The application of statistical pattern recognition methods for damage detection to field data

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1 IOP PUBLISHING Smart Mater. Struct. 17 (2008) (12pp) SMART MATERIALS AND STRUCTURES doi: / /17/6/ The application of statistical pattern recognition methods for damage detection to field data A Cheung 1, C Cabrera 1, P Sarabandi 1,KKNair 1,AKiremidjian 1 and H Wenzel 2 1 Department of Civil and Environmental Engineering, Stanford University, MC 4020, Stanford, CA , USA 2 VCE Holding GmbH, Hadikgasse 60, A-1140 Wien, Austria cheunga@stanford.edu, ccabrera@stanford.edu, psarabandi@stanford.edu, kknair@stanford.edu, ask@stanford.edu and Wenzel@vce.at Received 31 January 2008, in final form 12 September 2008 Published 30 October 2008 Online at stacks.iop.org/sms/17/ Abstract Recent studies in structural health monitoring have shown that damage detection algorithms based on statistical pattern recognition techniques for ambient vibrations can be used to successfully detect damage in simulated models. However, these algorithms have not been tested on full-scale civil structures, because such data are not readily available. A unique opportunity for examining the effectiveness of these algorithms was presented when data were systematically collected from a progressive damage field test on the Z24 bridge in Switzerland. This paper presents the analysis of these data using an autoregressive algorithm for damage detection, localization, and quantification. Although analyses of previously obtained experimental or numerically simulated data have provided consistently positive diagnosis results, field data from the Z24 bridge show that damage is consistently detected, however not well localized or quantified, with the current diagnostic methods. Difficulties with data collection in the field are also revealed, pointing to the need for careful signal conditioning prior to algorithm application. Furthermore, interpretation of the final results is made difficult due to the lack of detailed documentation on the testing procedure. (Some figures in this article are in colour only in the electronic version) 1. Introduction Structural health monitoring (SHM) for civil engineering applications is taking advantage of the latest technologies in sensors, wireless networks, and data analysis methods to protect civil infrastructure and preserve safety. SHM consists of damage diagnosis and residual life prognosis. The goal of damage diagnosis is to detect, localize, and quantify structural damage arising from a variety of sources, including long-term degradation such as corrosion and shortterm events such as earthquakes, and then to inform decisionmakers about the proper responsive action. Interest in using wireless sensing networks for structural health monitoring has increased as more research demonstrates successful application to increasingly complex structures. Wireless networks are desirable, because they are cheaper and easier to install and maintain than equivalent wired networks. However, they require that the power consumption be minimal thus making it necessary to limit data transmission (Straser and Kiremidjian 1998). One method of detecting damage in a structure is by measuring the structural response through strain or acceleration. The premise is that changes to structural properties caused by damage will change the way a structure responds to any excitation, including ground motions. Vibration based damage detection methods have traditionally been based on system identification techniques (Doebling et al 1996). Recent research has shown that statistical signal processing and pattern recognition techniques can be used to diagnose damage successfully. Worden et al (1999) used the Mahalanobis distance to identify damage applying outlier /08/ $ IOP Publishing Ltd Printed in the UK

2 analysis. Their work was followed by several papers by Farrar and Sohn (2000), Sohn et al (2001a, 2001b), Farrar et al (2004, 2005), Worden et al (2003), Manson et al (2003a, 2003b)Nairet al (2006) and Nair and Kiremidjian (2007). The advantage of using statistical methods is that a single vibration time history can be analyzed independently of all other signals collected elsewhere in the structure. This allows damage detection algorithms to be embedded at the sensor level, resulting in significant savings in power and computational time, both of which are necessary for the implementation of a fully wireless network. This method has been successfully applied to numerically simulated damage to an experimental structure, such as the ASCE Benchmark Structure (Nair et al 2006). However, computer simulations and even small-scale laboratory test structures cannot fully duplicate the dynamic response of actual structures. More importantly, the input ambient vibrations imposed on actual structures are much more random and unpredictable than those used in most computer and laboratory simulations. In order to test the effectiveness of damage detection algorithms on actual structures a suitable experiment must be designed. Such an experiment either requires a full or near fullscale test involving large facilities or an actual structure that can be subjected to controlled damage tests. For this