Reduced Preisach Model: Beyond Discrete Empirical Interpolation Method

Dan Wang,Hongtao Wu,Bai Chen,Yaoyao Wang,Linxiang Wang,Yonghua Lu

doi:10.1109/access.2019.2949252

Abstract

The Preisach model, which is formulated as a weighted superposition of hysteresis kernels, has been widely used for hysteresis modeling, especially in smart-material-based actuators. However, in the classical Preisach model, a trade-off is always required between the model accuracy and the number of the hysteresis kernels. To deal with this problem, a model order reduction technique based on the discrete empirical interpolation method (DEIM) has recently been proposed. The method can largely reduce the number of the hysteresis kernels while barely losing the model accuracy. It is noted that the kernel weight in the reduced DEIM-based model can be both positive and negative, which means that the monotonicity of the Preisach model could be lost. The monotonicity is a very important property especially when constructing the inverse Preisach model. Furthermore, the loss of the monotonicity can also deteriorate the model predictability. In the current paper, a modification strategy is proposed. In the modified reduced Preisach model, the DEIM is only employed to select the dominant hysteresis kernels while the corresponding weights of the selected hysteresis kernels are re-identified by solving a constraint optimization problem. Systematic simulation studies and experimental validation are carried out to demonstrate the effectiveness of the proposed strategy.

Highlights

Due to their intrinsic multi-physics coupling effects and excellent properties, smart materials and structures have been widely employed for engineering applications, such as different smart-material-based actuators, sensors, energy harvesters and vibration dampers [1]–[8]
The Preisach model has been successfully used for describing hysteresis nonlinearity in many different smart materials and structures, especially in various smart-material-based actuators, such as piezoelectric, magnetostrictive and shape memory alloy actuators [14]–[18]
It is noted that the re-constructed weights corresponding to the selected dominant hysteresis kernels in the reduced Preisach model using the discrete empirical interpolation method (DEIM) can be both positive and negative, which means that the monotonicity of the Preisach model could be lost

Summary

INTRODUCTION

Due to their intrinsic multi-physics coupling effects and excellent properties, smart materials and structures have been widely employed for engineering applications, such as different smart-material-based actuators, sensors, energy harvesters and vibration dampers [1]–[8]. J. Zhang et al proposed an optimal compression method based on the Kullback-Leibler (KL) divergence, which was utilized to measure the information loss in discretizing the Preisach model [21]. It is noted that the re-constructed weights corresponding to the selected dominant hysteresis kernels in the reduced Preisach model using the DEIM can be both positive and negative, which means that the monotonicity of the Preisach model could be lost. To preserve the monotonicity in the reduced model, a modified reduced Preisach model beyond the DEIM is proposed in the current paper. As for the weights corresponding to the selected dominant hysteresis kernels, instead of being constructed directly by the DEIM, they are re-identified by solving a constraint optimization problem.

PREISACH MODEL

PROBLEMS WITH RM-DEIM AND A MODIFICATION STRATEGY

SIMULATION STUDIES

EXPERIMENTAL VALIDATION

Findings

CONCLUSION