Debiprasad Ghosh Ph D Thesis

Structural Health Monitoring ofComposite Structures using

Magnetostrictive Sensors and Actuators.

A ThesisSubmitted for the Degree ofDoctor of Philosophyin the Faculty of Engineering

ByDebiprasad Ghosh

Department of Aerospace EngineeringIndian Institute of Science

Bangalore - 560 012India

July 2006

Declaration

I declare that the thesis entitled Structural Health Monitoring of Composite

Structures Using Magnetostrictive Sensors and Actuators submitted by me for

the degree of Doctor of Philosophy in the Faculty of Engineering of Indian Institute of

Science, Bangalore did not form the subject matter of any other thesis submitted by me

for any outside degree, and the original work done by me and incorporated in this thesis

is entirely done at the Indian Institute of Science, Bangalore.

Bangalore

July 2006

Debiprasad Ghosh

Dedicated to

My Extended Family Members

and

My Teachers

Acknowledgements

I express my deep sense of gratitude and appreciation to Prof. S. Gopalakrishnan for

his excellent supervision, active participation, sustained interest and critical suggestions,

without which the thesis would not have come into its present shape. He gave me the

highest freedom that any advisor can allow for his student. He has always been very kind

and encouraging and his door was always open to me.

I am grateful to Prof. A. V. Krishna Murti and Dr. M. Kumar, for giving me the

opportunity to work with them and many of their valuable suggestions.

It is a great honour to have the opportunity to express my profound gratitude to Prof.

B. Dattaguru and Prof. T.S. Ramamurthy for the encouragement they offered to me

throughout my stay in the Department.

I thank Prof. B.N. Raghunandan, Chairman, Department of Aerospace Engineering, for

providing the department facilities and solving other official issues. I am also thankful

to all the scientific and administrative staff of the department throughout my study and

research work.

I thank Prof. N. Balakrishnan and Prof. S.M. Rao, former Chairman, SERC, for providing

all the computational facilities. I also thank all the present and former staff of SERC, for

their numerous help.

I am grateful to Prof. Manohar, Prof. Chandrakishan, Department of Civil Enginnering,

IISc, for their excellent teaching in the course of structural dynamics and finite element

analysis.

I thank Prof. Basudeb Datta, Department of Mathematics, IISc, for lending me the book

Nonlinear electromechanical effects and applications.

I thank my colleagues Dr. Joydeban, Dr. Krishna Lok Singh, Dr. K.V.N. Gopal, Dr.

Debiprosad Roy Mahapatra, Adris Bisi, Dr. Abir Chakraborty, Mira Mitra, Gudla, Power,

Guru, Promad, Niranjan, Murugan and Narashima for their numerous help throughout my

research work. I am thankful to my colleagues Sivaganyam for his valuable contributions

i

and ideas while working together on numerous research problems.

I am grateful to the families of Prof. Aloknath Chakraborty, Prof. Chandra and Prof.

Phoolan Prasad for their kind help at my off-campus staying.

I am grateful to Debiprasad Panda, Abhijit Chakraborty (C), Sauvikda, Abhijit Das

(barda), Subhas Pal of North Bengal University, Argha Nandi of Jadavpure Univer-

sity, Nandan Pakhira, Abhijit Chaudhuri (sonu), Abhijit Sarkar (galu), Alakesh (bhuto),

Amitabha, Bikash dey, Goutam (kanu), Nilanjan, Subhra, Suchi, Himadri Nandan Bar,

Joysurya (chhana), Sabita, Pinaki Biswas, Priyanko Ghosh, Rajesh Murarka, Saikat

(mama), Samit Baxi, Sarmistha, Sandipan (Mota), Saugata chakraborty, Bhat mama,

Santanu Biswas, Debashish Sarkar, Sayan Gupta, Sunetra Sarkar, Shyama, Siladitya Pal,

Sitikantha Roy, Sonjoy Das (soda), Dipankar, Santanu, Pallav, Luna, Kaushik (bachcha),

Suppriyo, Rajib (pagla), Sovan (bachcha), Surajit Midya, Subhankar, Subimal Ghosh,

Ayas, Rangeet, Ansuman, Sagarika, Tapas, Dipanyita, Pankaj, Tripti, Arnab and Ripa

who made my stay in the campus most memorable one.

Last but not the least I would like to express deep respect for my parents, parents-in-law,

my wife, my daughter and the other family members for their endearing support during

my tenure in IISc.

SYNOPSIS

Structural Health Monitoring of Composite

Structures Using Magnetostrictive Sensors and

Actuators.

Ph.D Thesis

Debiprasad Ghosh

S.R. No. 115199406

Department of Aerospace Engineering

Indian Institute of Science

Bangalore - 560012, INDIA

Fiber reinforced composite materials are widely used in aerospace, mechanical, civil and

other industries because of their high strength-to-weight and stiffness-to-weight ratios.

However, composite structures are highly prone to impact damage. Possible types of

defect or damage in composite include matrix cracking, fiber breakage, and delamination

between plies. In addition, delamination in a laminated composite is usually invisible. It

is very difficult to detect it while the component is in service and this will eventually lead

to catastrophic failure of the structure. Such damages may be caused by dropped tools

and ground handling equipments. Damage in a composite structure normally starts as a

tiny speckle and gradually grows with the increase in load to some degree. However, when

such damage reaches a threshold level, serious accident can occur. Hence, it is important

to have up-to-date information on the integrity of the structure to ensure the safety and

reliability of composite components, which require frequent inspections to identify and

quantify damage that might have occurred even during manufacturing, transportation or

storage.

How to identify a damage using the obtained information from a damaged compos-

ite structure is one of the most pivotal research objectives. Various forms of structural

damage cause variations in structural mechanical characteristics, and this property is ex-

tensively employed for damage detection. Existing traditional non-destructive inspection

techniques utilize a variety of methods such as acoustic emission, C-scan, thermography,

shearography and Moir interferometry etc. Each of these techniques is limited in accuracy

and applicability. Most of these methods require access to the structure. They also require

a significant amount of equipment and expertise to perform inspection. The inspections

are typically based on a schedule rather than based on the condition of the structure.

Furthermore, the cost associated with these traditional non-destructive techniques can

be rather prohibitive. Therefore, there is a need to develop a cost-effective, in-service,

diagnostic system for monitoring structural integrity in composite structures.

Structural health monitoring techniques based on dynamic response is being used

for several years. Changes in lower natural frequencies and mode shapes with their special

derivatives or stiffness/flexibility calculation from the measured displacement mode shapes

are the most common parameters used in identification of damage. But the sensitivity of

these parameters for incipient damage is not satisfactory. On the other hand, for in service

structural health monitoring, direct use of structural response histories are more suitable.

However, they are very few works reported in the literature on these aspects, especially

for composite structures, where higher order modes are the ones that get normally excited

due to the presence of flaws.

Due to the absence of suitable direct procedure, damage identification from response

histories needs inverse mapping; like artificial neural network. But, the main difficulty in

such mapping using whole response histories is its high dimensionality. Different general

purpose dimension reduction procedures; like principle component analysis or indepen-

dent component analysis are available in the literature. As these dimensionally reduced

spaces may loose the output uniqueness, which is an essential requirement for neural

network mapping, suitable algorithms for extraction of damage signature from these re-

sponse histories are not available. Alternatively, fusion of trained networks for different

partitioning of the damage space or different number of dimension reduction technique,

can overcome this issue efficiently. In addition, coordination of different networks trained

with different partitioning for training and testing samples, training algorithms, initial

conditions, learning and momentum rates, architectures and sequence of training etc., are

some of the factors that improves the mapping efficiency of the networks.

The applications of smart materials have drawn much attention in aerospace, civil,

mechanical and even bioengineering. The emerging field of smart composite structures

offers the promise of truly integrated health and usage monitoring, where a structure can

sense and adapt to their environment, loading conditions and operational requirements,

and materials can self-repair when damaged. The concept of structural health monitoring

using smart materials relies on a network of sensors and actuators integrated with the

structure. This area shows great promise as it will be possible to monitor the structural

condition of a structure, throughout its service lifetime. Integrating intelligence into

the structures using such networks is an interesting field of research in recent years.

Some materials that are being used for this purpose include piezoelectric, magnetostrictive

and fiber-optic sensors. Structural health monitoring using, piezoelectric or fiber-optic

sensors are available in the literature. However, very few works have been reported in the

literature on the use of magnetostrictive materials, especially for composite structures.

Non contact sensing and actuation with high coupling factor, along with other prop-

erties such as large bandwidth and less voltage requirement, make magnetostrictive ma-

terials increasingly popular as potential candidates for sensors and actuators in structural

health monitoring. Constitutive relationships of magnetostrictive material are represented

through two equations, one for actuation and other for sensing, both of which are coupled

through magneto-mechanical coefficient. In existing finite element formulation, both the

equations are decoupled assuming magnetic field as proportional to the applied current.

This assumption neglects the stiffness contribution coming from the coupling between

mechanical and magnetic domains, which can cause the response to deviate from the time

response. In addition, due to different fabrication and curing difficulties, the actual prop-

erties of this material such as magneto-mechanical coupling coefficient or elastic modulus,

may differ from results measured at laboratory conditions. Hence, identification of the

material properties of these embedded sensor and actuator are essential at their in-situ

condition.

