Parameters Identification for Nonlinear Dynamic Systems Via Genetic Algorithm Optimization

Abstract

This paper presents a frequency domain method for the location, characterization, and identification of localized nonlinearities in mechanical systems. The nonlinearities are determined by recovering nonlinear restoring forces, computed at each degree-of-freedom (DOF). Nonzero values of the nonlinear force indicate nonlinearity at the corresponding DOFs and the variation in the nonlinear force with frequency (force footprint) characterizes the type of nonlinearity. A library of nonlinear force footprints is obtained for various types of individual and combined nonlinearities. Once the location and the type of nonlinearity are determined, a genetic algorithm based optimization is used to extract the actual values of the nonlinear parameters. The method developed allows simultaneous identification of one or more types of nonlinearity at any given DOF. Parametric identification is possible even if the type of nonlinearity is not known in advance, a very useful feature when the type characterization is difficult. The proposed method is tested on simulated response data. Different combinations of localized cubic stiffness nonlinearity, clearance nonlinearity, and frictional nonlinearity are considered to explore the method’s capabilities. Finally, the response data are polluted with random noise to examine the performance of the method in the presence of measurement noise.