Damage Detection Using Wavelet Transforms for Theme Park Rides

Damage Detection Using Wavelet Transforms for Theme Park Rides Amy N. Robertson, Hoon Sohn, and Charles R. Farrar Engineering Sciences and Applications Division Weapon Response Group Los Alamos National Laboratory Los Alamos, NM 87545 ABSTRACT In this study, an online monitoring system has been developed for amusement park rides. A specific type of damage is investigated, the delamination of an aluminum/polymer wheel on a roller coaster vehicle which rides on a rail. This wheel delamination can cause increased vibration in the wheel contact with the rail, leading to a more discontinuous response measured at the rail. Three different methods are reviewed for detecting the presence of damage in the acceleration response of the rail while the vehicle is passing over. Each method is based on extracting features from the wavelet transform of the dynamic signal. The first method examines the decay of the wavelet transform modulus across the scales at each time point, which is a measure of the regularity of the signal and is called the Holder Exponent. Low regularity indicates the presence of a discontinuity. The second method looks at chaining together ridges of high amplitude coefficients in the wavelet modulus (the modulus maxima) across the scales, and examining the length of the chains to indicate the presence of a discontinuity. The third method reviewed, wavelet variance, examines the time variation of each frequency band in the wavelet transform. The proposed methods are applied to the acceleration responses from a real-world theme park ride in Orlando, Florida to demonstrate their effectiveness. INTRODUCTION Currently every ride in theme parks must go through rigorous visual inspection on a daily basis to make sure it is as safe as possible before it opens every morning. Since 198 there have been over 47 amusements ride deaths in the United States, although most of these deaths are related to riders not following safety procedures (www.disneyforever.com). It seems that daily inspection might not be enough to prevent catastrophic disasters and that amusement park rides need to be continuously monitored. Ideally, the damage detection procedure should be continuous and automated, requiring minimum human intervention only when damage has occurred. The main objective of this study is to develop an online monitoring system for a specific roller coast ride, which can be installed on the rails to monitor incipient damage during its normal operation. The specifics of the roller coaster are not disclosed at this point because of a nondisclosure agreement with our industrial partner. Our customer identifies that the main failure mode of the ride system is the delamination between an inner aluminum wheel and its outer polymer layer on the roller coaster vehicle. However, because a sensing system cannot be easily installed on the moving wheels, a compromise is made to install the sensing system at one location on the rail track. The issue of the sensor placement limitation makes damage identification more challenging for this application. In this paper, a structural health monitoring system based on wavelet analysis has been developed and applied to data recorded from field testing of roller coaster rides in Orlando, Florida. This paper is organized as follows: first, the test configuration of the roller coaster rides and data recorded from the test are described. Second, a frequency analysis of the data is presented which will help in interpreting the wavelet transform results. Third, a brief description of wavelet transforms and the features that can be extracted from them for damage detection is given. Then, the experimental results based on the proposed structural health monitoring process are presented. Finally this paper concludes with findings of this study and recommendations for future testing. ROLLER COASTER TEST CONFIGURATION The data presented here were recorded from an actual roller coaster at a theme park in Orlando, Florida (see [1] for more detail. Data were acquired during test operation of the ride. As shown in Figure 1, three accelerometers were installed on the left rail of the roller coaster (Channels 1-3) and three accelerometers and a photosensor were installed on the right rail (Channels 4-7). The photosensor was used to indicate when the