Although, finite element method still remains most versatile, accurate and generally

applicable technique for numerical analysis, the method is computationally expensive for

wave propagation analysis of large structures. This is because for accurate prediction, the

finite element size should be of the order of the wavelength, which is very small due to high

frequency loading. Even in health monitoring studies, when the flaw sizes are very small

(of the order of few hundred microns), only higher order modes will get affected. This

essentially leads to wave propagation problem. The requirement of cost-effective compu-

tation of wave propagation brings us to the necessity of spectral finite element method,

which is suitable for the study of wave propagation problems. By virtue of its domain

transfer formulation, it bypasses the large system size of finite element method. Further,

inverse problem such as force identification problem can be performed most conveniently

and efficiently, compared to any other existing methods. In addition, spectral element

approach helps us to perform force identification directly from the response histories mea-

sured in the sensor. The spectral finite element is used widely for both elementary and

higher order one or two dimensional waveguides. Higher order waveguides, normally gives

a behavior, where a damping mode (evanescent) will start propagating beyond a certain

frequency called the cut-off frequency. Hence, when the loading frequencies are much be-

yond their corresponding cut-off frequencies, higher order modes start propagating along

the structure and should be considered in the analysis of wave propagations.

Based on these considerations, three main goals are identified to be pursued in this

thesis. The first is to develop the constitutive relationship for magnetostrictive sensor

and actuator suitable for structural analysis. The second is the development of differ-

ent numerical tools for the modelling the damages. The third is the application of these

developed elements towards solving inverse problems such as, material property identifica-

tion, impact force identification, detection and identification of delamination in composite

structure.

The thesis consists of four parts spread over six chapters. In the first part, linear,

nonlinear, coupled and uncoupled constitutive relationships of magnetostrictive materials

are studied and the elastic modulus and magnetostrictive constant are evaluated from

the experimental results reported in the literature. In uncoupled model, magnetic field

for actuator is considered as coil constant times coil current. The coupled model is

studied without assuming any explicit direct relationship with magnetic field. In linear

coupled model, the elastic modulus, the permeability and magnetostrictive coupling are

assumed as constant. In nonlinear-coupled model, the nonlinearity is decoupled and solved

separately for the magnetic domain and mechanical domain using two nonlinear curves,

namely the stress vs. strain curve and magnetic flux density vs. magnetic field curve.

This is done by two different methods. In the first, the magnetic flux density is computed

iteratively, while in the second, artificial neural network is used, where a trained network

gives the necessary strain and magnetic flux density for a given magnetic field and stress

level.

In the second part, different finite element formulations for composite structures

with embedded magnetostrictive patches, which can act both as sensors and actuators,

is studied. Both mechanical and magnetic degrees of freedoms are considered in the

formulation. One, two and three-dimensional finite element formulations for both coupled

and uncoupled analysis is developed. These developed elements are then used to identify

the errors in the overall response of the structure due to uncoupled assumption of the

magnetostrictive patches and shown that this error is comparable with the sensitivity

of the response due to different damage scenarios. These studies clearly bring out the

requirement of coupled analysis for structural health monitoring when magnetostrictive

sensor and actuator are used.

For the specific cases of beam elements, super convergent finite element formulation

for composite beam with embedded magnetostrictive patches is introduced for their spe-

cific advantages in having superior convergence and in addition, these elements are free

from shear locking. A refined 2-node beam element is derived based on classical and first

order shear deformation theory for axial-flexural-shear coupled deformation in asymmet-

rically stacked laminated composite beams with magnetostrictive patches. The element

has an exact shape function matrix, which is derived by exactly solving the static part

of the governing equations of motion, where a general ply stacking is considered. This

makes the element super convergent for static analysis. The formulated consistent mass

matrix, however, is approximate. Since the stiffness is exactly represented, the formulated

element predicts natural frequency to greater level of accuracy with smaller discretiza-

tion compared to other conventional finite elements. Finally, these elements are used for

material property identification in conjunction with artificial neural network.

In the third part, frequency domain analysis is performed using spectrally formu-

lated beam elements. The formulated elements consider deformation due to both shear

and lateral contraction, and numerical experiments are performed to highlight the higher

order effects, especially at high frequencies. Spectral element is developed for modelling

wave propagation in composite laminate in the presence of magnetostrictive patches. The

element, by virtue of its frequency domain formulation, can analyze very large domain

with nominal cost of computation and is suitable for studying wave propagation through

composite materials. Further more, identification of impact force is performed form the

magnetostrictive sensor response histories using these spectral elements.

In the last part, different numerical examples for structural health monitoring are

directed towards studying the responses due to the presence of the delamination in the

structure; and the identification of the delamination from these responses using artificial

neural network. Neural network is applied to get structural damage status from the

finite element response using its mapping feature, which requires output uniqueness. To

overcome the loss of output uniqueness due to the dimension reduction, damage space

is divided into different overlapped zones and then different networks are trained for

these zones. Committee machine is used to coordinate among these networks. Next, a

five-stage hierarchy of networks is used to consider partitioning of damage space, where

different dimension reduction algorithms and different partitioning between training and

testing samples are used for better mapping for the identification procedure. The results

of delamination detection for composite laminate show that the method developed in this

thesis can be applied to structural damage detection and health monitoring for various

industrial structures.

This thesis collectively addresses all aspects pertaining to the solution of inverse

problem and specially the health monitoring of composite structures using magnetostric-

tive sensor and actuator. In addition, the thesis discusses the necessity of higher order

theory in the high frequency analysis of wave propagation. The thesis ends with brief sum-

mary of the tasks accomplished, significant contribution made to the literature and the

future applications where the proposed methods addressed in this thesis can be applied.

List of Publications

Journal papers

1. Ghosh D. P. and Gopalakrishnan S.; Role of Coupling in constitutive relationships

of magnetostrictive material. Computers, Materials & Continua, Vol.-1, No. 3, pp.

213-228

2. Ghosh D. P. and Gopalakrishnan S.; Coupled analysis of composite laminate with

embedded magnetostrictive patches. Smart Materials and Structures 14 (2005)

1462-1473.

3. Ghosh D. P. and Gopalakrishnan S.; Super convergent finite element analysis of

composite beam with embedded magnetostrictive patches. Composite Structures

[in press].

4. Ghosh D. P. and Gopalakrishnan S.; Spectral finite element analysis of composite

beam with embedded magnetostrictive patches considering arbitrary order of shear

deformation and arbitrary order of poisson contraction. will be communicated

Conference papers

1. Ghosh D. P. and Gopalakrishnan S.; Structural health monitoring in a composite

beam using magnetostrictive material through a new FE formulation. In Proceed-

ings of SPIE vol. 5062 Smart Materials, Structures and Systems, edited by San-

geneni Mohan, B. Dattaguru, S. Gopalakrishnan, (SPIE, Bellingham, WA, 2003)

and page number 704-711. ; Dec12-14, 2002, Indian Institute of Science, Banga-

lore, India.

2. Ghosh D. P. and Gopalakrishnan S.; Time Domain Structural Health Monitoring

for Composite Laminate Using Magnetostrictive Material with ANN Modeling for

ix

Nonlinear Actuation Properties. Proceedings of INCCOM-2 & XII NASAS Sec-

ond ISAMPE national conference on composites and twelfth national seminar on

aerospace structures Sep 05-06, 2003, Bangalore, Karnataka, India

3. Ghosh D. P. and Gopalakrishnan S.; Identification of delamination size and location

of composite laminate from time domain data of magnetostrictive sensor and actu-

ator using artificial neural network. Proceeding of the SEC 2003, December 12-14,

structural engineering convention an international meet.

4. Ghosh D. P. and Gopalakrishnan S.; Time domain Structural Health Monitoring

with magnetostrictive patches using five-stage hierarchical neural network. Pro-

ceeding of the ICASI-2004, July 14-17,International Conference on Advances in

Structural Integrity.

5. Chakraborty A.; Ghosh D. P. and Gopalakrishnan S.; Damage Modelling And De-

tection Using Spectral Plate Element, International Congress on Computational

Mechanics and Simulation (ICCSM-2004). 9-12 December, 2004 at Indian Institute

of Technology Kanpur.

