Identification of Certain Polynomial Nonlinear Structures by Adaptive Selectively-Sensitive Excitation

Abstract

This paper presents a method for identification of certain polynomial nonlinear dynamic systems by adaptive vibrational excitation. The identification is based on the concept of selective sensitivity and is implemented by an adaptive multihypothesis estimation algorithm. The central problem addressed by this method is reduction of the dimensionality of the space in which the model identification is performed. The method of selective sensitivity allows one to design an excitation which causes the response to be selectively sensitive to a small set of model parameters and insensitive to all the remaining model parameters. The identification of the entire system thus becomes a sequence of low-dimensional estimation problems. The dynamical system is modelled as containing both a linear and a nonlinear part. The estimation procedure presumes precise knowledge of the linear model and knowledge of the structure, though not the parameter values, of the nonlinear part of the model. The theory is developed for three different polynomial forms of the nonlinear model: quadratic, cubic and hybrid polynomial nonlinearities. The estimation procedure is illustrated through simulated identification of quadratic nonlinearities in the small-angle vibrations of a uniform elastic beam.