Research On Nonlinear Hysteresis Modeling Of Electric Field-Polarization Of Piezoelectric Ceramics Based On DE-GWO Algorithm

Owing to the function of mutual conversion between mechanical energy and electric energy,piezoelectric ceramic,a kind of intelligent material,is widely used in underwater acoustics,ultrasonic wave and energy harvesting,etc.However,the ferroelectric hysteresis it has will cause harmonic distortion,oscillation and even instability of systems.To solve this problem,it is urgent to establish an accurate hysteresis model for this phenomenon.Since the output of piezoelectric ceramic is not only affected by the input history state,but also related to the rate of input change closely,a rate-dependent nonlinear dynamic hysteresis model accurately describing the polarization hysteresis caused by the electric field-polarization(P-E)has to be established.To address the above situation,a rate-dependent nonlinear dynamic hysteresis model for the electric field-polarization(P-E)hysteresis curve of Lead zirconate-titanate(PZT)piezoelectric ceramic is established by using an improved Bouc-Wen model in this paper.Due to the existence of differential terms within Bouc-Wen model and the unknown search range of parameters,parameter identification of Bouc-Wen model has always been a difficulty in its application.Based on Grey Wolf Optimizer(GWO)algorithm,an improved Grey Wolf algorithm(DE-GWO)is designed in this paper,then it is applied to parameter identification of Bouc-Wen model.First of all,since GWO algorithm has the advantages of simplicity implementation and fewer parameters for adjusting,this paper introduced the nonlinear adjustment strategy of time parameters a and improved position update rules to GWO algorithm,and then proposes DE-GWO algorithm mixed with the idea of difference vector.DE-GWO algorithm has achieved remarkable results in solving precision,avoiding local optimum,convergence rate and so on.In addition,it also balances exploration and exploitation capabilities of GWO algorithm,so as to further improve the performance of DE-GWO algorithm in mining the global optimal solution.Then,in order to verify the performance of DE-GWO algorithm,17 benchmark functions including unimodal functions,multimodal functions,and fixed-dimension multimodal functions as well as other intelligent optimization algorithms are used for comparison.The results show that DE-GWO algorithm has a great improvement in solving accuracy,avoiding local optimum and convergence rate.In addition,it also has advantages in dealing with large-scale function optimization problems.Finally,DE-GWO algorithm is applied to parameter identification of the improved Bouc-Wen model.According to the identification results,the relationships between the parameters and the frequency of input signal are established,then a rate-dependent nonlinear dynamic hysteresis model is found for the ferroelectric hysteresis of PZT piezoelectric ceramic.To verify the accuracy of this model,four groups of experimental data collected at input frequencies of 0.666 Hz,22 Hz,88 Hz and 133 Hz are used to detect the established model.The result shows that DE-GWO algorithm can identify the parameters within the improved Bouc-Wen model effectively and the rate-dependent nonlinear dynamic hysteresis model can accurately describe the nonlinear hysteresis relationship between the input electric field and the output polarization of piezoelectric ceramic.Furthermore,this model lays a foundation for the establishment of a controller to compensate the phenomenon as well.