HIGH FREQUENCY GUIDED WAVE VIRTUAL ARRAY SAFT R. Roberts Center for NDE, Iowa State University, Ames, IA 50014 A. Pardini, A. Diaz Pacific Northwest National Laboratory ABSTRACT. The principles of the synthetic aperture focusing technique (SAFT) are generalized for application to high frequency plate wave signals. It is shown that a flaw signal received in longrange plate wave propagation can be analyzed as if the signals were measured by an infinite array of transducers in an unbounded medium. It is shown that SAFT-based flaw sizing can be performed with as few as three or less actual measurement positions. INTRODUCTION This paper addresses the use of high frequency guided waves to inspect inaccessible regions of shell structures. The problem motivating this work is the inspection of the lower knuckle region of liquid nuclear waste storage tanks, as depicted in Fig.(l). The inspection seeks to detect stress corrosion cracking near the knuckle-to-bottom transition. The transducer is positioned on the tank wall, located up to two or more feet from the region to be inspected. Ultrasound propagates between the transducer and targeted inspection site through a series of multiple reflections between the inner and outer shell walls, using a shear wave launched into the steel shell at 70 degrees from perpendicular. The wall thickness is nearly one inch, and the transducer center frequency is 3.5 MHz, consequently the multiple reflections between the shell walls are easily isolated in time. The measurement is therefore viewed as a high frequency guided wave measurement. In work reported last year, a computational model was developed to predict and explain the complex signal features displayed by the signals received in this measurement. [1,2] In that work, it was seen that the signals consist of numerous discrete components, corresponding to varying numbers of multiple reflections between the shell walls. It was also seen how shell curvature complicates signal interpretation by introducing tangential incidence shadow boundaries, and focusing caustics due to "whispering gallery" modes of propagation at near-grazing incidence. In work this year, interest turned toward using the understanding of the modes of propagation in the shell to improve methods of flaw sizing. In particular, a method of flaw sizing is currently being employed in the inspection based on an adaptation of synthetic aperture focusing to the specific problem of sizing a perpendicular crack (oriented CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti © 2003 American Institute of Physics 0-7354-0117-9/03/S20.00 205 crack side view transmit B/\A B crack transducer top view FIGURE 1. Measurement geometry. geometry. receive FIGURE FIGURE 2. 2. T-SAFT T-SAFT measurement measurement configuration. configuration. perpendicular to the shell wall) in in aa thick thick shell shell structure, structure, depicted depicted in in Fig.(2). Fig.(2). This This adaptation exploits reflection from from the the inner inner shell shell wall wall to to collect collect data datascattered scattered primarily primarilyinin the direction of specular specular reflection from from the the crack. crack. In In this this method, method, aaseparate separate transmitter transmitter and receiver are initially positioned side-by-side, side-by-side, at at the the location location on on the the surface surface that that maximizes the maximizes the received received signal, signal, which which is is assumed assumed to to correspond correspond to to the the optimum optimumposition positionfor for reception of reception of the the corner corner trap trap signal, signal, depicted depicted by by position position A A in in Fig.(2). Fig.(2). The The transmitter transmitter and and receiver are are then scanned scanned in in tandem, tandem, that that is, is, at at equal equal rates rates in in opposite opposite directions, directions,with withdata data recorded at recorded at specified specified intervals intervals over over aa specified specified range range of of travel, travel, depicted depicted by by position position BB inin Fig.(2). Images Fig.(2). Images are are then then formed formed of of the the shell shell interior interior by by phasing phasing and andsumming summingthe thereceived received signals signals according according to to the the principles principles of of synthetic synthetic aperture aperture focusing. focusing. This This procedure procedure isis referred to to as referred as the the Tandem Tandem Synthetic Synthetic Aperture Aperture Focusing Focusing Technique Technique (T-SAFT). (T-SAFT). The The advantage advantage T-SAFT T-SAFT is is that that the the received received signals signals are are the the highest highest amplitude amplitude signals signals available available of of all all possible possible transducer transducer locations, locations, thus thus providing providing the the most most robust robust signal-to-noise signal-to-noise properties. In properties. In effect, effect, the the measurement measurement collects collects data data along along aa single single line line inin aa twotwodimensional dimensional data data space space (i.e. (i.e. the the position position of of transducers transducers A A and and B), B), over over which which the the signal signalhas has maximum amplitude. maximum amplitude. ItIt has has been been well well established established that that synthetic synthetic aperture aperture focusing focusing using using this data this data sub-set sub-set is is sufficient sufficient to to provide provide accurate accurate flaw flaw size size estimates.