ABSTRACT. Permanently mounted ultrasonic sensors are a key component of systems under development for structural health monitoring. Signal processing ...
ULTRASONIC SIGNAL PROCESSING FOR STRUCTURAL HEALTH MONITORING Jennifer E. Michaels and Thomas E. Michaels School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250
ABSTRACT. Permanently mounted ultrasonic sensors are a key component of systems under development for structural health monitoring. Signal processing plays a critical role in the viability of such systems due to the difficulty in interpreting signals received from structures of complex geometry. This paper describes a differential feature-based approach to classifying signal changes as either “environmental” or “structural”. Data are presented from piezoelectric discs bonded to an aluminum specimen subjected to both environmental changes and introduction of artificial defects. The classifier developed as part of this study was able to correctly identify artificial defects that were not part of the initial training and evaluation data sets. Central to the success of the classifier was the use of the Short Time Cross Correlation to measure coherency between the signal and reference as a function of time.
INTRODUCTION The use of ultrasound to monitor critical structures such as airplanes, bridges and buildings is an appealing possibility due to the potential for interrogating large areas with a small number of sensors. In particular, ultrasonic guided waves can travel long distances in suitable structures, and recent research has shown great promise in terms of detecting, locating and characterizing defects [1]. In contrast, traditional ultrasonic methods are generally not suitable for structural health monitoring due to the need for either large numbers of transducers or scanning to obtain adequate coverage. But successful use of guided waves requires a structure whose geometry supports propagation of specific modes. Other guided wave studies have been based upon larger numbers of embedded or surface mounted sensors transmitting and receiving short range signals that require analysis and identification of echoes reflected from boundaries [2]. Much of the work to date has concentrated on relatively simple geometries where the emphasis has been on generating modes or combinations of modes that are amenable to straightforward interpretation [3]. The approach considered here is to use permanently attached piezoelectric crystals for both transmission and reception of ultrasound, and to develop signal processing methods to aid in interpretation of the signals. Due to both the general purpose nature of the transducers and the complexity of realistic structures, complicated diffuse-like signals containing multiple modes are generated. The early time portion of the received signal has clearly identifiable arrivals, but in later times the signal becomes diffuse due to complicated interactions between multiple modes and multiple reflections from boundaries, even for homogeneous materials [4].
CP700, Review of Quantitative Nondestructive Evaluation Vol. 23, ed. by D. O. Thompson and D. E. Chimenti © 2004 American Institute of Physics 0-7354-0173-X/04/$22.00
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Ultrasonic monitoring of structures under realistic operating conditions is particularly difficult because both temperature changes and varying surface conditions (e.g. surface wetness) have as much or more effect on the ultrasonic signals as actual structural changes. A practical methodology for health monitoring is to (a) decide if there has been a change in the measured signal, (b) classify the change as either “environmental” or “structural”, and (c) characterize any structural changes in terms of type, size, location, severity, etc. The focus of the work presented here is to demonstrate the feasibility of the first two steps of detection and classification as these must be achievable before the third can be successful. MEASUREMENTS Measurements were made on a 6061 aluminum plate, 50.8 mm x 152.4 mm x 4.76 mm (2” x 6” x 3/16”), as illustrated in Figure 1(a). This specimen, although simple in both material and geometry, is of interest because reflections from the boundaries play a major role in the recorded signals and the geometry is not suitable for the use of guided waves. Two transducers were attached to the top surface of the specimen as shown in Figure 1(b). These transducers were constructed with longitudinally polarized, 2.25 MHz PZT disks, 12.5 mm diameter, and were attached to the specimen using cynoacrylate adhesive. A conventional ultrasonic pulser receiver (Panametrics 5072PR) was used for spike mode transducer excitation and waveform amplification. Waveforms were digitized with a sampling rate of 12.5 MHz and a resolution of 8 bits, and each recorded waveform was the average of 50 signals. The specimen was first subjected to environmental changes consisting of temperatures ranging from 9°C to 38°C (48°F to 100°F) and varying surface conditions. Surface conditions were changed by both wetting the top surface, and placing a small, oil-coupled aluminum block at various positions. The changes due to wetting the plate surface were not controlled because of the difficulty in applying a consistent pattern of water, but the changes due to positioning the oil-coupled block were consistent and thus could be repeated in conjunction with the introduction of flaws. Artificial flaws were introduced into the plate by first drilling a single hole, starting with a diameter of 1.98 mm (5/64”) and increasing the size up to a final diameter of 6.35 mm (1/4”). A second hole was later drilled in the same manner, as can be seen in Figure 1(b). Ultrasonic signals were recorded after each incremental change in diameter, and environmental changes were also applied. Table 1 provides a summary of all 275 recorded signals, with significant redundancy in order to assess measurement repeatability.
