Reliability analysis aims at estimating the failure probability of an engineering system. It often requires multiple runs of a limit-state function, which usually relies on computationally intensive simulations. Traditionally, these simulations have been considered deterministic, i.e., running them multiple times for a given set of input parameters always produces the same output. However, this assumption does not always hold, as many studies in the literature report non-deterministic computational simulations (also known as noisy models). In such cases, running the simulations multiple times with the same input will result in different outputs. Similarly, data-driven models that rely on real-world data may also be affected by noise. This characteristic poses a challenge when performing reliability analysis, as many classical methods, such as FORM and SORM, are tailored to deterministic models. To bridge this gap, this paper provides a novel methodology to perform reliability analysis on models contaminated by noise. In such cases, noise introduces latent uncertainty into the reliability estimator, leading to an incorrect estimation of the real underlying reliability index, even when using Monte Carlo simulation. To overcome this challenge, we propose the use of denoising regression-based surrogate models within an active learning reliability analysis framework. Specifically, we combine Gaussian process regression with a noise-aware learning function to efficiently estimate the probability of failure of the underlying noise-free model. We showcase the effectiveness of this methodology on standard benchmark functions and a finite element model of a realistic structural frame.

翻译：可靠性分析旨在评估工程系统的失效概率，通常需要多次执行极限状态函数，而这往往依赖于计算密集型仿真。传统上，这些仿真被认为是确定性的，即对给定输入参数集重复运行时将产生相同输出。然而，这一假设并非总是成立，文献中许多研究报告了非确定性计算仿真（也称为含噪模型）。在此类情况下，对相同输入重复运行仿真将得到不同输出。类似地，依赖真实世界数据的数据驱动模型也可能受到噪声影响。这一特性对可靠性分析构成了挑战，因为FORM和SORM等经典方法均针对确定性模型设计。为弥补这一空白，本文提出了一种对含噪声模型进行可靠性分析的新方法。在此类情况下，噪声为可靠性估计器引入了潜在不确定性，即使采用蒙特卡洛仿真，也会导致对真实潜在可靠性指标的错误估计。为克服这一挑战，我们提出在主动学习可靠性分析框架中使用基于去噪回归的代理模型。具体而言，我们将高斯过程回归与噪声感知学习函数相结合，以高效估计潜在无噪声模型的失效概率。我们通过在标准基准函数和现实结构框架的有限元模型上展示了该方法的有效性。