004.9:006.3

SMA; hysteresis; machine learning; ensemble model; Stacking Regressor; ElasticNet; Explainable AI (XAI); SHAP analysis; strain prediction; information technology.

Shape Memory Alloys are characterized by a nonlinear hysteretic behavior on the stress–strain (σ–ε) diagram, where the loop area determines the amount of energy dissipated per cycle. In this work, an ensemble Stacking machine learning model was developed to predict the hysteresis behavior of SMAs under cyclic loading at different frequencies (0.5, 1, 3, and 5 Hz). The model was constructed using experimental data from 100–250 loading cycles. Random Forest, Gradient Boosting, Extra Trees, k-Nearest Neighbors (kNN), Support Vector Regression (SVR), and Multilayer Perceptron (MLP) were employed as base algorithms. The ElasticNet model was selected as the meta-learner and tuned using GridSearchCV with GroupKFold validation. This approach ensured the combination of ensemble stability with adaptive selection of the most informative predictions from the base models. The obtained results showed a high accuracy in reproducing the stress–strain relationship: R² > 0.995, MSE < 0.0007, MAE < 0.02, and MAPE < 1.3 % on the test data. Validation on independent cycles 251 and 300 confirmed the model’s generalization ability, achieving R² > 0.974, MSE < 0.007, MAE < 0.06, and MAPE < 4.8 %. The interpretability of the model was provided by the SHAP method, which quantitatively determines the contribution of each input feature to the prediction. It was found that Stress is the dominant factor influencing the prediction, while UpDown defines the loading–unloading phase, and Cycle reflects the accumulation of cyclic effects. The developed ensemble Stacking model is an integral component of an information technology framework for predicting the hysteresis behavior of shape memory alloys using machine learning methods. The proposed approach provides not only high prediction accuracy but also a physically grounded interpretability of the results.

1. Sharma K., & Srinivas G. (2020Flying smart: Smart materials used in aviation industry. Materials Today: Proceedings, 27, pp. 244–250. Available at: https://doi.org/10.1016/j.matpr.2019.10.115.
2. Niu X., Yao X., & Dong E. (2025) Design and control of bio-inspired joints for legged robots driven by shape memory alloy wires. Biomimetics, 10 (6), pp. 378. Available at: https://doi.org/10.3390/biomimetics 10060378.
3. Schmelter T., Bade L., & Kuhlenkötter B. (2024) A two-finger gripper actuated by shape memory alloy for applications in automation technology with minimized installation space. Actuators, 13 (10), p. 425. Available at: https://doi.org/10.3390/act13100425.
4. Riccio A., Sellitto A., Ameduri S., Concilio A., & Arena M. (2021). Shape memory alloys (SMA) for automotive applications and challenges. In Shape Memory Alloy Engineering, pp. 785–808. Elsevier. Available at: https://doi.org/10.1016/b978-0-12-819264-1.00024-8.
5. Zhang H., Zhao L., Li A., & Xu S. (2024) Design and hysteretic performance analysis of a novel multi-layer self-centering damper with shape memory alloy. Buildings, 14 (2), p. 483. Available at: https://doi.org/ 10.3390/buildings14020483.
6. Iasnii V., Krechkovska H., Budz V., Student O., & Lapusta Y. (2024). Frequency effect on low‐cycle fatigue behavior of pseudoelastic NiTi alloy. Fatigue & Fracture of Engineering Materials & Structures. Available at: https://doi.org/10.1111/ffe.14331.
7. Tymoshchuk D., Yasniy O., Maruschak P., Iasnii V., & Didych I. (2024) Loading Frequency Classification in Shape Memory Alloys: A Machine Learning Approach. Computers, 13 (12), p. 339. Available at: https://doi.org/10.3390/computers13120339.
8. IBM. (n.d.-b). What is Explainable AI (XAI)? | IBM. https://www.ibm.com/think/topics/explainable-ai.
9. Hmede R., Chapelle F., & Lapusta Y. (2022) Review of neural network modeling of shape memory alloys. Sensors, 22 (15), p. 5610. Available at: https://doi.org/10.3390/s22155610.
10. He S., Wang Y., Zhang Z., Xiao F., Zuo S., Zhou Y., Cai X., & Jin X. (2023) Interpretable machine learning workflow for evaluation of the transformation temperatures of TiZrHfNiCoCu high entropy shape memory alloys. Materials & Design, 225, 111513. Available at: https://doi.org/10.1016/j.matdes.2022. 111513.