vehicle is passing over the sensing system and to trigger data acquisition from the accelerometers. All data are sampled at 12, Hz, and the sensitivity of all accelerometers is 1 mv/g. Fifty data sets were subsequently acquired from three different vehicles (trains 3, 4 and 6) with varying speeds, mass loading and damage conditions, as listed in Table 1. Each data set contains a time signal from one complete run of a train over the sensing system. Because the majority of the data in each signal corresponds to times when the train was far away from the sensors, the signals were trimmed. By inspecting the photosensor signal, the signals were trimmed to include only the sections where the train was over the sensing system. All of the trimmed signals are approximately 14, data points long. For the damaged cases, the left rear side-guide wheel of train 3 was replaced with several damaged wheels, as shown in Figure 2. The first wheel from the left in Figure 2 is an intact normal wheel, and the second wheel has a light-colored spot delamination. The third wheel is fully delaminated and was specially manufactured by coating the aluminum wheel with the polymer layer without putting any epoxy between them. Contradictory to our expectation, the polymer layer did not come off from the aluminum wheel even after several test runs. The final damage case was simulated by completely removing the polymer layer from the aluminum wheel (the fourth wheel in Figure 2). Five data sets were recorded from train 3 with the normal wheel (data sets 3, 6, 9, 12 and 15), two data sets with the partially delaminated wheel (data sets 19 and 21), two data sets with the fully delaminated wheel (data sets 37 and 4), and one data set with only the bare aluminum wheel (data set 48). All data from trains 4 and 6 were recorded with the normal wheel. (a) Installation of accelerometers on left rail (b) Installation of accelerometers and photosensor on right rail Figure 1: Location of six accelerometers and one photosensor Figure 2: Damage conditions of the left rear side-guide wheel

Note that damage was introduced only to train 3, and additional mass loading was introduced to train 3 by adding rock dummies on the vehicle (as indicated by the full loading condition in Table 1). In addition, at any given time point, there was only one test vehicle on the track. Two different levels of the ride speeds ( high and normal ) are experienced by the ride, but no quantitative information regarding the absolute speed of the train was provided at this point. Table 1: A list of collected test data sets ID # Time Train Loading Speed Wheel ID # Time Train Loading Speed Wheel 1 23:52 4 Empty Normal 26 1:5 4 Empty High 2 23:53 6 Empty Normal 27 1:6 6 Empty High 3 23:54 3 Full High New 28 1:8 4 Empty Normal 4 23:54 4 Empty Normal 29 1:1 6 Empty Normal 5 23:55 6 Empty Normal 3 1:11 4 Empty Normal 6 23:56 3 Full High New 31 1:12 6 Empty Normal 7 23:57 4 Empty Normal 32 1:13 4 Empty Normal 8 23:58 6 Empty Normal 33 1:14 6 Empty Normal 9 : 3 Full High New 34 1:16 4 Empty Normal 1 :1 4 Empty Normal 35 1:19 6 Empty Normal 11 :2 6 Empty Normal 36 1:2 4 Empty Normal 12 :3 3 Full Normal New 37 1:21 3 Full High Fully Delaminated 13 :5 4 Empty Normal 38 1:22 6 Empty Normal 14 :6 6 Empty Normal 39 1:23 4 Empty Normal 15 :7 3 Full Normal New 4 1:25 3 Full High Fully Delaminated 16 :8 4 Empty Normal 41 1:26 6 Empty Normal 17 :9 6 Empty Normal 42 1:27 4 Empty Normal 18 :35 4 Empty High 43 1:3 6 Empty Normal 19 :38 3 Full High Spot-delaminated 44 1:31 4 Empty Normal 2 :42 4 Empty High 45 1:37 6 Empty Normal 21 :46 3 Full High Spot-delaminated 46 1:4 4 Empty Normal 22 :48 4 Empty High 47 1:41 6 Empty Normal 23 :5 6 Empty High 48 1:42 3 Full High Bare Aluminum 24 :51 4 Empty Normal 49 1:43 4 Empty Normal 25 1:4 6 Empty High 5 1:44 6 Empty Normal FREQUENCY ANALYSIS Only one of the six acceleration channels shown in Figure 1, the channel 4 signal, was used for analysis. This channel measures acceleration in the lateral direction perpendicular to the right rail, and was chosen because it proved to be the most sensitive to damage in the wheel. It is speculated that the sensitivity of the channel 4 signal is attributed to the configuration of the accelerometers. The accelerometer sensors are placed near the tail of the track s downhill run, and there is a horizontal curve at the end of the hill, producing more centrifugal forces on the right rail rather than on the left rail. Furthermore, because the polymer delamination is introduced on the sideguide wheel, the channel 4 sensor, which measures the accelerometer in the lateral direction perpendicular to the rail, seems more influenced by damage than the sensors in the other directions. Therefore, only results from channel 4 are presented in this paper. Before the wavelet transform was employed, the frequency characteristics of Channel 4 from all 5 tests were analyzed using a Fourier transform. The frequency spectrum was calculated by subdividing the 14 point signals into 6 sections of 248 points each, and averaging the frequency spectrums of each section. Figure 3 shows the resulting 5 frequency spectrums as well as a zoomed-in view of the lower and upper frequencies. This closer view allows one to see that all tests performed with Train 3 (this includes the damaged case have a

