Inversion of Physically Recorded Ultrasonic Waveforms Using Adaptive Learning Network Models Trained on Theoretical Data

The objective of this work has been to demonstrate the feasibility of estimating automatically the size and orientation of subsurface defects in metals. The approach has been to (1) obtain computergene~ated spect~a from various elastic scattering theories, (2) use these sp.ectra to train empirical nonl1near Adapt1ve Learning Network (ALN) models, and (3) evaluate the theoretically trained ALN's on eight physically recorded defect specimens via a blind test. The results demonstrate that very good defect characterization is possible and that a fully automatic and general purpose NDE system can be implemented. An average orientation error of 10.2 degrees has been achieved and the defect average volume error is 17.5 percent. The ALN models were synthesized using theoretically generated spectral scattering data from the Born Approximation (BORN), the Extended Quasti-Static Approximation (EQSA), and the Scattering Matrix Method (SMM) digital computer programs. The type of defects simulated were oblate spheroidal voids in a Titanium alloy. The ultimate significance of this work is to further support the mounting evidence that theoretical computer models can be used as ultrasonic calibration data in place of building physical specimens. The capability of (1) simulating many difficult-to-produce defect/geometrfcal·reflector scenarios in various metal matrices and, (2) using the ALN methodology to develop automatic detection, characterization and sizing methods using the simulated ultrasonic echoes will yield tremendous economic benefits. Results: OF RESULTS RECOMMENDATIONS 1. The lowest average percentage errors made in estimates of the defect size parameters "A" and "B" were 20.0 and 5.9 percent, respectively. For the orientation parameters "a" and "f!", the errors were 6.7 and 5.1 percent, respectively. The error in estimating the def~ct volume computed from the individual estimates of "A" and "B", was 17.5 percent. Furthermore, the three-dimensional average orientation error over the eight experiments was only 10.2 degrees. These results demonstrate the feasibility of producing an automatic flaw characterization algorithm via ALN means. 2. It was found that the long wavelength A2 coefficient provides significant information relative to the size and orientation of spheroidal defects. For pitch-multiple-catch (PMC) data, A2 was successfully used in conjunction with other spectral features to estimate the shorter defect radius (A) and the defect's polar angle (aJ. Also, a favorable comparison existed between experimental and theoretically generated PMC data. This favorable comparison could not be observed for pulse-echo lPEJ data since the PE experimental data had been optimized to give maximum spectral bandwidth rather than reliable information in the low frequency llong-wavelength) regime. However, for the theoretical data, a correlation of 0.97 was found to exist between the defect's larger radius (BJ and the average value of A2 computed from the 341 inner ring ta=30°) PE transducers; also, a correlation of 0.96 existed between the defect's polar angle (a) and the ratio of inner to outer ring average value of A . These results clearly demonstrate the ~alue of A2 as a parameter for size and orientation estimates. 3. A completely automatic and ~eneral ALN processing algorithm has been developed for defect flaw characterization which also includes a fully automatic means of computing the long wavelength A2 coefficient. The algorithm employs deconvolution of the transducer characteristic so that the solution of problems can be achieved using~ commercially available 5 MHz search unit. 4. Use of the transducer arrangement in the pulse-echo (PE) mode yielded better results than the pitch-multiple-catch (PMCJ mode, at least when using ALN models trained on the BORN approximation data. This statement is supported by the fact that the average orientation error improved by 7.3 degrees when changing from a PMC to a PE transducer arrangement. Also, the total number of waveforms needed for PE array processing was a factor of 3 less than that of PMC. 5. A qualitative comparison of the PE scattering data generated by each of three theories lBORN, EQSA, and SMM) and experimental data was performed. The BORN and EQSA spectral shapes were found to be identical for bblate spheroidal void scatterers. The only observed difference between BORN and EQSA data was that EQ~A's spatial distribution of the total power feature {in the range of 0.4<ka<3.5) increasin~ the number of elements in thP. transmit/receive array; and {3} possibly, changing the transducer array to a more equispaced configuration. was more closely matched to the experimental 2. The present.study was concerned with evaluating three scattering theories on a common basis. In doing so, the SMM theory was considerably under-utilized because the phase information, not found in the BOHN or EQSA program, was discarded from analysis for the sake of maintaining a common basis for comparison. The additional information provided by the phase spectrum should be very useful in characterizing flaws. Therefore, it is recommended that the ~~M phase information be incorporated in all future work. data. The spectral bandwidth \i.e., the second spectral moment) for these two theories was also in good agreement with that observed from experiment. ~pectral data produced by the SMM theory possessed greater detail tnan that of the tlORN and EQ~A theories. In this respect, SMM spectra prov1dea a closer match to experimental spectra. Tne SMM data was the closest of three theor1es to faithfully mim1c the center frequency {first spectral moment) spat1al aistribution. 6. From a quantitative v1ewpoint, the three 3. J. Rose's transformation from frequency to R-space should be incorporated into the ALN procedure to test its utility for yielding further improvements in defect characterization. theories yielded almost identical orientation estimates, with an average error of approximately 12 degrees \Over a possible lBO degrees}. However, the average error in computing the defect's size varied among the three theories·. For BORN, EQSA, and SMM, the 4. ln the development of further flaw characterization systems, a "combined theory" data base might be considered, where the best features of each theory would be used for ALN model synthesis. ln this manner, a larger and more representative feature set could possibly be postulated. average size errors were 32, 26, and 54 microns, respectively. conclusions 1. use of theoretically generated data combined with ALN technology to accurately and automatically character1ze spheroidal-shaped 5. The present study is concerned with L~L mode scattering only; however, L~S mode scattering shoula also be considered in future work since the ripple period in the scattered shear wave spectrum is more observable than in the scattered longitudinal spectrum. flaws via ultrasonic inspection has been favorably established. 2. The EQSA theory, compared to the BOHN theory, provides a closer approximation to experimental scattering data. This is supported by the facts that {1) the EQSA-trained size 6. In order to realize a quantitative NDE flaw characterization system, the ability to discriminate between crack-like defects and ellipsoidal-shaped defects is necessary. A completely automatic ALN-based NDE system models were more accurate than BORN when evaluated on experimental data; and, {2) the EQSA total power spatial distributions were in excellent agreement with the experimentally observed distributions. The EQSA program {written by J. GubernatisJ is also very efficient in generating large data bases. It is therefore recommended that other groups interested in inversion techniques consider the EQSA theory in place of the ~ORN theory. The SMM theory provides the closest match to experiments than the other theories investigated. However, it is believed more analysis is needed to make best use of the "more detailed" spectral information. 3. The orientation estimates for BORN PE models are superior to the BORN PMC models probably because the BURN approximation is most accurate in the backscatter position. A qualitative observation to support this fact was that the radiation pattern {or polar plot) of the scattered energy was "sharper" {i.e., more peaked} for the PE mode than in the PMC mode and matc~ed experimental results more closely. Recommendations 1. improvements in estimating defect size and orientation can be achieved by \l) increasing the number of experiments in the training set from, say, 240 to aoout 1000; \2) 342 will need to character; ze both twoand threedimensional flaws. The present work has addressed three-dimensional defects. t similar effort should now be performed to characterize the size and orientation of twodimensional flaws. Also, an ability to discriminate between twoand three-dimensional flaws will be needed as illustrated in Fig. 1. It is recommended that the coming year's work focus on implementing the system shown in Fig.