Ultrasonic structural health monitoring: Strategies, issues and progress

Transcription

1 Invited Paper Ultrasonic structural health monitoring: Strategies, issues and progress Jennifer E. Michaels School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA ABSTRACT Several different strategies are being considered for ultrasonic structural health monitoring systems using a variety of approaches. Guided wave techniques for interrogating large plate-like structures have probably generated the most interest; these methods have the potential of monitoring large areas with a low sensor density while remaining sensitive to defects. The acousto-ultrasonic nondestructive evaluation method has motivated the use of long-time, reverberating waves which fill a structure and hence monitor large areas. Local methods based upon several different wave modes have been considered for monitoring known hot spots such as fastener holes and critical bonds. Presented here are examples of these three strategies where the purpose is to both show progress which has been made and illustrate key issues, mainly in the context of aerospace applications. The progress and problems thus far show both the promise of ultrasonic structural health monitoring and the significant challenges in moving from the laboratory to deployed systems. Keywords: Ultrasonics, Structural Health Monitoring, Damage Detection, Damage Characterization, Signal Processing. INTRODUCTION Ultrasonic nondestructive evaluation (NDE) methods have a long history of being used to assess the integrity of critical structures and components. Ultrasonic methods are currently being considered for a number of structural health monitoring (SHM) applications because of their proven ability to detect and characterize flaws. Furthermore, ultrasonic waves can propagate long distances while still remaining sensitive to damage, particularly guided waves such as Rayleigh and Lamb waves. Ultrasonic methods can be categorized as either active, where transducers act as both transmitters and receivers of elastic waves, or passive, where transducers act only as receivers, recording elastic waves generated by other mechanisms such as impacts, leaks and propagating cracks. The passive technique of acoustic emission is routinely applied to specific problems such as pressure vessel inspection and leak detection, and is also used for detecting and localizing external impacts to structures. Here we consider only active ultrasonic methods as applied to SHM. An active SHM method can be either direct or differential. A direct method is one in which the structural assessment is based solely upon the current measurement; many, if not most, NDE methods are direct by necessity since baseline and historical data are often not available. A differential measurement is one in which the current measurement is explicitly compared to one or more prior measurements. Furthermore, the output of either a direct or a differential method may be one point in a time series of measurements. If prior measurements were made and the data are available, analysis options are expanded considerably, particularly if the raw waveforms were recorded and saved. Active ultrasonic SHM methods can be further characterized as local or global. A local method is designed to monitor a known region of susceptibility to damage, such as a critical bond, fastener hole, or other specific location. The term hot spot is frequently used to refer to a local region of high stress concentration that is known to be a site of damage initiation. A global method, in contrast, is designed to interrogate a relatively large area; the monitored region may include hot spots, or there may be no specific locations within the monitored region that are known to be predisposed to damage initiation. It may not be necessary to determine the precise location of damage for a local SHM method since the local area is already known, whereas locating detected damage may be an important requirement for global monitoring of a large area. jennifer.michaels@ece.gatech.edu; phone ; Smart Sensor Phenomena, Technology, Networks, and Systems 28, edited by Wolfgang Ecke, Kara J. Peters, Norbert G. Meyendorf, Proc. of SPIE Vol. 6933, 6933Z, (28) X/8/$8 doi:.7/ Proc. of SPIE Vol Z-

