System Identification of Nonlinear Mechanical Systems Using Embedded Sensitivity Functions

A novel method of experimental sensitivity analysis for nonlinear system identification of mechanical systems is examined here. It has been shown previously that embedded sensitivity functions, which are quadratic algebraic products of frequency response function data, can be used to identify structural design modifications for reducing vibration levels. It is shown here that embedded sensitivity functions can also be used to characterize and identify mechanical nonlinearities. Embedded sensitivity functions represent the rate of change of the response with variation in input amplitude, and yield estimates of system parameters without being explicitly dependent on them. Frequency response functions are measured at multiple input amplitudes and combined using embedded sensitivity analysis to extract spectral patterns for characterizing systems with stiffness and damping nonlinearities. By comparing embedded sensitivity functions with finite difference frequency response sensitivities, which incorporate the amplitude-dependent behavior of mechanical nonlinearities, models can be determined using an inverse problem that uses system sensitivity to estimate parameters. Expressions for estimating nonlinear parameters are derived using Taylor series expansions of frequency response functions in conjunction with the method of harmonic balance for periodic signals. Using both simulated and experimental data, this procedure is applied to estimate the nonlinear parameters of a two degree-of-freedom model and a vehicle exhaust system to verify the approach.