Stochastic reduced order models for random vectors: Application to random eigenvalue problems

An improved optimization algorithm is presented to construct accurate reduced order models for random vectors. The stochastic reduced order models (SROMs) are simple random elements that have a finite number of outcomes of unequal probabilities. The defining SROM parameters, samples and corresponding probabilities, are chosen through an optimization problem where the objective function quantifies the discrepancy between the statistics of the SROM and the random vector being modeled. The optimization algorithm proposed shows a substantial improvement in model accuracy and significantly reduces the computational time needed to form SROMs, as verified through numerical comparisons with the existing approach. SROMs formed using the new approach are applied to efficiently solve random eigenvalue problems, which arise in the modal analysis of structural systems with uncertain properties. Analytical bounds are established on the discrepancy between exact and SROM-based solutions for these problems. The ability of SROMs to approximate the natural frequencies and modes of uncertain systems as well as to estimate their dynamics in time is illustrated through comparison with Monte Carlo simulation in numerical examples. © 2012 Elsevier Ltd. All rights reserved.

Duke Scholars

Author Wilkins Aquino Thomas Lord Department of Mechanical Engineering and Materia ...