Contents

Acknowledgements i

SYNOPSIS iii

List of Publications ix

List of Tables xix

List of Figures xxi

1 Introduction 1

1.1 Motivation and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Background: Structural Health Monitoring . . . . . . . . . . . . . . . . . . 2

1.2.1 Application Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1.1 Aerospace Application . . . . . . . . . . . . . . . . . . . . 4

1.2.1.2 Wind Turbine Blade Application . . . . . . . . . . . . . . 4

1.2.1.3 Bridge Structures . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1.4 Under Ground Structure . . . . . . . . . . . . . . . . . . . 5

1.2.1.5 Concrete Structure . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1.6 Composite Structure . . . . . . . . . . . . . . . . . . . . . 6

1.2.2 Sensors and Actuators . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.2.1 Piezoelectric Material . . . . . . . . . . . . . . . . . . . . 7

1.2.2.2 Optical Fiber . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.2.3 Vibrometer . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.2.4 Magnetostrictive Material . . . . . . . . . . . . . . . . . . 8

1.2.2.5 Nano sensor . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.2.6 Comparisons of different sensors . . . . . . . . . . . . . . . 9

xi

xii Contents

1.2.3 Solution Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.2.3.1 Static Domain . . . . . . . . . . . . . . . . . . . . . . . . 11

1.2.3.2 Modal domain . . . . . . . . . . . . . . . . . . . . . . . . 11

1.2.3.3 Frequency Domain . . . . . . . . . . . . . . . . . . . . . . 16

1.2.3.4 Time-Frequency Domain . . . . . . . . . . . . . . . . . . . 17

1.2.3.5 Impedance Domain . . . . . . . . . . . . . . . . . . . . . . 18

1.2.3.6 Time Domain . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.2.4 Levels of SHM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.2.4.1 Unsupervised SHM . . . . . . . . . . . . . . . . . . . . . . 19

1.2.4.2 Supervised SHM . . . . . . . . . . . . . . . . . . . . . . . 20

1.2.5 Damage Modelling in Composite Laminate . . . . . . . . . . . . . . 21

1.2.5.1 Matrix cracking . . . . . . . . . . . . . . . . . . . . . . . . 21

1.2.5.2 Techniques for Modelling of Delamination . . . . . . . . . 23

1.2.5.3 Multiple Delaminations . . . . . . . . . . . . . . . . . . . 25

1.2.6 Effective SHM Methodology . . . . . . . . . . . . . . . . . . . . . . 26

1.3 Background: Magnetostrictive Materials . . . . . . . . . . . . . . . . . . . 26

1.3.1 Initial History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

1.3.2 Rare Earth Material Era . . . . . . . . . . . . . . . . . . . . . . . . 28

1.3.2.1 Giant Magnetostrictive Materials . . . . . . . . . . . . . . 28

1.3.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.3.3.1 Thin Film and MEMS . . . . . . . . . . . . . . . . . . . . 29

1.3.3.2 Thick Film, Magnetostrictive Particle Composite . . . . . 30

1.3.4 Structural Applications . . . . . . . . . . . . . . . . . . . . . . . . . 30

1.3.4.1 Vibration and Noise Suppression . . . . . . . . . . . . . . 30

1.4 Artificial Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

1.4.1 The Biological Inspiration . . . . . . . . . . . . . . . . . . . . . . . 32

1.4.2 The Basic Artificial Model . . . . . . . . . . . . . . . . . . . . . . . 32

1.4.3 Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . 33

1.4.4 Neural Network Types . . . . . . . . . . . . . . . . . . . . . . . . . 34

1.4.4.1 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

1.4.4.2 Connection Type . . . . . . . . . . . . . . . . . . . . . . . 34

1.4.4.3 Learning Methods . . . . . . . . . . . . . . . . . . . . . . 34

1.4.4.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . 35

1.4.5 Multi Layer Perceptrons (MLP) . . . . . . . . . . . . . . . . . . . . 35

Contents xiii

1.4.5.1 Transfer / Activation Function . . . . . . . . . . . . . . . 36

1.4.6 The Back-propagation Algorithm . . . . . . . . . . . . . . . . . . . 37

1.4.6.1 Training of BP ANN . . . . . . . . . . . . . . . . . . . . . 37

1.4.6.2 Sequential Mode . . . . . . . . . . . . . . . . . . . . . . . 39

1.4.6.3 Batch Mode . . . . . . . . . . . . . . . . . . . . . . . . . . 39

1.4.6.4 Validation of Trained Network . . . . . . . . . . . . . . . . 39

1.4.6.5 Execution of Trained Network . . . . . . . . . . . . . . . . 40

1.4.7 Applications for Neural Networks . . . . . . . . . . . . . . . . . . . 40

1.5 Objectives and Organization of the Thesis . . . . . . . . . . . . . . . . . . 41

2 Constitutive relationship of Magnetostrictive Materials 43

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.1.1 Existing Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.1.1.1 Coupling between Actuation and Sensing Equations . . . . 44

2.1.1.2 Nonlinearity of Magnetostrictive Materials . . . . . . . . . 45

2.1.1.3 Hysteresis of Magnetostrictive Materials . . . . . . . . . . 46

2.2 Uncoupled Constitutive Model . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.2.1 Linear Uncoupled Model . . . . . . . . . . . . . . . . . . . . . . . . 50

2.2.1.1 Actuator Design - Some Issues . . . . . . . . . . . . . . . 52

2.2.1.2 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.2.1.3 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.2.2 Polynomial Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 54

2.2.3 ANN Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.2.3.1 Network Architecture . . . . . . . . . . . . . . . . . . . . 55

2.2.3.2 Study on Number of Nodes in Hidden Layer . . . . . . . . 55

2.2.3.3 Study on Learning Rate . . . . . . . . . . . . . . . . . . . 58

2.2.3.4 Sequential Training Mode . . . . . . . . . . . . . . . . . . 58

2.2.3.5 Training by Batch Mode . . . . . . . . . . . . . . . . . . . 59

2.2.3.6 Momentum Effect . . . . . . . . . . . . . . . . . . . . . . 59

2.2.3.7 Selected Network . . . . . . . . . . . . . . . . . . . . . . . 59

2.2.4 Comparative Study with Polynomial Representation . . . . . . . . . 63

2.3 Coupled Constitutive Model . . . . . . . . . . . . . . . . . . . . . . . . . . 65

2.3.1 Linear Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

2.3.2 Nonlinear Coupled Model . . . . . . . . . . . . . . . . . . . . . . . 74

xiv Contents

2.3.3 ANN Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

2.3.4 Comparison between Different Coupled Models. . . . . . . . . . . . 83

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

3 FEM with Magnetostrictive Actuators and Sensors 87

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87


3.2 3D Finite Element Formulation . . . . . . . . . . . . . . . . . . . . . . . . 88

3.2.1 Uncoupled Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.2.2 Coupled Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.3 Computation of Sensor Open Circuit Voltage . . . . . . . . . . . . . . . . . 92

3.3.1 Uncoupled Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.3.2 Coupled Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.4 Numerical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

