Bayesian system identification and chaotic prediction from data for stochastic Mathieu-van der Pol-Duffing energy harvester

Abstract

• An improved approximate Bayesian method is proposed. • The unknown parameters of chaotic VEH system are identified by improved approximate Bayesian method. • The 0-1 test is used to judge the chaotic occur based on the correlation of the response data In this paper, the approximate Bayesian computation combines the particle swarm optimization and sequential Monte Carlo methods, which identify the parameters of the Mathieu-van der Pol-Duffing chaotic energy harvester system. Then the proposed method is applied to estimate the coefficients of the chaotic model and the response output paths of the identified coefficients compared with the observed, which verifies the effectiveness of the proposed method. Finally, a partial response sample of the regular and chaotic responses, determined by the maximum Lyapunov exponent, is applied to detect whether chaotic motion occurs in them by a 0-1 test. This paper can provide a reference for data-based parameter identification and chaotic prediction of chaotic vibration energy harvester systems.