STRUCTURAL HEALTH MONITORING USING TIME SERIES …STRUCTURAL HEALTH MONITORING USING TIME SERIES METHOD COMBINING MODAL EXTRACTION TECHNIQUE Gayathri V G1, B Lakshmi K2, Rama Mohan

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Int. J. Struct. & Civil Engg. Res. 2014 Gayathri V G et al., 2014

STRUCTURAL HEALTH MONITORING USINGTIME SERIES METHOD COMBINING MODAL

EXTRACTION TECHNIQUE

Gayathri V G1, B Lakshmi K2, Rama Mohan Rao2, P Eapen Sakaria1, and Nagesh R Iyer2

1 Department of Civil Engineering, Saintgits College of Engineering, Kottayam, Kerala, India.2 CSIR – Structural Engineering Research Centre, Chennai, Tamil Nadu, India.

*Corresponding author:Gayathri V G [email protected]

ISSN 2319 – 6009 www.ijscer.comVol. 3, No. 4, November 2014

© 2014 IJSCER. All Rights Reserved

Int. J. Struct. & Civil Engg. Res. 2014

Research Paper

INTRODUCTIONStructural health monitoring problem is posedin a statistical pattern recognition frameworkwhich consists of four-parts: (i) the evaluationof a structure’s operational environment; (ii) theacquisi tion of structural responsemeasurements; (iii) the extraction of featuresthat are sensitive to damage; and (iv) thedevelopment of statistical models for featurediscrimination. This damage detectionapproach has shown great promise in theidentification of damage.

Structural Health Monitoring (SHM) is a process of continuous evaluation of a civil infrastructureby collecting information from a sensor network installed in the structure. It involves the processof observation of the system using the responses from a set of sensors, the extraction of damagesensitive features and the analysis of these features to determine the current health of thestructure. Blind Source Separation (BSS) is a powerful signal processing tool that is used toidentify the modal responses and mode shapes of a structure using the knowledge of responses.Time series method is used to know about the modal responses using time series modals theprediction can be done. An error index is used to identify the damage instant. Once the damageinstant is identified the undamaged and damaged parameters of the system can be identified.The identification of the damage instant and the location can be done in this proposed method.

Keywords: Structural Health Monitoring, Blind Source Separation, Sensors, Damage instant,Time Series Method

The various levels in the SHM process are

as mentioned below.

Level 1: Damage detection - Determination

of the damage present in the structure.

Level 2: Damage localization - Determination

of the geometric location of the damage.

Level 3: Damage quantif ication -

Quantification of the severity of the damage.

Level 4: Remaining life estimation - Prediction

of the remaining service life of the structure.

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LITERATURE REVIEWSadhu and Hazra (2012) presented a noveldamage detection algorithm is developedbased on blind source separation inconjunction with time-series analysis. BlindSource Separation (BSS), is a powerful signalprocessing tool that is used to identify themodal responses and mode shapes of avibrating structure using only the knowledgeof responses. In the proposed method, BSSis first employed to estimate the modalresponse using the vibration measurements.

Time-series analysis is then performed tocharacterize the mono-component modalresponses and successively the resulting time-series models are utilized for one-step aheadprediction of the modal response. With theoccurrence of newer measurementscontaining the signature of damaged system,a variance-based damage index is used toidentify the damage instant. Once the damageinstant is identified, the damaged andundamaged modal parameters of the systemare estimated in an adaptive fashion. The

Figure 1: Structural Health Monitoring – Overview

Figure 2: Levels of Structural Health Monitoring

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proposed method solves classical damagedetection issues including the identification ofdamage instant, location as well as the severityof damage. The proposed damage detectionalgorithm is verified using extensive numericalsimulations followed by the full scale study ofUCLA Factor building using the measuredresponses under Parkfield earthquake.

Ruigen Yao and Shamim N Pakzad (2012)presented a data-driven structural healthmonitoring based on sensor measurements.Modal parameters from system identificationare the most widely studied structural stateindicators adopted for this purpose; however,recent research has showed that they are notsensitive enough to local damage. In an effortto seek more effective alternatives, univariateautoregressive (AR) modeling on structuralresponse has been investigated in severalpublications, where model characteristics areused as damage indices. Although thesemethods are generally successful, they tendto generate false alarms when theenvironmental conditions are varying becauseresponses from only one location/sensor areconsidered. To strike a balance betweensensitivi ty and stabil ity, in this paperautoregressive with exogenous inputmodelling on measurements from severaladjacent sensing channels is presented andapplied to detect damage in a space trussstructure. The damage feature is extractedfrom the residuals obtained via fitting thebaseline model to data from the currentstructure. Also, damage localization isattempted by examining the estimated mutualinformation statistic between data fromadjacent sensing channels.

