Title: AL-SPCE -- Reliability analysis for nondeterministic models using stochastic polynomial chaos expansions and active learning Show Chinese title

Title: AL-SPCE — 使用随机多项式混沌展开和主动学习对非确定性模型进行可靠性分析

Abstract: Reliability analysis typically relies on deterministic simulators, which yield repeatable outputs for identical inputs. However, many real-world systems display intrinsic randomness, requiring stochastic simulators whose outputs are random variables. This inherent variability must be accounted for in reliability analysis. While Monte Carlo methods can handle this, their high computational cost is often prohibitive. To address this, stochastic emulators have emerged as efficient surrogate models capable of capturing the random response of simulators at reduced cost. Although promising, current methods still require large training sets to produce accurate reliability estimates, which limits their practicality for expensive simulations. This work introduces an active learning framework to further reduce the computational burden of reliability analysis using stochastic emulators. We focus on stochastic polynomial chaos expansions (SPCE) and propose a novel learning function that targets regions of high predictive uncertainty relevant to failure probability estimation. To quantify this uncertainty, we exploit the asymptotic normality of the maximum likelihood estimator. The resulting method, named active learning stochastic polynomial chaos expansions (AL-SPCE), is applied to three test cases. Results demonstrate that AL-SPCE maintains high accuracy in reliability estimates while significantly improving efficiency compared to conventional surrogate-based methods and direct Monte Carlo simulation. This confirms the potential of active learning in enhancing the practicality of stochastic reliability analysis for complex, computationally expensive models. Show Chinese abstract

Abstract: 可靠性分析通常依赖于确定性模拟器，这些模拟器对于相同的输入会产生可重复的输出。 然而，许多现实世界系统表现出内在的随机性，需要随机模拟器，其输出是随机变量。 这种固有的变异性必须在可靠性分析中加以考虑。 虽然蒙特卡洛方法可以处理这个问题，但其高昂的计算成本通常难以承受。 为了解决这个问题，随机代理模型已经出现，这些模型能够在较低成本下捕捉模拟器的随机响应。 尽管前景看好，但当前的方法仍然需要大量的训练集来生成准确的可靠性估计，这限制了它们在昂贵模拟中的实用性。 本文引入了一个主动学习框架，以进一步减少使用随机代理模型进行可靠性分析的计算负担。 我们专注于随机多项式混沌展开（SPCE），并提出了一种新的学习函数，针对与失效概率估计相关的高预测不确定性区域。 为了量化这种不确定性，我们利用了最大似然估计量的渐近正态性。 所得到的方法称为主动学习随机多项式混沌展开（AL-SPCE），应用于三个测试案例。 结果表明，AL-SPCE在保持可靠性估计的高准确性的同时，相比传统代理方法和直接蒙特卡洛模拟显著提高了效率。 这证实了主动学习在提高复杂、计算成本高的模型的随机可靠性分析实用性方面的潜力。