[3] estimates. [3] It It was was observed observed in in last last years years work work that that the the waveform waveform recorded recorded atat each each transmitter/receiver position transmitter/receiver position in in the the tank tank knuckle knuckle inspection inspection consists consists of of multiple multiple signal signal components components propagating propagating along along numerous numerous distinct distinct ray ray paths. paths. Application Application of ofT-SAFT T-SAFTtotothis this data data set set selects selects only only one one of of these these numerous numerous signals signals for forSAFT SAFTprocessing, processing,corresponding correspondingtoto the transmitted transmitted and the and received received rays rays oriented oriented at at the the nominal nominal transmission transmission angle angle of of the the transducer wedge. transducer wedge. A A question question was was raised raised regarding regarding the the potential potential of of improving improving the the inspection inspection by by performing performing aa SAFT SAFT image image construction construction that that utilizes utilizes all all the the ray ray paths paths contributing contributing to to the the recorded recorded waveforms. waveforms. This This paper paper reports reports on on the the examination examination of of this this question. question. It It is is shown shown that that aa potential potential exists exists for for substantially substantially reducing reducing the the number number of of data data collection collection positions positions needed needed for for adequate adequate flaw flaw sizing. sizing. The following section of this paper The following section of this paper presents presents aa generalization generalization of of the the concepts concepts underlying T-SAFT underlying T-SAFT imaging, imaging, appropriate appropriate for for long-range long-range propagation propagation in in aa thick thick shell. shell. Consideration Consideration is is restricted restricted to to the the case case of of planar planar shell shell geometry. geometry. Issues Issues to to be be addressed addressed inin the extension the extension of of the the work work to to curved curved shell shell geometries geometries are are discussed discussed in in the the paper paper summary. summary. 206 TECHNICAL TECHNICAL DEVELOPMENT DEVELOPMENT Discussion Discussion isis initiated initiated by by noting noting that that the the measurement measurement depicted depicted in in Fig.(2) Fig.(2) is is conceptually conceptually equivalent equivalent to to measurement measurement depicted depicted in in Fig.(3), Fig.(3), consisting consisting of of aa pair pair of of both both transmitting the top top and and bottom bottom of of aa transmitting and and receiving receiving transducers transducers placed placed symmetrically symmetrically on on the hypothetical specimen having twice the thickness of the specimen shown in Fig.(2). hypothetical specimen having twice the thickness of the specimen shown in Fig.(2). The The transmitting transmitting transducer transducer pair pair isis assumed assumed electronically electronically tied tied together, together, as as is is the the receiving receiving transducer are transducer pair. pair. The The transducers transducers positioned positioned on on the the bottom bottom of of the the specimen specimen in in Fig.(3) Fig.(3) are referred the bottom bottom of the referred to to as as “virtual” "virtual" transducers, transducers, associated associated with with the the reflection reflection from from the of the specimen specimen in in Fig.(2). Fig.(2). Fig.(3) Fig.(3) depicts depicts the the idea idea that that exploitation exploitation of of the the bottom bottom surface surface reflection reflection isis equivalent equivalent to to using using two-transducer two-transducer transmit transmit and and receive receive arrays arrays on on aa hypothetical specimen having twice the thickness. Next, consider that in the long-range hypothetical specimen having twice the thickness. Next, consider that in the long-range measurement, measurement, received received signals signals undergo undergo multiple multiple reflections reflections at at both both the the inner inner and and outer outer shell walls. Each reflection at the shell wall is equivalent to having a virtual shell walls. Each reflection at the shell wall is equivalent to having a virtual source source or or receiver receiver at at aa corresponding corresponding position position in in an an unbounded unbounded hypothetical hypothetical medium. medium. This This concept concept isis developed developed in in Fig.(4). Fig.(4). The The wave wave field field within within the the half-space half-space shown shown in in Fig.(4a) Fig.(4a) due due to to aa single two single source source isis equivalent equivalent to to the the wave wave field field in in the the unbounded unbounded medium medium arising arising from from the the two sources depicted in Fig.(4b), where the bottom source is a virtual source. Next, Fig.(4c) sources depicted in Fig.(4b), where the bottom source is a virtual source. Next, Fig.