Nonlinear Stochastic Parameter Estimation of a Random Duffing–van der Pol Oscillator Using Fokker–Planck Type Residual

Abstract

In this study, our proposed parameter estimation method is furtherly tested on a nonlinear random dynamical system. Our method assumes that a probability density function (PDF) data is measured from a random dynamical system whose model structure is known as a stochastic differential equation but having unknown parameter values. The Fokker–Planck equation (FPE) is derived from the random dynamical system with the help of Itô calculus. The measured PDF data and candidate parameter values are substituted into the FPE to calculate an FPE residual. The residual is minimized by our method to estimate the parameter values. The results of application to a random Duffing–van der Pol system show that our method is capable of estimating unknown parameters even when the system is nonlinear.