用分层克里金法高效优化高维不确定工程问题
Multi-level informed optimization via decomposed Kriging for large design problems under uncertainty
- 分层正交分解构建快速可扩展的代理模型
- 在相同资源下比现有方法快数个数量级且更准确
- 适合大规模复杂系统设计，尤其资源受限场景
工程设计常涉及大量决策变量与不可控参数，且不可避免的随机性与认知不确定性带来显著挑战。当前主流方法采用两阶段流程：先量化不确定性，再进行鲁棒或随机优化。然而，传统基于场景、代理模型辅助及数学规划的方法在大规模复杂问题中难以兼顾效率与精度。本文提出一种多层级方法，通过非侵入式、快速扩展的克里金代理模型，高效映射设计与参数联合空间。利用分层正交分解自适应更新多个代理模型，以挖掘最少但最具不确定性信息的数据。在分析测试平台上，该方法与最先进方法相比，在统计上同时实现数量级提升的速度与精度。
原文摘要 · Abstract (English)
Engineering design involves demanding models encompassing many decision variables and uncontrollable parameters. In addition, unavoidable aleatoric and epistemic uncertainties can be very impactful and add further complexity. The state-of-the-art adopts two steps, uncertainty quantification and design optimization, to optimize systems under uncertainty by means of robust or stochastic metrics. However, conventional scenario-based, surrogate-assisted, and mathematical programming methods are not sufficiently scalable to be affordable and precise in large and complex cases. Here, a multi-level approach is proposed to accurately optimize resource-intensive, high-dimensional, and complex engineering problems under uncertainty with minimal resources. A non-intrusive, fast-scaling, Kriging-based surrogate is developed to map the combined design/parameter domain efficiently. Multiple surrogates are adaptively updated by hierarchical and orthogonal decomposition to leverage the fewer and most uncertainty-informed data. The proposed method is statistically compared to the state-of-the-art via an analytical testbed and is shown to be concurrently faster and more accurate by orders of magnitude.
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