Uncertain linear structural systems in dynamics: Efficient stochastic reliability assessment

摘要

A numerical procedure for the reliability assessment of uncertain linear structures subjected to general Gaussian loading is presented. In this work, restricted to linear FE systems and Gaussian excitation, the loading is described quite generally by the Karhunen-Loeve expansion, which allows to model general types of non-stationarities with respect to intensity and frequency content. The structural uncertainties are represented by a stochastic approach where all uncertain quantities are described by probability distributions. First, the critical domain within the parameter space of the uncertain structural quantities is identified, which is defined as the region which contributes most to the excursion probability. Each point in the space of uncertain structural parameters is associated with a certain excursion probability caused by the Gaussian excitation.rnIn order to determine the first excursion probability of uncertain linear structures, an integration over the space of uncertain structural parameters is required. An extended procedure of standard Line sampling [P.S. Koutsourelakis, H.J. Pradlwarter, G.I. Schueller, Reliability of structures in high dimensions, part I: algorithms and applications, Probabilistic Engineering Mechanics 19(4) (2004) 409-417; G.I. Schueller, H.J. Pradlwarter, P.S. Koutsourelakis, A critical appraisal of reliability estimation procedures for high dimensions, Probabilistic Engineering Mechanics 19(4) (2004) 463-474] is used to perform the conditional integration over the space of uncertain parameters. The suggested approach is applicable to general uncertain linear systems modeled by finite elements of arbitrary size by using modal analysis as exemplified in the numerical example. Special attention is devoted to the efficiency of the proposed approach when dealing with realistic FE models, characterized by a large number of degrees of freedom and also a large number of uncertain parameters.