rep enma

Phil. Trans. R. Soc. A (2007) 365, 539560

doi:10.1098/rsta.2006.1935

Published online 13 December 2006

on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from Keywords: data normalization; environmental and operational variation;damage detection

1. Introduction

Structural health monitoring (SHM) is a problem which can be addressed at manylevels. Stated in its most basic form, the objective is to ascertain simply if damage ispresent or not. The basic premise ofmost damage detectionmethods is that damagewill alter the stiffness, mass or energy dissipation properties of a system, which inturn will alter the measured dynamic response of the system. During the normaloperation of a system or structure, measurements are recorded and features areextracted from data, which characterize the normal conditions. After training thediagnostic procedure in question, subsequent data can be examined to see if thefeatures deviate signicantly from the norm. That is, a simple damage classiersuch as outlier analysis (Worden 1997; Worden et al. 2000) can be employed fordeciding whether measurements from a system or structure indicate signicantdeparture from the previously established normal conditions. Ideally, an alarm issignalled if features increase above a pre-determined threshold.The basis for damage detection appears intuitive, but its actual application

poses many signicant technical challenges. Although many damage detectiontechniques are successfully applied to scale models or specimen tests inOn

*horted in the literature. Then, this paper presents research progresses that have bede in the area of data normalization.Effects of environmental and operationalvariability on structural health monitoring

BY HOON SOHN*

Civil and Environmental Engineering Department,Carnegie Mellon University, Pittsburgh, PA 15213, USA

Stated in its most basic form, the objective of structural health monitoring is to ascertainif damage is present or not based on measured dynamic or static characteristics of asystem to be monitored. In reality, structures are subject to changing environmental andoperational conditions that affect measured signals, and these ambient variations of thesystem can often mask subtle changes in the systems vibration signal caused by damage.Data normalization is a procedure to normalize datasets, so that signal changes causedby operational and environmental variations of the system can be separated fromstructural changes of interest, such as structural deterioration or degradation. This paperrst reviews the effects of environmental and operational variations on real structures astye contribution of 15 to a Theme Issue Structural health monitoring.

sohn@andrew.cmu.edu

539 q 2006 The Royal Socie

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on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from controlled laboratory environments, the performance of these techniques in eldis still questionable and needs to be validated. SHM applied to rotatingmachinery, often referred to as condition monitoring, is somewhat mature,having made the transition from a research topic to actual practice. Theobservation of this technology transition in rotation machinery makes uswonder, why is not the SHM technology penetrating into other market places?One of the main obstacles for deploying a SHM system for in-service structuresis the environmental and operational variation of structures. In fact, thesechanges can often mask subtler structural changes caused by damage. Often theso-called damage-sensitive features employed in these damage detectiontechniques are also sensitive to changes in environmental and operationalconditions of the structures.

(b)

D D D D

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Figure 1. Damage detection study of the I-40 Bridge over the Rio Grande in New Mexico, USA.(a) Introduction of damage in one of the bridge girders by electric saw cutting. (b) Four levels ofdamage introduced at the girder (the shaded area represents reduced cross-section).For instance, Farrar et al. (1994) performed vibration tests on the I-40 Bridgeover the Rio Grande in New Mexico, USA to investigate if modal parameterscould be used to identify structural damage within the bridge. Four differentlevels of damage were introduced to the bridge by gradually cutting one of thebridge girders, as shown in gure 1. The change of the bridges fundamentalfrequency is plotted with respect to the four damage levels, as shown in gure 2.Because the magnitude of the bridges natural frequency is proportional to itsstiffness, the frequency is expected to decrease as the damage progresses.However, the results in gure 2 belie the intuitive expectation. In fact, thefrequency value increases for the rst two damage levels, and then eventuallydecreases for the remaining two damage cases. Later investigation revealed that,beside the articially introduced damage, the ambient temperature of the bridgeplayed a major role in the variation of the bridges dynamic characteristics.Other researchers also acknowledged potential adverse effects of varyingoperational and environmental conditions on vibration-based damage detection(Cawley 1997; Ruotolo & Surace 1997; Roberts & Pearson 1998; Helmicki et al.1999; Rohrmann et al. 1999; Williams & Messina 1999; Cioara & Alampalli 2000;Sohn et al. 2001a,b).

Phil. Trans. R. Soc. A (2007)

the system. Damage detection is based on the premise that damage in thestructure will cause changes in the measured vibration data. Many existing

damage level

541Environmental and operational variability

on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from methods, however, neglect the important effect of changing environmental andoperational conditions on the underlying structure. For in-service structures, thevariability in dynamic properties can be a result of time-varying environmentaland operational conditions. Environmental conditions include wind, temperatureThis paper focuses on data normalization issues of SHM related to in-serviceinfrastructure. This paper starts by exposing data normalization issues reportedin the literature and identies technologies that seem promising for addressingthe data normalization problems.

2. Environmental and operational variability

Many techniques have been proposed to identify the extent and location ofdamage in in-service structures using changes in the dynamic characteristics of

Figure 2. The fundamental frequency change of the I-40 Bridge as a function of the four damagelevels shown in gure 1.2.30

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dam3and humidity, while operational conditions include ambient loading conditions,operational speed and mass loading. In this section, a brief summary of reportedexamples of the environmental and operational variability is provided.

