A New Method for Detecting the Time-Varying Nonlinear Damping in Nonlinear Oscillation Systems: Nonparametric Identification

Abstract

This paper presents an original method that can be used for identifying time-varying nonlinear damping characteristics of a nonlinear oscillation system. The method developed involves the nonparametric identification, in which only the system responses, namely, displacement and velocity need to be known for the identification. However, the method is concerned with a Volterra-type integral equation of the first kind, which leads to an instability of numerical solutions. That is, the solutions identified lack stability properties. In order to overcome the difficulty, a stabilization technique is applied to the identification process. A numerical example comprising a highly nonlinear system is examined to demonstrate the workability of the proposed method for the time-varying damping identification.