Time-varying parameter identification using orthogonal functions

Abstract

The identification of unknown parameters of mechanical systems is a typical case of inverse problem treated in engineering. Depending on the application, the parameters can be either constant or varying with respect to time. The present contribution is dedicated to the use of orthogonal function to expand the excitation and the responses together with the expansion of the time-varying parameters in such a way that by using an operational matrix of integration, the equations of motion are written as an algebraic equation. It is expected that the proposed technique can be used for the identification of crack parameters in rotating machinery. For this aim, two case-studies are provided: the first one deals with the identification of a nonlinear time varying stiffness element of a 3 d.o.f mechanical system; the second is focused on the identification of a cracked rotor. © 2008 IOP Publishing Ltd.