

it to change the structural properties and thus adapt to various disturbances. By

interpolating the isolation system into different levels of the structure, the storey isolation

system distributes the flexibility along the entire building which was concentrated at the

base level in the base isolation case and at a certain level in case of mid-storey isolation.

An NSGA-II was adopted to explore the best design parameters at each storey isolation

level when subjected to different earthquake excitations. As for the control method, a

Bang-Bang controller is utilised at each storey isolator to determine the current applied

at each control instant according to the relative movement between the adjacent floors.

Comparative numerical studies have been conducted using a five-storey benchmark

building model to evaluate the seismic protection performance of the fixed-based

building, passive base-isolated building, passive storey-isolated building, optimal storey-

isolated building and Bang-Bang controlled storey isolation system. Simulation results

indicate that both optimal and controlled storey isolation systems have considerably

superior vibration suppression performance than the other systems, with controlled

system being slightly better than the optimised one.

7.6 SUGGESTIONS FOR FUTURE WORK

7.6.1 Optimisation of Coil Configuration for Further Response Time

Reduction

To further reduce the response time of MRE isolator for better control synthesis, the

design of MRE isolator, especially the configuration of the coils, needs to be optimised.

For instance, as elaborated in Chapter 4, to reduce the time at fall edge, half of the coils

are used to generate the opposite magnetic field to cancel out the effect of the residual

magnetism. Hence, to achieve the same magnetic flux across the MRE material, twice the


276

current needs to be applied to the solenoid since only half of the coils are working during

normal time. In fact, according to the control law in field-quenching configuration, the

quenching coils are applied with full bus voltage when it comes to the fall edge to generate

a massive opposite magnetic field and thus reduce the current in the solenoid to the

desired value as soon as possible. Hence, it is not necessary that half of the coils be all

utilised as the quenching coil. To this end, the configuration of coils needs to be improved

and optimised to enhance the energy efficiency and further reduce response time of the

isolator. That means, the number of coils working at quenching condition, the bus voltage

and even the design of the laminated MRE structure need to be optimised to improve the

response time reduction performance. Furthermore, a dynamic simulation of magnetic

field in the isolator, especially on the cross-section of the laminated structure, needs to be

realised when the isolator is subjected to changing current.

7.6.2 Further Development of Control Algorithm

Real-time control is critical in capitalising the uniqueness of the MRE isolator to achieve

good seismic protection performance. More unconventional control algorithms should be

further explored. This thesis has already proposed control strategies based on either

classic optimal control like LQR control or algorithms averting the influence of isolator’s

nonlinearity like NFLC. Nevertheless, more straightforward control method may be

developed if we look at the working principle of the base isolation system. As mentioned,

the working principle of base isolation system lies in reducing lateral stiffness of the

foundation and thus shifting the natural frequency to avoid resonance to the input

excitation. As a matter of fact, this working mechanism can cut off the energy

transmission path between the structure and the ground. More specifically, the

transmissibility between the structural elements and ground needs to be maintained at a

low level at every time instant to achieve great control performance. To this end, a control

method, which can take advantage of the adaptive stiffness of the MRE isolator to tune

the structural transmissibility in each and every moment, has very considerable potential


277

to the ultimate solution of seismic isolation by eliminating the energy transmitted into the

structure via the base isolation level. More effort should be dedicated to the development

of a transmissibility control method. Meanwhile, in consideration of the inevitable time

delay in the control system, a new control algorithm that avoids rapid or frequent current

change or is able to compensate time delay should be developed in future study.

7.6.3 Optimisation of MRE Isolator Placement in Storey Isolation System

In this thesis, the control current applied on each MRE isolator in the storey isolation

system is optimised by the NSGA-II with DCD. However, when designing the storey

isolation system in high-rise structures, it is neither time/economically efficient nor

necessary to install the isolation system at each level of the structure. Therefore,

optimisations of the placement of MRE isolators in the structure can be an important

research in the future study. Meanwhile, the structure is simplified to a 2D model to

reduce the complexity of the system in this research but more complicated and

asymmetric architectural designs will be encountered in the real world application. As a

result, a 3D design of the isolation system, either base isolation or storey isolation, is of

great need. In this case, the MRE isolator could exert more influence to eliminate the

torsional motion as well as rocking movement of the structure.