3.4.1 Axial Deformation in a Magnetostrictive Rod . . . . . . . . . . . . 94

3.4.1.1 Uncoupled Analysis . . . . . . . . . . . . . . . . . . . . . 96

3.4.1.2 Coupled Analysis . . . . . . . . . . . . . . . . . . . . . . . 97

3.4.1.3 Degraded Composite Rod with Magnetostrictive Sensor/Actuator100

3.4.2 Finite Element Formulation for a Beam . . . . . . . . . . . . . . . . 100

3.4.2.1 Composite Beam with Magnetostrictive Bimorph . . . . . 104

3.4.2.2 Static Analysis . . . . . . . . . . . . . . . . . . . . . . . . 105

3.4.2.3 Frequency Response Analysis of a Healthy and Delami-

nated Beam . . . . . . . . . . . . . . . . . . . . . . . . . . 106

3.4.2.4 Time Domain Analysis . . . . . . . . . . . . . . . . . . . . 108

3.4.3 Finite Element Formulation of a Plate . . . . . . . . . . . . . . . . 111

3.4.3.1 Composite Plate with Magnetostrictive Sensor and Actuator116

3.4.4 Finite Element Formulation of 2D Plane Strain Elements . . . . . . 116

3.4.4.1 Composite Beam with Different Types of Failure . . . . . 118

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

4 Superconvergent Beam Element with Magnetostrictive Patches 122

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122


4.2 Super-Convergent Finite Element Formulations. . . . . . . . . . . . . . . . 124

4.2.1 FE Formulation for Euler-Bernoulli Beam. . . . . . . . . . . . . . . 124

Contents xv

4.2.1.1 Uncoupled Formulation . . . . . . . . . . . . . . . . . . . 126

4.2.1.2 Coupled Formulation . . . . . . . . . . . . . . . . . . . . . 129

4.2.2 FE Formulation for First Order Shear Deformable (Timoshenko)

Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

4.2.2.1 Uncoupled Formulation . . . . . . . . . . . . . . . . . . . 131

4.2.2.2 Coupled Formulation . . . . . . . . . . . . . . . . . . . . . 132

4.3 Numerical Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

4.3.1 Static Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

4.3.1.1 Euler-Bernoulli Beam . . . . . . . . . . . . . . . . . . . . 136

4.3.1.2 Timoshenko Beam . . . . . . . . . . . . . . . . . . . . . . 138

4.3.1.3 Single Element Performance for Static Analysis . . . . . . 139

4.3.2 Free Vibration Analysis. . . . . . . . . . . . . . . . . . . . . . . . . 141

4.3.2.1 Single Element Analysis. . . . . . . . . . . . . . . . . . . . 141

4.3.3 Super convergence Study. . . . . . . . . . . . . . . . . . . . . . . . 142

4.3.3.1 Free Vibration Analysis. . . . . . . . . . . . . . . . . . . . 142

4.3.3.2 Time History Analysis. . . . . . . . . . . . . . . . . . . . . 146

4.3.4 Material Property Identification . . . . . . . . . . . . . . . . . . . . 149

4.3.4.1 Elastic Modulus Identification . . . . . . . . . . . . . . . . 150

4.3.4.2 Magnetomechanical Coefficient Identification . . . . . . . 150

4.3.4.3 Material Properties Identification using ANN . . . . . . . 152

4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

5 Spectral FE Analysis with Magnetostrictive Patches 162

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162


5.2 FE Formulation of an nth Order Shear Deformable Beam with nth Order

Poissons Contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

5.2.1 Conventional FE Matrices . . . . . . . . . . . . . . . . . . . . . . . 173

5.3 Spectral Finite Element Formulation of Beam . . . . . . . . . . . . . . . . 173

5.3.1 Closed Form Solution for Cut-off Frequencies . . . . . . . . . . . . . 175

5.3.2 Finite Length Element . . . . . . . . . . . . . . . . . . . . . . . . . 176

5.3.3 Semi-Infinite or Throw-Off Element . . . . . . . . . . . . . . . . . . 177

5.3.4 Effect of the Temperature Field . . . . . . . . . . . . . . . . . . . . 178

5.3.5 Effect of the Actuation Current . . . . . . . . . . . . . . . . . . . . 179

xvi Contents

5.3.6 Solution in the Frequency Domain . . . . . . . . . . . . . . . . . . . 179

5.3.6.1 Strain Computation . . . . . . . . . . . . . . . . . . . . . 179

5.3.6.2 Magnetic Field Calculation. . . . . . . . . . . . . . . . . . 180

5.3.6.3 Stress and Magnetic Flux Density Calculation. . . . . . . 181

5.3.6.4 Computation of Sensor Open Circuit Voltage. . . . . . . . 181

5.3.6.5 Time Derivatives of any Variable. . . . . . . . . . . . . . . 181

5.4 Numerical Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . 182

5.4.1 Free Vibration and Wave Response Analysis . . . . . . . . . . . . . 182

5.4.1.1 Free Vibration Study . . . . . . . . . . . . . . . . . . . . . 184

5.4.1.2 Cut-Off Frequencies of Beam. . . . . . . . . . . . . . . . . 184

5.4.1.3 The Spectrum and Dispersion Relation . . . . . . . . . . . 188

5.4.1.4 Response to a Modulated Pulse . . . . . . . . . . . . . . . 196

5.4.1.5 Response to a Broad-band Pulse . . . . . . . . . . . . . . 203

5.4.2 Force Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

6 Forward SHM for Delamination 213

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

6.2 Delamination Modelling in Composite Laminate . . . . . . . . . . . . . . . 214

6.3 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

6.3.1 Tip Response Due to Tip Load . . . . . . . . . . . . . . . . . . . . 219

6.3.1.1 Varying Location . . . . . . . . . . . . . . . . . . . . . . . 219

6.3.1.2 Varying Size . . . . . . . . . . . . . . . . . . . . . . . . . 222

6.3.1.3 Symmetric Delaminations . . . . . . . . . . . . . . . . . . 222


6.3.2 Sensor Response for a Tip Load . . . . . . . . . . . . . . . . . . . . 227

6.3.2.1 Varying Size and Layer . . . . . . . . . . . . . . . . . . . . 230



6.3.3 Tip Response for Actuation . . . . . . . . . . . . . . . . . . . . . . 234


6.3.3.2 Varying Size . . . . . . . . . . . . . . . . . . . . . . . . . 238

6.3.4 Sensor Response for Actuation . . . . . . . . . . . . . . . . . . . . . 240


Contents xvii

6.3.4.2 Varying Size and Layer . . . . . . . . . . . . . . . . . . . . 242

6.3.5 SHM of a Portal Frame . . . . . . . . . . . . . . . . . . . . . . . . . 244

6.3.5.1 Thin Portal Frame . . . . . . . . . . . . . . . . . . . . . . 245

6.3.5.2 Thick Portal Frame . . . . . . . . . . . . . . . . . . . . . 248

6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

7 Structural Health Monitoring: Inverse Problem 255

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

7.2 SHM using Single ANN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

7.2.1 Difficulties in Single ANN . . . . . . . . . . . . . . . . . . . . . . . 259

7.3 Committee Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

7.3.1 Numerical Experiment using Committee Machine . . . . . . . . . . 263

7.3.2 Information Loss due to Dimension Reduction . . . . . . . . . . . . 267

7.4 Hierarchical Neural Network (HNN) . . . . . . . . . . . . . . . . . . . . . . 268

7.4.1 Five Stage HNN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

7.4.1.1 Neural Networks . . . . . . . . . . . . . . . . . . . . . . . 268

7.4.1.2 Ensemble Network . . . . . . . . . . . . . . . . . . . . . . 268

7.4.1.3 Validation Network . . . . . . . . . . . . . . . . . . . . . . 269

7.4.1.4 Expert in HNN . . . . . . . . . . . . . . . . . . . . . . . . 270

7.4.1.5 Committee Machine in HNN . . . . . . . . . . . . . . . . 271

7.4.2 Training Phase of HNN . . . . . . . . . . . . . . . . . . . . . . . . . 271

7.4.2.1 Training of ANN . . . . . . . . . . . . . . . . . . . . . . . 271

7.4.2.2 Training of Ensembler Network . . . . . . . . . . . . . . . 272

7.4.3 Testing Phase of HNN . . . . . . . . . . . . . . . . . . . . . . . . . 273

7.4.3.1 Testing of ANN . . . . . . . . . . . . . . . . . . . . . . . . 273

7.4.3.2 Testing of Ensembler Network . . . . . . . . . . . . . . . . 273

7.4.3.3 Testing of Validation Network . . . . . . . . . . . . . . . . 273

7.4.4 Execution Phase of HNN . . . . . . . . . . . . . . . . . . . . . . . . 274

7.4.4.1 Execution of ANN . . . . . . . . . . . . . . . . . . . . . . 274

7.4.4.2 Execution of Ensembler Network . . . . . . . . . . . . . . 274

7.4.4.3 Execution of Validation Network . . . . . . . . . . . . . . 274

7.4.4.4 Execution of Expert Network . . . . . . . . . . . . . . . . 275

7.4.4.5 Active Expert Network . . . . . . . . . . . . . . . . . . . . 275

7.4.5 Numerical Study of Five Stage Hierarchical ANN . . . . . . . . . . 276

xviii Contents

7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

8 Summary and Future Scope of Research 278

8.1 Contribution of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

8.1.1 Limitation of the Approach . . . . . . . . . . . . . . . . . . . . . . 282

8.2 Future Scope of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

Appendices 284

A Euler-Bernoulli Beam 285

B Timoshenko Beam 288

C Higher Order Theories 292

References 301

List of Tables

1.1 Comparison of different smart materials for SHM application. . . . . . . . 10

2.1 Constants 0 through 4 for different prestress levels [192]. . . . . . . . . . 54

2.2 Connection between input layer and hidden layer. . . . . . . . . . . . . . . 63

2.3 Connection between hidden layer and output layer. . . . . . . . . . . . . . 63

2.4 Coefficients for sixth order polynomial. . . . . . . . . . . . . . . . . . . . . 78

2.5 Connection between input layer and hidden layer. . . . . . . . . . . . . . . 83

2.6 Connection between hidden layer and output layer. . . . . . . . . . . . . . 85

3.1 Vertical Displacement of Cantilever Tip . . . . . . . . . . . . . . . . . . . . 105

4.1 Tip Deflection (mm) for Static Tip Load of 1 kN . . . . . . . . . . . . . . 140

4.2 Tip Deflection (mm) for Static Tip Load of 1 kN . . . . . . . . . . . . . . 140

4.3 Tip Deflection (mm) for Actuation Current . . . . . . . . . . . . . . . . . . 141

4.4 First Three Natural Frequencies (Hz) . . . . . . . . . . . . . . . . . . . . . 142

4.5 First Three Natural Frequencies (Hz) . . . . . . . . . . . . . . . . . . . . 142

4.6 First peak amplitude of training samples (mili-volt) . . . . . . . . . . . . . 154

4.7 Middle peak amplitude of training samples (mili-volt) . . . . . . . . . . . . 154

