This article presents an approach for modelling hysteresis in smart materials, specifically piezoelectric materials, that leverages recent advancements in machine learning, particularly in sparse-regression techniques. While sparse regression has previously been used to model various scientific and engineering phenomena, its application to nonlinear hysteresis modelling in piezoelectric materials has yet to be explored. The study employs the least-squares algorithm with a sequential threshold to model the dynamic system responsible for hysteresis, resulting in a concise model that accurately predicts hysteresis for both simulated and experimental piezoelectric material data. Several numerical experiments are performed, including learning butterfly-shaped hysteresis and modelling real-world hysteresis data for a piezoelectric actuator. Additionally, insights are provided on sparse white-box modelling of hysteresis for magnetic materials taking non-oriented electrical steel as an example. The presented approach is compared to traditional regression-based and neural network methods, demonstrating its efficiency and robustness. Source code is available at https://github.com/chandratue/SmartHysteresis.

翻译：本文提出了一种利用机器学习近期进展（尤其是稀疏回归技术）对智能材料（特别是压电材料）中的滞后现象进行建模的方法。尽管稀疏回归先前已用于建模各种科学和工程现象，但其在压电材料非线性滞后建模中的应用尚未被探索。本研究采用带序贯阈值的经典最小二乘算法来建模产生滞后的动态系统，从而得到能准确预测模拟和实验压电材料数据中滞后现象的简洁模型。我们执行了多项数值实验，包括学习蝴蝶形滞后以及建模压电致动器的实际滞后数据。此外，本文以非定向电工钢为例，提供了磁性材料滞后稀疏白箱建模的见解。将所提出的方法与基于传统回归和神经网络的方法进行了比较，证明了其高效性和鲁棒性。源代码见 https://github.com/chandratue/SmartHysteresis。