very different frequency spectrum in the lower frequencies than the remainder of the tests. The difference is likely caused by the change in loading for Train 3. Train 3 was fully loaded with weights during its runs while the remaining trains were run empty. Also notice that there is a set of tests that appear to have a different frequency spectrum in the upper frequencies. These tests correspond to the last six tests performed: numbers 45-5, which were all recorded on the same tape, id4. It is not known why the tests that appear on this tape should differ from the others becuase the testing conditions (empty, normal) appear to be similar to many of the other tests performed. 6 Complete Frequency Spectrum Mag. 4 2 1 2 3 4 5 Lower Frequencies Mag. 6 4 2 Trains 4,6 Train 3 5 1 15 2 25 3 Upper Frequencies Mag. 8 6 4 2 Data sets 1-44 Data sets 45-5 46 48 5 52 54 56 58 Frequency (Hz) Figure 3: Fourier transform of all 5 data sets: (a) Full frequency spectrum, (b) Lower frequencies, (c) Upper frequencies The differences between individual tests in the upper and lower frequencies can be seen more clearly in Figure 4. For this figure, the mean correlation coefficient between the frequency spectrum of each individual test and the remaining tests was determined. This number was then subtracted from the greatest correlation value amongst all the tests to reveal those tests which showed the least correlation with the others. A correlation was found both for the bottom half of the frequency spectrum and the upper half. Figure 4 shows clearly the large difference in the lower frequencies for tests performed with Train 3 (damage runs are also done with Train 3), and the large difference in the upper frequencies for tests recorded on tape id4. This observation brings our attention to the fact that any damage detection procedure employed needs to be able to distinguish changes in the features caused by damage from those caused by ambient operational and environmental variations of the system. The hope is that by focusing on the discontinuous nature of the signals using wavelets will provide this discrimination.

8 7 6 Lower Frequencies 1 9 8 Upper Frequencies No Damage Damage Train 3 Lack of correlation 5 4 3 2 1 Lack of correlation 7 6 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 Test # Test # Figure 4: Measure of degree of lack of correlation between individual test frequency spectrum and the others: shown for the upper and lower half of the frequency spectrum WAVELET TRANSFORM Wavelets are mathematical functions that decompose a signal into its constituent parts using a set of wavelet basis functions. This decomposition is very similar to Fourier transforms, which use dilations of sinusoids as the bases. The family of basis functions used for wavelet analysis is created by both dilations (scaling) and translations (in time) of a mother wavelet, thereby providing both time and frequency information about the signal being analyzed. The wavelet transform, WT(u,, is obtained by convolving the signal f(t) with the translations (u) and dilations ( of the mother wavelet: where 1 * t u WT ( u, = f ( t) ψ dt (1) s s t u ψ * 1 u, s ( t) = ψ s s (2) The frequency content of the wavelet transform is represented in terms of scales, which are inversely related to frequencies. The squared amplitude of the continuous wavelet transform is therefore called the scalogram. The relationship between scales and frequencies is easily found, and a time-frequency map can be formed from the scalogram. This two dimensional representation of the signal provides information on how the frequency content of the signal is changing with time. The wavelet transform (WT) was calculated for Channel 4 of all 5 Tests when the train was passing over. A complex Morlet wavelet of length 16 with 64 scales was used. The WT time-frequency representation was then used to extract features from the data in hopes of discriminating between undamaged and damaged test sets. These features include Holder exponents, modulus maxima, and wavelet variance, each of which will be reviewed in the following sections. The reviews are kept to a minimum due to the limited length of this paper, so the reader is referred to other papers in each section to learn more about the details of these methods.