(a ) Temperature effects

The effects of temperature variability on the measured dynamics response ofstructures have been addressed in several studies. It is intuitive that temperaturevariation may change the material properties of a structure. Wood (1992)reported that the changes of bridge responses were closely related to thestructural temperature based on the vibration test of ve bridges in the UK.Analyses based on the data compiled suggested that the variability of the asphaltelastic modulus due to temperature effects was a major contributor to thechanges in the structural stiffness.Temperature variation not only changes the material stiffness, but also alters

the boundary conditions of a system. Based on a eld test conducted on theSutton Creek Bridge in Montana, USA, Moorty & Roeder (1992) reported that

Phil. Trans. R. Soc. A (2007)

the effects of thermal stresses in a steel-stringer bridge while also recording trafc

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on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from loads by means of a weigh-in-motion roadway scale. It was concluded that thermalstresses far exceeded stresses caused by the recorded trafc.Finally, other studies on the inuence of temperature variation on in-service

structures have been reported (Churchward & Sokal 1981; Rohrmann et al. 1999;Cioara & Alampalli 2000; Peeters & De Roeck 2000).

(b ) Boundary condition effects

Changes in the structures surroundings or boundary conditions such asthermal expansion can produce more signicant changes in dynamic responsesthan damage. Using an analytical model of a cantilever beam, Cawley (1997)compared the effect of crack formation on the resonant frequency with the effectof the beams length on the resonant frequency. In this study, the crack wasintroduced at the xed end of the cantilever beam, and the length of the beamwas varied. His results demonstrated that the resonance frequency change causedby a crack, which was a 2% cut through the depth of the beam, was 40 timessmaller than that caused by a 2% increase in the beams length.Alampalli (1998) reported that, for a 6.76 by 5.26 m bridge span that they

tested, the natural frequency changes caused by the freezing of the bridgesupports were an order of magnitude larger than the variation introduced by anarticial saw cut across the bottom anges of both girders. Peeters & De Roeck(2000) found a highly nonlinear or a piecewise linear relationship between theambient temperature and the fundamental frequencies of the Z24 Bridge basedon a yearlong monitoring of data. In particular, the inuence of temperaturevariation became prominent when the temperature fell below the freezing point.Similar to Alampallis nding, it is possible that the piecewise linear relationshipwas mainly caused by the freezing of the bridge supports.the movements obtained from both the analytical model and the measured valuesshowed a signicant expansion of the bridge deck as temperature increased.Rohrmann et al. (1999) noted that when a bridge structure was obstructed fromexpanding or contracting, the expansion joints could be closed signicantlyaltering the boundary conditions.The temporal variation of the temperature also needs to be noted. Many

structures exhibit daily and seasonal temperature variations. Based on the modaltesting of Alamosa Canyon Bridge in NewMexico, USA, Doebling & Farrar (1997)showed that the rst mode frequency of the bridge varied approximately 5% duringthe 24 h cycle. Askegaard&Mossing (1988) tested a three-spanRC footbridge for a3-year period, and about 10% seasonal changes in the frequencies were repeatedlyobserved for each year. The authors concluded that the changes were partiallyattributed to the variation of ambient temperature.In reality, structureswill be subjected to different operational and environmental

variations simultaneously. Pirner & Fischer (1997) attempted to separatemechanically induced loadings from thermally induced ones in a TV tower inPrague, Czech Republic. The researchers concluded that it was impossible todirectly distinguish these loadings using time histories alone. They noted, however,that temperature changes producedmajor and slowly changing stresses while windloads produced faster changes. On the other hand, Helmicki et al. (1999) measuredPhil. Trans. R. Soc. A (2007)

believed that the damping ratio increased because the energy dissipation

543Environmental and operational variability

on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from capacity in the material and at the joint increased at higher trafc loading. Inaddition, it is speculated that the secondary structurevehicle interaction effectscould also inuence the dynamic characteristic of bridge structures.As part of an online monitoring system development for roller coasters, SohnIn particular, the changing boundary conditions would impose difculties onthe implementation of SHM systems, because it is often challenging to directlymeasure the boundary conditions of a structure.

(c ) Mass loading effects

Mass loading such as trafc loading would be another operational variable thatis difcult to precisely measure, but might be important for data normalization.The inuence of trafc loading on modal parameters of bridge structures hasbeen investigated (Kim et al. 1999; DeRoeck et al. 2002; Zhang et al. 2002). Theresearchers seem to agree that the mass loading effect of moving vehicles variesdepending on the vehicles mass relative to the magnitude of the bridge. Kimet al. (1999) reported that the measured natural frequencies of a 46 m long simplysupported plate girder bridge decreased by 5.4% as a result of heavy trafc.However, for the middle- and long-span bridges, changes in the measured naturalfrequencies due to different types of vehicle loading (heavy versus light) werehardly detectable. Zhang et al. (2002) found the damping ratios to be sensitive tothe trafc mass, especially when the deck vibration exceeded a certain level. It is

a side-guide wheel

a side-guide wheel

roller coaster vehicle

(a) (b)

