Robust design optimization by polynomial dimensional decomposition
 Xuchun Ren,
 Sharif Rahman
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This paper introduces four new methods for robust design optimization (RDO) of complex engineering systems. The methods involve polynomial dimensional decomposition (PDD) of a highdimensional stochastic response for statistical moment analysis, a novel integration of PDD and score functions for calculating the secondmoment sensitivities with respect to the design variables, and standard gradientbased optimization algorithms. New closedform formulae are presented for the design sensitivities that are simultaneously determined along with the moments. The methods depend on how statistical moment and sensitivity analyses are dovetailed with an optimization algorithm, encompassing direct, singlestep, sequential, and multipoint singlestep design processes. Numerical results indicate that the proposed methods provide accurate and computationally efficient optimal solutions of RDO problems, including an industrialscale lever arm design.
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 Title
 Robust design optimization by polynomial dimensional decomposition
 Journal

Structural and Multidisciplinary Optimization
Volume 48, Issue 1 , pp 127148
 Cover Date
 20130701
 DOI
 10.1007/s001580130883z
 Print ISSN
 1615147X
 Online ISSN
 16151488
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Design under uncertainty
 ANOVA dimensional decomposition
 Orthogonal polynomials
 Score functions
 Optimization
 Industry Sectors
 Authors

 Xuchun Ren ^{(1)}
 Sharif Rahman ^{(1)}
 Author Affiliations

 1. Department of Mechanical & Industrial Engineering, The University of Iowa, Iowa City, IA, 52242, USA