Principal components analysis for nonlinear model correlation, updating and uncertainty evaluation

Abstract

Principal Components Analysis of nonlinear systems is based on the singular value decomposition of a collection of response time-histories. The principal components are analogous to the modal response time-histories of linear structural analysis, except that the singular values are related to energy rather than frequency. This paper presents a theoretical basis for Principal Components Analysis, including the derivation of modal metrics for use in nonlinear model correlation, updating and uncertainty evaluation. A numerical example based on current experience will be presented to illustrate application to nonlinear model validation and verification.