reason, suitable experimental data are difficult to find. However, recent progressive damage tests performed on the Z24 bridge in Switzerland provide a large amount of experimental data with which damage detection algorithms can be tested (Wenzel 2005). The purpose of this study is to test the robustness of the damage detection algorithm based on autoregressive time series modeling and statistical pattern recognition techniques, which were developed by Nair et al (2006), Nair and Kiremidjian (2007), and Sohn et al (2001a, 2001b) in detecting and quantifying structural damage induced by pier, using acceleration data from the Z24 bridge progressive damage test. In addition, several modifications have been made to the original algorithm to enable more robust diagnosis. In particular, during the analysis of the data, it was found that a cumulative damage measure, which is the sum of the incremental damage measures between successive test cases, is able to characterize increasing damage in the form of pier. This paper is organized in the following manner. First, the statistical pattern recognition methods for damage detection are summarized. A new damage measure based on the Mahalanobis distance is introduced. Next, the bridge and data acquisition project are discussed. Finally, the cumulative damage measure is introduced, and the results obtained from testing the algorithm on the Z24 bridge data are presented and discussed. 2. Overview of the damage detection algorithm Statistical pattern recognition based damage detection algorithms are based on the hypothesis that a structure s vibration time history will change with the onset of damage (Sohn et al 2001a, 2001b, Nairet al 2006). Because the time histories have complex signatures making them difficult to compare, it is desirable to extract features from the signal referred to as damage sensitive features (DSFs), with which damage can be tracked. Nair et al (2006) have shown that decreases in a structure s stiffness due to damage will result in changes to AR coefficients for acceleration time series collected under ambient vibrations. Thus AR coefficients are an appropriate DSF. Damage is evaluated according to a pattern classification framework. A pattern classification algorithm, according to Sohn et al (2001a, 2001b) involves the following steps: (i) evaluation of a structure s operational environment, (ii) acquisition of structural response measurements and data processing, (iii) extraction of features that are sensitive to damage, and (iv) development of statistical models for feature discrimination. In this study the structural response measurements are acceleration time histories, and the DSFs are AR coefficients. Two methods for feature discrimination are proposed. Hypothesis testing using a t-test is performed as specified by Nair et al (2006); however it is shown that a normalized mean-difference value works just as well. In addition, a new multivariate damage measure (DM) based on the Mahalanobis distance is proposed. The Mahalanobis distance was used by Worden et al (1999) to determine outliers in a signal for damage detection purposes. In this paper the Mahalanobis distance is used to quantify damage extent. However, identifying damage location is complicated and is beyond the scope of this paper. Each step in the damage detection algorithm is explained in further detail in the following sections. 3. Data preprocessing Data preprocessing is done to remove or minimize dependence on variable environmental conditions and to identify conditions where sensors have probably malfunctioned. Acceleration time series collected from field experiments often show a drift in the signal. Linear drift is simple to correct. Nonlinear drift, however, is significantly more difficult to identify and correct (see Boore et al 2002). In this paper, time series exhibiting nonlinear drift were discarded while those exhibiting linear drift were detrended. Linear drift can be removed by fitting a line to the signal using least squares methods and then subtracting that line from the signal, thus removing the trend. After detrending, additional preprocessing is done to minimize the dependence on load and environmental conditions. Sohn et al (2001a, 2001b) show that normalizing and standardizing the acceleration time history x(t) by (x(t) μ) x(t) = (1) σ where μ is the mean of the signal and σ is its standard deviation, is required in order to minimize the effect of load and environmental conditions on the AR coefficients. All time histories examined in this study are filtered using equation (1) prior to application of the AR model. As with all experiments, sensors may malfunction and produce corrupt data. Review of the data collected at the Z24 bridge show that 298 out of approximately 4000 acceleration time histories collected during the test were 2