4.8 Middle peak location of training samples (micro-second) . . . . . . . . . . 154

4.9 Last peak amplitude of training samples (mili-volt) . . . . . . . . . . . . . 155

4.10 Last peak location of training samples (micro-second) . . . . . . . . . . . . 155

4.11 First peak amplitude of validation samples (mili-volt) . . . . . . . . . . . . 157

4.12 Middle peak amplitude of validation samples (mili-volt) . . . . . . . . . . . 157

4.13 Middle peak location of validation samples (micro-second) . . . . . . . . . 157

4.14 Last peak amplitude of validation samples (mili-volt) . . . . . . . . . . . . 160

4.15 Last peak location of validation samples (micro-second) . . . . . . . . . . . 160

xix

xx List of Tables

5.1 First 10 natural frequencies for 010 and 05/905 layup using 2D FEM . . . . 182

5.2 Propagation of modulated pulse with Un = 1,Wn = 0 beam assumption. . 199



6.1 Locations of different sensors and actuator . . . . . . . . . . . . . . . . . . 244

7.1 Performance of Committee Machine. . . . . . . . . . . . . . . . . . . . . . 263

8.1 Comparison with existing state-of-the-art . . . . . . . . . . . . . . . . . . . 281

List of Figures

1.1 Magnetostriction due to switching of magnetic domains. . . . . . . . . . . 27

1.2 Artificial Neural Network of 7-14-7 Architecture. . . . . . . . . . . . . . . . 38

2.1 Magnetostriction vs. magnetic field supplied by Etrema . . . . . . . . . . . 49

2.2 Magneto-mechanical coupling vs. magnetic field supplied by Etrema . . . . 50

2.3 Stress vs. strain relationship for different magnetic field level [Etrema] . . . 51

2.4 Elasticity vs. strain relationship for different magnetic field level [Etrema] . 51

2.5 Tangential coupling with bias field for different stress level. . . . . . . . . . 53

2.6 Coupling coefficient with bias field for different stress level. . . . . . . . . . 53

2.7 Study on the effect of number of node in hidden layer. . . . . . . . . . . . 56

2.8 Study on the effect of number of node in hidden layer. . . . . . . . . . . . 56

2.9 Test data from network and sample data set. . . . . . . . . . . . . . . . . . 57

2.10 Test data from network and sample data set. . . . . . . . . . . . . . . . . . 57

2.11 Effect of learning rate on training performance . . . . . . . . . . . . . . . . 60

2.12 Effect of learning rate on validation performance . . . . . . . . . . . . . . . 60

2.13 Effect of learning rate on batch mode training performance. . . . . . . . . 61

2.14 Effect of learning rate on validation performance for batch mode learning. . 61

2.15 Effect of momentum on training performance. . . . . . . . . . . . . . . . . 62

2.16 Effect of momentum on training performance. . . . . . . . . . . . . . . . . 62

2.17 Magnetostriction for different stress level. . . . . . . . . . . . . . . . . . . . 64

2.18 Coupling coefficient for different stress level. . . . . . . . . . . . . . . . . . 64

2.19 Magnetostriction for different stress level. . . . . . . . . . . . . . . . . . . . 66

2.20 Ratio of two permeabilities (r) with different values of permeability vs.

modulus of elasticity (a) and modified elasticity (b), considering d=15X109

m/Amp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

xxi

xxii List of Figures

2.21 Ratio of two permeabilities (r) with different values of coupling coefficient

vs. constant strain permeability (a) and constant stress permeability (b),

considering Q=15GPa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

2.22 Ratio of two permeabilities (r) with different values of coupling coefficient

vs. modulus of elasticity (a) and modified elasticity (b), considering =

7X106 henry/m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

2.23 Nonlinear curves (a) Strain vs. Stress curve (b) Magnetic field vs. Magnetic

flux density curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

2.24 Nonlinear curves in different stress level (a) Magnetic field vs. Strain (b)

Magnetic field vs. Magnetostriction. . . . . . . . . . . . . . . . . . . . . . . 80

2.25 Nonlinear curves for different field level (a) Stress vs. Strain (b) Modulus

vs. Strain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

2.26 Artificial neural network architecture . . . . . . . . . . . . . . . . . . . . . 83

2.27 Nonlinear curves for different stress level (a) Strain vs. Magnetic field (b)

Magnetic flux density vs. Magnetic field. . . . . . . . . . . . . . . . . . . . 84

3.1 Various elements with node and degrees of freedom. . . . . . . . . . . . . . 95

3.2 Composite Rod With Magnetostrictive Sensor and Actuator . . . . . . . . 99

3.3 Open Circuit Voltages at Magnetostrictive Sensor . . . . . . . . . . . . . . 99

3.4 Laminated Beam With Magnetostrictive Patches. . . . . . . . . . . . . . . 104

3.5 Frequency Response Function . . . . . . . . . . . . . . . . . . . . . . . . . 107

3.6 Actuation History with Frequency content . . . . . . . . . . . . . . . . . . 109

3.7 Cantilever Tip Velocity for 00 ply angle . . . . . . . . . . . . . . . . . . . . 110

3.8 Cantilever Tip Velocity for 900 ply angle. . . . . . . . . . . . . . . . . . . . 112

3.9 Sensor Open Circuit Voltage for 00 ply angle . . . . . . . . . . . . . . . . . 113

3.10 Sensor Open Circuit Voltage for 900 ply angle . . . . . . . . . . . . . . . . 114

3.11 Multiple delaminated plate with magnetostrictive sensor and actuator . . . 117

3.12 Sensor open circuit voltage for plate with multiple delaminations . . . . . . 117

3.13 Laminated composite beam with sensor, actuator and crack . . . . . . . . 119

3.14 Sensor open circuit voltages for matrix crack in laminated composite beam 119

3.15 Sensor Open Circuit Voltages for Fiber Breakage . . . . . . . . . . . . . . . 120

3.16 Sensor Open Circuit Voltages for Internal Crack . . . . . . . . . . . . . . . 120

4.1 10 layer composite cantilever beam with different layup sequence . . . . . . 137

4.2 Natural Frequency for Cantilever Beam with [010] Layup sequence . . . . . 143

List of Figures xxiii

4.3 Natural Frequency for Cantilever Beam with [05/905] Layup sequence . . . 143

4.4 Natural Frequency for Beam with Coupled, [m/08/m] Layup sequence . . . 144

4.5 Natural Frequency for Beam with Uncoupled, [m/08/m] Layup sequence . 144

4.6 Natural Frequency for Beam with Coupled, [m/04/904/m] Layup sequence 145

4.7 Natural Frequency for Beam with Uncoupled, [m/04/904/m] Layup sequence145

4.8 50 kHz Broadband Force History with Frequency Content (inset) . . . . . . 147

4.9 Effect of Beam Assumption on Tip Response [010] . . . . . . . . . . . . . . 147

4.10 Superconvergent Study of ScFSDT elements . . . . . . . . . . . . . . . . . 148

4.11 Open circuit voltage for Coupled, [m/08/s] Layup sequence . . . . . . . . . 149

4.12 Sensor voltage for coupled, [m/04/904/s] with varying elasticity . . . . . . 151

4.13 Sensor voltage for Coupled, [m/04/904/s] with varying coupling coefficient 151

4.14 Open circuit voltage for Coupled, [m/04/904/s] layup sequence . . . . . . . 152

4.15 Training Histories of different ANN architectures . . . . . . . . . . . . . . 156

4.16 ANN with Different architectures . . . . . . . . . . . . . . . . . . . . . . . 158

4.17 Training Performance of 5-4-2 ANN architectures . . . . . . . . . . . . . . 159

4.18 Validation Performance of 5-4-2 ANN architectures . . . . . . . . . . . . . 159

5.1 Error in Natural Frequency for Different Beam Assumptions . . . . . . . . 183

5.2 Cut-Off Frequencies for [010] Layup with different beam assumptions. . . . 185

5.3 Cut-Off Frequencies for [m/04/904/m] layup with different beam assump-

tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

5.4 Spectrum Relationships and Group Speeds for [010]. . . . . . . . . . . . . . 189

5.5 Spectrum Relationships and Group Speeds for [010]. . . . . . . . . . . . . . 190

5.6 Spectrum Relationships and Group Speeds for [m/04/904/m]. . . . . . . . 192

5.7 Group Speed for [m/04/904/m] Layup sequence. . . . . . . . . . . . . . . . 194

5.8 Group Speed for [m/04/904/m] Layup sequence. . . . . . . . . . . . . . . . 195

5.9 Modulated pulse of 200 kHz frequency . . . . . . . . . . . . . . . . . . . . 197

5.10 Group Speed and Modulated Pulse Response for [m/04/904/m] Layup with

Un = 1,Wn = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198


Un = 2,Wn = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200


Un = 4,Wn = 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

5.13 Broadband response of 010 layup sequence. . . . . . . . . . . . . . . . . . . 204

5.14 Broadband response of [m/04/904/s] layup sequence (s for sensor layer). . 205

xxiv List of Figures

5.15 25 kHz Broadband Force Reconstruction for [m/04/904/m] layup. . . . . . 211

6.1 Modelling of Delamination in Finite Element Formulation. . . . . . . . . . 215

6.2 Comparison between Beam and 2D Modelling of Delamination . . . . . . . 217

6.3 Composite Beam with Sensor and Actuator . . . . . . . . . . . . . . . . . 218

6.4 100mm Delamination at Mid Layer and Different Distance from Support. . 220

6.5 20mm Delamination at Mid Layer and Different Distance from Support. . . 221

6.6 Delamination at Mid span of Mid Layer with Different sizes. . . . . . . . . 223

6.7 Delamination at Mid span of Top Layer with Different sizes. . . . . . . . . 224

6.8 Symmetric Delaminations at Top and Bottom Layers. . . . . . . . . . . . . 225

6.9 Symmetric Delaminations at 0.3mm Layers. . . . . . . . . . . . . . . . . 2266.10 Multiple Delaminations Increasing towards the Depth. . . . . . . . . . . . 228

6.11 20, 50 and 100mm Delamination at mid and top Layer near Support. . . . 229

6.12 100mm Top Layer Delamination for Different Distance from Support. . . . 231

6.13 100mm Mid Layer Delamination for Different Distance from Support. . . . 232

6.14 100mm Bottom Layer Delamination for Different Distance from Support. . 233

6.15 20mm Top Layer Delamination for Different Distance from Support. . . . . 235