Figure 3. (a) A roller coaster vehicle and a test wheel. (b) A zoomed left rear side-guide wheel.et al. (2004) studied the effect of passenger loading on their time-series-baseddamage detection algorithm. A specic type of damage investigated was thedebonding between an inner aluminiumwheel and an outer polymer layer of a rollercoaster ridewhile the vehiclewas on a rail (gure 3).The acceleration-time responsesignals were recorded from the roller coasters at one position of the roller coastertrack. Datawere subsequently acquired during a test operation from three differentvehicles (trains 3, 4 and 6) with varying speeds, mass loading and damageconditions. Note that only train 3 was loaded with rocks on the seats to simulatepassenger loading, while trains 4 and 6 were tested with the seats empty.Then, the auto-regressive (AR) and moving average (MA) coefcients of the

auto-regressive with exogenous input (ARX) model were plotted separately ingure 4a,b, respectively. In gure 4a, a clear separation between the ARcoefcients from train 3 and those of trains 4 and 6 was observed. Although a

Phil. Trans. R. Soc. A (2007)

0.62 0.000.985 0.099 0.995 1.000 1.0051.65 1.60

t th

1.55 1.50 1.45

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on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from Fujino et al. (2000) observed that the dynamic behaviour of cable-stayed orsuspension bridges is amplitude dependent. For instance, the fundamentalfrequency of a suspension bridge reduced as the wind speed increased. On theother hand, themodal damping increasedwhen thewindvelocity exceeded a certainlevel. Mahmoud et al. (2001) used continuously measured vibration data from theHakucho Suspension Bridge in Japan to study the dynamic behaviour of asuspension bridge. It was found that the vertical amplitude of the bridge response ismore thorough investigation is required, it seems that two distinctive clusters ingure 4a, one from train 3 and the other from trains 4 and 6, were caused bydifferent mass loading conditions between train 3 and trains 4 and 6. A lessobvious, but similar, conclusion can be drawn from gure 4b. The results fromgure 4 clearly highlight that variation due to different mass loading was muchbigger than that due to wheel debonding.

(d ) Wind-induced variation effect

The wind-induced vibration plays an important role for long-span bridges. As abridge vibrates in the wind, the energy input from the wind-induced vibrationbecomes larger than the energy dissipated by damping, causing utter or buffeting.

the first AR coefficient the first MA coefficient

Figure 4. Separation of train 3 and trains 4 and 6 data using principal component analysis ofAR-ARX (4,2,2) model coefcients. (a) Using AR coefcients. (b) Using MA coefcients.0.74(a) (b)

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train 3 (damaged)train 4train 6almost a quadratic function of the wind speed and damping ratio is vibrationamplitude dependent. In particular, the lower natural frequencies were signi-cantly affected by wind speeds. However, the dependency of mode shapes on thevibration amplitude was mainly observed for higher modes and near the tower.

3. Data normalization methods

Since data can be measured under varying conditions, the ability to normalizethe data becomes very important to the SHM process. This section contains newtechnical developments that attempt to tackle the aforementioned environ-mental and operational issues of SHM.When the environmental or operating variability is an issue, there are three

different situations for data normalization. First, when direct measurements ofthe varying environmental or operational parameters are available, various kinds

Phil. Trans. R. Soc. A (2007)

545Environmental and operational variability

on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from undamaged (T2)

undamaged (T3) undamaged (T4)

undamaged (T1)need measure of the environmental variable

damaged (T1)change of the feature distribution as afunction of an environmental parameter T

undamaged (T2)

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(a)

(b) of regression and interpolation analyses can be performed to relate measurementsrelevant to structural damage and those associated with environmental andoperation variation of the system (Rohrmann et al. 1999; Peeters & De Roeck2000; Worden et al. 2002; Fritzen et al. 2003). For example, the dependency oftwo-dimensional features on some environmental variable T can be approxi-mated by using regression analysis, as shown in gure 5a, when a large set ofextracted features and measured environmental variables are available. Notethat there might be some damage cases, which cannot be distinguished from theundamaged conditions unless the environmental variable is measured (e.g. thedamage case shown in gure 5a).On the other hand, there are situations in which direct measurements of these

operational and environmental parameters are impractical or difcult to achieveand damage produces changes in the extracted features, which are orthogonalto the changes caused by the operational and environmental variation of thesystem (gure 5b). For this situation, it may be possible to distinguish changescaused by damage from those caused by the operational and environmentalvariation of the system without measuring the operational and environmentalparameters. Several researchers have tackled this situation by implicitly

two-dimensional feature space

undamaged (T1)damaged (T2)

measurement of the environmentalvariable may not be necessary

Figure 5. Three conceptional situations exist for data normalization: (a) direct measurements ofthe varying environmental or operational parameters are available, (b) direct measurements ofthese parameters are impractical or difcult to achieve, but damage produces changes orthogonalto changes caused by damage, and (c) features that are mainly sensitive to damage but insensitiveto operational and environmental variations can be extracted (not shown in the gure).