(4c) depicts the depicts the the first first reflection reflection from from top top bounding bounding surface surface of of aa plate. plate. Fig.(4d) Fig.(4d) depicts depicts the equivalent virtual source in a hypothetical unbounded medium. Thus, the wave field in equivalent virtual source in a hypothetical unbounded medium. Thus, the wave field in aa plate plate arising arising from from the the first first two two reflections reflections of of aa source source positioned positioned at at the the surface surface is is equivalent equivalent to to the the wave wave field field arising arising from from aa three three source source array array in in aa hypothetical hypothetical unbounded unbounded medium. medium. Continuing number of of multiple multiple Continuing the the conceptual conceptual construction construction for for the the theoretically theoretically infinite infinite number reflections between plate walls, it is seen that the wave field within the plate is equivalent reflections between plate walls, it is seen that the wave field within the plate is equivalent transmit receive B/\A/ Virtual Virtual transducers transducers transmit receive FIGURE using virtual virtualtransducers. transducers. FIGURE 3. 3. Equivalent Equivalent T-SAFT T-SAFT configuration configuration using (a) (b) (c) (d) Virtual transducer FIGURE in (a, (a, b) b) half-space half-space and and (c, (c, d) d) plate. plate. FIGURE 4. 4. Virtual Virtual transducer transducer concepts concepts in 207 flaw focal plane focal &3ost& FIGURE 5. 5. Virtual Virtual array for plate. FIGURE plate. usec US6C FIGURE FIGURE 6. 6. Signal Signal components componentsfrom fromvirtual virtualarray. array. to the the wave wave field field arising arising from from an an infinite infinite array array of virtual sources in a hypothetical to hypothetical unbounded medium, spaced two plate thicknesses apart, as depicted in Fig.(5). A similar unbounded medium, spaced similar construction holds holds in in considering considering aa receiver on the plate surface: surface: the received construction received signal signal in in response to to aa source source with with in in aa plate plate is is equivalent equivalent to to that that obtained obtained from from an an infinite infinite array response array of of virtual receivers receivers in in an an unbounded unbounded medium, medium, spaced spaced two virtual two plate plate thicknesses thicknesses apart. apart. Using the the concept concept of of virtual virtual source source and and receiver receiver arrays, arrays, the Using the constituents constituents of of the the complex signal obtained in a long-range plate measurement can be interpreted complex signal obtained in a long-range plate measurement can be interpreted as as transmission and and reception reception between between the the various various virtual virtual array array elements. transmission elements. This This notion notion is is demonstrated in in Fig.(6), Fig.(6), which which displays displays the the pulse-echo pulse-echo waveform waveform predicted demonstrated predicted by by the the computational model model for for aa 75 75 percent percent through-wall through-wall crack crack in computational in aa 11 inch inch thick thick plate plate 32 32 inches inches from aa 3.5 3.5 MHz MHz 70 70 degree degree shear shear wave wave transducer. transducer. The The signal signal constituents constituents are are identified identified by from by number-pairs, corresponding corresponding to to transmission transmission and and reception reception by number-pairs, by elements elements of of the the transmitting transmitting and receiving receiving arrays. arrays. For For example, example, the the component component designated designated 7-8 and 7-8 designates designates transmission transmission by element 7 and reception by element 8 in the virtual array depicted by element 7 and reception by element 8 in the virtual array depicted in in Fig.(5). Fig.(5). Viewing the the ultrasonic ultrasonic response response in in Fig.(6) Fig.(6) as as resulting Viewing resulting from from transmission transmission and and reception at an infinite array of measurement positions, the question arises reception at an infinite array of measurement positions, the question arises "can “can the the signals signals from the the virtual virtual array array positions positions be be phased phased and and summed summed to synthesize aa focused from to synthesize focused beam beam response similar similar to to conventional conventional SAFT SAFT imaging?” imaging?" A difficulty to response A difficulty to be be considered considered in in such such an an attempt isis the the fact fact that, that, unlike unlike in in conventional conventional SAFT SAFT data data collection, collection, the attempt the signals signals from from the the transmitting and and receiving receiving positions positions are are obtained obtained all transmitting all at at once, once, as as if if the the transmitters transmitters and and receivers are electronically tied together. However, it is noted that, because receivers are electronically tied together. However, it is noted that, because of of the the high high frequency nature nature of of the the measurement, measurement, signals signals from from the discrete measurement frequency the discrete measurement positions positions can can be isolated in time to a significant degree. This fact suggests an algorithm