CRACK SIZING USING A NEURAL NETWORK CLASSIFIER TRAINED WITH DATA OBTAINED FROM FINI1E ELEMENT MODELS

CRACK SIZING USING A NEURAL NETWORK CLASSIFIER TRAINED WITH DATA OBTAINED FROM FINI1E ELEMENT MODELS Kornelija Zgonc, Jan D. Achenbach and Yung-Chung Lee Center for Quality Engineering and Failure Prevention Northwestern University Evanston, IL 60208-3020 INTRODUCTION Ultrasonic inspection of riveted joints carried out by human operator is cumbersome and time consuming. An automated signal classification system would provide better reliability and accuracy in the detennination of crack size and orientation. In this paper, we discuss a neural network designed for use in ultrasonic signal classification. The network can give classification results in a short time which makes possible real time ultrasonic inspection. An automated crack sizing system was presented earlier for similar applications [1] and the present paper is an extension of that work. The latest improvement is the use of numerically obtained ultrasonic data to train the neural network classifier (NNC). The NNC has to be trained with the ultrasonic data that has previously been collected or numerically calculated. To build an appropriate data base, many experiments would have to be perfonned to get the infonnation about all possible sizes and orientations of cracks. The preparation of the required number of model cracks, which are generally simulated by EDM notches, and the subsequent testing are both impractical and costly. The solution is to obtain the required data by numerical simulation. In our work, finite element models (FEM) were applied to simulate the experiments. The FEM is selected mostly because the modeling can be extended to the 3-D case which will be required to simulate a riveted joint. Preliminary results are provided by a 2-D approximation. To match the FE model to experiments a thin aluminum plate is used as a specimen. However, FE models can provide only approximate solutions as it is difficult to model signal attenuation in real materials. Experimental data serve, therefore, to provide calibration coefficients to numerically obtained solutions. EXPERIMENTAL SYSTEM CONFIGURATION The crack characterization is perfonned by the self-compensating technique [1]. This technique outputs results that are independent of the unpredictable coupling of the transducer to the specimen. The measured ultrasonic data are used to calculate the ratio of similar frequency components of ultrasonic back-and forward-scattered waves from the crack. This ratio between the reflected signals and through-transmitted signals is related to the crack size and will be further referred to as the R!T ratio. To discriminate reflection from the crack and the rivet hole, time-of-flight delay is considered to determine multiple gates in the time domain. A schematic of the experimental setup is depicted in Figure 1. The specimen is an aluminum plate (Alclad 2024-T3 alloy) of thickness 1 mm and the hole diameter is 5 mm. EDM notch lengths are selected as 0.5 mm, 1.0 mm, 1.5 mm, 2.0 mm, 2.5 mm, and 3.0 mm. The EDM notch lengths are selected as 0.5 mm, 1.0 mm, 1.5 mm, 2.0 mm, 2.5 mm, and 3.0 mm. Review of Progress in Quantitative Nondestructive Evalumion, Vol. 14 Edited by D.O. Thompson and D.E. Chimenti, Plenum Press. New York. 1995 779