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FIGURE 1. Aluminum specimen used for all measurements; (a) drawing; (b) photograph.
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TABLE 1. Summary of recorded signals. Signals 1-27 28-33 34-53 54-73 74-94 95-129 139-149 150-168 169-219 220-239 240-263 264-275
Description Undamaged specimen, temperature varied from 9°C (48°F) to 38°C (100°F) Undamaged specimen, temperature varied from 31°C (88°F) to 26°C (78°F) Undamaged specimen, 23°C (73°F) Undamaged specimen, 22°C (72°F) Undamaged specimen, temperature varied from 10°C (50°F) to 32°C (90°F) Undamaged specimen, heated and surface wetted, then cooling off and drying Undamaged specimen, 24°C (75°F) Undamaged specimen, varied surface conditions via contact with oiled block Hole #1, drilled in increments combined with various environmental effects Specimen with hole #1, 23°C (73°F) Specimen with hole #1, varied surface conditions Hole #2, drilled in increments
Figure 2 illustrates typical signals from the specimen as follows: (a) undamaged and nominal environmental conditions (room temperature and dry, free surface), (b) undamaged at 10°C (50°F), and (c) hole #1 and nominal environmental conditions. For all of the signals the start time was 10 µsec and the total time window was 1000 µsec, which is sufficient to capture most of the energy of the ultrasound field; a longer window would not yield significant additional information due to the limited 8 bit resolution of the digitizer. Note that the 1000 µsec time window is equivalent to a longitudinal wave in aluminum traveling 6,350 mm (250 inches), which is over 40 times the length of the specimen. For reference, the calculated first arrival of the longitudinal wave occurs at 16.3 µsec, the first shear arrival is at 32.4 µsec, and the Rayleigh wave arrival is at 34.8 µsec. These arrivals are consistent with the recorded waveforms, and no attempt was made to identify additional arrivals due to the large number of combinations of edge reflections. The general trend and appearance of the three signals in Figure 2 are very similar, as is true for all of the recorded signals, although subtle differences are clearly evident. There are no obvious characteristics of the time domain signals that distinguish between environmental and structural conditions. Many signals were also examined in the frequency and timefrequency domains, and again there were no obvious distinguishing features.
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FIGURE 2. Recorded waveforms from (a) the undamaged specimen at room temperature and with a dry, free surface, (b) the undamaged specimen at 10°C (50°F), and (c) the specimen after the drilling of hole #1.
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ANALYSIS Due to the complexity of the recorded signals and the subtlety of the changes, a differential feature-based approach to analysis was taken, in contrast to the usual approach of calculating time and frequency domain features from a single signal [5]. The interpretation here of “differential” is that all methods and features explicitly incorporate comparison to a reference signal, and that if there are no changes from this reference, the condition of the structure is classified as unchanged. Although this approach may seem obvious, quantitatively incorporating it into the signal processing steps required careful consideration. Change Detection The first step was to determine whether or not a change had occurred compared to a recorded reference signal. The reference signal is not necessarily the room temperature baseline, but would typically be a signal recorded from the undamaged specimen under similar environmental conditions. It is anticipated that any practical system would be continually updating a history of baseline data, and during real-time monitoring, recorded signals would be compared to a sequence of recent historical data. For this study, the energy of the difference between the signal and the reference was calculated and compared to a threshold to decide if there was a change. The threshold level was determined by calculating energy difference values for signals recorded at nominally the same conditions vs. different conditions, and setting the level so as to always detect the changed conditions. Training and Evaluation Data Sets As is customary for development of a feature-based classifier, two sets of labeled data were constructed for training and evaluation. Given the original 275 signals, there are 2 theoretically N -N = 75,350 different ways of defining signal-baseline pairs; even given that some of these combinations do not make sense (e.g. using a signal from a drilled hole as a reference), there is a rich set of data from which to select signal pairs. From these possibilities, the training data set consisted of 43 signal pairs, of which 28 were due to environmental changes (class 1) and 15 to structural changes (class 2). The environmental conditions included both temperature changes and surface condition variations, and the structural changes consisted of various sizes of hole #1 combined with environmental effects. The evaluation data set was constructed in a similar manner but with different signal pairs. The hole #2 signals were not used for either data set, but were reserved for additional testing. Feature Calculation and Evaluation A set of features was defined and calculated in order to reduce the dimensionality of the data. The differential approach taken here required that all of the features be defined relative to a reference signal. For example, instead of using “Peak Amplitude” as a feature, the peak amplitude value would be scaled by the peak amplitude of the reference signal. Table 2 summarizes the 24 features that were calculated; all of them are relative to a reference signal and are either identically zero (features 11-14, 22, 23) or one (all other features) if the measured signal and the reference signal are the same.