Phil. Trans. R. Soc. A (2007)

was observed in the fundamental frequency. Similar observations were reported

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on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from for the next three fundamental frequencies as well.A similar linear regression analysis was applied to vibration signals obtained

from the Alamosa Canyon Bridge in New Mexico, USA to relate the change ofthe bridges fundamental frequency to the temperature gradient of the bridge(Sohn et al. 1998). The measured fundamental frequency of the Alamosa CanyonBridge in New Mexico varied approximately 5% during a 24 h test period, andthe change of the fundamental frequency was well correlated to the temperaturedifference across the bridge deck. Because the bridge was approximately alignedin the north and south direction, there was a large temperature gradient betweenthe west and the east sides of the bridge deck throughout the day.modelling the underlying relationship between the environmental variables andthe damage-sensitive features (Ruotolo & Surace 1997; Manson 2002; Kullaa2003; Sohn et al. 2003b). Others have attempted to divide baseline datasets intosubsets, each corresponding to a different operational and environmental condition(Sohn & Farrar 2001; Sohn et al. 2001a,b).Finally, there are other researchers who attempt to explicitly extract features

that are mainly sensitive to damage but insensitive to operational andenvironmental variations (Manson 2002; Sohn et al. 2003a). In this section, thesenovel approaches to address the data normalization issue are briey introduced.

(a ) Regression analysis

Peeters (2000) performed a regression analysis of the natural frequencies of theZ24 Bridge on temperature to lter out the temperature effects from themeasured frequencies. The Z24 Bridge in Switzerland was monitored duringalmost one year before it was articially damaged. A bilinear relationship wasobserved between the measured frequencies and temperature. There was a clearlinear relationship above the freezing temperature (08C) and a different linearcorrelation below the freezing temperature. It was demonstrated that thisbilinear behaviour was attributed to the asphalt layer on the deck. Although theasphalt layer did not contribute to the overall stiffness at warm temperatures, itadded signicant stiffness to the bridge at cold temperatures. In this study, onlydata corresponding to above freezing temperatures were used for the linearregression analysis.In particular, to take into account the thermal inertia of the asphalt and

the concrete, a dynamic linear regression model called ARX was tted to themeasured frequencytemperature data to reconstruct the dependence of themeasured frequencies on temperature. Single-input and single-output (SISO)ARX models were constructed for the rst four fundamental frequencies,describing the relation between one input temperature and one output frequency.Although multi-input and single-output (MISO) ARX models were alsoinvestigated, no signicant improvement over the SISO model was observed.Once the ARX model was constructed, the prediction error was used as a

damage-sensitive feature. If the residual error exceeds a condence intervalestablished from the baseline training datasets, it is likely that the bridgeundergoes abnormal conditions that it had not experienced during the trainingphase. In this study, the damage introduced was the incremental settlement ofone of the bridge piers. As shown in gure 6, a drastic shift of the prediction errorPhil. Trans. R. Soc. A (2007)

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)A simple linear lter using the temperature readings across the bridge asinputs was constructed and was able to predict the frequency variation, as shownin gure 7. The rst dataset from 1996 was used to train the adaptive lter, whilethe second dataset from 1997 was used to test the prediction performance. Alinear lter with two spatially separated and two temporally separatedtemperature measurements reproduced the variation of the frequencies of therst dataset. Based on the trained lter system, a prediction interval of thefrequency for a new temperature prole was computed and the predictionperformance was tested using the second dataset. Results indicated that a linearadaptive lter with four temperature inputs (two temporal and two spatial

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Figure 6. Damage diagnosis using ARX model, which models the relation between the measuredfundamental frequency and temperature (Peeters 2000).

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Figure 7. Reproduction of the rst mode frequency using a linear lter.

Phil. Trans. R. Soc. A (2007)

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on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from dimensions) could reproduce the natural variability of the frequencies withrespect to time of day reasonably well. Then, the regression model was also usedto establish condence intervals of the frequencies for a new temperature prole.It is worthwhile to compare the regression approaches performed by Peeters

(2000) and Sohn et al. (1998). While Peteers work emphasizes the thermaldynamics of the bridge by using a single temperature measurement with multipletime lags (the temporal variation of temperature), the work by Sohn et al. (1998)used temperature readings from multiple thermocouples to take into account thetemperature gradient across the bridge (the spatial variation of temperature) aswell as the temporal variation. The comparison of these two approaches clearlydemonstrates that data normalization is problem-specic; one kind for eachindividual structure.Because the Alamos Canyon Bridge examined by Sohn et al. (1998) is oriented

in a northsouth direction and it is located in southern New Mexico, where thetemperature can easily go above 458C, the bridge experiences a large temperaturegradient across the bridge throughout the day. Therefore, it is feasible that thespatial variation of the bridge temperature might have been the main drivingfactor for the frequency variation. On the other hand, the magnitude of the Z24Bridge, which had a 30 m long main span and two 20 m long side spans with8.6 m width, is certainly larger than the 7.3 m wide and 15.2 m long span of theAlamos Canyon Bridge tested. Therefore, it is possible that it took a longer timebefore the temperature affected the dynamic properties of the bridge and thetime-lag information of the temperature was more important for the Z24 Bridgethan the Alamos Canyon Bridge.

