Polynomial, Non-Polynomial, and Orthogonal Polynomial Generating Functions for Nonlinear System Identification

摘要

Traditional methods for identifying models of nonlinear systems use integer power series to construct nonlinear feedback forces, which act together with the external forces on an appropriately chosen nominal linear system model. Two primary disadvantages to using ordinary polynomial series in practice are that nonlinear characteristics in engineered structures and material constitutive laws are generally not governed by integer power series; and limitations on measurement dynamic range restrict the number of terms in the series and hence the fidelity of the nonlinear model. This paper addresses these disadvantages by discussing and implementing non-integer power series, normalized polynomial series, and orthogonal polynomial series for nonlinear structural dynamic system identification. The first of these generating series can describe general nonlinear stiffness and damping characteristics, whereas the second and third types of series help to avoid poor numerical conditioning associated with ordinary integer power series.