Wenjia Liu et al. (2013) investigated thetime series representation methods andsimilarity measures for sensor data featureextraction and structural damage patternrecognition. Both model-based time seriesrepresentation and dimensionality reductionmethods are studied to compare theeffectiveness of feature extraction for damagepattern recognition. The evaluation of featureextraction methods is performed by examiningthe separation of feature vectors amongdifferent damage patterns and the patternrecognition success rate. In addition, theimpact of similarity measures on the patternrecognition success rate and the metrics fordamage localization are also investigated. Thetest data used in this study are from theSystem Identification to Monitor CivilEngineering Structures (SIMCES) Z24 Bridgedamage detection tests, a r igorousinstrumentation campaign that recorded thedynamic performance of a concrete box-girderbridge under progressively increasingdamage scenarios. A number of progressivedamage test case datasets and damage testdata with different damage modalities areused. The simulation results show that both timeseries representation methods and similaritymeasures have significant impact on thepattern recognition success rate.

METHODOLOGYThe basic problem statement of BSS is givenby BSS method along with the time-seriesanalysis is proposed to detect the damage inthe structural system. Time series models areused to characterize the sources that areobtained from the past observations and thefuture sources are predicted. An error is

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evaluated between the true and predictedmeasurements and subsequently the damage

is identified. With the arrival of newermeasurements containing the signature of

Flowchart of the Proposed Method

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structural damage, significant difference isobserved between the predicted and truemeasurement, which is used as a damageindicator. Once the damage is detected, themeasurements prior to the damage arediscarded and the modal parameters of thedamaged state are estimated based on thecurrent measurements. The damage andundamaged modal parameters are estimated.

The method involves the following stepsmainly

1. Estimation of the mixing matrix

2. Estimation of the source matrix

3. Time series modeling and one step aheadprediction of the sources

4. Identification of the damage location

FLOWCHART OF THE PROPOSEDMETHODOnce the sources are extracted using the BSSmethod with the measurement up to (k – 1) th

time instant, the sources can be predicted fork th time instant using their time-series models.

Where are the AR parameters

Sk = x�

1S

k-1 + x�

2S

k-2 + x�

3S

k-3 + a

t

Once the sources are predicted, one-stepahead response can be estimated using:

xk1

= Ak-1

Sk

where A k-1

is the mixing matrix based on themeasurements up to (k –1) th time instant. Withthe occurrence of new measurement at k thtime instant, i.e, x

kthe error between the

predicted (i.e., xk1

) and true measurement (xk)

can be estimated. Therefore, by utilizing asuitable error index, damage can be estimatedusing the true and predicted measurement. The

variance-based error index can be defined as:

R(0,k)-R1(0,k)Ei,k=

R(0,k)

k

n=0R(0,k) = x(n)/k ,

k

n=0R(0,k) = x1(n)/k are the variances of

the true and the predicted measurement of i th

floor location at k th time instant.

When the error index Ei,k

attains a valuemore than a specified tolerance e then itsignifies that the modelling of s based on themeasurements up to (k–1)th time instant isinappropriate. This particular scenariohappens when there are significant changesin the system and leads to a situation whenthe damage occurs. Under such situation, themeasurements up to (k–1)th time instantrepresents the system response ofundamaged state. On the other hand, thecurrent measurements hereby represent theresponse of damaged state. Therefore themeasurements up to (k–1)th time instant (i.e.,damage instant td) is separated out and theBSS method is employed separately toundamaged and damaged data sets toestimate the modal parameters of undamaged(Su, Au) and damaged system (Sd, Ad)respectively. In this way, time series analysis-based error index is implemented in theframework of BSS to characterize thesuccessive damage and undamaged states.

Identification of Damage Location

Once the mode shapes of the damaged (Ad)and the undamaged (Au) systems areestimated, the damage location can besubsequently identified considering thedifference between the modal co-ordinates of

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the mode shapes under undamaged anddamaged condition. The following equationsare used to find out the location damage:

Damaged states:

1 2 3

2

2d d dd

z z zZ

S

where zd1

, zd2

, zd3

are the modal coordinatesfor the successive time instants correspondingto the damaged mode shape matrix and Sbeing the distance between the adjacentsensors in the structure.

