讲座题目:Polynomial Dimensional Decomposition for Design under Uncertainty
报告人：Ren Xuchun Mechanical Engineering Department at Georgia Southern University
The various kind of uncertainties poses extreme difficulty to the already challenging design optimization problem of complex engineering systems. This talk presents the recently developed computational method, referred to as polynomial dimensional decomposition (PDD), foruncertainty qualification including stochastic moment analysis/reliability analysis and stochastic design optimization.The PDD methodexploitsthe dimensionalhierarchylurking behind a probabilistic response, leading to accurate and efficient estimates for reliability and moments. Applied to the statistical moments, the method provides mean-square convergent analytical expressions of design sensitivities of the first two moments of a stochastic response. Integrated with the saddlepoint approximation or Monte Carlo simulation, it leading to analytical formulae or embedded MCS formulation for calculating design sensitivities of probability distribution and component reliability. Both the statistical moments or failure probabilities and their design sensitivities are determined concurrently from a single stochastic analysis or simulation. Numerical examplesillustratethe accuracy of the proposed methods. Applications to robust shape design, reliability-based shape design, and stochastic topology sensitivities of complex structures subject to a large number of random inputs show that the new method developed provides computationally efficient solutions for industry scale design problems.
Dr. Ren is an Assistant Professor of Mechanical Engineering at Georgia Southern University. He received his bachelor and master degrees in Mechanical Engineering and Engineering Mechanics, respectively, from Dalian University and Technology in 1997 and 2000, and one doctoral degree in Engineering Mechanics from Tsinghua University and one in Mechanical Engineering from the University of Iowa. The focus of Dr. Ren’sresearchis to develop rational design methodologies based on novel simulation methods and statistical methods for use in complex engineering problems. His goal is to study, discover, and demonstrate new ways in which engineers can explore new design concept for complex engineering systems. Current research in his group involves topics such as robust or reliability-based topology optimization, advanced methods for uncertainty quantification, robust or reliability-based shape optimization, deterministic design optimization, and advanced modeling/simulation techniques for complex engineering system.