Robust design optimization under dependent random variables by a generalized polynomial chaos expansion
Robust design optimization under dependent random variables by a generalized polynomial chaos expansion
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DOI：
10.1007/s00158-020-02820-z
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发表时间：
2021-03
影响因子：
3.9
通讯作者：
Dongjin Lee;S. Rahman
中科院分区：
文献类型：
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作者：
Dongjin Lee;S. Rahman
针对输入随机变量具有任意相依概率分布的复杂工程系统的鲁棒设计优化问题，提出了一种新的计算方法。该方法建立在广义多项式混沌展开（GPCE）上，用于确定依赖输入随机变量的一般输出函数的二阶矩统计量，GPCE和得分函数之间的创新耦合，用于计算相对于设计变量的二阶矩灵敏度，以及标准的基于梯度的优化算法，建立直接GPCE，单步GPCE，和多点单步GPCE设计过程。提出了与统计矩分析同步进行设计灵敏度分析的新的解析公式。数值结果表明，所提出的方法不仅准确，而且计算效率高的几个数学和简单的RDO问题的最优解。最后，转向节随机形状优化设计的成功验证了多点单步GPCE方法在解决工业规模工程问题中的作用。
New computational methods are proposed for robust design optimization (RDO) of complex engineering systems subject to input random variables with arbitrary, dependent probability distributions. The methods are built on a generalized polynomial chaos expansion (GPCE) for determining the second-moment statistics of a general output function of dependent input random variables, an innovative coupling between GPCE and score functions for calculating the second-moment sensitivities with respect to the design variables, and a standard gradient-based optimization algorithm, establishing direct GPCE, single-step GPCE, and multi-point single-step GPCE design processes. New analytical formulae are unveiled for design sensitivity analysis that is synchronously performed with statistical moment analysis. Numerical results confirm that the proposed methods yield not only accurate but also computationally efficient optimal solutions of several mathematical and simple RDO problems. Finally, the success of conducting stochastic shape optimization of a steering knuckle demonstrates the power of the multi-point single-step GPCE method in solving industrial-scale engineering problems.