2 Three stages of SHM may be thought of as detection (existence of damage), localization (location of damage), and characterization (details about the damage). A fourth stage, not strictly SHM but closely related, is prognosis (expected progression of damage). A big challenge of SHM is how to quantify results at these various stages. Quantifying SHM requires, as a minimum, estimating the uncertainty in the probability of detection, damage location, and degree of damage; there are very few applications to date for which a complete uncertainty analysis has been performed. This paper presents an overview of three ultrasonic SHM methods that have been developed recently in the QUEST (Quantitative Ultrasonic Evaluation, Sensing and Testing) Laboratory at Georgia Tech, and uses these examples to illustrate various SHM strategies and show some progress which has been made. These examples also motivate a discussion on what are some of the key issues that still need to be addressed before ultrasonic SHM methods are implemented on critical aerospace structures. 2. GUIDED WAVES FOR LARGE AREA MONITORING Guided wave techniques for both NDE and SHM have been the subject of much research because of their ability to travel long distances as compared to bulk waves. Rose [] gives an overview of the use of guided waves for NDE applications, and Cawley and Simonetti [2] specifically address the use of guided waves for SHM. Simple and inexpensive piezoelectric elements, both circular and rectangular, effectively generate guided waves in plate-like structures [3,4], and their arrangement in a spatially distributed array is appealing for SHM applications. Wang et al. [5] used a four-transducer distributed piezoelectric array to general images of damage by applying delay-and-sum beamforming to the differenced signals, an approach based upon times-of-arrivals from damage. Michaels and Michaels [6] extended this idea by generating and fusing multiple images at multiple frequencies. Zhao et al. [7] considered a mathematically simpler algorithm based upon spatially distributing signal difference coefficients but using a larger number of transducers. More recently, an imaging method based upon time-differences-of-arrival has been employed and compared to the time-of-arrival method [8]. Here we consider the time-of-arrival method as shown in Figure. Let d ij (t) be the envelope of the differenced signal from transmitter i and receiver j; that is, the current signal minus a no-damage baseline signal. If dispersion is neglected, then the delay-and-sum approach synthetically focuses the signals from all transmit-receive pairs on each point (x,y) in the image plane. The arrival time t ij of the signal scattered from damage is the total propagation time from the transmitter to the damage to the receiver, and d ij (t ij (x,y)) corresponds to the amplitude of the signal scattered from the point (x,y). The image value at (x,y) is the square of the sum of the delayed signals over all transducer pairs, where N is the total number of transducers, 2 N (, ) N E x y dij ( tij ( x, y)). () i j i ( x, y ) 2 ( x2, y2) (, x y) 3 ( x3, y3) Fig.. Propagation paths between a point (x,y) in the image plane and three transducers acting as transmitters and receivers. Proc. of SPIE Vol Z-2

3 Figure 2 is an image, generated as per Eq. (), of a 3 long notch cut through the thickness of a flat plate at the 9 o-clock position of an existing 6 diameter hole; the plate thickness was Although the damage is clearly detected, there are lower amplitude artifacts in the image. The ones toward the center within the region bounded by the transducers are essentially side lobes of the beamforming process. Additional artifacts result from geometrical reflections, which are from the plate edges in this example, causing the higher amplitude artifacts in the periphery of the image away from the point of damage. If the geometrical reflectors are outside of the region bounded by the transducers, they can be somewhat suppressed by exponential windowing of the signals beginning at the time of the direct arrivals, )/ w' ( t) w( t) e ( t d t t u( t t ). (2) Here w(t) is the signal prior to windowing, t is the time of the direct arrival, t d is the exponential decay constant, u(t) is the step function, and w (t) is the windowed signal. Figure 2 is of the same 3 notch as that of 2 but after exponential windowing with t d = s. 6 r Fig. 2. Images of a 3 through notch in a flat plate created by delay-and-sum beamforming. No exponential windowing, and after exponential windowing with t d = s. The circles denote the transducers, and the + symbol corresponds to the center of the 6 hole from which the notch originated. The color scale is linear. Imaging methods are not limited to damage localization and can also play a significant role in detection of damage. For example, if the resulting image is very low in amplitude, it suggests that there are no significant scatterers. However, absolute amplitude levels may be difficult to establish, and high amplitude images may also result from variable environmental factors such as temperature and surface conditions. Thus, it is useful to extract parameters from images and then track the parameters as a function of time (i.e., structural usage) to detect damage even in the presence of other factors. Figure 3 illustrates the first step in this process, which is to identify contiguous regions of an image that exceed a threshold, which is set here to 75% of the peak amplitude. For this example there are 7 regions, and such parameters as the total area and centroid location can be calculated for each one, as well as for all regions together. Figure 4 shows plots of several image parameters versus the data set number both before and after introduction of artificial damage; the data sets are in time order but are not equally spaced in time. Figure 4 shows the number of contiguous regions for which the amplitude exceeds 75% of the peak, and Figure 4 shows both the area of the largest amplitude region and the total area. There were temperature variations prior to onset of damage, and the image parameters exhibit significant variations. After damage is introduced, the image parameters stabilize even though there are subsequent temperature variations, indicating that the image itself has stabilized. Thus, the likelihood of the damage being correctly detected and localized is high. Proc. of SPIE Vol Z-3

