Identifying the stiffness and damping of a nonlinear system using its free response perturbed with Gaussian white noise

Abstract

Measurement uncertainty can affect the accuracy of estimating parameters of vibrating systems. This article is concerned with the development of a method for estimating parameters from the free vibration response of a nonlinear system in which the response signal is contaminated with Gaussian white noise. The backbone curve and envelope of the response are first estimated from the free vibration signal. An algorithm based on the Bayesian approach is then used to identify the stiffness and damping parameters of a nonlinear system excited at a single resonant frequency. A numerical example is provided to illustrate the proposed method, which is then applied to the experimental data from a nonlinear vibration absorber system that was excited at its first resonant frequency. The proposed approach provides the distribution and confidence intervals of the parameter estimates, which is an improvement on methods that provide a single number for each estimate. As the signal-to-noise ratio decreases, the variances of the posterior distributions increase as do the confidence intervals, reflecting greater uncertainty in the parameter estimates. The approach is effective provided that the signal-to-noise ratio is greater than about 10.