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TABLE 2. Summary of features used for classification of environmental vs. structural changes. Feature 1 2 3 4 5 6,7,8 9,10 11 12,13,14 15 16 17,18,19 20,21 22,23 24
Description Relative energy Relative amplitude Relative center of energy -- time domain Relative cross correlation peak amplitude Relative curve length Relative time domain 1st, 2nd and 3rd moments Relative energy in time domain, +/- 5% and +/- 10% of reference time center Energy of difference between normalized envelopes 1st, 2nd and 3rd moments of absolute value of difference between normalized envelopes Relative center frequency Normalized inner product of amplitude spectrum with reference spectrum Relative frequency domain 1st, 2nd and 3rd moments Relative energy in frequency domain, +/- 5% and +/- 10% of reference frequency center Slope and error of local time shift vs. time as determined by Short Time Cross Correlation Normalized Short Time Cross Correlation peak at T=910 µsec
One measure of a single feature’s ability to separate two classes is the Fisher Discriminant Ratio [6], 2 (µ − µ ) FDR = 12 2 2 (1) (σ 1 + σ 2 ) where µ1 and µ2 are the means and σ1 and σ2 are the variances of the two classes (environmental and structural, respectively). The FDR is large for a specific feature if the classes have a large difference in means combined with small variances. A plot of the FDR for the 24 features is shown in Figure 3, where it can be seen that feature 24 has by far the largest FDR, and thus is most effective in separating the classes. The FDR is useful for evaluating the effectiveness of a single feature, but combinations of features have the potential for being more effective than single features. With a total of N 24 features, there are a total 16,777,215 (2 -1) different combinations of features that could be used to form a classifier, clearly too many to empirically evaluate. However, if features are considered two at a time, there are only 276 combinations, which is a realistic number to exhaustively test. Pairs of features were evaluated using a linearly separable classifier implemented with a neural network consisting of a single hard-limit perceptron [6]. The training data set was used to construct the classifier, and the evaluation data set was used to verify its performance. There were no pairs of features that perfectly classified both the training data set and the evaluation data set, but it was noted that the best performing pairs all included feature 24, which is not surprising considering its high FDR.
FIGURE 3. Fisher Discriminant Ratio (FDR) for the 24 calculated features.
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Features were then evaluated in groups of three for the 276 combinations containing feature 24. There were ten of these combinations that perfectly classified all data in both the training and evaluation sets. A comprehensive data set was prepared to further evaluate these ten 3-feature classifiers as well as additional classifiers comprised of four and more features that were determined by trial and error. Features were calculated for 779 signal pairs in order to evaluate the performance of the classifiers on data very unlike the training and evaluation data sets. This comprehensive data set included many more conditions than were originally considered. For example, signal pairs with temperature differences of up to 11°C (20°F) were included, as compared to a maximum difference of 7°C (12°F) for the training data, and hole signals were paired with reference signals at different environmental conditions. Of these 779 pairs, 526 were environmental changes and 253 were structural changes. RESULTS Classifier Performance Classifier performance for a given data set can be evaluated via a 2x2 confusion matrix. The upper and lower diagonal elements of this matrix are the number of correctly classified environmental and structural changes, respectively. The upper right element corresponds to the number of structural changes (i.e. potential flaws) that are misclassified as environmental changes, and the lower left element is the number of false alarms; i.e. environmental changes misclassified as structural changes. Confusion matrices for four of the classifiers that were evaluated using the comprehensive data set are shown in Figure 4: (a) the best two-feature classifier, (b) the best three-feature classifier, (c) a typical four-feature classifier, and (d) the best classifier of the ones comprehensively tested. The best classifier in Figure 4(d) was deemed as such because it had the lowest number of misclassified structural changes. Most of these misclassifications were signal pairs where the reference signal was not from the undamaged specimen but was after the hole was started. Most of the false alarms were due to temperature changes greater than those represented in the training and evaluation data sets being classified as structural changes. Other misclassifications of both types were generally due to the reference signal being at a much different temperature than the signal being classified, or extreme surface condition combinations. As an additional means of evaluating performance, signal pairs from the second hole were evaluated using this best classifier. There were 11 hole #2 signals corresponding to 11 increments of increasing hole size. Features were calculated using both a reference signal from the undamaged specimen with nominal environmental conditions, and a reference signal after hole #1 was drilled to full size. Correctly classified were 21 of the 22 signal pairs, with the only one misclassified being the smallest hole size (1.98 mm (5/64”) diameter) with the reference signal from the specimen with hole #1 (not the undamaged specimen). (a) 439
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FIGURE 4. Confusion matrices for classifiers comprised of (a) features 1 and 24, (b) features 10, 22 and 24, (c) features 5, 6, 20 and 24, and (d) features 2, 5, 6, 9, 10, 20, 22 and 24.