6.16 Multiple Delaminations Increasing towards the Depth . . . . . . . . . . . . 236

6.17 100mm Delamination at Top layer for 50 Hz and 5kHz Actuation. . . . . . 237

6.18 100mm Delamination at Mid layer for 50 Hz and 5kHz Actuation. . . . . . 237

6.19 100mm Delamination at Bottom layer for 50 Hz and 5kHz Actuation. . . . 237

6.20 Delamination at Top layer near support for 50 Hz and 5kHz Actuation. . . 239

6.21 Delamination at Mid layer near support for 50 Hz and 5kHz Actuation. . . 239

6.22 Delamination at Bottom layer near support for 50 Hz and 5kHz Actuation. 239

6.23 100mm Delamination at Top layer for 50 Hz and 5kHz Actuation. . . . . . 241

6.24 100mm Delamination at Mid layer for 50 Hz and 5kHz Actuation. . . . . . 241

6.25 100mm Delamination at Bottom layer from support to 200mm for 50 Hz

and 5kHz Actuation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

6.26 Delamination at Top layer near support for 50 Hz and 5kHz Actuation. . . 243

6.27 Delamination at Mid layer near support for 50 Hz and 5kHz Actuation. . . 243

6.28 Delamination at Bottom layer near support for 50 Hz and 5kHz Actuation. 243

6.29 Delaminated Composite Portal Frame with Sensors and Actuator . . . . . 244

6.30 Sensor Responses for Different Beam Assumptions. . . . . . . . . . . . . . 246

6.31 Sensor Responses for Different Locations of Sensors with EB Assumption. . 247

6.32 Sensor Responses for Different Locations of Sensors with FSDT Assumption.249

List of Figures xxv

6.33 Sensor Responses for Different Locations of Sensors with 2D Model. . . . . 250

6.34 Sensor Responses for Different Beam Assumptions. . . . . . . . . . . . . . 251

6.35 Sensor Responses for Different Locations of Sensors with 2D Model. . . . . 252

7.1 Delaminated composite beam with sensor and actuator. . . . . . . . . . . . 258

7.2 ANN of 10-5-1 Architecture. . . . . . . . . . . . . . . . . . . . . . . . . . . 259

7.3 ANN Architecture 10-5-2-1. . . . . . . . . . . . . . . . . . . . . . . . . . . 259

7.4 Training Performance of ANNs. . . . . . . . . . . . . . . . . . . . . . . . . 260

7.5 Testing Performance of ANNs. . . . . . . . . . . . . . . . . . . . . . . . . . 261

7.6 ANN Architecture 10-5-2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

7.7 Committee Machine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

7.8 Training Performance of Different Span Experts. . . . . . . . . . . . . . . . 264

7.9 Training Performance of span experts . . . . . . . . . . . . . . . . . . . . . 265

7.10 Removal of Noisy Expert. . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

7.11 Partition of Sample Set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

7.12 Training, Validation and Execution of 5 stage HNN. . . . . . . . . . . . . . 272

7.13 Performance of HNN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276

Chapter 1

Introduction

1.1 Motivation and Scope

Composites have revolutionized structural construction. They are extensively used in

aerospace, civil, mechanical and other industries. Present day aerospace vehicles have

composites upto 60 % or more of the total material used. More recently, materials, which

can give rise to mechanical response when subjected to non-mechanical loads such as

PZTs, magnetostrictive, SMAs, have become available. Such materials may broadly refer

to as functional materials. With the availability of functional materials and the feasibility

of embedding those into or bonding those to composite structures, smart structural con-

cepts are emerging to be attractive for potential high performance structural applications

[236]. A smart structure may be generally defined as one which has the ability to deter-

mine its current state, decides in a rational manner on a set of actions that would change

its state to a more desirable state and carries out these actions in a controlled manner in a

short period of time. With such features incorporated in a structure by embedding func-

tional materials, it is feasible to achieve technological advances such as vibration and noise

reduction, high pointing accuracy of antennae, damage detection, damage mitigation etc.

[128, 45].

Various damages like crack or delamination in composite structures are unavoidable

during service time due to the impact or continual load, chemical corrosion and aging,

change of ambient conditions, etc. These damages will cause a change in the strain/stress

state of the structure and hence its vibration characteristics. By continuously monitoring

one or more of these response quantities, it is possible to assess the condition of the

structure for its structural integrity. Such a monitoring of the structure is called structural

health monitoring. Health monitoring application has received great deal of attention all

over the world, due to its significant impact on safety and longevity of the structure.

1

2 Chapter 1. Introduction

To implement health monitoring concept, it is necessary to have a number of sensors

to measure response parameters. These response will then be post-processed to asses

the condition of structure. Such a system was built by Lin and Chang [232], when

they developed a built-in monitoring system for composite structures using a network

of actuators or sensors. The engineering community has great interest in the development

of new real-time, in-service health monitoring techniques to reduce cost and improve

safety. With the current NDE techniques, the complex mechanical systems need to be

taken out of service for an extended period of time for the inspection. The inspection

becomes even more lengthy and expensive for inaccessible locations. Also, on the same

preventive basis, structures are often withdrawn from service early, even if the structure is

still capable of performing its task. It is estimated that nearly 27 percent of an aircrafts

life cycle cost is spent on inspections and repairs (Kessler et al. [178]). With an on-line,

self actuated system, such costs can be dramatically reduced. Furthermore, the impact

of such an in-situ SHM system is that it not only increases safety and performance, but

also enables converting schedule based into condition based maintenance, thus reducing

both down time and costs (Bray and Roderick [46]).

The overall objective of this thesis is how magnetostrictive sensor responses can be

used to identify the health condition of the composite structures. So, the central question

is how responses can be obtained for both healthy or damaged structures, which is forward

analysis; and how these obtained responses can be mapped with the damage state of the

structure, which is inverse problem. Hence, different 1D, 2D and 3D finite element is

formulated to get magnetostrictive sensor responses for healthy and damaged structures

with mapping of different artificial neural networks for identification of damages. Sensing

and actuation properties are characterized using available experimental results. Optimal

location of sensors are studied in structural health monitoring framework. In addition,

in-situ sensor properties and applied forces on structures are identified from truncated

sensor responses.

1.2 Background: Structural Health Monitoring

The safety and performance of all commercial, civil, and military structural systems dete-

riorate with time. Further more, it is very important to confirm the structural condition

immediately by nondestructive inspection or other method when the structure receives

the foreign object collision. Structural damage detection at the earliest possible stage is

1.2. Background: Structural Health Monitoring 3

very important in the aerospace industry to prevent major failures and for this reason it

has attracted a lot of interest. However, it is not practical to assume experts are always

available to explain the measured data. With the advances in sensor systems, data ac-

quisition, data communication and computational methodologies, instrumentation-based

monitoring has been a widely accepted technology to monitor and diagnose structural

health and conditions for civil, aerospace and mechanical structural systems. The process

of implementing a damage detection strategy for aerospace, civil, and mechanical engi-

neering infrastructure is referred to as Structural Health Monitoring (SHM). Followings

are some of the facts attributed to SHM:

SHM is the whole process of the design, development and implementation of tech-niques for the detection, localization and estimation of damages, for monitoring the

integrity of structures and machines.

Because of current manual inspection and maintenance scheduling procedures aretime consuming, costly, insensitive to small variations in structural health, and prone

to error in severe and mild operating environments, there is an urgent economic and

technological need to deploy automated structural diagnostic instrumentation for

seamless evaluation of structural integrity and reliability.

SHM offers the promise of a paradigm shift from schedule-driven maintenance tocondition-based maintenance of structures.

The concept of SHM is a technology that automatically monitors structural condi-tions from sensor information in real-time, by equipping sensor network and diag-

nosis algorithms into structures.

The key requirements of a health monitoring system are that it should be able todetect damaging events, characterize the nature, extent and seriousness of the dam-

age, and respond intelligently on whatever timescale is required, either to mitigate

the effects of the damage or to effect its repair.

Doebling et al. [100, 101] provide one of the most comprehensive reviews of the

technical literature concerning the detection, location, and characterization of structural

damage through techniques that examine changes in measured structural-vibration re-

sponse.


1.2.1 Application Areas

1.2.1.1 Aerospace Application

SHM for Aerospace structures are studied by many researchers. Qing et al. [317] had

developed a hybrid piezoelectric/fiber optic diagnostic system for quick non-destructive

evaluation and long term health monitoring of aerospace vehicles and structures. The

SHM system for the Eurofighter Typhoon had been reported by Hunt and Hebden [164].

Fujimoto and Sekine [125] presented a method for identification of the locations and

shapes of crack and disbond fronts in aircraft structural panels repaired with bonded

FRP composite patches for extension of the service life of aging aircrafts. Zingoni [428]

had stated the essentiality of SHM, damage detection and long-term performance of aging

structures. Tessler and Spangler [366] formulated a variational principle for reconstruction

of three-dimensional shell deformations from experimentally measured surface strains,

which could be used for real-time SHM systems of aerospace vehicles. Epureanu and Yin

[115] had explored nonlinear dynamics of aeroelastic system and increased the sensitivity

of the vibration based SHM system. Baker et al. [26] reported the development of life

extension strategies for Australian military aircraft, using SHM of composite repairs and

joints. Balageas [27] had reported research and development in SHM at the European

Research Establishments in Aeronautics.

1.2.1.2 Wind Turbine Blade Application

Ghoshal et al. [133] had tested transmittance function, resonant comparison, operational

deflection shape, and wave propagation methods for detecting damage on wind turbine

blades.

