Parameter Identification And Chaos Prediction Of High-dimensional Stochastic System

Chaos is an important part of nonlinear science and has been applied in many academic and engineering fields.In recent years,the development of self-powered technology has promoted the deep integration of human life and wireless sensor network products,among which chaotic vibration energy harvester technology has become a hot topic in the field of self-powered research because of its high energy conversion rate.One of the key problems in converting vibration energy into electrical energy in wireless sensor networks is to deeply understand the dynamics of chaotic vibration energy harvester systems and reveal the chaotic development of the systems.However,for most chaotic systems,we lack reliable information about the parameters.Therefore,in this paper,we take the Mathieu-van der Pol-Duffing vibrational energy harvester system coupled with a piezoelectric device and a circuit as an example,and investigate the two aspects of parameter identification and chaos prediction of this system:Ⅰ.Parameter identification based on the response information of a high-dimensional chaotic systemIn this section,the problem of difficult identification of physical parameters of high-dimensional chaotic vibration energy harvester is investigated.First,a mathematical model of the Mathieu-van der Pol-Duffing vibration energy harvester is established.The particle swarm optimization technique is used to calculate the global optimal solutions of all unknown parameters using the input and output data of the system,and the prior distribution of each unknown parameter is determined.Then,the developed approximate Bayesian calculation method is used to update the prior distribution to the approximate posterior distribution,and the mean statistic is used as the estimated value of every unknown parameter.Finally,the error between the identified parameters and the real ones is calculated,and the maximum error is no more than 2%.The effectiveness of the method is further verified by comparing the real system with the corresponding response output path of the identified system.Ⅱ.Chaos prediction based on the response information of high-dimensional stochastic chaotic systemIn this section,the chaotic behavior of the system is predicted based on the partial response information of the Mathieu-van der Pol-Duffing vibration energy harvester under stochastic chaotic periodic excitation.First,the necessary condition for the occurrence of chaotic motion in the stochastic system is studied qualitatively using the mean square criterion by the stochastic Melnikov method.Subsequently,the chaotic behavior of the system is investigated by calculating the maximum Lyapunov exponent,phase diagram and Poincarémap of the stochastic vibration energy harvester for different noise intensities.Finally,we propose a 0-1 test technique based on partial corresponding information to predict the chaotic behavior of the system,and the prediction results are consistent with the qualitative and quantitative analysis of the chaotic behavior of the system.In conclusion,this paper provides a suitable analytical scheme for the problem of identifying parameters of high-dimensional chaotic systems and predicting chaos in high-dimensional chaotic systems under stochastic excitation.