Figure 5: Wavelet Transform of Test Run 48 HOLDER EXPONENT ANALYSIS The Holder Exponent is a measure of the regularity of a signal. Regularity is related to the smoothness of the signal. If a signal is highly continuous (e.g. a sine wave), it has a large Holder exponent value, but a discontinuous signal such as a step function will have a low Holder exponent value. The regularity may be measured at each time point in the signal by using a time-frequency transform, such as the wavelet transform used here. Thus, the time-variation of the Holder exponent (regularity) may be examined. Past experience has shown that the Holder exponent is sensitive to damage that introduces high frequency components into the measured response [2]. The Holder regularity is defined as follows. If a signal f (t) has a Holder exponent α over [a,b], then there exists A > such that [3]: WT( u, As α + 1/ 2 ( u, [ a, b] (3) where WT ( u, is the wavelet transform modulus of f(t). The exponent α can be calculated at a specific time point by finding the slope of the log of the modulus at that time versus the log of the scale vector s: log WT ( u, = log( A) + ( α + 1/ 2)log( (4) log WT ( u, m = 1/ 2 = α (5) log( The Holder Exponent (HE) will be used here to examine the vibration response of the track. If a rattle is present in the track, such as when a train is moving across, the response can become fairly discontinuous. A discontinuity has a regularity of zero or lower. Therefore, a discontinuity can be identified in the time varying HE function as points where the HE values are low, or drop significantly. If damage is present in one of the wheels of the roller coaster, it is believed that an even larger rattle will be induced into the track, causing even more discontinuities in

the measured acceleration response of the track. Therefore, the aim of this analysis is to identify damage by the presence of increased discontinuous behavior in the track response. A time-varying Holder exponent function was calculated from each of the 5 wavelet transforms. The analysis of these functions unfortunately did not show the damaged sets to have lower Holder exponents than the other data sets, which was expected. It was found, though, that by decimating the time signals by 1/1 using the Matlab function, decimate.m, and focusing on the lower frequencies ( 5.71 Hz) contained in the last 23 scales, this analysis became more effective. Figure 6 shows the number of times that the time-varying Holder exponent drops below a prescribed threshold for each test. The threshold in this case was determined by fitting the Holder exponents from the first five tests to an extreme value distribution [6] and finding the value associated with a confidence interval of 9%. Tests 4 and 48 show the most exceedances and are associated with a fully delaminated and bare wheel respectively. Similar results are seen in Figure 7, which displays the mean value of the time-varying Holder exponent function for each test run. The decimation and selection of frequency band for investigation both contribute to creating an analysis that focuses on a specific frequency band of interest in the lower frequency range. Typically Holder exponent analysis is based on the influx of high frequency information into the signal due to discontinuities. However, as was shown in the frequency analysis section above, Tests 45 to 5 show a significant increase in high frequency content over the other tests. Therefore, taking a standard approach to Holder exponent analysis would only identify Tests 45 to 5 as those with damage. Since we have been forced to examine a subsection of the frequency range, Holder exponents are probably not the most effective approach to be used here. 4 35 No Damage Train 3 Damage -.5 Number of Exceedences 3 25 2 15 1 5 Mean of HE -1-1.5-2 -2.5 1 2 3 4 5 Test No. Figure 6: Number of Minima Values in HE Function Below 9% Threshold 1 2 3 4 5 Test No. Figure 7: Mean Value of Time-Varying Holder Exponent Function MODULUS MAXIMA Mallat and Hwang [4] first introduced a method for detecting discontinuities in a signal by examining the evolution of the maxima of the modulus of the wavelet transform across the scales. A modulus maximum (s,u ) is defined as a local maximum of the modulus of the wavelet transform WT(s,u ) at a fixed scale, s. A full definition is given by Mallat and Hwang in [4]: A local extremum of the wavelet transform of f(t) is any point (s,u ) such that:

WT( s, u) x = (6) A local maximum is any point (s,u ) such that WT ( s, u) < WT( s, u ) when u belongs to either the right or the left neighborhood of u, and WT ( s, u) WT ( s, u ) when u belongs to the other side of the neighborhood of u. (This statement does not make sense to me.) A maxima line is any connected curve in the scale-time space along which all points are modulus maxima. Points of sharp variation in a signal (such as impulses or jump create maximum points in the wavelet transform. The first step for finding these discontinuities is to identify the modulus maxima of the wavelet transform. Next, these maxima must be chained together by stepping through the scales of the wavelet transform and finding maxima points that are close to one another in time. Only maxima lines that continue from the coarser scales to the finer scales have the possibility of being associated with a discontinuity. Noise produces modulus maxima in a signal at the higher scales, but does not usually progress to the lower. Instead, true discontinuities are identifiable by their presence at all scales. The length of the maxima line will therefore be the criterion used for identifying a discontinuous point in the roller coaster signals. maxfreq < 11 3 No Damage Train 3 Damage 25 # of Exceedences 2 15 1 5 5 1 15 2 25 3 35 4 45 5 Test # Figure 8: Number of Maxima Lines that Extend through the Frequency Spectrum, Threshold =.5 A modulus maxima map was formed for each of the 5 wavelet transforms. The same problems arise for analyzing the data using maxima lines as occurred for the Holder exponent analysis. Tests 45 to 5, with their increase in high frequency content, also end up having the largest number of maxima lines. Even if the effects of the high frequency information in Tests 45-5 could be alleviated, it was difficult to separate the undamaged runs on Train 3 from the damaged ones. In the end, the best results were found by first thresholding the maxima of the wavelet transform so that no values below 5% of the maximum value in the wavelet transform remained. Figure 8 shows the number of maxima that extended through the frequency range up to the 11 th scale, which equates to a frequency of 2181 Hz. All scales were not used here since none of the maxima lines from the thresholded wavelet transform extended through all 64 scales. The only damaged case that stands out is Test 48, which is the bare aluminum wheel, though Tests 19 and 4 also have a large number of long maxima lines present.

Wavelet Variance A third application of the WT is to look at what can be called the wavelet variance of the data. This was shown to be effective in finding the location of damage in an 8 DOF spring-mass system [5]. This method is based on the assumption that if damage is present, it will cause a change in the frequency content of the signal over time. By measuring the standard deviation across the time span of the WT for each frequency band, the level of damage present can be found. The formula used for determining this feature value, ST, is shown below. ST ( f j ) = n ( WT ( f j, ti ) WT ( f j )) i = 1 n 1 2 (7) where W T ( f j ) is the mean of the wavelet transform across time at a given frequency. Figure 9 shows the wavelet variance estimates for all 5 tests at all frequencies (scale. Just as with the frequency analysis, the higher frequencies of tests 45-5 have the same unique pattern in the upper frequencies, and the wavelet variance of all Train 3 runs in the lower frequencies look similar. The wavelet variance measure has provided a good means of dimension reduction of the data. Our original signals are approximately 14 time points long, and we have now represented that information with a 64-point feature pattern. It was decided therefore to take the approach of trying to classify these 64-point wavelet variance patterns into two groups: damaged and undamaged. Wavelet Variance 1.1 1.9.8.7.6.5.4.3.2.1 1 2 3 4 5 6 Frequency (Hz) Figure 9: Wavelet Variance Measurement for All 5 Tests Classification of the wavelet variance patterns was performed using an auto-associative neural network. An auto associative neural network (ANN) is formed by training a feed-forward neural network with network outputs that are simply the reproduction of the network inputs. The network consists of an internal bottleneck layer, two additional hidden layers, and the output layer [7]. The bottleneck layer contains fewer nodes that the input or output, therefore forcing the network to represent the data more compactly. In this case, a network with a 7:(5:2:5):7 layer construction was used. This means that the input to the network would now be represented with only 2 feature parameters.