3 Figure 1. Example of corrupt time history. Figure 3. Example of an acceptable time history. 4. Feature extraction using the autoregressive model Figure 2. Example of corrupt time history. corrupted, representing only 7% of the database. These records exhibited erratic patterns, or had sections of signals missing, or had their peaks clipped. While filtering could potentially remove some of these problems, it was felt that filtering may also remove important information from the data, thus potentially leading to erroneous results. Figures 1 3 show two examples of corrupt and one acceptable time histories. The signal in figure 1 appears to be clipped, while the signal in figure 2 is also clipped but at a constant value across the signal. As stated earlier, however, the majority of data did not display such problems and could be used in this analysis. Identification and correction of corrupted time histories, whether possible or not, is beyond the scope of this paper. Because the damage detection algorithm is a local sensor based algorithm, discarding corrupt signals does not affect the results presented in this paper. The AR model was presented in great detail in Nair et al (2006) but is briefly summarized here for clarity. Let x i (t) be acceleration data from sensor i. x i (t) is divided into different chunks x ij (t) where i denotes the sensor number and j denotes the chunk. x ij (t) is standardized and normalized as described in section 3. Once preprocessing is complete, the optimal AR order must be estimated. In previous studies the autoregressive moving average (ARMA) model was used for modeling the vibration signal (Nair et al 2006, Nair and Kiremidjian 2007). When analyzing the data, it was observed that results obtained from using the AR algorithm are not significantly different than those obtained using an ARMA algorithm. Therefore, to simplify the computations, the AR algorithm is used. The AR model is given by the following equation: x ij (t) = p α k x ij (t k) + ε ij (t) (2) k=1 where x ij (t) is the normalized acceleration signal of the jth chunk of the ith sensor, α k is the kth AR coefficient, p is the AR model order, and ε ij (t) is the residual term. The Burg algorithm (Brockwell and Davis 2003) is used to estimate the AR coefficients. Running the AR model on each chunk from a single sensor produces N vectors of AR coefficients of length p, wheren is the total number of chunks from one sensor. Thus it follows that total signal length N =. (3) chunk length The optimal chunk length is determined by calculating the mean and standard deviation of the AR coefficients at different chunk length, and then determining at which point they begin to stabilize. Figure 4 shows a plot of the mean of the 1st AR coefficient at varying chunk lengths. A 3

4 Figure 4. Variation of AR coefficient value with chunk size. Figure 6. AR residual values over length of one chunk. Figure 5. Optimal AR model order selection using AIC. Figure 7. ACF of residuals. chunk length of 400 was found to be optimal in this study. The optimal AR order can be estimated using the Akaike Information Criterion (AIC) as described in Nair et al (2006). The optimal order is found to be in the range of 6 8, as shown in figure 5. In this study, an AR order of 8 is used. Subsequently, the residuals of the AR model are tested to determine if they are independent and identically distributed. This is important, because the original acceleration signals are assumed to be a result of ambient vibrations and are therefore assumed to be linear stationary signals. Figure 6 plots the residuals of the AR model superimposed over a plot of the actual acceleration signal. The variance of the residuals grows and shrinks slightly with the amplitude of the acceleration signal. Aside from that, the residuals appear to be independent and have zero mean. A plot of the ACF (figure 7) shows that there are no significant trends in the residuals. At lags greater than zero, the ACF value drops vary an insignificant amount. 5. Feature discrimination The next step is to determine whether the feature vector has migrated from an undamaged baseline case to a potentially damaged state referred to as the test case. If the feature vector is determined to have migrated sufficiently in a statistically significant sense then it is concluded that damage has occurred. It should be noted that for each baseline or test case, it is not merely one feature vector but rather N feature vectors that are being tracked. Thus, it is desirable to determine whether the cluster mean has migrated. Previous research has done this by using a standard t-test (Nair et al 2006). However, it will be shown in this study that a normalized difference in means of 4

5 the baseline and test case suffice to show whether sufficient migration has occurred. In order to perform the calculations, however, the proper damage sensitive feature must first be formulated. As stated before, the DSF is a function of the AR coefficients, but defining this function is not trivial. After extensive study of the data, it was observed that the first AR coefficient alone is sufficient to capture the migration of the feature vectors. More complex combinations of AR coefficients tested did not significantly improve the performance of the algorithm. The standard t-test can be used to determine whether the AR coefficient mean has changed significantly. The null hypothesis H 0 is that the AR coefficients from the base case and test case are given by the same distribution. The t-statistic is calculated according to the following formula: AR AR Base Case Test Case AR t = (μ 2 μ 1 ) (4) 1 Sp n n 2 (n 1 1)σ1 2 Sp = + (n 2 1)σ2 2 (5) n 