that be isolated in time to a significant degree. This fact suggests an algorithm that computes computes the transit transit time time to to aa specified specified focal focal point point of of interest interest for for aa given given transmitter-receiver the transmitter-receiver pair, pair, and "clips" a gated portion from the received waveform about that and “clips” a gated portion from the received waveform about that time time position. position. The The gated signals signals obtained obtained in in this this fashion fashion for for all all transmitter-receiver transmitter-receiver pairs gated pairs are are then then summed summed to to form the the synthesized synthesized response response to to aa beam beam focused focused at form at the the specified specified focal focal point. point. Such Such an an algorithm was was implemented implemented to to synthesize synthesize the scanning of algorithm the scanning of aa focused focused beam beam over over aa focal focal plane oriented perpendicular to the bounding surfaces of a one inch thick plate, plane oriented perpendicular to the bounding surfaces of a one inch thick plate, as as depicted depicted in Fig.(5). Fig.(5). For For each each point point on on the the focal focal plane, plane, the the transit transit time time between between transmitter in transmitter and and receiver positions were computed, and gated signal segments centered about receiver positions were computed, and gated signal segments centered about that that transit transit time were summed for numerous transmitter-receiver pairs. The algorithm did not sum time were summed for numerous transmitter-receiver pairs. The algorithm did not sum contributions from all transmitter-receiver pairs, as many of these pairs have negligible contributions from all transmitter-receiver pairs, as many of these pairs have negligible signal amplitudes. Rather, only pairs oriented close to receiving specular reflections from signal amplitudes. Rather, only pairs oriented close to receiving specular reflections from 208 the crack face (i.e. to within the angular aperture of the transducer) were included in the sum. This restriction is similar to the concept underlying the T-SAFT data collection, which restricts data collection to orientations suitable for receiving specular crack face reflections. The results of the phased time-gating summation procedure are first presented for a wave packet obtained from a 0.2-inch deep crack extending from the inner shell wall in a 1-inch thick plate measured at 32 inches, using the same transducer as in Fig.(6). The procedure was carried out for points on a focal plane coinciding with the crack, ranging from s = -1 to 1 inch, where s is the distance from the inner shell wall. A synthetic waveform was constructed using the time gating procedure described above for each calculation point on the focal plane. The peak amplitude of the synthetic waveforms was then plotted as a function of position s, shown in Fig.(7). It is noted that the response for negative s mirrors that for positive s, due to the fact that, for a given transmit-receive pair and position s, yielding a particular transit time, there will be a corresponding transmitreceive pair yielding the same transit time to the position -s. It is expected that the response will have its 50 percent maximum amplitude when the focused beam is halfway on the crack. Note that the synthetic focused response has a half-amplitude point slightly less than 0.25 inches, slightly beyond the actual edge of the crack. The slight overestimation of the crack size is due to the relative dimensions of the synthetic focused beam and the crack: when the crack dimension becomes small enough, the response begins to appear less as a measure of the crack dimension and more as a measure of beam width. The slight over-estimation of the crack size signifies the onset of this phenomenon. It will be seen that the over-estimation is significantly less for larger cracks. The minimum beam width obtainable when constructing a synthetic focus is determined by the width of the angular aperture of the transducer used in data collection. Hence improved resolution of smaller cracks would require a transducer having a wider angular aperture be used in data collection. Side lobes *M -0,75 4M»0 «OJ§ «0 0,25 OJO -34,0 O -16.0 FIGURE 8. Virtual array geometry for Fig.(7). FIGURE 7. SAFT-computed crack profile. 209 2.0 Side lobes -34.0 -16.8 FIGURE 10. SAFT crack profile for Fig.(9). FIGURE 9. Virtual array for two probes. Although the synthetic focused response obtained by time gating the wave packet provided a good estimate of the crack dimension, the result in Fig.(7) is severely contaminated by artifacts that could be mistaken for crack signals. These artifacts are the result of side lobe generation in the synthetic focus. Generally speaking, side lobes are generated in phased array focusing when there is insufficient spatial density of array elements. The density of the array elements used in obtaining Fig.(7) is depicted in Fig.(8), which shows the rays connecting the transducers in the virtual array to the root of the crack. The artifacts seen in Fig.(7) indicate that the angular gaps between the rays in Fig.