PSI - Issue 81

Dmytro Tymoshchuk et al. / Procedia Structural Integrity 81 (2026) 35–40

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Table 3. Prediction errors (cycles 251 and 300) Prediction errors

Frequency, Hz

0.3

0.5

3

5

251

300

251

300

251

300

251

300

0.0007 0.0039 0.0003 0.0006 0.0005 0.0020 0.0004 0.0095 0.0203 0.0537 0.0134 0.0218 0.0178 0.0375 0.0155 0.0788 0.9997 0.9985 0.9993 0.9986 0.9986 0.9952 0.9982 0.9653 0.0065 0.0206 0.0047 0.0075 0.0090 0.0210 0.0084 0.0591

Mean squared error (MSE) Mean absolute error (MAE) Coefficient of determination ( R 2 )

Mean absolute percentage error (MAPE)

The results confirm that the Voting model is capable not only of accurately reproducing the experimental hysteresis curves on the test data but also of generalizing underlying patterns when predicting new cycles. Therefore, ensemble approach is reliabile and has a promising potential for predicting the functional properties of SMAs.

3.3. Prediction of SMA Hysteresis Behavior

The developed ensemble Voting model made it possible to reproduce the complex hysteresis behavior of SMAs over a wide range of cyclic loading frequencies. Figure 2 presents a comparison between the experimental and predicted hysteresis loops generated by the ensemble Voting model for the 251st and 300th cycles at a loading frequency of 0.3 Hz. a b

Fig. 2. Comparison of experimental and predicted hysteresis loops for the 251st (a) and 300th (b) cycles at a loading frequency of 0.3 Hz.

It can be observed that the model reproduces the curve shapes with high accuracy during both the loading and unloading stages, successfully capturing the characteristic nonlinear relationships caused by phase transformations. Minor deviations in the more distant 300th cycle can be attributed to material fatigue accumulation; however, the overall agreement between the predicted and experimental data remains high. Similar hysteresis loops were obtained for other loading frequencies, confirming the stability and robustness of the ensemble approach in modeling the behavior of shape memory alloys under various operating conditions. 4. Conclusions In this study, an ensemble Voting machine learning model was developed to predict the hysteresis behavior of shape memory alloys under repeated cyclic loading at different frequencies. The results confirm that the proposed approach achieves high accuracy in reproducing experimental curves, as evidenced by the low error values (MAE < 0.022, MSE < 0.0008) and a high coefficient of determination (R 2 > 0.998). The model retained its generalization capability on extrapolated cycles, confirming its reliability for long-term predictions. It was found that tree-based algorithms and the multilayer perceptron contributed the most to the ensemble’s predictions, effectively capturing the nonlinear dependencies inherent in SMA behavior. These findings highlig ht the promising potential of ensemble models for predicting the fatigue life and functional properties of SMAs in real-world engineering applications.