Nonlinear Hysteresis Parameter Identification of Piezoelectric Actuators Using an Improved Gray Wolf Optimizer with Logistic Chaos Initialization and a Levy Flight Variant

Piezoelectric tilt mirrors are crucial components of precision optical systems. However, the intrinsic hysteretic nonlinearity of the piezoelectric actuator severely restricts the control accuracy of these mirrors and the overall performance of the optical system. This paper proposes an improved Gray Wolf Optimization (GWO) algorithm for high-accuracy identification of hysteresis model parameters based on the Bouc-Wen (BW) differential equation. The proposed algorithm accurately describes the intrinsic hysteretic nonlinear behavior of piezoelectric tilt mirrors. A logistic chaotic mapping method is introduced for population initialization, while a nonlinear convergence factor and a Levy flight strategy are incorporated to enhance global search capabilities during the later stages of optimization. These modifications enable the algorithm to effectively identify BW model parameters for piezoelectric nonlinear systems. Compared to conventional Particle Swarm Optimization (PSO) and standard GWO, the improved algorithm demonstrates faster convergence, higher accuracy, and superior ergodicity, making it a promising tool for solving optimization problems, such as parameter identification in piezoelectric hysteresis systems. This work provides a robust approach for improving the precision and reliability of piezoelectric-driven optical systems.