Application of Reduced Order Models for the Stochastic Design Optimization of Dynamic Systems

Abstract

This paper addresses the need for numerical stochastic techniques in the analysis and design optimization of dynamic systems. Most stochastic analysis techniques result in a heavy computational burden, the cost of which is amplied if embedded into a design optimization framework. Therefore, this work seeks to alleviate the computational costs of analyzing dynamic systems through employing reduced order modeling. Reduced order models are computationally less expensive than full order models for a specic design, due to the signican t reduction in degrees of freedom. The key to utilizing reduced order models in stochastic analysis and optimization lies in making them adaptable to design changes and variations in random parameters. The application of an extended reduced order model, which is a reduced order model that accounts for parameter changes, is tested on a linear structural dynamics system, and the method is included into a stochastic analysis and design optimization framework. Stochastic analyses are performed on a dynamic system using a Monte Carlo simulation, the rst-order reliability method, and Monte Carlo simulation based on a polynomial chaos expansion. In all cases the stochastic analysis utilizing the extended reduced order model is compared against that for the full order model. As a nal example a reliability-based design optimization problem that takes into account uncertainties in design variable is performed on the dynamic system.