1.2.1.3 Bridge Structures

Structural health monitoring of bridge had been studied by various researcher [66, 67, 68,

185, 223, 224, 225, 226, 227, 242, 276, 290, 298, 308, 359, 365, 411, 412]. DeWolf et al. [97]

had reported their experience in non-destructive field monitoring to evaluate the health

of a variety of existing bridges and shown the need and benefits in using non-destructive

evaluation to determine the state of structural health. Moyo and Brownjohn [277] had

analyzed in-service civil infrastructure based on strain data recorded by a SHM system

installed in the bridge at construction stage. Bridge instrumentation and monitoring

for structural diagnostics is been done by Farhey [118]. The strain-time histories at


critical locations of long-span bridges during a typhoon passing the bridge area were

investigated by Li et al. [223, 224, 225] using on-line strain data acquired from the SHM

system permanently installed on the bridge. Ko and Ni [185] had explored the technology

developments in the field of long term SHM and their application to large-scale bridge

projects, in order to secure structural and operational safety and issue early warnings

on damage or deterioration prior to costly repair or even catastrophic collapse. Patjawit

and Nukulchai [308] conducted laboratory tests to demonstrate the sensitivity of Global

Flexibility Index for SHM of highway bridges. Li et al. [226] had studied the reliability

assessment of the fatigue life of a bridge-deck section based on the statistical analysis of

the strain-time histories measured by the SHM system permanently installed on the long-

span steel bridge. Li et al. [223, 224, 225] had determined the effective stress range and

its application on fatigue stress assessment of existing bridges. Tennyson et al. [365] had

described the design and development and application of fiber optic sensors for monitoring

of bridge structures.

1.2.1.4 Under Ground Structure

A low-cost fracture monitoring system for underground sewer pipelines had been reported

by Todoroki et al. [367] using sensors made of fabric glass and carbon black-epoxy com-

posite materials. Bhalla et al. [42] had addressed technology associated with SHM of

underground structures. An experimental program was carried out by Mooney et al.

[274] to explore the efficacy of vibration based SHM of earth structures, e.g., foundations,

dams, embankments, and tunnels, to improve design, construction, and performance.

1.2.1.5 Concrete Structure

SHM of concrete structure is performed by many researchers [41, 292, 359]. Corrosion of

the reinforcing bars in concrete beams was monitored by Maalej et al. [241] using fiber op-

tic sensor. Both semi-empirical and experimental results for one-way reinforced concrete

slab were studied by Koh et al. [187] using Fast Fourier Transform and the Hilbert Huang

Transform. Chen et al. [75] used coaxial cables as distributed sensors to detect cracks in

reinforced concrete structures from the change in topology of the outer conductor under

strain conditions. Bhalla and Soh [41] discuss the feasibility of employing mechatronic

conductance signatures of surface bonded piezoelectric-ceramic (PZT) patches in moni-

toring the conditions of reinforced concrete structures subjected to base vibrations, such

as those caused by earthquakes and underground blasts. Nojavan and Yuan [292] have


proposed SHM systems using electromagnetic migration technique to image the damages

in reinforced concrete structures. Taha and Lucero [359] examined fuzzy pattern recog-

nition techniques to provide damage identification using the data simulated from finite

element analysis of a prestressed concrete bridge without a priori known levels of damage.

1.2.1.6 Composite Structure

Fibre reinforced laminate composites are widely used nowadays in load-bearing structures

due to their light weight, high specific strength and stiffness, good corrosion resistance and

superb fatigue strength limit. While composite materials enjoy different advantages, they

are also prone to a wide range of defects and damage which may significantly reduce their

structural integrity. Internal damages such as delamination, fiber breakage and matrix

cracks are caused easily in the composite laminates under external force such as foreign

object collision. Such damages induced by transverse impact can cause reductions in the

strength and stiffness of the materials, even if the damages are tiny. Hence, there is a

need to detect and locate damage as it occurs.

Wang et al. [387] investigated the interaction between a crack of a cantilevered

composite panel and aerodynamic characteristics by employing Galerkins method for one-

dimensional beam vibrating in coupled bending and torsion modes. Prasad et al. [312]

used Lamb wave tomography for SHM of composite structures. Iwasaki et al. [167] had

implemented unsupervised statistical damage detection method for SHM delaminated

composite beam. Dong and Wang [103] had presented the influences of large deformation

for geometric non-linearity, rotary inertia and thermal load on wave propagation in a

cylindrically laminated piezoelectric shell. Verijenko and Verijenko [380] had studied

smart composite panels with embedded peak strain sensors for SHM. Takeda [362] had

presented a methodology for observation and modelling of microscopic damage evolution

in quasi-isotropic composite laminates. Kuang et al. [195] used polymer-based sensors for

monitoring the static and dynamic response of a cantilever composite beam. Chung [88]

had reviewed the use of smart materials in composite. Takeda [360] reported the summary

of the structural health-monitoring project for smart composite structure systems as a

university-industry collaboration program.


1.2.2 Sensors and Actuators

1.2.2.1 Piezoelectric Material

Piezoelectric are class of sensor/actuator materials, which are available in various forms.

It is available in the form of crystals, polymers or ceramics. Polymer form is normally

called PVDF (PolyVinylidine DiFluoride) and is available as very thin films, which are

extensively used as sensor material. In ceramic form, it is called PZT (Lead Zirconate

Titanate), which is used both as sensor and actuator.

PZT has been used by many researchers [41, 72, 130, 103, 131, 317, 329, 350, 385]

for SHM. Koh et al. [186] reported an experimental study for in situ detection of disbond

growth in a bonded composite repair patch in which an array of surface-mounted lead

zirconate titanate elements (PZT) had been used. Bonding piezoelectric wafers to either

end of the fasteners, Barke et al. [30] had shown a technique capable of detecting in situ

damage in structural grades of fasteners. Han et al. [145] had presented a vibration-

based method of detection of the crack in the structures by using piezoelectric sensors

and actuators glued to the surface of the structure. Wang and Huang [391] reported a

theoretical study of elastic wave propagation in a cracked elastic medium induced by an

embedded piezoelectric actuator. Wang and Huang [390] provided a theoretical study of

crack identification by piezoelectric actuator. Gex et al. [131] presented low frequency

bending piezoelectric actuator for fatigue tests and damage detection. Qualitative exper-

imental results of fatigue tests and damage detection were presented and low frequency

bending piezoelectric actuator was used by Gex et al. [130] for SHM. Ritdumrongkul et al.

[329] used PZT actuator-sensor in conjunction with numerical model-based methodology

in SHM to quantitatively detect damage of bolted joints.

1.2.2.2 Optical Fiber

Fiber-optic sensors are gaining rapid attention in the field of SHM [68, 94, 154, 173, 210,

219, 234, 278, 357]. Tsuda et al. [374] studied damage detection of CFRP using fiber

Bragg gratings sensors. Murayama et al. [280] studied SHM of a full-scale composite

structure using fiber optic sensors. High-speed dense channel fiber optic sensors based

on Fiber Bragg Grating (FBG) technology was used by Cheng [74] for SHM. Xu et al.

[410] introduced an approach for delamination detection using fiber-optic interferometric

technique. Long gage and acoustic sensors types of optical fibers were used for SHM

of large civil structural systems by Ansari [20]. Suresh et al. [357] had presented fiber


Bragg grating based shear force sensor in SHM. Tennyson et al. [365] had described

the development and application of fiber optic sensors for monitoring bridge structures.

Chan et al. [68] investigated the feasibility of SHM using FBG sensors, via monitoring

the strain of different parts of a suspension bridge. Fiber bragg grating strain sensors was

developed by Moyo et al. [278] for SHM of large scale civil infrastructure. Kang et al.

[173] had studied the embedding technique of fiber Bragg grating sensors into filament

wound pressure tanks used for SHM. Embedded optical fiber Bragg grating sensors was

used by Herszberg et al. [154] for SHM. Ling et al. [234] had studied the dynamic

strain measurement and delamination detection of composite structures using embedded

multiplexed FBG sensors through experimental and theoretical approaches and revealed

that the use of the embedded FBG sensors is able to actually measure the dynamic strain

and identify the existence of delamination of the structures. Li et al. [227] had presented

an overview of research and development in the field of fiber optical sensor SHM for civil

engineering applications, including buildings, piles, bridges, pipelines, tunnels, and dams.

Cusano et al. [94] described the design of a fiber Bragg grating sensing system for static

and dynamic strain measurements leading to the possibility to perform high frequency

detection for on-line SHM in civil, aeronautic, and aerospace applications. Fluorescent

fiber optic sensors were used by McAdam et al. [262] for preventing and controlling

corrosion in aging aircraft.

1.2.2.3 Vibrometer

Scanning laser vibrometer [221, 345, 356] are used for SHM mainly for their non-contact,

distributed sensing.

1.2.2.4 Magnetostrictive Material

Sensing of delamination in composite laminates using embedded magnetostrictive mate-

rial was studied by Krishna Murty, A. V. et al. [192]. Saidha et al. [335] presented an

experimental investigation of a smart laminated composite beam with embedded/surface-

bonded magnetostrictive patches for health monitoring applications. Theoretical and

experimental investigation had been done by Giurgiutiu et al. [134] for SHM of magne-

tostrictive composite beams. Hison et al. [156] reported magnetoelastic sensor prototype

for on-line elastic deformation monitoring and fracture alarm in civil engineering struc-

tures.


