Parameter-identification investigations on the hysteretic Preisach model improved by the fuzzy least square support vector machine based on adaptive variable chaos immune algorithm

Abstract

In order to solve the hysteretic character of the piezoelectric material for application, the initial weight factors of the hysteretic units are calculated by the Preisach theory and the first-order reversal curves test data, a hysteretic Preisach model based on the improved fuzzy least square support vector machine (improved FLS-SVM) is established. In the established model, the fuzzy least square support vector machine is introduced to calculate more weight factors of the hysteretic units and the adaptive variable chaos immune algorithm is introduced to optimize the penalty factor and the kernel parameter of the FLS-SVM (the penalty factor c ¼ 35 and the kernel parameter ¼ 1.35 are obtained). Moreover, the quadratic polynomial interpolation method is used to eliminate the sawtooth phenomenon. The validity of established model reveals that fuzzy least square support vector machine method based on adaptive variable chaos immune algorithm (FLS-SVMAVCIA) is more accurate than FLS-SVM method according to application results of the real actuators (the absolute mean error of the FLS-SVMAVCIA model is less than 1 mm and its maximum error is less than 2 mm). As a result, the hysteretic phenomenon can be effectively eliminated by the hysteretic Preisach model based on the FLS-SVMAVCIA method.

Adaptive backstepping fuzzy sliding mode vibration control of flexible structure

“…In order to eliminate the chattering, the discontinuous control component in equation (20) can be replaced by a smooth sliding mode component tanhðsÞ, which can create a small boundary layer about the switching surface in which the system trajectory will remain.…”

“…Theorem 1. If the updated control law (20), with the adaptation law of the fuzzy system designed as equation (24), is applied to the nonlinear uncertain system such as flexible structure defined by equation (8), then the system's tracking error can converge to zero and the vibration can be suppressed . And the unknown model uncertainties and external disturbances can be approximated by fuzzy system so as to improve the robustness of the dynamic system.…”

Modeling and Identification of Rate Dependent Hysteresis in Piezoelectric Actuated Nano-Stage: A Gray Box Neural Network Based Approach

“…Parameter identification of NARMAX model by using least-squares support vector machine is presented in [23]. In [22] a fuzzy least square support vector machine technique which can overcome the slow convergence problem of least-squares support vector machine is presented. An adaptive least squares support vector regression based method is proposed in [21], where the particle swarm optimization is used to optimize the hyperparameters.…”

Hysteresis modeling of piezoelectric micro-positioning stage based on convolutional neural network

“…They use hysteresis operators and differential equations to characterize hysteresis, respectively. For example, the Preisach model 4,5 and the Prandtl–Ishlinskii (PI) model 6–8 are operator-based models and the Bouc–Wen model 9–11 is a differential model. PI model is widely used for hysteresis modeling because it is relatively simple, and its analytical inverse model can be obtained.…”