AR時系列解析を用いた2次+3次非線形系のばね定数の同定

抄録

The authors proposed the identification method of nonlinear spring coefficient using Auto-Regressive time series analysis and Krilov-Bogoliubov-Metropolsky method (KBM method) in a previous paper. Especially, the conventional works had independently deal with the case of second order nonlinearity and the case of third order nonlinearity. However, there is a problem that conventional work didn’t consider the case of second + third order nonlinearity. In this paper, the system identification method in asymmetric nonlinear system included second order and third-order nonlinearity is investigated. At first, formulation of identification problem is conducted. The identification problem is described using the KBM method. Regression problem is formulated using the difference between instantaneous natural angular frequency and linear natural angular frequency. Identification experiment is conducted using numerical investigation based on 4th Runge-Kutta method. Here, second-order nonlinear coefficient is considered in two cases, positive case and negative case, respectively. In both cases, the estimation values of our proposed method are good agreement with the true values.