带CVaR约束的风险规避设计优化：基于多保真度尾区校正方法
Risk-averse design optimization with CVaR constraints via multifidelity tail-region correction
- Hanyang University（汉阳大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文针对带CVaR约束的风险规避设计优化中HF评估成本高的问题，提出基于DD-GPCE的多保真度尾区校正方法，在桁架、阀门测试中实现了HF样本高效且性能优异的CVaR约束设计。
中文摘要 AI 辅助
带条件风险价值（CVaR）约束的风险规避设计优化需要准确的尾部分布估计，但重复的高保真度（HF）评估成本高昂。本文提出一种多保真度（MF）尾区校正方法，采用维度分解广义多项式混沌展开（DD-GPCE）作为全局代理模型，并将有限的HF预算分配给对CVaR影响最大的响应。估计的DD-GPCE系数的协方差量化了有限样本预测不确定性，定义了基于置信区间的尾区；在该区域内，采用两阶段策略，先探索预测不确定性高的位置，再利用校正诱导偏移大的位置。采用相同多项式基的Tikhonov正则化残差展开生成统一的尾区校正代理模型。针对十杆桁架的测试显示，该方法得到的设计接近粗蒙特卡洛采样（crude-MCS）参考结果，且HF评估量仅为所考虑的MF重要性采样配置的1/72至1/274；针对吸气阀的测试中，该方法在满足阀门开启要求的同时，使质量降低1.05%，弯曲CVaR降低17.68%，鼓胀CVaR降低21.53%。结果表明，通过局部MF校正可实现准确且HF样本高效的CVaR约束设计。
英文摘要
Risk-averse design optimization with conditional value-at-risk (CVaR) constraints requires accurate tail estimates, but repeated high-fidelity (HF) evaluations are costly. We propose a multifidelity (MF) tail-region correction method that uses dimensionally decomposed generalized polynomial chaos expansion (DD-GPCE) as a global surrogate and directs a limited HF budget to responses that most strongly influence CVaR. Covariance of the estimated DD-GPCE coefficients quantifies finite-sample prediction uncertainty and defines a confidence-interval-based tail region. Within this region, a two-stage strategy explores locations with high prediction uncertainty and then exploits locations with large correction-induced shifts. A Tikhonov-regularized residual expansion using the same polynomial basis yields a unified tail-corrected surrogate. For a ten-bar truss, the method produced a design close to the crude-MCS reference with approximately 72 to 274 times fewer HF evaluations than the considered MF importance sampling configurations. For a suction valve, it reduced mass by 1.05% and bending and bulging CVaR by 17.68% and 21.53%, respectively, while satisfying the valve-opening requirement. The results demonstrate accurate, HF-sample-efficient CVaR-constrained design through localized MF correction.