Oscilloscope Computer Pulser Receiver 5055 PR Ultrasonic transducer #1 9 Ultrasonic transducer #2 Fig. 1 Experimental setup for self-compensating technique. The pulser-receiver generates pulses which are converted into compression waves by the two ultrasonic transducers mounted on the sides of the plate (see Figure 1.). The transducers serve also as receivers and they detect both back and forward scattered waves. The back scattered field contains partially reflected waves from the crack and the forward scattered field is transmitted past the crack. The transducers' center frequency is 3.5MHZ and the aperture is 0.5 inch (12.7 mm). The received signals are digitized in the oscilloscope and sent to the personal computer for further evaluation. The rivet hole is positioned asymmetrically with respect to the transducers position to prevent the overlap between the received signals in the time domain. From the received signals, amplitude spectra are calculated, which are further used to calculate the R!f ratio for a suitable frequency component. For this particular application a frequency of 2.5MHz was chosen. The reason for selecting this particular frequency is that lower frequencies waves are much less affected by the small cracks. At higher frequencies multiple modes start to propagate and the 2-D assumption (plane-stress case) would be invalid. Since only one mode propagates in a 2-D case let us check first the frequency spectra for our specific experimental configuration. Examining the Rayleigh-Lamb frequency spectra [4] for the longitudinal modes, the frequency range where only one mode is propagating can be determined. The solutions of the frequency equation (1) tan [1j[(Q2 _2)!] _---=2 -:- = tan [ Ij[(Q2/K2_1;2) 2 1 1 42(Q2/K2_2)2(Q2 _2)2 (Q2_21;2)2 (1) where 1C is the material constant, Q the dimensionless frequency and the dimensionless wave number, 1 K = cl = [2(1-V)]2 (2) ct 1-2v are shown in Figure 2. We can see that for frequencies below 2.7 MHz, which corresponds to n = 1.74, a single mode propagates (see Figure 2.). As suggested in [1] the scan ofrff ratios along the crack should be obtained to discriminate between a small normal crack and bigger inclined crack. The scanning positions used both in numerical modeling and experiments are shown in Figure 3. After time-dependent signals are measured, a FFf is applied in the time gates of equal 780

7.0.if. if 6.0..::: 5.0..., N * II 4.0 --L(O) _.._. LD(I) 3.0..., :;:::.. 8 2.0 * II a 1.0 0.00 0.5 1 1.5 2 2.5 = 2h*k/1t. v=o.34 Fig. 2 Rayleigh-Lamb frequency spectra for the aluminum plate of thickness Imm. Ultrasonic transducer #1 Ultrasonic V 12 transducer #2 L- ---I I 4 5 6 7 8 9 10 II 12 13 14 15 I I I I I I I I I I I I Fig. 3 Scanning positions and schematic example of wave paths: Vll and V22 are reflected signals, V21 and Vl2 through-transmitted signa1. size. After that, averaging in a small frequency interval around 2.5 MHz, the data describing both reflected and transmitted signals is extracted. The final result which is stored in the data base is the Rtf curve for the selected EDM size. The R!f curves stored in the data base are depicted in Figure 4. The signal processing scheme is shown in Figure 5. The results show that different EDM notch sizes give different peak amplitudes of the Rtf curves. NUMERICAL MODELING SYSlEM 2-D FE models are used to obtain the necessary numerical data. To calculate R/f curves both the back and forward scattered fields are needed. Besides deciding on standard FE modeling parameters such as time step, mesh size, etc., a difficult problem in ultrasonic inspection simulation is how to model the transmitters and receivers. As a transmitter signal a realistic transducer signal is used which has been determined experimentally by a pulseecho experiment through an isotropic aluminum block. The excitation signals, as functions of time and frequency, are depicted in Figure 6. The receiver output signal R(t) is roughly approximated by a weighted average [2] over 11 nodal points as shown in equation (3), 1 11 R(t) = -11. I Wi r x(t) 1=1 (3) 781