The input and output to the ANN was the wavelet variance parameters from the 7 highest scales, corresponding to frequencies from to about 14 Hz. The lower frequency range was found to be the most sensitive to damage, as was seen with the Holder exponent analysis as well. Training of the neural network was performed with 2 data sets, including 3 of the 5 undamaged sets from Train 3, but none of the damaged sets. The remaining 3 data sets were then used to test the network. The output of the network should be the same as the input, and the difference between the two is the error in using the trained ANN to represent the data. Since the network was trained with undamaged data, it is assumed that the damaged cases would produce a larger amount of error. Figure 1 shows the error associated with each of the 5 data sets, formed by taking the average error across 1 repetitions of the training/testing procedure. For each iteration, a different random sampling of data sets were used for training, but always with the restriction that 3 of the 5 undamaged Train 3 runs are used for training and none of the damaged cases. Figure 1 clearly shows data sets 19, 37, and 48 to have significantly larger error than the remainder of the data sets. The other two damaged sets, 21 and 4, have higher error than most, but not as significant..8.7 No Damage Train 3 Damage Error.6.5.4.3.2.1 1 2 3 4 5 Test # Figure 1: Error in Auto-Associative Neural Network, Average of 1 Tests CONCLUSION This paper applies wavelet based damage detection methods to field data collected from roller coaster rides at a theme park in Orlando, Florida. The damage of main interest is the delamination of one wheel on the roller coaster vehicle. In order to detect this damage in 5 of the 5 data sets, variation in the data caused by damage needed to be separated from variations caused by ambient operational and environmental conditions of the system. The approach used was to look for an increase in the discontinuous nature of the signal to indicate the presence of damage. However, this approach tends to focus on the upper frequency content of the signal, and Tests 45-5 had a very unique upper frequency signature compared to the remainder of the data sets. Therefore, the lower frequency information was focused on instead. The variation in this frequency range was dominated by the change in loading conditions for Train 3. However, each of the three wavelet features extracted, Holder exponents, modulus maxima, and wavelet variance, showed some promise in distinguishing the damaged data sets from the remainder of the Train 3 runs. The discrimination of the wavelet variance using an auto-associative neural network gave the best results, with 3 of the 5 damaged sets appearing as outliers. This analysis could be improved if more test runs were available with more variation in loading, and if an explanation for the variations of the upper frequencies in tests 45-5 could be provided.

REFERENCES 1. Sohn, H., et al. (24) Online Damage Detection for Theme Park Rides, Proceedings of the 22nd International Modal Analysis Conference, Ann Arbor, MI. 2. Robertson, A.N., Farrar, C.R., and Sohn, H. (23) Singularity Detection for Structural Health Monitoring Using Holder Exponents, Mechanical Systems & Signal Processing, Vol. 17, no. 6, pp.1163-1184. 3. Struzik, A. (21) Wavelet Methods in (financial) time-series processing, Physica A, v. 296, pp. 37-319. 4. Mallat, S. and Hwang, W.L., (1992) Singularity detection and processing with wavelets, IEEE Transactions on Information Theory, vol. 38, pp. 617-643. 5. Robertson, A.N. (22) Investigation of the Morlet Wavelet for Nonlinearity Detection, Proceedings of the 2 th International Modal Analysis Conference, Los Angeles, CA. 6. Worden, K., et al., 22, Extreme Value Statistics for Damage Detection in Mechanical Structures, Los Alamos National Lab Publication LA-1393-MS. 7. Sohn, Hoon; Worden, Keith; and Farrar, Charles R. (23) Statistical Damage Classification under Changing Environmental and Operational Conditions, Journal of Intelligent Materials Systems and Structures, Vol. 13, no. 9, pp. 561-574.