(b ) Subspace-based identication method

Fritzen et al. (2003) modied an existing subspace-based identication method(Peeters & De Roeck 1999) for temperature compensation. For damage diagnosisbased on the subspace-based identication method, the following residual error isrst computed:

zZ vecsT0H 1;where z is the residual error;H0 andH1 are the Hankel matrices of the baseline andtest structures obtained from either impulse time signals or frequency responsefunctions, respectively;S0 is the left singular vector of the baselineHankelmatrixH0;and vec(.) is the stack operator rearranging a matrix into a column vector. Theresidual errorbasically compares the response spaces spannedby thebaseline system,H0, and the system in question,H1. Therefore, if damage occurs, this residual errorwill increase because the response spaces spanned by the damaged system will bedifferent from those spanned by the baseline system. Therefore, statistical analysiscan be performed on the residual error for damage diagnosis.To address the temperature calibration issue, the left singular vectors

corresponding to various temperature values are stored in a reference database.Then, when a newHankel matrix is constructed at anymeasured temperature value,the residual error is computed by selecting the left singular vector corresponding tothe same temperature from the previously established reference database.This method has been tested using only numerical simulations. Note that this

approach is based on the assumption that damage produces changes orthogonalto the response spaces spanned by the baseline data. However, other operationalPhil. Trans. R. Soc. A (2007)

sensitive to damage than the conventional novelty detection approach, where the

549Environmental and operational variability

on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from mean vector and covariance matrix were constructed spanning all environmentalconditions of interest. However, it was reported that when the training data werenot properly sampled, the covariance matrix may not be positive semi-deniteproducing negative Mahalanobis distances. This problem was addressed byand environmental conditions may produce changes orthogonal to the existingbaseline conditions, and damage may produce changes along the response spacespanned by the baseline signal.

(c ) Novelty detection

Novelty detection rst builds an internal representation of the systems normalcondition, and then examines subsequent data to see if they signicantly departfrom a normal condition. The discordancy of a candidate outlier is measured by thefollowing squaredMahalanobis distancemeasureD (Barnett&Lewis 1994; Farrar&Worden 2007; Worden & Manson 2007):

DZ xKxTCxKx;where x is a vector of the potential outlier; x and C are the mean vector andcovariance matrix of the baseline system, respectively. Once the Mahalanobisdistance is computed, it is checked against a threshold value. Note that thisnovelty detection addresses only the simplest level of damage identication, i.e.whether damage is present or not.One major advantage of this novelty detection is that statistical model

building for damage classication is based only on data from the undamagedsystem. However, the success or failure of the novelty detection is contingent onthe accuracy of the description of the normal condition. In reality, the normalcondition of the system may experience a wide range of variation due tooperational and environmental changes of the system.Worden et al. (2002) tackled this issue via the construction of a reference set

parameterized by environmental and operational variables. That is, new data areevaluated only with respect to reference data obtained from the sameenvironmental conditions. It is assumed that the environment is parameterizedby a single measurable variable T. Thus, the mean vector and the covariancematrix become functions of the underlying environmental parameter, and thefunctional relationships are approximated by polynomial regression models

xiZXn

jZ0

aji Tj and C ij Z

Xn

kZ0

akijTk ;

where xi and Cij are the ith entity of the mean vector and the ij th entity of thecovariance matrix, respectively; n is the polynomial order; and aji and a

kij are the

regression coefcients estimated by least-squares regression.Now the monitoring strategy becomes clear. When a new set of data is

measured at an environmental value at T and is tested for novelty, theappropriate x and C are estimated from the regression model at the sameenvironmental value, and they are used to compute the Mahalanobis distance.The effectiveness of this approach is demonstrated by using simulated data froma lumped-mass system. It was shown that the regression approach was morePhil. Trans. R. Soc. A (2007)

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on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from introducing an interpolation approach to data normalization. The interpola-tion approach guaranteed that the estimated covariance matrix be positivesemi-denite.Manson (2002) used the same novelty detection for damage identication, but

took an alternative approach for data normalization. His approach for datanormalization is based on the premise that there might be a subset of features,which are more sensitive to damage yet insensitive to environmental variations.Therefore, his approach focuses on isolating those feature components that aresensitive to damage. In this study, Lamb-wave propagation data from acomposite plate were used similar to the work by Worden (2002). Theinstrumented composite plate was placed in an environmental chamber andLamb-wave signals were recorded every minute. Initially, the chambertemperature was held at a constant temperature of 258C, and the temperaturewas uctuated between 10 and 308C. At the end of the test, a 10 mm hole was

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Figure 8. Diagnosis using the conventional novelty detection (Manson 2002).drilled in the plate between two sensors.The rst half of the data measured at 258C was stored as a training dataset,

and the rest of the data was tested against the training dataset for novelty. Thediagnosis using the conventional novelty detection method is shown in gure 8.Most of the data points from the second half of the constant temperature set(the rst segment in gure 8) were below the threshold. The datasets from thedamage case (the last segment in gure 8) were all substantially over thethreshold, so were the data from the temperature-cycled case (the middlesegment in gure 8). This is certainly an undesirable situation.To address this issue, two approaches were used. The rst method calculated a

univariate novelty index for each feature variable instead of the multivariateMahalanobis distance, while the second method made use of the minorcomponents taken from a principal component analysis (PCA) of the multi-variate feature space. The rst approach was straightforward. By examiningindividual feature variable, the rst method identied a subset of the featurevariables which were insensitive to temperature variation yet sensitive todamage. The second approach rst performed a PCA on the training data from

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on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from different temperature conditions. Then, assuming that the variance in the datawas primarily produced by temperature variation, the original feature space wasprojected on to a reduced feature space using minor principal componentscorresponding to the smallest singular values. An improved diagnosis based onthis PCA is shown in gure 9. All data from the temperature-cycled case withoutdamage (the middle segment in gure 9) have been classied as undamaged,while the actual damage cases are agged as such.

