System identification of nonlinear system subjected to white random excitation using Fokker-Planck equation

Abstract

This paper proposes an identification method of symmetry nonlinear system using Fokker-Planck equation. The proposed identification method will be derived from the least square estimation based on probability density function of Fokker-Planck equation. In order to estimate the probability density function, response of target nonlinear system is supposed to be subject to a constrained Gaussian Mixture Model, which has a constraint about symmetrical distribution. The estimation algorithm will be derived by using a method of maximum logarithmic likelihood, i.e. ExpectationMaximization algorithm. In a numerical simulation based on a nonlinear one degree-of-freedom system subjected to white random excitation, the estimation result of probability density function shows good agreement with the ground truth. In addition, relationship between restoring force and displacement shows good agreement with the ground truth.