1 + n 2 2 where μ 1 and μ 2 are the mean of the AR coefficients from the base case and test case, σ 1 and σ 2 are their standard deviations, and n 1 and n 2 are the number of observations within each group. Using the cdf of the t-distribution, p values are calculated from the t-statistic, representing the probability of observing the current data, given that the null hypothesis is true. A level of significance α can be set at which the null hypothesis is either rejected or accepted. The problem with this framework is that the level of significance α necessary in order to conclude that damage has or has not occurred is not predetermined. Concluding that the AR coefficients represent two separate populations is not useful if that does not correspond to physical damage. What is desired is the threshold of how far apart the AR coefficient clusters need to be in order to conclude that damage has occurred. Thus, a form of supervised learning is required by which the damage detection algorithm uses training data where the damage state is known beforehand in order to determine this threshold. Since a supervised learning approach is necessary anyway, another approach is to simply take the difference in means between the two AR coefficient clusters, and then determine a damage threshold, thereby avoiding the t-test altogether. A normalized mean distance measure γ is chosen, given by the formula γ = μ 1 μ 2 (6) σ 1 + σ 2 where μ 1 and μ 2 are the mean of the AR coefficients from the base case and test case respectively, σ 1 and σ 2 are their standard deviations respectively. Another method of measuring the migration of the feature vector clusters is by computing the centroid to centroid distance between the undamaged cluster and test cluster. One advantage of using this method is that by considering the multivariate centroid distance, the effects of several AR coefficients can be considered in this damage measure. It is Figure 8. AR coefficient cloud migration plotted in 3D AR coefficient space. observed that the magnitude of the first three AR coefficients is significantly larger than the magnitude of subsequent AR coefficients; therefore only the first three AR coefficients are kept and the others are discarded. Thus the distance between two clusters in three-dimensional AR coefficient space is measured. A new damage measure (DM) based on the Mahalanobis distance is proposed. The Mahalanobis distance between two clusters is given by the equation = (X Y ) T (X Y ) (7) where X and Y are the centroids of each cluster, and is the covariance matrix of one of the clusters. In order to take into account both clusters covariance matrices and their cross covariance matrix, the DM is given by the equation DM = (μ undamaged μ damaged ) T S inv (μ undamaged μ damaged ) (8) where S inv = ( undamaged + damaged 2 cross ) 1 (9) μ undamaged is the centroid of the undamaged data set, μ damaged is the centroid of the damaged data set, undamaged is the covariance matrix of the damaged data set, damaged is the covariance matrix of the damaged data set, and cross is the cross covariance matrix between each data set. Figure 8 shows a plot of AR coefficient clouds from two separate damage setups. The signals are sample measurements of the ambient response of the Z24 bridge that was subjected to varying degrees of damage as described in greater detail in the application section of this paper. As the clouds migrate with damage, the value of the DM increases. Again, in order to detect damage, a form of supervised learning must be used, where the algorithm is trained to recognize damaged and undamaged data sets and thus develops a threshold value beyond which it is concluded that damage has occurred. Also note that the magnitude of the DM can be used to measure damage extent. This will be explained in further detail in the section presenting algorithm results. 5

6 Figure 9. The Z24 bridge with the Koppigen pier circled. Figure 10. Diagram of crack formation near Koppigen pier. 6. Damage detection algorithm summary In summary, the damage detection algorithm is composed of the following steps. (1) Collect acceleration data from sensors located on an undamaged structure. (2) Compute and store the AR coefficients as described above, including data preprocessing. (3) Collect acceleration data from the same sensors at some later point in time. (4) Compute the AR coefficients as described above, including data preprocessing. (5) Perform feature discrimination techniques calculate the p value (or γ value) or the DM and compare the result with a previous training set to determine whether the AR coefficient cluster has migrated sufficiently to conclude that damage has occurred. 7. Application of damage algorithm to the Z24 bridge in Switzerland The damage detection algorithm was tested on data collected from a progressive damage test on the Z24 bridge in Switzerland. The purpose of this study is to test the efficacy of the damage detection algorithm described above in discriminating between different controlled damage states to which the bridge was subjected. The Z24 bridge spans the A1 Berne-Zurich motorway linking Koppigen with Utzenstorf in Switzerland. The threespan structure has a total length of 58 m, subdivided in three spans of 14, 30 and 14 m, respectively. The superstructure 6

