PSI - Issue 40

V.S. Kanakin et al. / Procedia Structural Integrity 40 (2022) 194–200 Kanakin V.S. et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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Figure 4a shows the effect of the number of neurons on the values of the average relative deviation and the coefficient of variation when the neural network is trained according to the experimental data shown in Fig. 2. Figure 4b demonstrates the effect of the number of neurons on the accuracy of predicting the behavior of the flow stress curve for temperatures of 350 and 450  С and strain rates of 0.8 and 4 s − 1 . These temperature – rate deformation conditions are not used in training. As it can be seen from Fig. 4a, the neural network approximates the flow stress curves with good engineering accuracy, even with 25 neurons. However, the average relative deviation in predicting rheological behavior at temperatures of 350 and 450  С is more than 10%, which is not enough for acceptable engineering accuracy. The best result in training was obtained when 275 neurons were used. However, the coefficient of variation during verification is 35%; this indicates a strong spread of the deviations of the experimental data from the calculated ones. The lowest value of the coefficient of variation was obtained for the neural network with the number of neurons equal to 200 (see Fig. 4b). At the same time, the average relative deviation  during verification is 7%, and this corresponds to acceptable engineering accuracy. As a result of the computational experiments described above, the neural network scheme with the architecture parameters shown in the Table was selected. In Fig. 2, red lines show the results of approximating the flow stress curves of the AlMg6/10% SiC MMC at temperatures ranging from 300 to 500 °C and strain rates ranging from 0.1 to 5 s − 1 by the proposed neural network architecture. The average relative deviation  of the calculated data from the approximated ones is 1.6%, which is a good engineering accuracy. Figure 5 shows the data obtained during neural network verification for the specimens deformed at temperatures of 350 and 450 °C and strain rates of 0.8 and 4 s − 1 .

Fig. 4. The influence of the number of neurons on the average relative deviation  and the coefficient of variation  during identification (a) and verification (b) of the neural network.

Table 1. Neural network architecture. Parameters

Value

Learning algorithm Number of neurons Number of epochs Activation function

Backpropagation

200

10000 logistic

Learning rate

0.001

Number of hidden layers

1