4 'e Fig. 3. Normalized image (linear color scale), and its binary counterpart using a 75% threshold. Number of Regions (75% Threshold) Data Set Number 4.5 x Flaw Area Peak Amplitude Region Total for All Regions 3 sq Data Set Number Fig. 4. Time history of image parameters. Number of regions, and total area and area of peak amplitude region. These results illustrate just one strategy for using guided waves for SHM incorporating a spatially distributed array. Guided wave SHM methods are by no means limited to this configuration; for example, spatially compact arrays have been considered [9,], and guided wave SHM methods have been applied to pipes []. Proc. of SPIE Vol Z-4

5 3. DIFFUSE-LIKE WAVES FOR DAMAGE DETECTION IN COMPLEX COMPONENTS A limitation of guided wave methods in general is that they are restricted to structural components which support their propagation. A further limitation to many if not most guided wave methods is the necessity of identifying and interpreting individual echoes, either from structural features or scattered from damage. However, it is quite easy to excite ultrasonic waves that reverberate throughout a complex structure using the same piezoelectric transducers as are used to generate guided waves; this idea is the basis of the acousto-ultrasonic NDE method [2]. The incident wave essentially floods the structure with energy after large numbers of reflections, effectively interrogating the entire structure. The signals, however, are very complex and much more difficult to interpret compared to guided waves as can be seen by the typical signal of Figure 5. It is well-known that these types of signals are generally very sensitive to damage, but unfortunately they are also very sensitive to changing temperatures and environmental conditions [3,4]. Because of this sensitivity to other factors, combined with the difficulty in analyzing the received signals, highly reverberating diffuse-like waves are not typically considered for SHM Time ( s) Fig. 5. Typical diffuse-like reverberating signal with an initial concentration of energy followed by a gradual decay. Rather than use individual echo arrivals to detect and localize damage, one strategy is to quantify how long-time signals have changed relative to a baseline via one or more differential features [5,6]. A differential feature is a parameter calculated from a pair of signals, where one signal is the baseline and the other is the signal of interest. Each differential feature is explicitly defined such that it is zero if the two signals are identical; i.e., the signal hasn t changed from the baseline. For example, a damage index is typically a differential feature. The challenge is to identify features which are sensitive to damage but are insensitive to benign changes. As an example, results are shown here from an experiment where a small aluminum specimen was instrumented with four piezoelectric sensors. Artificial damage was introduced in the form of a drilled hole in combination with benign surface wetting; the signal of Fig. 5 is from one transducer pair of this specimen. The strategy is to compute multiple differential features from the six total transducer pairs, and apply threshold and data fusion techniques to ascertain whether or not damage is present. A suary is presented here, and details may be found in [7]. Seven differential features are computed from the time domain signals, the local temporal coherence [4], and from a matching pursuit wavelet decomposition [8]. They are: () normalized mean squared error, (2) drop in correlation coefficient, (3) loss of temporal coherence, (4) differential curve length, (5) average peak-to-peak amplitude changes from the matching pursuit decomposition, (6) standard deviation of the time changes from the matching pursuit decomposition, and (7) ratio of amplitude changes in different frequency ranges from the matching pursuit decomposition. Each of these features is zero when the signal and baseline are identical, and increases as the signal changes from the baseline. The efficacy of each feature in terms of discriminating damage from benign signal changes may be evaluated via a receiver operating characteristic (ROC) curve when sufficient data are available, as is the case for this controlled experiment. A threshold is associated with each feature to separate damage from no damage. If the threshold is very low, then virtually everything is classified as damage and the probability of detection (POD) approaches %, but at the expense of false alarms. In contrast, if the threshold is set very high, there are virtually no false alarms but at the expense of a greatly reduced POD. If POD is plotted against the false alarm rate (probability of false alarm) as the Proc. of SPIE Vol Z-5