1.2.2.5 Nano sensor

Watkins et al. [392] had studied on single wall carbon nanotube-based SHM sensing

materials. Collette et al. [91] had developed nano-scale electrically conductive strain

measurement device potential for SHM. This nano-sensor based SHM has great potential

in the coming years.

1.2.2.6 Comparisons of different sensors

In high frequency structural application like, SHM, frequency bandwidth of the material

is most important criteria for both sensing and actuation mechanism. Although shape

memory alloy gives high strain of 2-8%, its bandwidth limitation is one of the main

disadvantages for SHM application.

Actuator: The maximum force exerted by any material is necessarily limited by

its maximum stress. In order to maximize the actuation force, it is generally desirable

to employ a material with a large maximum stress capable of large actuation strains. It

seems unlikely that both parameters can be optimized in the same materials. As a result,

the maximum actuation force of future materials may not be vastly greater than the forces

achievable at present. Low-stiffness materials with large actuation strains can provide an

effective source of actuation for certain type of structural applications. Ferromagnetic

Shape-Memory Alloys can produce relatively large strains, limited mainly by the yield

strength of the metal. Given the trade-off between stiffness and strain, perhaps the more

important physical limit to consider in SHM application is the maximum actuation stress

that is achievable by a material. PZT actuators typically provide displacements of 0.13%

strains. Their large bandwidth is another great advantage; operation in the gigahertz

frequency range is even possible. They have good linearity, and since they are electrically

driven, can be directly integrated with the composite structures. The devices and material

are moderately priced compared to other actuators. Piezoceramics specific weigh near 7.5-

7.8 and have a maximum operating temperature near 300C. The main disadvantage of

piezoelectric actuators is the high voltage requirements, typically from 1 to 2 kV. Further,

as the size of the actuators increases, so does the required voltage, making them favorable

only for small-scale devices. Being ceramic, PZT actuators are also brittle, requiring

special packaging and protection. Other disadvantages are the high hysteresis and creep,

both at levels from 15-20%. Electrostrictive materials can provide 0.1% strain and operate

from 20 to 100 kHz. They have specific weigh near 7.8 with operating temperatures near

300C. Finally, their low hysteresis (


Table 1.1: Comparison of different smart materials for SHM application.PZT 5H PVDF PMN Terfenol-D Nitinol

Actuation Piezoceramic Piezo electro- magneto- SMAmechanism (31) film strictive strictive

Maximum strain (%) 0.13 0.07 0.1 0.2 8Modulus (GPa) 60 2 64 30 28/90Specific Weight 7.5 1.78 7.8 9.25 7.1Hysteresis (%) 10 >10


modulus but with a high coupling coefficient. For those applications that can tolerate low

mechanical stiffness, PVDF is generally chosen over a piezoceramic material because of its

low modulus and relatively low cost, despite its relatively low electromechanical coupling

coefficient. Flexibility and manufacturability of PVDF sensor has made them popular

for use as thin-film contact sensors and acoustic transducers. The main advantage of

magnetostrictive sensing is that the fundamental technology is non-contact in nature so

that the sensors can last indefinitely and can be inserted inside the composite layers.

1.2.3 Solution Domain

Literature for SHM can be divided according to their solution domain. These are the

following:

1.2.3.1 Static Domain

In the presence of damage, stiffness matrix of the structure changes. Due to this change,

displacement of the structure due to static load changes. This change is one of the criteria

used for the detection of damage. Jenkins et al. [169] introduced a static deflection based

damage detection method. They mention that the other methods are relatively insensitive

to many instances of localized damage such as fatigue crack or notch, which results in very

little changes in the system mass or inertia. Zhao and Shenton [235] presented a novel

damage detection method based on best approximation of dead load stress redistribution

due to damage.

For self-equilibrating static load (usually generated from smart actuator), the effect

of load far away from the actuator has negligible effect on the static response, even in the

presence of damage. Hence, the change of structural properties distant from the actuator

cannot be sensed through static self-equilibrating load. Hence, the use of smart actuator

for SHM in static domain is limited to the proximity of actuator only.

1.2.3.2 Modal domain

Since modal parameters depend on the material property and geometry, the change in

natural frequencies, mode shape curvature etc. can be used to locate the damage in

structures without the knowledge of excitation force, when linear analysis is adequate.

The amount of the literature pertaining to the various methods for SHM based on modal

domain is quite large [58, 66, 177, 197, 197, 221, 242, 290, 342, 378, 379]. New and


sophisticated strategies for damage identification using modal parameters is studied ex-

tensively (e.g. [Ratcliffe, [320]; Lam et al., [208]; Ratcliffe and Bagaria, [321]; Ratcliffe

[322]; Chinchalkar, [77]). Lakshminarayana and Jebaraj, [206] used the first four bending

and torsional modes and corresponding changes in natural frequencies to estimate the lo-

cation of a crack in a beam. It is reported that if the crack is located at the peak/trough

positions of the strain mode shapes, then percentage change in frequency would be higher

for corresponding modes. It is also found that if the crack is located at the nodal points of

the strain mode shapes, then the percentage change in frequency values would be lower for

corresponding modes. Uhl [376] presented different approaches for identification of modal

parameters for model-based SHM. Khoo et al. [182] presented modal analysis techniques

for locating damage in a wooden wall structure. Ching and Beck [78] used modal identifi-

cation for probabilistic SHM. Verboven et al. [378] applied total least-squares algorithms

for the estimation of modal parameters in the frequency-domain. Caccese et al. [58] stud-

ied the detection of bolt load loss in hybrid composite/metal bolted connections using

low frequency modal analysis. Sodano et al. [342] used macro-fiber composites sensor to

find modal parameters for SHM of an inflatable structure. Chan et al. [66] updated finite

element model of a large suspension steel bridge using modal characteristics for SHM of

the bridge. Laser vibrometer, designed for modal analysis was used for crack detection in

metallic structures by Leong et al. [221].

The presence of delamination changes the structural dynamic characteristics and

can be traced in natural frequencies, mode shapes, phase, dynamic strain and stress

wave patterns etc. Significant research has been reported on the effect of delamination

on natural frequencies and mode shapes and strategies have been developed to identify

location of delamination using changes in these modal parameters (Tracy and Pardoen,

[371]; Gadelrab, [127]; Schulz at al., [338]; Zou et al., [430]; Chinchalkar, [77]). Tracy and

Pardoen, [371] found that if the delamination is in a region of mode shape where the shear

force is very high, there will be considerable degradation in natural frequency, which is

otherwise not significant. Hence, by studying the mode shapes and the corresponding

natural frequencies, estimation on the location of delamination can be made.

Resonant Frequencies / Natural Frequencies: The resonant frequencies are defined

as the frequencies at which the magnitude of the frequency response at a measured de-

grees of freedom approaches infinity, which is also called as natural frequency. Adams,

et al. [4] illustrated a method to detect damage from changes in resonant frequencies.

Wang and Zhang [389] estimate the sensitivity of modal frequencies to changes in the


structural stiffness parameters. Zak et al. [420] examined the changes in resonant fre-

quencies produced by closing delamination in a composite plate. In particular, the effects

of delamination length and position on changes in resonant frequencies were investigated.

Williams and Messina [396] formulate a correlation coefficient that compares changes in a

structures resonant frequencies with predictions based on a frequency-sensitivity model

derived from a finite element model. Hearn and Testa [152] developed a damage detection

method from ratio of changes in natural frequency for various modes.

Antiresonance frequencies: The antiresonance frequencies are defined as the frequen-

cies at which the magnitude of the frequency response at measured degrees of freedom

approaches zero [310]. To calculate antiresonance frequencies of a dynamic system, He

and Li [151] developed an accurate and efficient method for undamped systems. The rea-

sons for looking to the antiresonance frequencies are that these antiresonance frequencies

can be easily and accurately measured in a similar way as for the natural frequencies.

Furthermore, a system can have much greater number of antiresonance frequencies than

natural frequencies because every different FRF between an actuator and a sensor con-

tains another set of antiresonance frequencies. Williams and Messina [396] considered

anti-resonance frequencies for their damage detection technique. Lallement and Cogan

[207] introduced the concept of using antiresonance frequencies to update FE models.

Mottershead [275] showed that the antiresonance sensitivities to structural parameters

can be expressed as a linear combination of natural frequency and mode shape sensitivi-

ties, and furthermore that the dominating contributors to the antiresonance sensitivities

are the sensitivities of the nearest frequencies and corresponding mode shapes. It is con-

cluded that the antiresonance frequencies can be a preferred alternative to mode shape

data.

Mode Shapes: Doebling and Farrar [99] examine changes in the frequencies and

mode shapes of a bridge as a function of damage. This study focuses on estimating the

statistics of the modal parameters using Monte Carlo procedures to determine if damage

has produced a statistically significant change in the mode shapes. Stanbridge, et al. [343]

also use mode shape changes to detect saw-cut and fatigue crack damage in flat plates.

They also discuss methods of extracting those mode shapes using laser-based vibrometers.

Another application of SHM using changes in mode shapes can be found in (Ahmadian

et al. [13]). West [393] used mode shape information (Modal Assurance Criteria) for the

location of structural damage. Ettouney