Prediction of SMA Hysteresis Behavior: A Deep Learning Approach with Explainable AI

This article presents an approach to predicting the hysteresis behavior of shape memory alloys (SMAs) using a Temporal Convolutional Network (TCN) deep learning model, followed by the interpretation of the results using Explainable Artificial Intelligence (XAI) methods. The experimental dataset was prepared based on cyclic loading tests of nickel-titanium wire at loading frequencies of 0.3, 0.5, 1, 3, and 5 Hz. For training, validation, and testing, 100–250 loading-unloading cycles were used. The input features of the models were stress σ (MPa), cycle number (Cycle parameter), and loading-unloading stage indicator, while the output variable was strain ε (%). The data were divided into groups based on the cycle number, ensuring no overlap between samples and correctly assessing the model’s generalization ability. TCN network hyperparameters are optimized using the Hyperband algorithm. The model’s accuracy was evaluated using mean squared error (MSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and the coefficient of determination (R²). On the test dataset, the models achieved MSE ≤ 0.0002, MAE ≤ 0.0055, MAPE ≤ 0.0038, and R² ≥ 0.9997, confirming the high accuracy of reproducing the stress-strain loop shape. The extrapolation ability was evaluated on additional cycles not used during training. For a frequency of 1 Hz, the following results were obtained: for cycle 260, MSE = 0.0001, MAE = 0.0081, MAPE = 0.0032, R² = 0.9997; for cycle 350, MSE = 0.0004, MAE = 0.0178, MAPE = 0.0073, R² = 0.9989, for cycle 450 MSE = 0.0017, MAE = 0.0315, MAPE = 0.0124, R² = 0.9964. This dynamic reflects a physically justified increase in errors with increasing cycle number, due to the accumulation of functional fatigue effects. To interpret the model’s performance, the SHapley Additive exPlanations (SHAP) method was used, which made it possible to quantitatively assess the contributions of input features to the prediction. Stress is the dominant factor, and the significance of the Cycle parameter increases with increasing cycle distance, s consistent with the evolution of the hysteresis loop under the influence of functional fatigue of the material.