E-<... 40 >< 30 Ei" 20 1:1 3.0mm 2.5mm 2.0mm 60.. 1.5mm 1.0mm 50 0.5mm 10 0 0 2 4 6 8 10 12 14 16 Scanning Position [0.5x 10-1 inch increment] Fig. 4 Experimentally obtained R!f curves for EDM notch sizes from 0.5 to 3.0 mm. where wi denotes the i-th weight and rx(t) the nodal velocity in the x direction. The frequency of the excitation signal is 3.5 MHz and therefore the mesh of the plate has to be very fine to capture such a high frequency. The plate specimens used in the experiments are 2 inch (50.8 mm) wide in the x direction and 7 inch (177.8 mm) long in the y direction. To reduce the number of computations, the plate is "cut" in the y direction and silent boundary conditions are imposed at both plate edges in the y direction. The length of numerically modeled plate in the y direction is 1.4 inch (35.5 mm). The total number of elements is 44550 of which 297 are positioned in the x direction and 150 in the y direction. The selected number of elements ensures approximately 10 elements per longitudinal wave length AL in the x direction and about 7 elements per AL in the y direction. Material parameters, the longitudinal and transverse wave velocities, are selected in correspondence to a plane stress case for a thin aluminum plate: longitudinal plate wave velocity CL = 5397 mis, transverse plate wave velocity or = 3100 mls. An example of wave scattering calculated by FEM is depicted in Figures 7.a, 7.b, 7.c, and 7.d. In Figure 7.a, a simultaneous excitation from both sides of the plate can be seen as two waves propagating toward each other. As the waves propagate further all four values needed to calculate the R!f ratio [1] can be evaluated: VII, VI2, V2I, and V22. The first is the partial wave reflection V1I from the model crack recorded at the near side of the plate (Figure 7.b), second and third are through-transmitted wave signals, V2I and V12, from one side of the plate to the other, shown in Figure 7.c, and the fourth is the partial wave reflection V22 from the model crack recorded at the other side of the plate (Figure 7.d). Figures 7.a - d show contour plots of particle velocity in the x direction for selected time intervals which are chosen by a time-of-flight approach [1] to extract the needed information for the R!f calculation. After acquiring all the data in a manner similar to the experiments, R!f curves can be calculated. These R!f curves do not match in amplitude with experimental data and they need to be calibrated. To perform appropriate amplitude modification, known experimental data are used to account for material attenuation. The resulting modeled R/T curves are shown in Figure 8. A satisfactory agreement can be noticed between numerical and experimental results by comparing Figure 4. and Figure 8. 782

( Processing Phase ) ( I I Ultrasonic Measurement Neural Network Classifier 1::;= NNC NNCOutput Crack Length in mm I_I=== r " Learning Phase ) TRAINING FEM Analysis PERFORMANCE TESTING Test Experimental Signals..., Fig. 5 Ultrasonic signals processing system. 3.2 0.8 2.2 0.6 1.2 u 0.4 8 '0 0.2 -.S u 'a 0.2 e -0.8 '0 > 0-1.8-2.8-0.2 2.5 2.9 3.3 3.8 4.2 1 2 3 4 5 6 time [Ils] frequency [MHz] 7 Fig. 6 Transmitter time and frequency dependent excitation signals used in FE modeling. NEURAL NETWORK CLASSIFIER After the desired numerical and experimental data are obtained and corresponding R!f curves stored the NN classifier can begin to learn. Its training is perfonned by numerically obtained R!f curves for model crack sizes of 1.0, 2.0, and 3.0 mm. The case of no crack is simulated by crack size of 0.0 mm which enables the NN classifier to appropriately evaluate also crack sizes between 0.0 mm and 1.0 mm. The NN is then trained to map the collected R!f curves to encoded crack size patterns [3] which are easily convertible into actual crack sizes in mm. The desired outputs of the NN classifier in the learning phase are presented in Table I. The NN classifier is designed to perfonn shift-invariant mapping which is required in our particular application due to the unknown reference scanning position. The NN classifier scheme is shown in Figure 9. The first two layers consist of pre-processing units which are specifically connected [I] to perfonn shift-invariance and the next three layers represent the 783

x x 2.0- ----------------, - 1.5-1.5-1.0-1.0-0.5-0.5-2.0-1--- --, 0.0 -+-----r---""'t""--,r rl...-..,_ 0.0 0.5 1.0 1.5 Y x Figure 7.a Time = 1.48 Ils 0.0 -t----.----r---r---"t,--"r'-""-y 0.0 0.5 1.0 1.5 x Figure 7.b Time = 3.60 Ils 2.0-2.0-1.5-1.5-1.0-1.0-0.5-0.5-0.0 -I----.---""T""'---r-----r,---+--...-. 0.0 0.5 1.0 1.5 Y Figure 7.c Time = 10.62 Ils 0.0 -t--.,--,.---,--,---r----,t- 0.0 0.5 1.0 1.5 Y Figure 7.d Time = 15.42 Ils 784