(8) are too large to form a single focused lobe with the plate thickness. To fill in the gaps, a second measurement is taken in which a receiving transducer is placed two inches from the first transducer, that is, at 30 inches from the crack. The rays connecting the virtual array positions for the two transducers are shown in Fig.(9), indicating how the second measurement fills in the angular gaps. The synthetic focusing is now performed by wave packet gating of the pulseecho signal from the first transducer, and the pitch-catch signal for transmission from the first transducer to the second transducer. Again, synthetic waveforms are constructed corresponding to each of the points of focus on the focal plane, and the peak amplitude of these signals is plotted versus position on the focal plane. The result of this two-transducer computation is shown in Fig.(lO). A significant reduction in side lobe artifacts is seen. The side lobe artifacts seen in Fig.(lO) can be reduced yet further by including a third measurement position. A result is shown in which a third transducer is employed, this time at a position 2 inches farther from the first transducer, or at 34 inches from the flaw. A plot of the rays connecting the virtual transducer positions to the root of the crack in this case is presented in Fig.(ll). The increased density in angular aperture coverage is evident. The crack response profile shown in Fig.(12) correspondingly shows yet a further reduction in side lobe artifacts. It is evident that, at a distance of 32 inches to the flaw, accurate flaw sizing can be performed using two or three measurement positions, through exploitation of the virtual array properties of the high frequency guided wave signals. 210 Results are next presented comparing the virtual array SAFT response for cracks having depths of 0.2, 0.5, and 0.8 inches. The synthetic scanned focused beam response is computed using data collected from three transducer positions, identical to the procedure presented in Fig.(12). The comparison, shown in Fig.(13), only plots the response from s = 0 to s = 1 inch, corresponding to the physical dimension of the plate thickness. Results are shown in Figs.(13a and b) for cracks rooted in the inner and outer shell walls, respectively. It is seen that the 50 percent amplitude points on the response curves agrees quite well with the dimension of the crack, particularly for the larger cracks (0.5 and 0.8 inch deep). It is interesting to note that another means to increase the angular density of the SAFT acquisition is to increase the distance between the transducer and flaw. Results similar to Fig.(12) are reported in [4] using a single transducer positioned at a distance of 72 inches. 8&8 8,?i FIGURE 12. SAFT crack profile for Fig.(l 1). FIGURE 11. Virtual array for three probes. (a) crack FIGURE 13. SAFT crack profiles for cracks rooted in (a) inner wall, (b) outer wall. 211 SUMMARY The results presented here indicate that the physics of guided wave propagation potentially allow for SAFT imaging using a significantly reduced number of actual measurement positions. This results from the fact that the bounding surfaces of the wave guide transmit and return energy between transducer and flaw over the entire angular aperture of the transducer. In conventional SAFT applications, the transducer must be physically translated to obtain full aperture information. In the guided wave application, a single measurement periodically samples the entire angular aperture at a spatial interval twice the plate thickness. The corresponding angular sampling density consequently increases as distance to the flaw increases. In the measurement this work is supporting, the plate structure is curved. Therefore future work needs to generalize the concepts presented here to curved shell geometry. A complication introduced in the case of a curved shell is the fact that the SAFT sources no longer appear to be point sources, but rather extended sources distributed over caustic surfaces. It is conceivable, however, that an appropriate generalization would be possible. Successful development of SAFT algorithms exploiting the virtual transducer array properties associated with high frequency guided waves would significantly improve the effectiveness of the tank knuckle measurement, by decreasing the amount of data collection necessary to perform flaw evaluation. Currently, data is collected by scanning two transducers over the SAFT aperture as described in Fig.(2). Replacing this procedure with a stationary array of, say, 3 to 5 transducers would significantly simplify data collection and reduce acquisition time. ACKNOWLEDGEMENT Funded by the Tank Focus Area Program, Office of Environmental Management, Office of Science and Technology, US Department of Energy. REFERENCES 1. R. Roberts, A. Pardini, and A. Diaz, "A Model for High Frequency Guided Wave Inspection of Curved Shells," in Review of Progress in QNDE, 21, eds. D.O. Thompson and D.E. Chimenti, (American Institute of Physics, 2002). Pp. 165-172. 2. A. Pardini, et. al "Development of a Remotely Operated NDE System for Inspection of Hanford's Double Shell Waste Tank Knuckle Regions", PNNL-13682, Sept., 2001. 3. S. Doctor, et. al "Development and Validation of a Rel-Time SAFT-UT System for the Inspection of Light Water Reactor Components, PNL-5822, May, 1986. 4. A. Pardini, et. al. "Remotely Operated NDE System for Inspection of Hanford's Waste Tank Knuckle Regions", PNNL-14072, Sept., 2002. 212
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