PSI - Issue 72

Oleh Yasniy et al. / Procedia Structural Integrity 72 (2025) 188–194

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Table 1 shows the prediction errors for the loading and unloading stages for the MLP neural network modeling of SMA hysteresis behavior for four frequencies.

Table 1. Prediction errors

Prediction errors (%)

The loading stage, MLP 3-54-1

The unloading stage, MLP 3-39-1

Mean absolute error (MAE) Mean squared error (MSE)

0.0115 0.0002 0.4253

0.0123 0.0003 0.4659

Mean absolute percentage error (MAPE)

A low MAE value confirms that the model's predictions deviate little from the actual values. Also, a low MSE value means the model rarely makes large deviations between predicted and actual values. This indicates not only the model overall accuracy but also that large errors are rare. The low MAPE value shows that the model's predictions are characterized by small relative errors, regardless of the scale of the data. These results show that the ANN model accurately predicts material behavior during the loading and unloading. Both stages have low error values, which indicates the high accuracy of the models in general. To further evaluate the performance of the artificial neural network model, there were used the data from the 1025th loading-unloading cycle, which was not included in the training, test, or validation samples but was reserved for additional testing. This approach made it possible to assess better the model ability to predict material behavior beyond the data on which it was trained. Fig. 2 shows the dependence between the experimental values of material strain and the predicted values . obtained during model testing on the 1025th loading-unloading cycle at a frequency of 0.1 Hz. a b

Fig. 2. The predicted versus true strain  , obtained using the ANN method for the loading (a) and unloading (b) stage at a frequency of 0.1 Hz.

These graphs indicate the high accuracy of the MLP model. Similar dependencies were also obtained for frequencies of 0.5, 1 and 5 Hz. Table 2 shows the values of the prediction errors for the loading and unloading stages of the simulation of the hysteresis behavior of the nickel-titanium alloy for 1025 th cycle and four frequencies. Fig. 3 shows the hysteresis loop for 1025 th loading-unloading cycle built using ANN and the corresponding experimental data at a frequency of 0.1 Hz.