7.6.4 Experimental Investigation of the MRE Base Isolation System on

Full-Scaled Civil Infrastructures

This thesis has already investigated and experimental evaluated the MRE isolation

system’s seismic protection performance on a three-storey building model subjected to

various benchmark earthquakes. To further demonstrate the feasibility of the MRE

isolator in civil applications, experimentations on a full-scaled structure equipped with

the MRE base isolation system would be worthwhile to conduct. This will involve the

design or selection of a widely acknowledged structure model, resolution of energy


278

supplement issue for the isolator, improvement of vertical capacity of individual isolator

or arrangement of MRE isolators at the base level to support the self-weight of the larger

scaled structure.

Reference

279

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APPENDIX

Appendix A PEAK RESPONSES UNDER FOUR EARTHQUAKES

Figure A-1 Peak responses under four earthquakes (scaling factor = 5%)


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0.2

Rel

ativ

e di

spla

cem

ent (

mm




0.1

0.2

0.3

0.4

0.5

Peak

shea

r/W



Appendix

296

Appendix B EVALUATIVE INDICES

Figure B-1 Evaluative indices J1 ~ J6 under four earthquakes (earthquake scaling factor = 5%)

J1 J2 J3 J4 J5 J60

20

40

60

80

100

Inde

x va

lue/



J1 J2 J3 J4 J5 J60

50

100

150

Inde

x va

lue/

%

Kobe Earthquake


J1 J2 J3 J4 J5 J60

50

100

150

Inde

x va

lue/

%



J1 J2 J3 J4 J5 J60

20

40

60

80

Inde

x va

lue/

%



Appendix

297


J1 J2 J3 J4 J5 J60

20

40

60

80

100

Inde

x va

lue/



J1 J2 J3 J4 J5 J60

50

100

150

Inde

x va

lue/

%

Kobe Earthquake


J1 J2 J3 J4 J5 J60

50

100

150

Inde

x va

lue/

%



J1 J2 J3 J4 J5 J60

20

40

60

80

Inde

x va

lue/

%



Appendix

298


J1 J2 J3 J4 J5 J60

20

40

60

80

100

Inde

x va

lue/



J1 J2 J3 J4 J5 J60

50

100

150

Inde

x va

lue/

%

Kobe Earthquake


J1 J2 J3 J4 J5 J60

50

100

150

Inde

x va

lue/

%



J1 J2 J3 J4 J5 J60

20

40

60

80

Inde

x va

lue/

%



Appendix

299

Figure B-4 Evaluative indices J7 ~ J9 at worst case scenario (earthquake scaling factor = 5%)

Figure B-5 Evaluative indices J7 ~ J9 at worst case scenario (earthquake scaling factor = 10%)

Figure B- 6 Evaluative indices J7 ~ J9 at worst case scenario (earthquake scaling factor = 20%)

0 10 20 30 40

Lyapunov

Frequency

LQR

Bang-Bang

NSGA-NFLC

Passive-on

Value of J7 (%)0 2 4 6 8

Value of J8 (%)0 2 4 6

Value of J9 (%)

0 20 40 60 80

Lyapunov

Frequency

LQR

Bang-Bang

NSGA-NFLC

Passive-on

Value of J7 (%)0 2 4 6 8

Value of J8 (%)0 5 10

Value of J9 (%)

0 50 100 150

Lyapunov

Frequency

LQR

Bang-Bang

NSGA-NFLC

Passive-on

Value of J7 (%)0 2 4 6 8

Value of J8 (%)0 5 10 15 20

Value of J9 (%)

Appendix

300

Appendix C SELECTED TIME HISTORY RESPONSES

Figure C-1 Time history of top floor acceleration with different control algorithms (0.05 El-

Centro)

0 10 20 30 40 50-0.04

-0.02

0

0.02

0.04

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.04

-0.02

0

0.02

0.04

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.05

0

0.05

Acc

eler

atio

n (g

)

Passive-offLQR

0 10 20 30 40 50-0.04

-0.02

0

0.02

0.04

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.04

-0.02

0

0.02

0.04

Time (s)

Acc

eler

atio

n (g

)

Passive-offLyapunov

Appendix

301


Centro)

0 10 20 30 40 50-0.1

-0.05

0

0.05

0.1A

ccel

erat

ion

(g)


0 10 20 30 40 50-0.1

-0.05

0

0.05

0.1

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.1

-0.05

0

0.05

0.1

Acc

eler

atio

n (g

)

Passive-offLQR

0 10 20 30 40 50-0.1

-0.05

0

0.05

0.1

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.1

-0.05

0

0.05

0.1

Time (s)