7 Μ Figure 11. Location of sensors across bridge deck. consists of a two-cell closed box girder with tendons in the three webs. Both main piers were built as concrete diaphragms, fully connected with the superstructure. The bridge was subjected to a number of progressive damage tests. Three damage scenarios are examined in this study: of one bridge pier, removal of posttensioning anchor heads, and cutting of tendons. In order to simulate, one section of one pier was cut away and replaced by mechanical jacks, which were gradually lowered. Damaged was introduced to the structure by gradually settling the Koppigen pier up to 95 mm. The location of the pier is circled in figure 9. This produced cracks in the deck as shown in figure 10. The cracks marked in red occurred when the increased from 40 to 80 mm. The cracks marked in blue occurred when the increased from 80 to 95 mm. After the tests, the Koppigen pier was raised back to its initial height and another reference case data were collected. Two additional damage test data were gathered after removing the post-tensioning anchor heads and cutting the bridge tendons. Although additional damage tests were performed on the Z24 bridge, they are not considered in this study. Acceleration data were recorded by sensors at various locations on the bridge, at ambient vibration conditions, after the bridge was subjected to each damage setup. Data were collected at a sampling rate of 100 Hz. Figure 11 shows the locations of the accelerometers on the bridge deck. The sensing equipment was installed in nine sections on the deck. Fifteen sensors were placed on each of the nine sections of the deck for a total of one hundred and thirtyfive sensors (however, due to sensor malfunction, a portion of the collected data is discarded). Acceleration was collected in the longitudinal, transverse, and vertical direction; however, only results using vertical acceleration signals are presented for simplicity. Results for longitudinal and transverse acceleration data are similar to the results obtained for the vertical accelerations. The following data sets are analyzed in this study: Test case Description 1 A reference case collected after cutting of the Koppigen pier, installation of the mechanical jacks and re-leveling the bridge to original height. 2 After 20 mm pier. 3 After 40 mm pier. 4 After 80 mm pier. Cracks were observed to have developed on the bottom of the bridge girder. 5 After 95 mm pier. Further cracking was observed. 6 A second reference case collected after restoring the Koppigen pier to its original height. 7 After removal of post-tensioning anchor heads. 8 After cutting of tendons. For the computation of damage measures, the pier damage cases (test cases 2 5) are compared to the reference (test case 1). The removal of posttensioning anchor heads (test cases 7 and 8) and cutting of tendon tests are compared to the second reference (test case 6). 8. Analysis results Table 1 shows the normalized damage measure γ,asdefined by equation (6), calculated from data collected from sensors located across the bridge deck for test cases 2 5 and 7 8. The table lists the results for three of the fifteen sensors in each section on the deck and the sensor location number is listed in the first column. After review of all the data, some of the data were discarded due to problems identified in preprocessing. Table 2 shows the multivariate damage measure, as defined by equation (8), for the same sensor locations. In addition, 7

8 Location Table 1. Standardized differences in mean γ values for various sensor locations. 20 mm 40 mm 80 mm Damage case 95 mm Removal of post-tension anchor heads Cutting of tendons Location 20 mm Table 2. DM values for various sensor locations. 40 mm 80 mm Damage case 95 mm Removal of post-tension anchor heads Cutting of tendons the damage measure for three sensors at different locations on the bridge is plotted in figures The locations are chosen to provide a broad overview of the effect of damage on the AR coefficients at different locations on the bridge deck. Figures 12 and 13 show the γ and DM damage measures respectively for a sensor located near the bridge abutment. Figures 14 and 15 show both damage measures for a sensor at the bridge midspan, and figures 16 and 17 show both damage measures for a sensor located above the bridge pier. The locations of these sensors are shown in figure 11. These results indicate that the algorithm detects damage in the Z24 bridge through a pattern classification framework with AR coefficients as the features. It is worth noting that the post-tension anchor head removal and tendon cutting damage cases (test cases 7 8) are consistently different than the pier damage cases (test cases 2 5), even though the 8