6 threshold is varied from one extreme to the other, the resulting ROC curve may be used to evaluate the efficacy of the feature; two example curves from two different transducer pairs are shown in Figure 6. An ideal feature has one or more threshold levels that perfectly separate the damage and no damage cases, resulting in an ROC curve which makes a perfect right angle in the upper left corner of the plot. For the examples of Figure 6, the better features correspond to curves which approach this shape. Damage data are needed to generate an ROC curve, whereas thresholds can be set prior to damage initiation from statistics of the calculated features under normal operating conditions by specifying a desired false alarm rate. P -.. MS E.8 Pxy Corr. DCL MPP2P.4 MPSTD MPPatio.2 U False Alarm Rate U False Alarm Rate Fig. 6. Examples of ROC curves from two different transducer pairs for evaluating features. The net result of the feature calculation and evaluation process is multiple detection decisions one for each feature and transducer pair (42 total for this example). Since the waves have reverberated throughout the entire structure, there should be a single detection decision. A variety of strategies are possible to fuse the individual results, such as neural networks and other machine learning algorithms, but here we consider a simple two-stage voting strategy. For each sensor pair, an N of 7 voting process is used, and these results are fused at the structure level by a subsequent M of 6 vote. All voting combinations are considered, along with 5 feature false alarm rates ( to 5% in % increments), for a total of 242 combinations. For each combination, both the POD and false alarm rate can be calculated from the data, and results are shown in Figure 7 in the form of an ROC-like curve. = 'a a a. a Selected Operating Best Point Result 8 92 False Alarm Rate False Alarm Rate Fig. 7. POD vs. false alarm rate for all combinations of feature false alarm threshold and vote counts. Full view, and zoomed region showing the selected operating point. Proc. of SPIE Vol Z-6

7 The selected operating point, shown in the zoomed region of Figure 7, corresponds to a feature false alarm rate of 2%, N= of 7 votes for feature fusion, and M=3 of 6 votes for sensor fusion. The complete decision process is illustrated by the chart of Figure 8. The resulting probability of detection is 96.3% with an overall false alarm rate of 3.9%. F T Feature Fusion of 7 votes F 7 T 7 Transducer pair -2 Sensor Fusion Damage Declaration Feature False Alarm Rate of 2% F T 6 Feature Fusion F 7 T 76 Transducer pair of 6 votes Fig. 8. Chart illustrating the data fusion process for features and sensors to obtain a final detection decision. The primary advantages of using long-time reverberating waves are twofold: () complete coverage of complex structures using a small number of sensors, and (2) potentially increased detection sensitivity because the reverberating waves pass through areas of damage multiple times, resulting in a compounding effect. Two disadvantages are increased sensitivity to benign changes, and lack of localization information. For structural components which support guided waves but also have complex geometry, it is possible to combine the advantages of reverberating waves for detection and guided waves for localization [9]. 4. LOCAL ULTRASONIC METHOD FOR HOT SPOT MONITORING An example of so-called hot spot monitoring is the use of a high frequency ( MHz) ultrasonic method configured to monitor fastener holes for fatigue cracks. The ultrasonic technique is illustrated in Figure 9, where the path of wave propagation is shown. The angle beam path between the transmitter and receiver passes through the center of the hole being monitored, which blocks the direct arrival of the shear wave. The only energy reaching the receiver is that which is diffracted around both sides of the hole. As cracks form and are opened and closed under varying loads, the ultrasonic signal is modulated by the applied load, and a normalized energy ratio is calculated which quantifies the energy received under load to that received under no load. Cracks are detected by monitoring the energy ratio for a significant drop, and crack sizes are estimated by the magnitude of the drop. Figure illustrates the drop in energy with load when a crack is present, and Figure shows the energy ratio as a function of fatigue cycles. Additional details about the method can be found in several papers [2,2]. Since transducers are permanently mounted and cannot be manually or automatically articulated as is the case for NDE methods, there is significant variance in the ultrasonic energy ratio verses crack size curve, where size can refer to area, length or depth. An ultrasonic measurement model was developed to quantify the variance using Monte Carlo methods to both model the wave propagation via rays and to capture the response to large numbers of simulated crack profiles [22]. Figure shows the resulting curve that relates crack depth to ultrasonic energy ratio, and Figure shows the standard deviation. A POD curve can be constructed directly from these results as shown in Figure 2. Proc. of SPIE Vol Z-7

8 Incident Ultrasound Re-radiated Creeping Wave Sound travels around hole as a surface wave (creeping wave) and is leaked to receiver MHz, 7 Shear Transmitter MHz, 7 Shear Receiver Cracks at 2: and 6: positions block the creeping waves Fig. 9. Ultrasonic technique to monitor fastener holes for fatigue cracks. Energy (%) 9 8 Normalized Energy Ratio Load (%) Fatigue Cycles ('s) Fig.. Typical energy versus load curve when a crack is present, and typical energy ratio versus cycles behavior.. Energy Ratio Energy Ratio ( ) Depth ().5.5 Depth () Fig.. Ultrasonic measurement model for monitoring fastener holes. Ultrasonic energy ratio versus crack depth, and standard deviation of the energy ratio versus crack depth. Proc. of SPIE Vol Z-8

