Reliability-based design optimization under dependent random variables by a generalized polynomial chaos expansion
Reliability-based design optimization under dependent random variables by a generalized polynomial chaos expansion
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DOI：
10.1007/s00158-021-03123-7
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发表时间：
2021-12
影响因子：
3.9
通讯作者：
Dongjin Lee;Sharif Rahman
中科院分区：
文献类型：
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作者：
Dongjin Lee;Sharif Rahman
针对输入随机变量服从任意相依概率分布的复杂机械系统，提出了一种新的可靠性优化设计计算方法。它涉及到一个广义多项式混沌扩展（GPCE）的可靠性分析依赖输入随机变量，一种新的融合的GPCE近似和得分函数估计的灵敏度的失效概率相对于设计变量，和标准的基于梯度的优化算法，导致在一个多点单步设计过程。该方法，指定为多点单步GPCE方法或简单的MPSS-GPCE方法，产生的解析公式计算的失效概率及其设计灵敏度同时从一个单一的随机模拟或分析。因此，MPSS-GPCE方法提供了解决具有大设计空间的工业规模问题的能力。数学函数或基本工程问题的数值结果表明，新方法提供了更准确或计算效率比现有的方法或参考解决方案的设计方案。最后，以某型喷气发动机压气机叶片根部为例进行了优化设计，验证了该方法的有效性。
This article brings forward a new computational method for reliability-based design optimization (RBDO) of complex mechanical systems subject to input random variables following arbitrary, dependent probability distributions. It involves a generalized polynomial chaos expansion (GPCE) for reliability analysis subject to dependent input random variables, a novel fusion of the GPCE approximation and score functions for estimating the sensitivities of the failure probability with respect to design variables, and standard gradient-based optimization algorithms, resulting in a multi-point single-step design process. The method, designated as the multi-point single-step GPCE method or simply the MPSS-GPCE method, yields analytical formulae for computing the failure probability and its design sensitivities concurrently from a single stochastic simulation or analysis. For this reason, the MPSS-GPCE method affords the ability to solve industrial-scale problems with large design spaces. Numerical results stemming from mathematical functions or elementary engineering problems indicate that the new method provides more accurate or computationally efficient design solutions than existing methods or reference solutions. Furthermore, the shape design optimization of a jet engine compressor blade root was successfully conducted, demonstrating the power of the new method in confronting practical RBDO problems.