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Stochastic design optimization accounting for structural and distributional design variables

机译：考虑结构和分布设计变量的随机设计优化

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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.
机译：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，该方法用于鲁棒性设计优化（RDO）和基于可靠性的设计优化（RBDO），该设计受混合设计变量（包括分布和结构设计变量）的影响设计/方法/方法-该方法包括对高维随机响应进行新的增强的PDD，以进行统计矩和可靠性分析；增强的PDD，得分函数和有限差分近似的积分，用于计算前两个时刻的灵敏度以及关于分布和结构设计变量的失效概率；发现-针对力矩的设计敏感度提出了新的闭式公式，该公式与力矩同时确定。针对故障概率的设计敏感性，提出了与嵌入式增强型PDD的嵌入式蒙特卡罗模拟相结合的有限差分近似法。原始性/价值-结合多点，单步设计过程，该新方法可提供解决通常的随机设计问题的有效方法，该问题要求设计空间较大的混合设计变量。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问题提供了准确而计算有效的灵敏度估计和最佳解决方案。

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