Undamaged states:

1 2 3

2

2u u uu

z z zZ

S

where zu1

, zu2

, zu3

are the modal coordinatesfor the successive time instants correspondingto the undamaged mode shape matrix and Sbeing the distance between the adjacentsensors in the structure.

RESULTS AND DISCUSSIONCase Study 1: Response of a 20-Storey Shear BuildingThe modal response of a 20-storey shearbuilding was studied using the method of BSS.Sensors were placed in each storey. Theacceleration data was generated choosing aparticular storey to be damaged one. AR timeseries model was employed. The damageinstant was detected and the modal curvaturesfor the damaged and undamaged responseswere identified. The building response wasstudied under different signal noise levels andat different temperature conditions. Plots weremade for the modal responses depicting thedamage locations. The damage elementschosen include both single and multiplestoreys. Both single and multiple damage

locations were separately studied and plotsdepicting the damage locations were obtained

A typical storey damage matrix is shownbelow:

The damage storey was the tenth storey:

Damage Matrix

Figure 3: Mode(1)

Figure 4: Mode(2)

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beam of 10 m length was studied using the

method of BSS. The total number of elements

in the beam was taken as 11 .The size of the

beam was taken as 0.35 x 0.5 m. Sensors

were placed at each node except at both end

of the beam. The total numbers of nodes were

taken as 12 (elements+1). The acceleration

data was generated choosing a particular

element to be damaged. AR time series model

was employed. The damage instant was

detected and the modal curvatures for the

damaged and undamaged responses were

identified. Plots were made for the responses

depicting the damage locations. The damage

elements chosen include both single and

multiple locations. Both single and multiple

damage locations were separately studied

and plots depicting the damage locations were

obtained.

A typical damage matrix is shown below:

Figure 5: Mode(3)

Figure 6: Mode(4)

Figure 7: Mode(5)

Case Study 2: Response of a SimplySupported Beam

The modal response of a simply supported The damage element was the fourth storey:

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Figure 7: Plots Representing the Location of Damage

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CONCLUSIONBlind source separation-based damage

detection method in conjunction with time-

series analysis is proposed in this work. Blind

source separation is first utilized to estimate

the modal responses using the vibration

measurements. Time-series model (AR

model) is then employed for one-step ahead

prediction of the past measurements. The

proposed error index is used to identify the

damage instant. Once the damage instant is

identified, the damage and undamaged modal

parameters of the system are estimated in an

adaptive fashion utilizing in the framework of

blind source separation. Classical damage

detection issues including identification of

damage instant, location and severity of

damage are addressed using the proposed

method. Case studies include the study on the

modal responses of a 20 storey shear building

and a 10 m span simply supported beam. The

results are thus analyzed and plots of the

damage locations were made.

ACKNOWLEDGMENTThe paper is being published with the kindpermission of The Director, CSIR-SERC,Chennai.

REFERENCES1. Hoon Sohn, Jerry A Czarnecki, Charles

R and Farrar P E (2000), “Structural

Health Monitoring Using StatisticalProcess Control”, Journal of StructuralEngineering, Vol. 126, pp. 1356-1363.

2. Kuroiwa T and Iemura H (2008),“Vibration-Based Damage DetectionUsing Time Series Analysis”, EarthquakeEngineering, Vol. 12, pp. 12-17.

3. Michael L Fugate (2001), “Vibration-based damage detection usingStatistical process control” MechanicalSystems and Signal Processing, Vol.15,No. 4, pp. 707-721.

4. Nair K K, and Kiremidjian (2003),“Application of time series analysis instructural damage evaluation”,Proceedings of the InternationalConference on Structural HealthMonitoring, pp.14-16.

5 Ruigen Yao and Shamim N Pakzad(2011), “Statistical Modeling Methods forStructural Damage Identification”, Vol. 8,pp. 25-26.

6. Sadhu A and Hazra B (2013), “A noveldamage detection algorithm using time-series analysis-based blind sourceseparation”, Shock and Vibration, Vol.20, pp. 423-438

7. Zhang Q W (2007), “Statistical damageidentification for bridges using ambientvibration data”, Computers andStructures, Vol. 85, pp. 476-485

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STRUCTURAL HEALTH MONITORING USING TIME SERIES …STRUCTURAL HEALTH MONITORING USING TIME SERIES METHOD COMBINING MODAL EXTRACTION TECHNIQUE Gayathri V G1, B Lakshmi K2, Rama Mohan