Identification of nonlinear spring coefficient in asymmetric nonlinear system using auto-regressive time series analysis

Abstract

The author proposed the identification method of symmetric nonlinear system based on the Auto-Regressive analysis and the method of averaging in a previous paper. However, there is a problem that conventional methods including the one in the previous paper cannot address the identification of asymmetric vibrating systems. In this paper, the system identification in asymmetric nonlinear system is investigated. At first, formulation of identification problem is conducted. The identification problem is described using the method of Krilov-Bogoliubov-Metropolsky is considered the two-order approximation. The description contains the amplitude dependency however coefficient of the sign cannot discriminate. Therefore, this paper proposes a new system identification method to solve these problems by identifying appropriate sign of nonlinear parameters based on movement of center-of-vibration. Identification experiment is conducted using numerical investigation, Runge-Kutta method. A nonlinear coefficient is considered in two cases: positive number and negative number. In both cases, the proposed method gives good estimated results which show good agreement with the true values. Moreover, identification experiment is conducted using the cantilever system subjected to the magnetic force. The proposed method gives estimated results which shows good agreement with the true experiment values.