Surrogate-based reliability analysis for noisy models - Sudret, Bruno; Moustapha, Maliki; Pires, Anderson; ICASP14; Marelli, Stefano (My University, 2023)
Reliability analysis ultimately aims at estimating the probability of failure of a system. In this context, limit-state functions represent the system performance, i.e., whether it fails or not, and consist of potentially expensive-to-evaluate models that enable the classification of the state of the system through their sign. Additionally, as failure is generally a rare event, estimating the probability of failure often requires many evaluations of the limit-state function. Surrogate models are commonly employed to circumvent the high computational cost of reliability assessment. They are computationally inexpensive models that act as a proxy to the limit-state function and can be combined with active learning methods. In this framework, the rationale is to employ a learning function to iteratively select the best set of points to train the surrogate model. The objective is to obtain a proxy that properly assesses the system performance, i.e., predicts the sign of the limit-state function accurately. In parallel, the use of data-driven models built from machine learning techniques has recently increased in engineering practice. Due to the uncertainty in measurements, however, the data used in these models is intrinsically noisy, leading to possible misclassifications of points close to the limit-state surface, which may corrupt the estimation of the probability of failure. Estimating the actual probability of failure reduces to denoising the noise-corrupted data-driven limit-state function. In this paper, we propose using regression-based surrogate models to this aim. They are robust-to-noise and enable the accurate estimation of the noise-free probability of failure at an affordable cost, even when the surrogate is trained with noise-corrupted data. Using synthetic data, we demonstrate that Monte Carlo simulation fails to estimate the true underlying probability of failure. To do so, we propose a methodology for corrupting noise-free models for the purpose of benchmarking. Finally, we showcase the performance of the proposed approach by employing Gaussian process regression and polynomial chaos expansions in well-known reliability benchmark problems that are extended to a noisy version. We conclude that regression-based surrogate models are suitable to denoise corrupted models and estimate their actual probability of failure.
14th International Conference on Applications of Statistics and Probability in Civil Engineering(ICASP14)
PUBLISHED