research paper structural damage diagnostic … · structural damage diagnostic techniques using...

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Int. J. Struct. & Civil Engg. Res. 2014 Rakhy Joy et al., 2014

STRUCTURAL DAMAGE DIAGNOSTIC

TECHNIQUES USING TIME SERIES

Rakhy Joy1*, A Rama Mohan Rao2 and P Eapen Sakaria3

Damage is a change introduced into a system that adversely affects current or future performanceof that system. Structural Health Monitoring (SHM) is used for detection, localization and extendsof damage. This paper is to detect the damage occurred in a structure using time series. It alsoaims to detect the severity of damage occurred in a structure. Here Mahalanobis distance methodis used to detect damage in engineering systems. And thus damage index is obtainedcorresponding to each sensor. Damage index is found for both simply supported beam andcantilever beams. To prove the accuracy of work experimental data is taken from undamagedand damaged condition. And Damage index is found out. The information obtained from monitoringis generally used to plan and design maintenance, increase the safety, verify hypotheses, reduceuncertainty and to widen the knowledge concerning the structure being monitored.

1 Saintgits College of Engineering, Pathamuttom.

2 Structural Engineering Research Centre, Chennai.

3 Civil Engineering Department, Saintgits College of Engineering, Pathamuttom.

*Corresponding author:Rakhy Joy � [email protected]

ISSN 2319 – 6009 www.ijscer.com

Vol. 3, No. 1, February 2014

© 2014 IJSCER. All Rights Reserved

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

Research Paper

Keywords:Damage index, Mahalanobis distance, Structural health monitoring, Time series

INTRODUCTION

Structural health monitoring is a process aimedat providing accurate and in time informationconcerning structural condition andperformance. The information obtained frommonitoring is generally used to plan and design.Vibration responses of structures havebecome one of the most common types ofinformation for damage identification andstructural health monitoring of structures,especially bridges. Vibration Responses aremeasured using Accelerometers. Time series

techniques are reliable and economical indamage assessment. The use of model (AR,ARMAX, and ARX) fitted using a set of datameasured on the healthy structure can provideparametric information which can be useful fora further prognostic step. Time series is anordered sequence of values of a variable atequally spaced time intervals. Time seriesdata is normally used to obtain anunderstanding the underlying forces andstructure that produced the observed data andto fit a model and proceed to forecasting,

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monitoring or even feedback and feed forwardcontrol.

LITERATURE REVIEW

Mustafa gula, F Necaticatbasa, Michaelgeorgiopoulosb found time series analysis isone of the methods, which is implemented instatistical pattern recognition applications toSHM. Auto-Regressive (AR) models are highlyutilized for this purpose. In this study, AR modelcoefficients are used with different outlierdetection and clustering algorithms to detectthe change in the boundary conditions of asteel beam.

A number of different boundary conditionsare realized by using different types andamounts of elastomeric pads. The advantagesand the shortcomings of the methodology arediscussed in detail based on the experimentalresults in terms of the ability of it to detect thestructural changes and localize them. Timeseries analysis, i.e., Auto-Regressive modelscoefficients are extracting using Mahalanobisdistance based outlier detection algorithms isused to discriminate different structuralconditions. The methodology is applied tolaboratory test data where ambient vibrationtests are conducted on a steel beam withdifferent boundary conditions. In this analysisnormalization is applied to each channel of thedata before constructing the Auto Regressive(AR) models. After normalizing (averaging) thedata, AR models are fitted to the averageddata. Then the coefficients of these models areused as the damage indicating features andthey are fed to the outlier detection andclustering algorithms.

The random response of a system at aparticular time consists of three components,

which are the step response due to the initialdisplacements, the impulse response frominitial velocity, and a random part due to theload applied to the structure. By taking averageof data segments, every time the response hasan initial displacement bigger than the triggerlevel, the random part due to random load willeventually vanish and become negligible.Additionally, since the sign of the initial velocitycan be assumed varying randomly in time, theresulting initial velocity will also be zero leavinga pseudo-free response of the system. It is animportant to improve the methodology topinpoint the location of the change.

METHODOLOGY

The methodology uses auto-regressivemodels in conjunction with a Mahalanobisdistance-based outlier detection algorithm. Inthe proposed methodology, free vibrationresponse from the ambient vibration data istaken. It’s a modified methodology byimplementing the normalizing for the ambientvibration data before constructing the ARmodels. Ambient vibration (acceleration) datais used to obtain pseudo-free responses bymeans. Then AR models of these freeresponses are constructed. The coefficientsof these AR models are used as the damagefeatures. Finally, the Mahalanobis distance-based outlier detection algorithm is used toseparate different states of the structuredamage indicator, defined using the distancebetween AR models, and is proposed. Areference AR model, which is fitted to thevibration response of the structure undernormal operation conditions, represents thehealthy structure. If the structure is damaged,a different model is to be used to representthe damaged structure, and the distance

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between the two models is correlated with thelocation and severity of the damage. Forefficiently distinguishing between the damagedstructure and the undamaged one, it isnecessary to define an appropriate distancebetween AR models of damaged andundamaged structures. The Mahalanobisdistance for AR models is adopted here torelate a common distance that is widelyaccepted in system identification forcomparing healthy and damaged AR modelsand the AR model is shown in Figure 1.

obtaining the coefficients of the AR models,they are fed to the outlier detection algorithmwhere the Mahalanobis distance between thetwo different data sets is calculated.