60 iii 3.0 mm -eb-2.5mm.. 2.0mm 50 - -1.5mm 40 1.0 mm 0.5 mm 30 20 10 o o 2 4 6 8 10 12 14 16 Scanning Position [0.5xlO- 1 inch increment] Fig. 8 RJT curves obtained by FE modeling of the EDM notches. Table I. Desired NN classifier outputs in the learning phase. EDMnotch QytI;mlynill QYlI!J.U ynil 2 QYlI!Ylynil 3 QYlI!Ylynil 4 size [mm] Omm Imm 2mm 3mm 0.0 1 0 0 0 1.0 0 1 0 0 2.0 0 0 1 0 3.0 0 0 0 1 Table II. NN Classifier generalization capabilities. EDM Average Average output output output output notch error error unit 1 unit 2 unit 3 unit 4 size learning testing Omm Imm 2mm 3mm [mm] phase phase r%l r%l 0.0 3.09 FEM 5.14 EX 0.5 0.42 EX 0.58 EX 0.24 EX 0.02 EX 1.0.87 FEM 5.92 EX 1.5 0.27 EX 0.47 EX 0.51 EX 0.15 EX 2.0 1.81 FEM 6.47 EX 2.5 0.05 EX 0.13 EX 0.58 EX 0.47 EX 3.0 1.03 FEM 6.19 EX standard back-propagation type of neural network [3]. A more detailed description of the computations performed by a particular NNC layer can be found in reference [1]. Once the network is trained, its performance is tested by experimental data used in amplitude calibration pre-processing (see Table II.). The trained NN classifier can be further utilized to estimate crack sizes from RIT curves that have not been used in the learning phase. The results showing the generalization capabilities [1] of the system are shown in the right portion of Table II. 785

(Rln l (Rff)2 (R/T)3 Omm notch 1 mmnotch 2mmnotch (RlT)14 3 mmnotch (RlTh5 CONCLUSION Fig. 9 Five-layer neural network classifier architecture. An ultrasonic data processing system has been developed and applied to the detection and sizing of ED M notches emanating from rivet holes. A shift-invariant neural network is successfully used to classify RIT curves for different EDM notches that are used to model cracks. A set of training data for the NN is obtained by 2-D FE models. The results show that numerical results can be applied to train the NN classifiers and that the ultrasonic data processing system gives a good prediction of the EDM notch sizes. To obtain even better generalization capabilities of the classifier would require a larger number of numerically obtained data. The data processing system is general and can be applied also to other nondestructive testing problems. In practice, plate waves are used to perform inspection around riveted joints. Therefore, future work will concentrate on 3-D FE modeling which will more accurately simulate real applications. ACKNOWLEDGMENTS This work was sponsored by the FAA Center for Aviation Systems Reliability, operated by the Ames Laboratory, USOOE, for the Federal Aviation Administration by Iowa State University and Northwestern University. REFERENCES 1. I.Komsky, K.Zgonc, and J.D.Achenbach, Review in Progress in QNDE, Vol. 13, eds. D.O Thompson and D.E Chimenti (Plenum, New York, 1994, p. 895 2. R.Ludwig and W.Lord, " A Finite Element Formulation for the Study of Ultrasonic NDT System", IEEE Trans. on UFFC, Vol 35, No.6, p.809 3. R.H.Nielsen, Neurocomputing, Addison-Wesley Publishing Company, 1990 4. ld. Achenbach, Wave propagation in elastic solids, North-Holland, 1990 (sixth printing) p.226 786