9 Figure 12. γ values for sensor located near abutment. Figure 15. DM values for sensor located at midspan. Figure 13. DM values for sensor located near abutment. Figure 16. γ values for sensor located above bridge pier. Figure 14. γ values for sensor located at midspan. Figure 17. DM values for sensor located above bridge pier. values of the damage measures γ and DM are not consistently in the same direction for each test case at each location. Thus, it is concluded that the AR coefficients are capable of detecting changes in the structure of the bridge, and that different types of structural damage will have different effects on the AR coefficients implying that the algorithm can potentially be used to correlate the damage measures to the type of damage. In addition to computing the damage measure of each damage case compared to a baseline case, the incremental change in damage measure between each damage case is shown in figure 18. This is done for the three-dimensional multivariate damage measure defined by equations (8). The damage measure difference is denoted as DM i ( γ i in the one-dimensional damage measure), which is the DM measured 9

10 Location Table 3. Incremental damage measure DM values for various sensor locations. 20 mm 40 mm 80 mm Damage case 95 mm Removal of post-tension anchor heads Cutting of tendons Figure 18. DM values for sensor located at midspan. Figure 19. DM values for sensor located at midspan. between damage case i and damage case i 1. In the one-dimensional case, the sum of all γ i from i = 2to some k will closely approximate the value of γ k, the damage measure from case k to the baseline case. However, with a multivariate distance measure, it is possible to have migration of AR coefficients between two distinct damage cases in a direction such that the distance of each damage state to the baseline remains unchanged. The incremental change in the damage measure will capture the change from one damage state to the next, and it is desirable to show that effect as well. Table 3 lists the values of DM for representative sensors on the bridge deck for test cases 2 5 and 7 8, and figure 18 plots the DM for one sensor for the same test cases. As is observed in figure 18, the incremental damage measure is large for the 20, 40, and 80 mm pier cases (test cases 2 4) while it is small for 95 mm (test case 5). This makes sense since the incremental damage caused by from 80 to 95 mm may also be relatively small. The change in amount is smallest for the mm case; in addition, once cracking occurs, additional cracking may not change the bridge s structural response as much as the initial cracking. For the post-tensioning anchor head removal and cutting of tendons (test cases 7 8), because only two damage cases are analyzed, it is difficult to detect any trend. After computing the incremental damage measures, a total damage measure can be defined by summing the previous incremental damage measures. The cumulative damage measure k i=n DM i is defined as the sum of all DM i from i = n to k, wheren is some test case immediately following a baseline reference case, and k is the test case of interest. Table 4 lists the values of the cumulative damage measure for representative sensors on the bridge deck. Figure 19 shows the cumulative damage measure for the same sensor as 10

11 Location Table 4. Cumulative damage measure values for various sensor locations. 20 mm 40 mm 80 mm Damage case 95 mm Removal of post-tension anchor heads Cutting of tendons shown in figure 18. It is observed that this measure increases monotonically, which corresponds to the monotonically increasing pier applied during the damage tests. However, since the DM as defined by equation (8) isalways positive, the summed incremental damage measure will always increase monotonically. Therefore, use of this measure to diagnose damage must be done with care, since noise among many unchanged test cases will also result in a monotonically increasing damage measure. The incremental damage measures must be analyzed first relative to the measurement noise in order to determine when use of the cumulative damage measure is appropriate. 9. Conclusion This study demonstrates that a damage detection algorithm based on a pattern classification framework can detect structural changes caused by damage. While previous studies applied the algorithm primarily to laboratory or numerically simulated data, this investigation is based on data collected from a real structure subjected to various types of damage. The two damage measures used to identify and potentially quantify damage are based on (a) the distance between the mean values of the AR coefficients normalized to the square root of the sum of the variances of the baseline and damaged cases denoted as γ, and (b) the Mahalanobis distance between the baseline and the damaged structure denoted as DM also referred to as the multivariate damage measure. It is found that γ will change sign depending on the type of damage. More specifically, for many of the sensor locations, it is observed that the γ value has a different sign and magnitude for the of the bridge pier than the γ value for the cut tendon or anchor head removal. The multivariate damage measure DM as defined is positive for all damage states and no correlation could be found between the degree of damage and the damage measure. In order to improve the ability of the algorithm to correlate the damage measure to the degree of damage a new measure is introduced that uses the incremental change in the structure, which will result in an incremental change in the damage measure. The new damage measure is defined as the sum of the incremental changes and is defined as the cumulative