(d ) Singular value decomposition

Ruotolo & Surace (1997) note that test structures can be subjected toalterations during normal operating conditions, such as changes in mass. Tohandle this situation, a damage detection method based on singular valuedecomposition (SVD) is proposed to distinguish between changes in the working

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Figure 9. Diagnosis using the modied novelty detection, using minor PCA components(Manson 2002).conditions and the onset of damage. Let vi be the feature vector collected at ndifferent normal congurations (iZ1, 2,., n). When a new feature vector vc iscollected, the whole feature vectors can be arranged in a matrix M,

M Z v1v2.vnvc: 3:1If the structure is intact, the new feature vector vc will be close to one of theexisting feature vectors vi, and the rank of the matrix M estimated by SVDshould remain unchanged by adding vc toM. On the other hand, if the structureexperiences damage, the rank of the matrixM will increase by 1. This approachis based on the premise that any structural damage will produce orthogonalchanges to the feature space expanded by the existing baseline data.

(e ) Auto-associative neural network

Sohn et al. (2003b) developed a combination of time-series analysis, neuralnetworks and statistical inference techniques for damage classication, explicitlytaking into account ambient variation of the system. First, a time predictionmodel called an auto-regressive and auto-regressive with exogenous inputs(AR-ARX) model is t to vibration signals measured during normal operating

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on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from conditions of the structure. Through this AR-ARX model tting, the AR andARX coefcients corresponding to various operational conditions are obtained.Note that the parameters of the AR-ARX model should be constant if theseparameters are obtained using time signals from a time-invariant system.However, when there are operational and environmental variations of thesystem, these AR-ARX coefcients are not constant anymore and they will be afunction of these ambient variations.Next, data normalization is performed based on an auto-associative neural

network, where target outputs are simply inputs to the network. Using theextracted features, which are the parameters of the AR-ARX model previouslyextracted from the normal conditions of the structure, as inputs, the auto-

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Figure 10. Schematic of an auto-associative neural network.associative neural network is trained to characterize the underlying dependency ofthe extracted features on the unmeasured environmental and operational variationsby treating these environmental and operational conditions as hidden intrinsicvariables in the neural network. Once the network is trained properly, the outputlayer of the auto-associative neural network will reproduce the extracted features inthe input layer. That is, the dependence of the extracted features on environmentaland operational variations is registered in the trained neural network.The auto-associative network consists of mapping, bottleneck and de-mapping

layers (gure 10). The bottleneck layer contains fewer nodes than input oroutput layers forcing the network to develop a compact representation of theinput data. Kramer (1991) shows that this auto-associative neural network is arealization of a general nonlinear principal component analysis (NLPCA). WhilePCA is restricted to mapping only linear correlations among variables, NLPCAcan reveal the nonlinear correlations present in data. If nonlinear correlationsexist among variables in the original data, NLPCA can reproduce the originaldata with greater accuracy and/or with fewer factors than PCA.Finally, when a new time signal is recorded from an unknown state of the

system, the parameters of the time prediction model are computed for the newsignal and fed to the trained neural network. When the structure undergoes

Phil. Trans. R. Soc. A (2007)

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experimental study of an eight-degree-of-freedom (DOF) spring-mass system,as shown in gure 11. Damage is simulated by placing a bumper between twoadjacent masses, so that the movement of one mass is limited relative to anadjacent mass. Figure 12 shows the hardware used to simulate nonlinear damage.When one end of a bumper, which is placed on one mass, hits the other mass,impact occurs. This impact simulates damage caused by the impact from theclosing of a crack during vibration. Random excitation was accomplished with a215 N peak force electro-dynamic shaker. The root mean square (r.m.s.)

mass 1mass 8

Figure 11. An 8-DOF system attached to a shaker with accelerometers mounted on each mass.amplitude level of the input was varied from 3 to 7 V. The response of anindividual mass is recorded by an accelerometer attached to each mass. Thechallenge in this example is to distinguish signal changes caused by the insertionof the bumper from those caused by varying excitation levels.Figure 13 shows a typical relationship between the output of the bottleneck

layer and the excitation level obtained from the network corresponding to mass 2.Here, the output of the bottleneck layer is an averaged output of multipletime-series corresponding to each input level. The bottleneck output is closelyrelated to the excitation level, in that the relationship is linear and this is sufcientto reconstruct the input at the output layer. Similar results are also observed fromthe networks associated with the other measurement points. This result impliesthat the auto-associative neural network is trained properly to capture theunderlying dependence of the measured time signals on the excitation levels.Finally, a hypothesis testing technique called a sequential probability ratio test issuccessfully performed on the normalized features to automatically infer thedamage state of the system. Additional details can be found in Sohn et al. (2003b).