11. Sridharan S., Velayutham R., Behera S., & Murugesan J. (2025). Machine Learning-Based Temperature-Induced Phase Transformation Temperature Prediction of Ti-Based High-Temperature Shape Memory Alloy. Journal of Materials Engineering and Performance. Available at: https://doi.org/10.1007/s11665-025-11236-z.
12. Thiercelin L., Peltier L., & Meraghni F. (2024) Physics-informed machine learning prediction of the martensitic transformation temperature for the design of “NiTi-like” high entropy shape memory alloys. Computational Materials Science, 231, 112578. Available at: https://doi.org/10.1016/j.commatsci.2023. 112578.
13. Lam T.-N., Jiang J., Hsu M.-C., Tsai S.-R., Luo M.-Y., Hsu S.-T., Lee W.-J., Chen C.-H., & Huang E.-W. (2024) Predictions of Lattice Parameters in NiTi High-Entropy Shape-Memory Alloys Using Different Machine Learning Models. Materials, 17 (19), 4754. Available at: https://doi.org/10.3390/ma17194754.
14. Liu C., & Su H. (2024) Machine learning aided prediction of martensite transformation temperature of NiTi-based shape memory alloy. Materials Today Communications, 41, 110720. Available at: https://doi. org/10.1016/j.mtcomm.2024.110720.
15. Iasnii V., Bykiv N., Yasniy O., & Budz V. (2022) Methodology and some results of studying the influence of frequency on functional properties of pseudoelastic SMA. Scientific journal of the Ternopil national technical university, 107 (3), pp. 45–50. Available at: https://doi.org/10.33108/visnyk_tntu2022.03.045.
16. StackingRegressor. (n.d.). Available at: https://scikit-learn.org/stable/modules/generated/sklearn.ensemble. StackingRegressor.html.
17. RandomForestRegressor. (n.d.). Available at: https://scikit-learn.org/stable/modules/generated/sklearn. ensemble.RandomForestRegressor.html.
18. Clark B., & Lee F. (n.d.). What is Gradient Boosting? | IBM. Available at: https://www.ibm.com/think/ topics/gradient-boosting.
19. ExtraTreesRegressor. (n.d.). Retrieved from Available at: https://scikit-learn.org/stable/modules/generated/ sklearn.ensemble.ExtraTreesRegressor.html.
20. Nearest Neighbors. (n.d.). Available at: https://scikit-learn.org/stable/modules/neighbors.html.
21. Support Vector Machines. (n.d.). Available at: https://scikit-learn.org/stable/modules/svm.html.
22. Haykin S. (2009). Neural networks and learning machines (3rd ed.). Hamilton, ON, Canada: Prentice Hall.
23. ElasticNet. (n.d.). Available at: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model. ElasticNet.html.
24. Metrics and scoring: quantifying the quality of predictions. (n.d.). Available at: https://scikit-learn.org/ stable/modules/model_evaluation.html#model-evaluation.
25. GitHub – shap/shap: A game theoretic approach to explain the output of any machine learning model. (n.d.-b). Available at: https://github.com/shap/shap.

1. Sharma K., & Srinivas G. (2020Flying smart: Smart materials used in aviation industry. Materials Today: Proceedings, 27, pp. 244–250. Available at: https://doi.org/10.1016/j.matpr.2019.10.115.
2. Niu X., Yao X., & Dong E. (2025) Design and control of bio-inspired joints for legged robots driven by shape memory alloy wires. Biomimetics, 10 (6), pp. 378. Available at: https://doi.org/10.3390/biomimetics 10060378.
3. Schmelter T., Bade L., & Kuhlenkötter B. (2024) A two-finger gripper actuated by shape memory alloy for applications in automation technology with minimized installation space. Actuators, 13 (10), p. 425. Available at: https://doi.org/10.3390/act13100425.
4. Riccio A., Sellitto A., Ameduri S., Concilio A., & Arena M. (2021). Shape memory alloys (SMA) for automotive applications and challenges. In Shape Memory Alloy Engineering, pp. 785–808. Elsevier. Available at: https://doi.org/10.1016/b978-0-12-819264-1.00024-8.
5. Zhang H., Zhao L., Li A., & Xu S. (2024) Design and hysteretic performance analysis of a novel multi-layer self-centering damper with shape memory alloy. Buildings, 14 (2), p. 483. Available at: https://doi.org/ 10.3390/buildings14020483.