9 .8 POD (%) Crack Depth () Fig. 2. Probability of detection curves corresponding to different energy ratio thresholds for crack detection. One way to reduce the measurement uncertainty is to combine the measurement model with a crack growth model in a state estimation framework. Here Paris s Law is used as the crack growth model, and an extended Kalman filter is applied for state estimation. The uncertainty in the crack growth law is estimated by considering several of the constants in Paris s equation to be random variables. As illustrated by the two examples of Figure 3, crack depth estimates using this methodology are generally improved over those using the measurement model alone. Additional details can be found in [22,23]..8.6 SHM Estimate Meas. Model Measured Depth.4.2 SHM Estimate Meas. Model Measured Depth Depth ().4.2 Depth () KCycles (Cycles/) KCycles (Cycles/) Fig. 3. Two examples showing a comparison of measurement model results (solid line), crack size estimates from the state estimation framework (dashed line), and depth measured optically from destructive testing (diamond). The specific local monitoring example shown here illustrates the strategy of adapting an NDE angle beam technique to in situ monitoring. As is often done for NDE, a model-assisted approach was taken to quantify damage and its uncertainty. Unlike NDE, time history information is available, which makes it possible to apply a state estimation approach for combining measurements with crack growth laws to reduce uncertainty. Proc. of SPIE Vol Z-9

10 5. DISCUSSION Although there has been a significant increase in SHM research over the past decade, there are still numerous issues that prevent widespread adoption of SHM methods. Some of these issues are identified and discussed below. Calibration. Protocols for quantifying the output of an SHM system are generally not available. Not only does the SHM output have to be related to some aspect of damage, it is critical that the uncertainty also be quantified. The largely experimental approaches taken by the NDE counity are generally not possible because of the in situ requirements for SHM sensors. However, more recently considered model-assisted approaches to probability of detection [24] have more applicability to SHM, as illustrated here by the example of Section 4. Full 3D modeling of wave propagation is still prohibitive for most applications, but that situation is changing rapidly as computing capabilities continue to improve. In the meantime, approximate models can capture many characteristics of the wave propagation and, when combined with appropriate experiments, may offer a practical approach to quantifying SHM for specific applications. Validation. The issue of validation is directly related to the problem of considering real defects in real structures. Many if not most laboratory experiments are not realistic in terms of either or both of the defects and the structure. Large scale in situ validation tests are time consuming and expensive, but it is unlikely that many SHM systems will be implemented without them. Environmental Effects. Benign environmental effects such as temperature, load variations, and surface conditions are well-known to cause significant changes in ultrasonic signals, often exceeding the changes due to damage. Temperature changes have been considered by several researchers [25,26], and the resulting effects are better understood than those due to other environmental variations. Load variations are not necessarily benign because their cumulative effects cause damage; however, a single load cycle can usually be thought of as benign. Load changes, unlike temperature changes, are generally anisotropic; like temperature changes, they cause changes in propagation times of individual ultrasonic echoes. It may be possible to ultrasonically monitor both temperature and loading, and use these variations to help characterize damage as was done in the example of Section 4 for uniaxial loads. Surface condition changes are more problematic in terms of predicting their effect on received ultrasonic signals because of the range of expected variability of, for example, wetting from rain. Aging Effects. Many aging effects, relating to the sensors, the structures, and their coupling, are not well-understood. For example, sealants are coon in aerospace structures, and it is expected that benign aging of the sealant material will significantly affect ultrasonic responses. Other age-related effects, which may be spatially distributed, may not be benign. Crack growth may also take place over the same time scales. The general problem of separating and characterizing changes taking place over the same long time scales has not been effectively addressed for most SHM applications. Use of Time History Data. One primary advantage of SHM methods as compared to NDE is the availability of time history data. There is no generally accepted way of incorporating this time history information into an overall condition monitoring strategy. Various baseline comparison strategies, such as those described in this paper, are one way of using historical data, but there has been little work done on strategies for adaptively updating baseline information. Before time history data can be effectively used, it is necessary to characterize expected time dependent behavior for not only growth of damage but also sensor degradation, structural aging processes, and environmental changes. Then probabilistic methodologies such as novelty detection and Bayesian state estimation can be applied. 6. SUMMARY AND CONCLUSIONS This paper illustrates several strategies for improving the ability of specific ultrasonic SHM methods to be quantified. These strategies include using damage localization results to assist detection, monitoring signal and image features as a function of time, evaluating receiver operating characteristic (ROC) curves to quantify the efficacy of multiple features for damage detection, fusing results from multiple features and sensors to improve detection performance, developing model-assisted measurement models for quantifying assessment of damage, and employing Bayesian state estimation methods that use expected crack growth behavior to improve measurement results. Although these strategies have been shown to be effective, mainly in the laboratory for specific problems, there is currently no one coherent quantification strategy that can be applied across the board to ultrasonic SHM applications. Proc. of SPIE Vol Z-