Acc

eler

atio

n (g

)

Passive-offLyapunov

Appendix

302


Centro)

0 10 20 30 40 50-0.2

-0.1

0

0.1

0.2

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.2

-0.1

0

0.1

0.2

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.2

-0.1

0

0.1

0.2

Acc

eler

atio

n (g

)

Passive-offLQR

0 10 20 30 40 50-0.2

-0.1

0

0.1

0.2

Acc

eler

atio

n (g

)


0 10 20 30 40 50-0.2

-0.1

0

0.1

0.2

Time (s)

Acc

eler

atio

n (g

)

Passive-offLyapunov

Appendix

303

Figure C-4 Time history of base displacement with different control algorithms (0.05 El-Centro)

0 10 20 30 40 50

-5

0

5

Dis

plac

emen

t (m

m)


0 10 20 30 40 50

-5

0

5

Dis

plac

emen

t (m

m)


0 10 20 30 40 50-5

0

5

Dis

plac

emen

t (m

m)

Passive-offLQR

0 10 20 30 40 50-5

0

5

Dis

plac

emen

t (m

m)


0 10 20 30 40 50

-5

0

5

Time (s)

Dis

plac

emen

t (m

m)

Passive-offLyapunov

Appendix

304


0 10 20 30 40 50

-10

-5

0

5

10

Dis

plac

emen

t (m

m)


0 10 20 30 40 50

-10

-5

0

5

10

Dis

plac

emen

t (m

m)


0 10 20 30 40 50-10

-5

0

5

10

Dis

plac

emen

t (m

m)

Passive-offLQR

0 10 20 30 40 50-10

-5

0

5

10

Dis

plac

emen

t (m

m)


0 10 20 30 40 50-10

-5

0

5

10

Time (s)

Dis

plac

emen

t (m

m)

Passive-offLyapunov

Appendix

305


0 10 20 30 40 50-20

-10

0

10

20

Dis

plac

emen

t (m

m)


0 10 20 30 40 50-20

-10

0

10

20

Dis

plac

emen

t (m

m)


0 10 20 30 40 50-20

-10

0

10

20

Dis

plac

emen

t (m

m)

Passive-offLQR

0 10 20 30 40 50-20

-10

0

10

20

Dis

plac

emen

t (m

m)


0 10 20 30 40 50-20

-10

0

10

20

Time (s)

Dis

plac

emen

t (m

m)

Passive-offLyapunov

Appendix

306

Appendix D CONTROL FORCE AND CORRESPONDING CURRENT

Figure D-1 Control force and corresponding control current with frequency control (Earthquake


0 2 4 6 8 10

-300

0

300

Con

trol f

orce

(N)

Kobe Earthquake


0 2 4 6 8 10

-100

0

100

Con

trol f

orce

(N)



0 2 4 6 8 10

-150

0

150

Time (s)

Con

trol f

orce

(N)



0 2 4 6 8 10

-100

0

100C

ontro

l for

ce (N

)El Centro Earthquake


Cur

rent

(A)

0

5

Cur

rent

(A)

0

5

Cur

rent

(A)

0

5

Cur

rent

(A)

0

5

Appendix

307



0 2 4 6 8 10

-150

0

150

Con

trol f

orce

(N)



0 2 4 6 8 10

-600

0

600

Con

trol f

orce

(N)

Kobe Earthquake


0 2 4 6 8 10

-100

0

100

Con

trol f

orce

(N)



0 2 4 6 8 10

-300

0

300

Time (s)

Con

trol f

orce

(N)



Cur

rent

(A)

0

5

Cur

rent

(A)

0

5

Cur

rent

(A)

0

5

Cur

rent

(A)

0

5

Appendix

308



0 2 4 6 8 10

-250

0

250

Con

trol f

orce

(N)



0 2 4 6 8 10

-1000

0

1000

Con

trol f

orce

(N)

Kobe Earthquake


0 2 4 6 8 10

-200

0

200

Con

trol f

orce

(N)



0 2 4 6 8 10

-600

0

600

Time (s)

Con

trol f

orce

(N)



Cur

rent

(A)

0

5

Cur

rent

(A)

0

5

Cur

rent

(A)

0

5

Cur

rent

(A)

0

5

Documents

Investigation of Adaptive Base Isolation System Utilising Magnetorheological Elastomer · 2017-12-01 · Investigation of Adaptive Base Isolation System Utilising Magnetorheological