Stochastic design optimization accounting for structural and distributional design variables

• Published in: Engineering computations Vol. 35; no. 8; pp. 2654 - 2695
• Main Authors: Ren, Xuchun, Rahman, Sharif
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Publishing Limited 27.11.2018; Emerald Group Publishing Limited
• Subjects: Algorithms; Approximation; Computer simulation; Decomposition; Design engineering; Design optimization; Design standards; Euclidean space; Finite difference method; Mathematical functions; Methods; Monte Carlo simulation; Polynomials; Probability; Probability theory; Random variables; Reliability analysis; Robust design; Sensitivity; Sensitivity analysis; Statistical analysis; Structural design; Distributional design variables; Augmented polynomial dimensional decomposition; Structural design variables; Stochastic design optimization
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/EC-10-2017-0409

Purpose This paper aims to present a new method, named as augmented polynomial dimensional decomposition (PDD) method, for robust design optimization (RDO) and reliability-based design optimization (RBDO) subject to mixed design variables comprising both distributional and structural design variables. Design/methodology/approach The method involves a new augmented PDD of a high-dimensional stochastic response for statistical moments and reliability analyses; an integration of the augmented PDD, score functions, and finite-difference approximation for calculating the sensitivities of the first two moments and the failure probability with respect to distributional and structural design variables; and standard gradient-based optimization algorithms. Findings New closed-form formulae are presented for the design sensitivities of moments that are simultaneously determined along with the moments. A finite-difference approximation integrated with the embedded Monte Carlo simulation of the augmented PDD is put forward for design sensitivities of the failure probability. Originality/value In conjunction with the multi-point, single-step design process, the new method provides an efficient means to solve a general stochastic design problem entailing mixed design variables with a large design space. Numerical results, including a three-hole bracket design, indicate that the proposed methods provide accurate and computationally efficient sensitivity estimates and optimal solutions for RDO and RBDO problems.