Identification and parameter estimation of a bilinear oscillator using Volterra series with harmonic probing

Identification of non-linear systems is mainly limited to polynomial form non-linearities. Among the non-polynomial forms, bilinear oscillator constitutes an important class of non-linear systems and it has been used for modeling of various physical systems, particularly for structural elements with a breathing crack. An identification procedure is presented here for the class of bilinear oscillator, using higher order FRFs derived from Volterra series under harmonic excitation. The procedure addresses the problem of both; identification of the non-linearity structure as well as estimation of the bilinear parameter, which can be correlated to the crack severity and structural degradation. The procedure is illustrated with numerical simulation and the estimation results indicate that even a weakly bilinear state introduced by a small crack size can be accurately identified and measured.