Stochastic design optimization accounting for structural and distributional design variables
Stochastic design optimization accounting for structural and distributional design variables
复制标题
DOI：
10.1108/ec-10-2017-0409
复制
发表时间：
2018-11
影响因子：
1.6
通讯作者：
Xuchun Ren;S. Rahman
中科院分区：
文献类型：
--
作者：
Xuchun Ren;S. Rahman
目的本文旨在提出一种新方法，称为增强多项式维分解（PDD）方法，用于基于分布和结构设计变量的混合设计变量的鲁棒设计优化（RDO）和基于可靠性的设计优化（RBDO）。设计/方法/方法 该方法涉及一种新的增强型 PDD，用于统计矩和可靠性分析的高维随机响应；增强 PDD、得分函数和有限差分近似的集成，用于计算前两个矩的敏感性以及相对于分布和结构设计变量的失效概率；和标准的基于梯度的优化算法。研究结果提出了新的封闭式公式，用于与力矩同时确定的力矩的设计灵敏度。针对失效概率的设计敏感性，提出了与增强 PDD 的嵌入式蒙特卡洛模拟相结合的有限差分近似。独创性/价值结合多点、单步设计过程，新方法提供了一种有效的方法来解决涉及大设计空间的混合设计变量的一般随机设计问题。包括三孔支架设计在内的数值结果表明，所提出的方法为 RDO 和 RBDO 问题提供了准确且计算高效的灵敏度估计和最优解决方案。
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.