damage measure. It is observed that the incremental change in damage measure reflects the incremental amounts of for all cases. In addition, the cumulative damage measure is found to be correlated to the total monotonically increasing. The application of this measure to the tendon cutting and anchor head removal also showed good results; however, these damage states are independent of each other and may not reflect a gradual increase in damage. Since only two damage states were investigated, a pattern could not be discerned on that basis. The cumulative damage did show that additional damage had resulted in the structure when both damage conditions were present. Overall, the cumulative damage measure is found to be more robust than the two previously used damage measures. Care, however, must be taken to determine the influence of noise on such incremental changes to avoid false positive damage diagnoses. More specifically, summing incremental changes due to noise will result in a large cumulative damage even though damage may not have taken place. It is emphasized that the damage detection algorithm proposed in this study will require in practice a training data set in order to better distinguish between damaged and undamaged samples. Since training data typically would not be available, a numerical simulation may be needed to identify different damage states and use the simulated data as the training set. Furthermore, a library of a structure s different damage 11

12 patterns can be built over time for purposes of training damage detection algorithms and these can be repeated for various structures. The effects of damage to a large structure are often complex with numerous locations of damage and varied types and amounts of damage. Thus, as the complexity of the structure increases, the damage measures are likely to identify the damage occurrence; however, the correlation to the type of damage will become increasingly more difficult. However, careful examination of the structure and the types of damage that can occur locally in close proximity of a sensor can be helpful in narrowing down the many options to a manageable size. Furthermore, use of different sensors and sensors specialized for specific type of damage (e.g. corrosion sensors, strain sensor, in addition to vibration sensors) can greatly enhance our ability to more reliably predict the amount and type of damage. Acknowledgments This research was partially supported by the National Science Foundation through an NEES Grant and by a grant from the National Institute from Standards and Technology, ATP Contract. The authors gratefully acknowledge their support. References Boore D M, Stephens C D and Joyner W B 2002 Comments on baseline correction of digital strong-motion data: examples from the 1999 hector mine, California earthquake Bull. Seismol. Soc. Am Brockwell R J and Davis R A 2003 Introduction to Time Series and Forecasting 2nd edn (Berlin: Springer) p 456 Doebling S W, Farrar C R, Prime M B and Shevitz D W 1996 Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review Los Alamos National Laboratory Report LA MS Farrar C R and Sohn H 2000 Pattern recognition for structural health monitoring Workshop on Mitigation of Earthquake Disaster by Advanced Technologies (Las Vegas, NV, Nov. Dec.) Farrar C R, Sohn H and Park G 2004 A statistical pattern recognition paradigm for structural health monitoring Proc. 9th ASCE Joint Specialty Conf. on Probabilistic Mechanics and Structural Reliability (Albuquerque, NM, July) Farrar C R, Worden K, Manson G and Park G 2005 Fundamental axioms of structural health monitoring Proc. 5th Int. Workshop on Structural Health Monitoring (Stanford, CA, Sept.) Manson G, Worden K and Allman D J 2003a Experimental validation of structural health monitoring methodology II: novelty detection on a laboratory structure J. Sound Vib Manson G, Worden K and Allman D J 2003b Experimental validation of structural health monitoring methodology III: novelty detection on a laboratory structure J. Sound Vib Nair K K and Kiremidjian A S 2007 Time series based structural damage detection algorithm using gaussian mixtures modeling ASME J. Dyn. Syst. Meas. Control Nair K K, Kiremidjian A S and Law K H 2006 Time series based damage detection and localization algorithm with application to the ASCE benchmark structure J. Sound Vib Sohn H, Farrar C R, Hunter H F and Worden K 2001a Applying the LANL statistical pattern recognition paradigm for structural health monitoring to data from a surface-effect fast patrol boat Los Alamos National Laboratory Report LA MS Sohn H, Farrar C R, Hunter N F and Worden K 2001b Structural health monitoring using statistical pattern recognition techniques ASME J. Dyn. Syst. Meas. Control (Special issue on Identification of Mechanical Systems) Straser E G and Kiremidjian A S 1998 A modular wireless damage monitoring system forstructures Report No. 128 John A Blume Earthquake Engineering Center, Stanford, CA Wenzel H 2005 personal communication Worden K, Manson G and Allman D J 2003 Experimental validation of structural health monitoring methodology I: novelty detection on a laboratory structure J. Sound Vib Worden K, Manson G and Fieller N R 1999 Damage detection using outlier analysis J. Sound Vib