CAREER: High Performance Computational Method for Stochastic Design Problems

Purdue University, West Lafayette IN

Investigators

Abstract

The importance of uncertainty analysis and stochastic modeling has received increasing amount of attention in recent years, especially from the Computational Mathematics society. Extensive research efforts have been devoted to uncertainty quantification and stochastic computations, and novel numerical methods have been developed to efficiently deal with large and complex systems with uncertainty. Although these methods have been demonstrated to be highly effective in predicting the behavior of complex stochastic systems, the design industry has not taken full advantage of these developments, and the design procedures in many disciplines remain almost exclusively deterministic. The research objective of this proposal is to develop new mathematical and numerical methods for multidisciplinary design problems with uncertain inputs, with an emphasis on the efficiency and accuracy of the new methods so that they are applicable to large-scale, realistic engineering applications. This objective will be attained through three major efforts: (1) employing rigorous mathematical theory to form a unified framework that allows one to conduct systematical analysis and error estimates; (2) employing the state-of-the-art stochastic algorithms to construct a set of high performance design algorithms for two major classes of uncertainty-based design: robust design and reliability design; and (3) extending the new methods to large-scale complex systems and developing fast and parallel solvers. Quantifying uncertainty is of paramount importance in almost all aspects of science and engineering. It is of particular significance in modern-day strategic planning and risk management where decisions are made in a constantly changing landscape with many unknown factors. Examples such as epidemic control, aircraft optimization under extreme conditions, optimal response following natural disasters, etc, are abundant. Such problems are essentially design and optimization in a complex and multidisciplinary environment, with substantial uncertainty interacting in a highly nonlinear fashion in the systems and parameters. While simulation based design tools continue to be advanced at rapid rates, little attention has been paid to incorporation of state-of-the-art mathematical techniques in stochastic analysis and uncertainty quantification. The traditional approaches, e.g., those by using safety factors to accommodate uncertainty in a gross manner, are becoming increasingly obsolete and often result in overly conservative decisions. This project is valuable for its multi-disciplinary influence, its fundamental contribution to uncertainty-based design problems, and more importantly, its high performance stochastic design algorithms the provide better and sharper analysis for decision makers. The project will unite a collection of uncertainty-based design techniques scattered over various engineering applications with the cutting-edge stochastic computation framework. It is a true synergy of Computational Mathematics tools and practical demands, and can be extended to a large class of design and optimization problems.