6. Iasnii V., Krechkovska H., Budz V., Student O., & Lapusta Y. (2024). Frequency effect on low‐cycle fatigue behavior of pseudoelastic NiTi alloy. Fatigue & Fracture of Engineering Materials & Structures. Available at: https://doi.org/10.1111/ffe.14331.
7. Tymoshchuk D., Yasniy O., Maruschak P., Iasnii V., & Didych I. (2024) Loading Frequency Classification in Shape Memory Alloys: A Machine Learning Approach. Computers, 13 (12), p. 339. Available at: https://doi.org/10.3390/computers13120339.
8. IBM. (n.d.-b). What is Explainable AI (XAI)? | IBM. https://www.ibm.com/think/topics/explainable-ai.
9. Hmede R., Chapelle F., & Lapusta Y. (2022) Review of neural network modeling of shape memory alloys. Sensors, 22 (15), p. 5610. Available at: https://doi.org/10.3390/s22155610.
10. He S., Wang Y., Zhang Z., Xiao F., Zuo S., Zhou Y., Cai X., & Jin X. (2023) Interpretable machine learning workflow for evaluation of the transformation temperatures of TiZrHfNiCoCu high entropy shape memory alloys. Materials & Design, 225, 111513. Available at: https://doi.org/10.1016/j.matdes.2022. 111513.
11. Sridharan S., Velayutham R., Behera S., & Murugesan J. (2025). Machine Learning-Based Temperature-Induced Phase Transformation Temperature Prediction of Ti-Based High-Temperature Shape Memory Alloy. Journal of Materials Engineering and Performance. Available at: https://doi.org/10.1007/s11665-025-11236-z.
12. Thiercelin L., Peltier L., & Meraghni F. (2024) Physics-informed machine learning prediction of the martensitic transformation temperature for the design of “NiTi-like” high entropy shape memory alloys. Computational Materials Science, 231, 112578. Available at: https://doi.org/10.1016/j.commatsci.2023. 112578.
13. Lam T.-N., Jiang J., Hsu M.-C., Tsai S.-R., Luo M.-Y., Hsu S.-T., Lee W.-J., Chen C.-H., & Huang E.-W. (2024) Predictions of Lattice Parameters in NiTi High-Entropy Shape-Memory Alloys Using Different Machine Learning Models. Materials, 17 (19), 4754. Available at: https://doi.org/10.3390/ma17194754.
14. Liu C., & Su H. (2024) Machine learning aided prediction of martensite transformation temperature of NiTi-based shape memory alloy. Materials Today Communications, 41, 110720. Available at: https://doi. org/10.1016/j.mtcomm.2024.110720.
15. Iasnii V., Bykiv N., Yasniy O., & Budz V. (2022) Methodology and some results of studying the influence of frequency on functional properties of pseudoelastic SMA. Scientific journal of the Ternopil national technical university, 107 (3), pp. 45–50. Available at: https://doi.org/10.33108/visnyk_tntu2022.03.045.
16. StackingRegressor. (n.d.). Available at: https://scikit-learn.org/stable/modules/generated/sklearn.ensemble. StackingRegressor.html.
17. RandomForestRegressor. (n.d.). Available at: https://scikit-learn.org/stable/modules/generated/sklearn. ensemble.RandomForestRegressor.html.
18. Clark B., & Lee F. (n.d.). What is Gradient Boosting? | IBM. Available at: https://www.ibm.com/think/ topics/gradient-boosting.
19. ExtraTreesRegressor. (n.d.). Retrieved from Available at: https://scikit-learn.org/stable/modules/generated/ sklearn.ensemble.ExtraTreesRegressor.html.
20. Nearest Neighbors. (n.d.). Available at: https://scikit-learn.org/stable/modules/neighbors.html.
21. Support Vector Machines. (n.d.). Available at: https://scikit-learn.org/stable/modules/svm.html.
22. Haykin S. (2009). Neural networks and learning machines (3rd ed.). Hamilton, ON, Canada: Prentice Hall.
23. ElasticNet. (n.d.). Available at: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model. ElasticNet.html.
24. Metrics and scoring: quantifying the quality of predictions. (n.d.). Available at: https://scikit-learn.org/ stable/modules/model_evaluation.html#model-evaluation.
25. GitHub – shap/shap: A game theoretic approach to explain the output of any machine learning model. (n.d.-b). Available at: https://github.com/shap/shap.