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Figure 12. A typical bumper used to simulate nonlinear damage.

0.5yercollar

spring It should be noted that auto-associative neural network is not the only way torealize NLPCA. Malthouse (1998) suggested principal curves (Hastie & Stuetzle1989) as an alternative strategy for NLPCA, and Jia et al. (2000) use an input-training neural network for the same purpose. In particular, Worden (2002)showed that the principal curves could be used to infer a measurement of anenvironmental parameter in the context of damage detection.

(f ) Factor analysis

Kullaa (2003) proposed a data normalization technique based on factoranalysis (Johnson & Wichern 1998). Similar to the previous two approaches, it isassumed that data normalization can be performed without measuringenvironmental parameters.A factor analysis is one form of multivariate analyses, which attempt to reveal

the correlation among multiple sets of variables. In particular, the factor analysisassumes that there are a smaller number of underlying factors that describe thevariation of the measured variables and the measured variables are subjected to

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layer at mass 2.

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unsuccessful without factor analysis (Kullaa 2004).

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on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from (g ) Lamb-wave propagation method

Since the 1960s, the ultrasonic research community has studied Lamb wavesfor the non-destructive evaluation of plates (Bourasseau et al. 2000). Lamb wavesare mechanical waves with wavelength of the same order of magnitude as thethickness of the plate. Because the Lamb waves travel long distances and can beapplied with conformable piezoelectric (PZT) actuators/sensors that requirelittle power, it may prove suitable for online SHM. In particular, the recentadaptation of wavelet analysis to Lamb-wave techniques has allowed theapplication of Lamb-wave techniques to composite structures to ourish (Okaforet al. 1994; Staszewski et al. 1999 a,b; Badcock & Birt 2000; Monnier et al. 2000;Lemistre & Balageas 2001; Kessler 2002). The advances in sensor and hardwaretechnologies for efcient generation and detection of Lamb waves and theincreased usage of solid composites in load-carrying structures, particularly inaircraft industries, have led to the explosion of studies that use Lamb waves fordetecting defects in composite structures. For online continuous monitoring, it isimportant to demonstrate that the Lamb-wave-based methods are robust whenused under varying environmental and operational conditions.Sohn et al. (2003a) developed a damage detection algorithm based on wavelet

transform to extract features that are less sensitive to changing boundaryconditions and temperature variations. In this study, a Morlet wavelet with anarrowband driving frequency is designed as the input waveform (gure 14a).Figure 14b shows the time response of one PZT patch when the Morlet inputwaveform is generated at another PZT patch. The solid line represents therandom errors as shown in the following:

yZLxC3;

where y is a n!1 vector of the measured variables; L is a n!m factor loadingmatrix (nOm); x is am!1 vector of unobservable common factors; and 3 is a n!1vector of unique factors. By using numerical simulations, Kullaa attempted tomodel the dependency of the rst four natural frequencies (themeasured variables)on the temperature (the latent common factor) by using factor analysis. Note thatif the latent common factor represents the temperature parameter, then the uniquefactors, 3, are variables independent of the common factors and can be used fordamage diagnosis. That is, if the structural condition deteriorates, the previouslytrained factor analysis cannot explain the multivariate correlation of the newlycollected data, causing an increase in the unique factors. This paradigm is similar tothe previous auto-associative neural network approach. One major difference isthat while the auto-associative neural network can model nonlinear relationshipsamong the measured variables, this factor analysis is limited to linear relationshipsamong variables. The author also attempted to model nonlinear relationships bymixing different linear factor models over different data spaces. At this point, thisapproach was tested only with a nite element model of a vehicle crane.Operational variation was simulated by changing the conguration of the cranevehicle, and damage was simulated by stiffness reduction. The rst ve modalparameters of the crane were used as the damage-sensitive features. All damagecases were identied using factor analysis, whereas damage detection wasPhil. Trans. R. Soc. A (2007)

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on April 8, 2015http://rsta.royalsocietypublishing.org/Downloaded from baseline signal, and the dashed line shows the response time signal whendelamination is within a direct line of the actuator and sensor path.The response signal is composed of several wave modes owing to wave

scattering at the boundaries. In gure 14b, the rst mode, which looks like a sinewave modulated by a cosine function, is the rst arrival of the Ao modeassociated with the direct path of the wave propagation. The second mode isanother Ao mode that is reected from the edge of the plate. The observation ofgure 14b clearly reveals that the rst Ao mode is the most sensitive to thedelamination damage. Based on these observations, a damage index is dened asthe function of a signals attenuation at a limited time span (a signal portioncorresponding to the rst Ao mode) and at a specic frequency (the inputfrequency of the signal). Note that the attenuation is correlated to the amount ofenergy dissipated by damage. In other words, the proposed damage indexmeasures the degree of the test signals energy dissipation compared with thebaseline signal, especially at the rst Ao mode and the input frequency value.Next, the insensitivity of the proposed damage index to the boundary

condition of the panel was investigated. One edge of the plate is clamped using analuminium plate, as shown in gure 15a, and the associated response signal forthe wave path of patches 2 and 3 is shown in gure 15b. It is clearly demonstratedthat the clamped boundary condition only changes the second Ao wave of thesignal reected from the clamped edge of the plate (the second modulated sinewave in gure 15b). However, it does not affect the performance of the proposeddamage detection algorithm at all, because the damage index is based on thesignals attenuation only at the rst Ao mode.Although the data normalization issue is explicitly taken into account in this