Detection can be considered as thedetection of damages in the sensors, whichdeviate from other sensors so that they areassumed to be generated by another systemor mechanism detection is one of the mostcommon pattern recognition concepts amongthose applied to SHM problems. In this study,Mahalanobis distance-based detection isused to detect the novelty in the data. One ofthe most common is based on deviationstatistics and it is given by the following.

di dzi

σ−= ...(2)

where zi is the outlier index for univariate data,di is the potential outlier and, d and σ are thesample mean and standard deviation,respectively. The multivariate equivalent of thisdiscordance test for nxp (where n is the numberof the feature vectors and p is the dimensionof each vector) data set is known as theMahalanobis squared distance.

The mahalanobis squared distance will bereferred as mahalanobis distance after thispoint and it is given as

( ) ( )1

1

Tzi xi x xi x

−= − −∑ ...(3)

where zi is the outlier index form ultivariatedata, xi is the potential outlier vector and x isthe sample mean vector and σ is the samplecovariance matrix. By using the aboveequations, the outliers can be detected if theMahalanobis distance of a data vector ishigher than a pre-set threshold level. The

Figure 1: Obtaining the Feature SetsUsing Time Series Modeling

An AR model estimates the value of afunction at time t based on a linear combinationof its prior values. The model order (generallyshown with p) determines the number of pastvalues used to estimate the value at t. Thebasic formulation of a Pth order AR model isdefined as follows.

...(1)

where x(t) is the time signal, f is the modelcoefficients and e(t) is the error term. After

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flowchart of the damage detectionmethodology using the proposed damageindicator is shown in Figure 2.

history response is computed using finiteelement analysis with Newmark’s timemarching scheme. The sampling rate isconsidered as 1000 samples per second.From the data collected from sensors wecreate acceleration time histories which arereferred as Y data (for damaged andundamaged conditions). Here we use somealgorithms in mat lab to get Y data.

Damage is identified by analyzing the errorsobtained between the undamaged time seriesand the curve obtained by auto regression fordamaged structure. Y data (undamaged)sample is divided as reference and healthydata. Damage datasets are created from Ydata (damaged condition). Damage featureswere extracted using errors from fittingautoregressive models with exogenous inputsto collected time histories. Autoregressivemodels were fitted to all the segmented datasamples in reference, healthy and damagedatasets.

Damage index is used to determine thedamage occurred in a structure. Higher thedamage, greater is damage index. Using thiswe can determine damage occurred or not.You also need to determine the severity ofdamage.

Damage index = Ratio of variance ofprediction errors from healthy, reference anddamage sets.

Several test cases are considered by givingdifferent temperature for different elements andacceleration responses for each case areobtained. Similar way 30 sets of responsesare obtained. Now the Mahalanobis distancesbetween AR models of different combinationof response sets are obtained. The peak

Figure 2: Flowchart for the DamageDetection Methodology

Numerical experiments have beenconducted to test and verify the damagediagnostic technique using the AR modeldiscussed. It is expected that the proposedalgorithm will be more reliable in robustlyidentifying the damage instant and also thespatial location of damage in the structure.Numerical examples of a simply supportedbridge girder and a cantilever beam arepresented to demonstrate the effectiveness ofthe damage indicator derived by comparingAR models of baseline data and the currentdata.

A simply supported and a cantilever beamgirder with a span of 10 m are considered.For the purpose of numerical simulationstudies, the beam is discretised into 20elements. The material and geometricalproperties are also given. The beam is excitedusing random dynamic loading which isstochastic in nature. The acceleration time

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values of Mahalanobis distance from eachcombination are taken to obtain the UpperControl Limit (UCL).

UCL = Mean + (3 x SD)

In the numerical studies, vibrationresponses are generated through Finiteelement code in MATLAB. To illustrate theeffectiveness of the proposed method ofdamage detection, the experimental data of abenchmark structure from Los Alamos NationalLaboratory (LANL) laboratory is considered.Experimental data include undamagedcondition and damaged condition from abenchmark structure.

The structure tested is a three-story framestructure model as shown in Figure 3.

are mounted on the aluminum blocks that areattached by hot glue to the plate and column.

