Time-Dependent Meta-Models for Dynamic Systems with Nonparametric Excitations  
Author Gordon J. Savage
Co-Author(s) Young Kap Son
Abstract This paper presents a simple way to provide very fast and accurate simulations of dynamic nonlinear systems excited by nonparametric excitations. A meta-model is created from both a matrix of nonparametric training excitations and a corresponding matrix of responses provided by the mechanistic model. Application of singular value decomposition separates out the so-called space information from the time information in both matrices. The novelty of the methodology herein lies in the recognition that any of the well-known parametric metamodels may be invoked to relate the pair of left-singular vector matrices. This link, plus basic linear algebra using the remaining singular value decomposition matrices, creates the meta-model in the form of three weight matrices that in turn provide the approximate response for an arbitrary excitation. The efficacy of the method is shown through an investigation of a nonlinear, double mass-spring-damper, system. For testing purposes, sets of excitations have been developed from the Weibull pulse. Least-squares and Kriging meta-models are applied and compared. The sources of errors are identified and ways to mitigate them are discussed.
Keywords Dynamic systems, Nonlinear, Time-dependent meta-model, Nonparametric, Singular Value Decomposition
    Article #:  23-054
Proceedings of the 23rd ISSAT International Conference on Reliability and Quality in Design
August 3-5, 2017 - Chicago, Illinois, U.S.A.