Parameter estimation of a random Duffing–van der Pol system via Fokker–Planck type residual

Abstract

In this study, our proposed method, which estimates un-known parameter values of stochastic differential equation (SDE) models without explicit description of probability density function (PDF) data, is furtherly tested on a non-linear random vibration system. In our proposed method, it is assumed that a measured PDF is obtained from a random dynamical system whose structure is described by a known SDE model with unknown parameter values. With the help of Itô calculus, the Fokker–Planck equation (FPE) is derived from the SDE model. The measured PDF and candidate parameter values are substituted into the FPE to calculate a FPE residual. Our method is applied to a random Duffing–van der Pol (DVP) system. The resulting FPE residuals show that our method is capable of the unknown parameter estimation for the parameters having sufficient sensitivity of the FPE residuals.