IDENTIFICATION OF CERTAIN POLYNOMIAL NONLINEAR STRUCTURES BY ADAPTIVESELECTIVELY-SENSITIVE EXCITATION

This paper presents a method for identification of certain polynomial nonlinear dynamic systems by adaptive vibrational excitation. The iden tification is based on the concept of selective sensitivity and is imp lemented by an adaptive multihypothesis estimation algorithm. The cent ral problem addressed by this method is reduction of the dimensionalit y of the space in which the model identification is performed. The met hod of selective sensitivity allows one to design an excitation which causes the response to be selectively sensitive to a small set of mode l parameters and insensitive to all the remaining model parameters. Th e identification of the entire system thus becomes a sequence of low-d imensional estimation problems. The dynamical system is modelled as co ntaining both a linear and a nonlinear part. The estimation procedure presumes precise knowledge of the linear model and knowledge of the st ructure, though not the parameter values, of the nonlinear part of the model. The theory is developed for three different polynomial forms o f the nonlinear model: quadratic, cubic and hybrid polynomial nonlinea rities. The estimation procedure is illustrated through simulated iden tification of quadratic nonlinearities in the small-angle vibrations o f a uniform elastic beam.