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Figure 14. Lamb-wave time signals from the tested composite plate. (a) An input Morletwaveform. (b) Response strain time signals.study, the procedure developed has only been veried on relatively simplelaboratory test specimens. To fully verify that the proposed approach is trulyrobust, it will be necessary to test the proposed approach for a wide range ofoperational and environmental cases and for different representative damagetypes, such as ply crack, bre breakage and through-hole penetrations.From a similar Lamb-wave inspection study, the short- and long-term

stability of the normal condition data is investigated by Manson et al. (2000).For the short-term study, the Lamb-wave responses were recorded once everyminute for a period of just over 18 h. For the long-term test, signals wererecorded every 10 min over a period of 11 days. During the rst test, no articialtemperature variation was introduced. However, temperature was uctuated byincreasing room temperature using a heater during the second test period. Based

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change, humidity changed the amplitude of the Lamb-wave response. However,

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4. Conclusions and discussions

Currently, various sensors are available to measure parameters relevant toambient conditions of a structure and, in fact, several in-service structures arereported to have been instrumented with thermocouples, anemometers andhumidity sensors. However, the information gathered from these sensors is stillnot directly applied to existing damage detection algorithms. It is the authorsopinion that SHM systems will not be accepted in practical applications unlesson this long-term stability test, the authors conrmed that the effect oftemperature upon the normal condition dataset is one of great importance. Forinstance, observations, which were agged as coming from a damaged structure,may actually have been agged due to a shift in the normal condition set.Conversely, actual damage may not be agged for the same reason.The authors also investigated the long-term stability against humidity

variation (Manson et al. 2001). The authors report that while temperaturevariation mainly produced a phase shift of the signal with a slight amplitude

without clampwith clamp

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Figure 15. Change of the response signal as a result of a boundary condition change. (a) One edgeof the plate is clamped with an aluminium plate. (b) The response signals of the actuator (no. 2)and sensor (no. 3) pair.robust techniques are developed to explicitly account for environmental andoperational constraints/conditions of the systems to be monitored. However,there are few proven techniques that are able to address these issues properly.The developments presented here will allow some progress in in-service

monitoring of aerospace, automotive, civil and mechanical systems, which aresubject to various operational and environmental conditions. Such a monitoringsystem will be less prone to false-positive indication of damage. To minimize thisfalse indication of damage and to develop a more robust monitoring system, it iscritical that training datasets are collected over a wide range of environmental andoperational conditions of the system. Otherwise, the damage classiers presentedmay not be able to make any denite statement regarding the existence of damagebecause abnormal operational conditions can have similar effects as that of damageon the monitoring system. In addition, for real world applications, a hybridapproach from all three categories will most probably be necessary.

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identication. In Proc. DAMAS 97: structural damage assessment using advanced signal

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Soc. A 365, 303315. (doi:10.1098/rsta.2006.1928)Farrar, C. R., Baker, W. E., Bell, T. M., Cone, K. M., Darling, T. W., Duffey, T. A., Eklund, A. &

Migliori, A. 1994 Dynamic characterization and damage detection in the I-40 bridge over theRio Grande. Los Alamos National Laboratory Report: LA-12767-MS.

Fritzen, C. R., Mengelkamp, G. & Guemes, A. 2003 Elimination of temperature effects on damagedetection within a smart structure concept. In Proc. 4th Int. Workshop on Structural HealthMonitoring, Stanford University, CA, pp. 15301538.

Fujino, Y., Abe, M., Shibuya, H., Yanagihara, M. & Sato, M. 2000 Monitoring of Hakuchosuspension bridge using ambient vibration. In Proc. Workshop on Research and Monitoring ofLong Span Bridges. Hong Kong, pp. 142149.

Hastie, T. & Stuetzle, W. 1989 Principal curves. J. Am. Stat. Assoc. 84, 502516. (doi:10.2307/2289936)Overall, it is the opinion of the author that sufcient evidence exists topromote the need for data normalization procedures for damage detection instructures. It is clear, however, that the development of data normalizationprocedures needs to be more focused on specic applications and industries thatwould benet from this technology, such as the health monitoring of bridges,offshore oil platforms, airframes and other structures in elds. Additionally,research should be focused more on tests of real structures in their operatingenvironment, rather than laboratory tests of representative structures. Owing tothe magnitude of such projects, more cooperation will be required betweenacademia, industry and government organizations. If specic techniques can bedeveloped to quantify and extend the life of structures, the investment made inthis technology will clearly be worthwhile.

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Effects of environmental and operational variability on structural health monitoringIntroductionEnvironmental and operational variabilityTemperature effectsBoundary condition effectsMass loading effectsWind-induced variation effect

Data normalization methodsRegression analysisSubspace-based identification methodNovelty detectionSingular value decompositionAuto-associative neural networkFactor analysisLamb-wave propagation method

Conclusions and discussionsReferences