用高斯-埃尔米特积分法分离模型不确定性，提升物理可靠性分析精度。
Accounting for Uncertainty in Machine Learning Surrogates: A Gauss-Hermite Quadrature Approach to Reliability Analysis
- 通过高斯-埃尔米特积分解耦输入随机性与模型近似误差
- 在三个案例中保持高效计算且预测更可信
- 适合需要高可靠性的工程仿真与风险评估场景
机器学习代理模型正被广泛用于替代昂贵的物理计算模型进行可靠性分析。然而，其引入的模型近似误差所导致的认知不确定性，会与输入变量的随机性相互耦合，从而影响可靠性预测的准确性。本文提出一种基于高斯-埃尔米特积分的方法，以解耦这两种嵌套不确定性：先利用一阶和二阶可靠性方法在随机输入条件下评估条件失效概率，再对认知不确定性不同实现下的概率进行积分整合。三个实例表明，该方法在保持计算效率的同时，相比忽略模型不确定性的传统方法，能提供更可靠的预测结果。
原文摘要 · Abstract (English)
Machine learning surrogates are increasingly employed to replace expensive computational models for physics-based reliability analysis. However, their use introduces epistemic uncertainty from model approximation errors, which couples with aleatory uncertainty in model inputs, potentially compromising the accuracy of reliability predictions. This study proposes a Gauss-Hermite quadrature approach to decouple these nested uncertainties and enable more accurate reliability analysis. The method evaluates conditional failure probabilities under aleatory uncertainty using First and Second Order Reliability Methods and then integrates these probabilities across realizations of epistemic uncertainty. Three examples demonstrate that the proposed approach maintains computational efficiency while yielding more trustworthy predictions than traditional methods that ignore model uncertainty.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。