Trial of identification of Non-linear 1-dof system based on the maximum likelihood estimation using the analytical solution of Fokker-Plank equation

Abstract

In this research, the system identification based on the maximum likelihood estimation method using the analytical solution of the Fokker-Plank equation is discussed in case of a nonlinear one-degree-of-freedom system. In previous work, an author was already reported about the verification result of the fundamental operation. However, there is a problem which the previous study didn’t consider the estimation accuracy loss by non-stationary response. Therefore, it is necessary understanding of the relationship between estimation accuracy and non-stationary response. In this paper, the moment equation analysis was conducted in order to understanding of the estimation accuracy mechanism. The non-stationarity and steady-state values are obtained from the moment equations. As the result, relaxation time of transient behavior was revealed in a case. Furthermore, the squared error surface is calculated based on each theoretical values about the moment.