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Feature Performance A key result of the feature evaluation is the importance of feature 24. This feature is derived from a local cross correlation which we refer to as the Short Time Cross Correlation, or STXC. The STXC between two signals x1(t) and x2(t) is defined as:
STXC (T ,τ ) =
T +∆T
∫
x1 (t ) w(t − T ) x2 (t + τ )w(t + τ − T )dt.
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T −∆T
In this equation T is time, τ is the cross correlation lag, 2∆T is the window width, and w(t) is a suitable window function of length 2∆T centered at t=0. As can be seen from the above equation, the STXC is simply the cross correlation between corresponding windows of two signals centered at time T. Similarly to the short time Fourier transform, the STXC can be displayed as an image where time (T) is the horizontal axis and cross correlation lag (τ) is the vertical axis. If the windowed signals are the same or similar, the cross correlation will exhibit a distinctive peak; if they are different, then the cross correlation will appear more random in nature. Thus, the shape of the STXC as a function of time is a measure of the coherency of the two signals. Local cross correlations have been used by other researchers to measure time dependent time shifts [7,8]. This property of the STXC can be seen in Figure 5, where 5(a) shows the STXC between a signal due to an environmental change and a nominal reference signal, and 5(b) shows the STXC between a signal after hole #1 was drilled and the same reference signal. For both plots, the STXC is normalized by the square root of the product of the local autocorrelation peaks. In Figure 5(a), the STXC contains a distinct peak throughout the entire time window, whereas for 5(b), it does not, indicating that the two signals lose coherency as time progresses. Feature 24 is the peak of the normalized STXC at T=910 µsec using a 200 µsec time window. Features 22 and 23 are also derived from the STXC; in particular, they are the slope and error from fitting a line to the time of the STXC peak. Temperature changes exhibit a linear time shift, as predicted by diffuse wave theory [8], whereas the time shift for other changes was observed to be negligible for this study.
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FIGURE 5. Short Time Cross Correlation of (a) signal from environmental changes (warm plus wetted surface) with nominal reference signal, and (b) signal from hole #1 with nominal reference signal.
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SUMMARY AND CONCLUSIONS
Permanently mounted ultrasonic sensors have been demonstrated to be sensitive to both structural and environmental changes. As expected, environmental effects such as changing temperature and surface conditions affect the ultrasonic signal as much or more as structural changes. This paper has proposed and successfully demonstrated a differential approach for classifying structural vs. environmental changes that is based upon quantitatively comparing a measured signal to a reference signal. Key to this approach is the concept of “differential features” whereby all calculated features are relative to a reference signal. Initial classifier results are promising with excellent performance for conditions incorporated into the training data and reasonable performance for other conditions. The best classifier was able to correctly identify a defect that was not part of the training data. The importance of a single feature derived from a local cross correlation has led to the definition of the Short Time Cross Correlation, which has been demonstrated as an effective tool for evaluating signal coherence and local time shift as a function of time. Time dependent coherency was shown to be useful in discriminating structural changes and environmental effects for the experimental data presented here. Future work must concentrate in three main areas: (a) further development and demonstration of a complete methodology for ultrasonic structural health monitoring, (b) extension of classifier results to more complicated geometries, additional materials, and characterization of structural changes, and (c) further investigation into applications of the Short Time Cross Correlation as both a measure of signal coherency and local time shift. REFERENCES
1. Rose, Joseph L., “Standing on the Shoulders of Giants: An Example of Guided Wave Inspection,” Materials Evaluation, 60, 53-59 (2002). 2. Giurgiutiu, Victor, Zagrai, Andrei and Bao, Jung Jung, “Piezoelectric Wafer Embedded Active Sensors for Aging Aircraft Structural Health Monitoring,” Structural Health Monitoring, 1, 41-61 (2002). 3. Lowe, M. J. S., Alleyne, D. N. and Cawley, P., “Defect detection in pipes using guided waves,” Ultrasonics, 36, 147-154 (1998). 4. Weaver, Richard and Lobkis, Oleg, “On the emergence of the Green’s function in the correlations of a diffuse field: pulse-echo using thermal phonons,” Ultrasonics, 40, 435-439 (2002). 5. Case, Timothy J and Waag, Robert C., “Flaw Identification from Time and Frequency Features of Ultrasonic Waveforms,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 43, 592-600 (1996). 6. Schalkoff, Robert, Pattern Recognition, John Wiley & Sons, Inc., New York, 1992, pp. 89-104. 7. Lubinski, Mark A., Emelianov, Stanislav Y. and O-Donnell, Matthew, “Speckle Tracking Methods for Ultrasonic Elasticity Imaging Using Short-time Correlation,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 46, 82-96 (1999). 8. Weaver, Richard and Lobkis, Oleg, “Temperature dependence of the diffuse field phase,” Ultrasonics, 38, 491-494 (2000).
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