Figure 3: Basic Dimensions of the3 Story Frame Structure

The structure is instrumented with 24piezoelectric single axis accelerometers, twoper joint as shown in Figure 4. Accelerometers

Figure 4: Floor Layoutas Viewed from Above

This configuration allows relative motionbetween the column and the floor to bedetected. The nominal sensitivity of eachaccelerometer is 1 V/g. A 10 mV/lb forcetransducer is also mounted between the stingerand the base plate. This force transducer isused to measure the input to the base of thestructure. A commercial data acquisitionsystem controlled from a laptop PC is used todigitize the accelerometer and forcetransducer analog signals. The data sets thatwere analyzed in the feature extraction andstatistical modeling portion of the study werethe acceleration time histories. In each testcase, three separate data sets were collectedwith the shaker input level at 2, 5 or 8 V.

RESULTS AND DISCUSSION

A. With Simply Supported Beam

Girder

This is the graph plotted between sensornumber and damage index. Graph includes 19sensors and corresponding damage index is

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plotted. Here, the damage index is theMahalanobis distance between the ARmodels. Here the UCL is found to be 4.6 and itis shown in Figure 5. Damage index for thetenth element is crossing the UCL.

And here also damage condition at fifth andfifteenth element shift beyond UCL and it isshown in the Figure 8.

Figure 5: Damage at the10th Element, 50% Damage

And here also damage condition at fifth andfifteenth element shift beyond UCL and it isshown in the Figure 6.

Figure 6: Damage at the 5th and 15th

Element, 40 and 70% Damage

B. With Cantilever Beam Girder

Here the damage is simulated into cantileverbeam girder by reducing the stiffness of tenthelement. Here the UCL is found to be 3.96.Damage index for the tenth element is crossingthe UCL and it is shown in the Figure 7.

Figure 7: Damage at the 10th

Element, 50% Damage

Figure 8: Damage at the 5th and 15th

Element, 35 and 65% Damage

In order to prove the method, theundamaged and damaged data are taken fromLANL laboratory. Tests are done for differentvolt condition and damage condition and it isshown in the Figure 9. And the Figure 10

Figure 9: Single Damage-bolt wereRemoved Between Bracket

and Plate -Volt2

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represents damage at both locations and it isa case with volt2. Here 3rd and 4th sensors gotdamaged.

From the Figure13 it is shown that theIntensity of damage is high at the nineteenthsensor.Which means that Damage is induced

Figure 10: Damage at both Locations-Brackets was Completely Removed-Volt2

Here Intensity of damage is high at the thirdsensor. Which means that Damage is inducedat the third floor of position A and Plate isdamaged.

This is the case with 5 V. Here damagecondition is Single Damage-bolt wereremoved between Bracket and Plate and it isshown in the Figure 11.

Figure 11: Single Damage-boltwere Removed Between Bracket

and Plate -Volt5

The Figure 12 gives the Damage at bothlocations 11th and 12th sensor got damaged.

Figure 12: Damage at Both Locations-Brackets was Completely Removed-Volt5

Figure 13: Single Damage-bolt wereRemoved Between Bracket

and Plate -Volt8

Figure 14: Damage at Both Locations-Brackets was Completely Removed-Volt8

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at the first floor of position A and Plate isdamaged.

And for the Damage at both locations 19th

and 20th sensor got damaged. This is shownin the Figure 14.

CONCLUSION

1. The main advantage is the sensitivity of thetime-series coefficients to changes incharacteristics of dynamic response. Thisadvantage has resulted in the use of time-series models for damage identificationpurposes.

2. The application of time series analysismethods to Structural Health Monitoring(SHM) is a relatively new but promisingapproach. Time series methods areinherently suited to SHM where data issampled regularly over a long period oftime, which is typical for monitoringsystems.

3. The use of model (AR) fitted using a set ofdata measured on the healthy structure canprovide parametric information which can beuseful for a further prognostic step. Mostcurrently available damage detectionmethods are global in nature and globaldamage measures are not sensitive to minordamage and local damage. Furthermore,such methods involve finite elementmodeling and system identification methods,which can be computationally expensive.Here there is no need for the modeling.

4. The efficiency of the proposed methodologyto identify the presence of damage isvalidated in this study, using a simplysupported beam girder, cantilever beamgirder and 3-storey bookshelf benchmark

structure from LANL as numericalexamples. From the results it is shownclearly, that the damage indicator hasefficiently identified presence of thedamage even from the noisy data andenvironmental variabilities.

FUTURE WORK

As an extension off the study on time seriesmethod, it is planned to propose more timeseries method and carry out experimentalworks to validate the results and conclusionsobtained analytically.

ACKNOWLEDGMENT

The authors thanks Dr. Rama Mohan Rao, chiefscientist, SERC-Chennai, Prof. Eapen Skaria,Head of the Civil Engineering Department forthe help provided during preparation of thepaper.

REFERENCES

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