Issue 53

Y. Lu et alii, Frattura ed Integrità Strutturale, 53 (2020) 325-336; DOI: 10.3221/IGF-ESIS.53.25 332 error range is -0.029mm~0.011mm, the maximum relative error is 0.029mm, and the minimum relative error is 0.003mm. The GA-BPNN prediction error range is -0.016mm~0.004mm, the maximum relative error is 0.016mm, and the minimum relative error is 2.69*10 -6 mm. Figure 7: GA-BPNN predictive output Figure 8: Comparison of neural network errors The detailed comparison of BPNN and GA-BPNN is given below. Fig. 9 shows the training performance of two neural networks. It can be seen from Fig. 9 that the training error, validation error and test error of the network are decreasing with time, the generalization error is gradually smaller, the generalization ability is improved, and the test curve and the verification curve are consistent. When the circle position in the figure is reached, the generalization error reaches a minimum. The BPNN converges after 4 epochs, and the GA-BPNN converges after 6 epochs. GA-BPNN has a longer convergence time than BPNN because the evolution process of the population takes a long time, and the larger the initial size range of the population size, the number of iterations, the weight and the threshold, the longer the convergence time. Fig. 10 shows the validation results of the trained BPNN. It is noticed from the figure that the gradient index and mutation index of the BPNN is smaller than that of the GA-BPNN. Fig. 11 is the regression analysis of the expected output of the network and the actual training results. It can be seen from Fig. 11 that the correlation coefficient of BPNN is 0.97074, and the correlation coefficient of GA-BPNN is 0.97843, indicating that GA-BP network has better regression performance and better generalization capabilities. Tab. 4 lists the MSE (mean squared error), RMSE (root mean square error) and MAE (mean absolute error) prediction errors. From Tab. 4 we can see that the prediction precision of the GA-BPNN is higher than that with BPNN. For the two patterns, the prediction mean absolute error of BPNN is 0.0095. Contrast with it, the prediction mean absolute error of GA-BPNN is 0.0054. As a result, we can see that the GA-BPNN algorithm has better performance than BPNN. This comparison indicates that taking the advantage of the GA optimization, the BPNN could be trained well with high generalization ability and hence the forecasting performance is superior to the unoptimized neural networks. Xu [21] has studied welding deformation based on the traditional method of elastoplastic deformation. In his study, a three-dimensional finite element model for laser welding of a thin plate was established based on the thermal-elastic- plastic FEM approach to simulate the temperature field and deformation of the 316L stainless steel in the pulsed laser welding process. A moving volumetric heat source was applied to simulate the laser energy input during the welding process. Meanwhile, the welding deformation was measured by a laser displacement sensor. And the computed results were compared with the measured results.