11 In suary, there is generally no argument that a variety of ultrasonic methods have been demonstrated to be effective for detecting and characterizing damage in the context of structural health monitoring. However, airframe manufacturers and maintainers are generally reluctant to install ultrasonic SHM systems in existing or new aircraft, except perhaps under special circumstances. This reluctance does not stem from lack of sensors and instrumentation, although technology is improving rapidly in that regard, nor does it stem from the inability of ultrasonic methods to detect damage. The primary limiting factors are those of calibration and validation, partially because of a lack of understanding of environmental and aging effects, but more fundamentally because of the complex interactions between elastic waves and structural damage, which currently limit our ability to quantify the output of an SHM system. These issues are more tractable for local SHM methods, and thus local ultrasonic methods may be the first to enjoy widespread acceptance and implementation. ACKNOWLEDGEMENTS The work reported here could not have been accomplished without the support and direct assistance of many people; these include Mr. Adam Cobb, Dr. Yinghui Lu and Prof. Thomas Michaels. The support of the National Science Foundation under contract number ECS-423 is gratefully acknowledged, as is the support of the Defense Advanced Research Projects Agency (DARPA), Defense Sciences Office, Structural Integrity Prognosis System Program, contract No. HR-4-3, to Northrop Gruan, Integrated Systems. The work supported by DARPA, reported in Section 4, is approved for public release with unlimited distribution. REFERENCES [] [2] [3] [4] [5] [6] [7] [8] [9] [] [] [2] [3] J. L. Rose, Guided wave nuances for nondestructive evaluation, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 47(3), (2). P. Cawley and F. Simonetti, Structural health monitoring using guided waves potential and challenges, Proceedings of the 5 th International Conference on Structural Health Monitoring, DEStech Publications, 53-5 (25). V. Giurgiutiu, A. Zagrai and J. Bao, Piezoelectric wafer embedded active sensors for aging aircraft structural health monitoring, Structural Health Monitoring An International Journal,, 4-6 (22). G. Park, C. R. Farrar, F. Lanza di Scalea and S. Coccia, Performance assessment and validation of piezoelectric active-sensors in structural health monitoring, Smart Materials and Structures, 5, (26). C. H. Wang, J. T. Rose and F.-K. Chang, A synthetic time-reversal imaging method for structural health monitoring, Smart Materials and Structures, 3, (24). J. E. Michaels and T. E. Michaels, Guided wave signal processing and image fusion for in situ damage localization in plates, Wave Motion, 44, (27). X. Zhao, H. Gao, G. Zhang, B. Ayhan, F. Yan, C. Kwan and J. Rose, Active health monitoring of an aircraft wing with embedded piezoelectric sensor/actuator network: I. Defect detection, localization and growth monitoring, Smart Materials and Structures, 6, (27). J. E. Michaels, A. J. Croxford and P. D. Wilcox, Imaging algorithms for locating damage via in situ ultrasonic sensors, Proceedings of the 28 IEEE Sensor Applications Symposium, Atlanta, Georgia (28). P. Wilcox, Omni-directional guided wave transducer arrays for the rapid inspection of large areas of plate structures, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 5(6), (23). V. Giurgiutiu and J. Bao, Embedded-ultrasonics structural radar for in situ structural health monitoring of thin-wall structures, Structural Health Monitoring An International Journal, 3(2), 2-4 (24). J. K. Van Velsor, H. Gao and J. L. Rose, Guided-wave tomographic imaging of defects in pipe using a probabilistic reconstruction algorithm, Insight, 49(9), (27). A. Vary, Acousto-ultrasonic characterization of fiber-reinforced composites, Materials Evaluation, 4(6), (982). A. L. Gyekenyesi, L. M. Harmon and H. E. Kautz, The effect of experimental conditions on acousto-ultrasonic repeatability, Proc. SPIE, 474, (22). Proc. of SPIE Vol Z-

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