发表机构
University of São Paulo; University of Michigan; Federal University of Paraná（圣保罗大学; 密歇根大学; 巴拉那联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出结合广义分层抽样（GSS）与随机多项式混沌展开（SPCE）的框架，用于结构性能导向风险优化，可准确估算结构响应分布尾部并减少非线性模型评估次数。
AI 中文摘要
元模型对于降低随机荷载下结构性能导向风险优化（PBRO）中嵌套可靠性分析与优化循环的计算负担至关重要。在此背景下，随机仿真器尤为实用，因其能在考虑仿真器内在随机性的同时近似响应分布。在这类方法中，随机多项式混沌展开（SPCE）颇具吸引力，因为它无需在固定输入条件下重复非线性分析。然而，SPCE在准确表征结构响应分布尾部的极端响应方面可能存在局限。为解决这一局限，本研究提出了一种将广义分层抽样（GSS）与SPCE相结合的框架。GSS方案根据灾害强度将输入空间划分为若干层，以提升极端响应的表征能力，同时在每层内训练独立的SPCE仿真器。随后，利用全概率定理对各层估算的条件超越概率进行重组，以评估概率约束。所提出的GSS-SPCE框架被应用于两层钢结构建筑中屈曲约束支撑横截面积的优化设计，目标是在满足规定概率性能约束的同时最小化初始建造成本。结果表明，该框架能准确估算结构响应分布，包括其尾部区域，同时大幅减少PBRO所需的非线性模型评估次数。
英文摘要
Metamodels are instrumental in reducing the computational burden associated with nested reliability analyses and optimization loops in Performance-Based Risk Optimization (PBRO) of structures under stochastic loads. In this context, stochastic emulators are particularly useful because they approximate response distributions while accounting for the intrinsic stochasticity of the simulator. Among these methods, Stochastic Polynomial Chaos Expansion (SPCE) is especially attractive because it does not require replications of nonlinear analyses at fixed input conditions. However, SPCE may present limitations in accurately representing extreme responses in the tails of structural response distributions. To address this limitation, this study proposes a framework that combines Generalized Stratified Sampling (GSS) with SPCE. The GSS scheme partitions the input space into strata according to the intensity of the hazard, improving the representation of extreme responses, while independent SPCE emulators are trained within each stratum. The conditional exceedance probabilities estimated in each stratum are then recombined using the total probability theorem to evaluate the probabilistic constraints. The proposed GSS-SPCE framework is applied to the optimal design of buckling-restrained brace cross-sectional areas in a two-story steel building. The objective is to minimize the initial construction cost while satisfying prescribed probabilistic performance constraints. Results show that the proposed framework accurately estimates structural response distributions, including their tail regions, while substantially reducing the number of nonlinear model evaluations required for PBRO.
