Submit

Login Login

Register Register

Home / Journals / CMC / Online First / doi:10.32604/cmc.2026.077062
Journal Menu
Special Issues
Table of Content

All issues

Online First

2026

2025

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

Open Access

ARTICLE

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

Dmytro Tymoshchuk1,*, Oleh Yasniy1, Iryna Didych2, Pavlo Maruschak3,*, Yuri Lapusta4
1 Department of Artificial Intelligence Systems and Data Analysis, Ternopil Ivan Puluj National Technical University, Ternopil, Ukraine
2 Department of Computer-Integrated Technologies, Ternopil Ivan Puluj National Technical University, Ternopil, Ukraine
3 Department of Automation of Technological Processes and Production, Ternopil Ivan Puluj National Technical University, Ternopil, Ukraine
4 Université Clermont Auvergne, CNRS, Clermont Auvergne INP, Institut Pascal, Clermont-Ferrand, France
* Corresponding Author: Dmytro Tymoshchuk. Email: email; Pavlo Maruschak. Email: email
(This article belongs to the Special Issue: Machine Learning in the Mechanics of Materials and Structures)

Computers, Materials & Continua https://doi.org/10.32604/cmc.2026.077062

Received 01 December 2025; Accepted 22 January 2026; Published online 04 February 2026

Abstract

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.

Keywords

SMA; hysteresis; cyclic loading; TCN; SHAP; XAI; machine learning; neural networks

  • 97

    View

  • 15

    Download

  • 0

    Like

Related articles
Copyright© 2026 Tech Science Press
© 1997-2026 TSP (Henderson, USA) unless otherwise stated

Share Link