Reliability analysis for non-deterministic limit-states using stochastic emulators

Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments are repeatable, i.e., they produce consistent outputs for a given set of inputs. However, real-world systems often exhibit stochastic behavior, leading to non-repeatable outcomes. These so-called stochastic simulators produce different outputs each time the model is run, even with fixed inputs. This paper formally introduces reliability analysis for stochastic models and addresses it by using suitable surrogate models to lower its typically high computational cost. Specifically, we focus on the recently introduced generalized lambda models and stochastic polynomial chaos expansions. These emulators are designed to learn the inherent randomness of the simulator's response and enable efficient uncertainty quantification at a much lower cost than traditional Monte Carlo simulation. We validate our methodology through three case studies. First, using an analytical function with a closed-form solution, we demonstrate that the emulators converge to the correct solution. Second, we present results obtained from the surrogates using a toy example of a simply supported beam. Finally, we apply the emulators to perform reliability analysis on a realistic wind turbine case study, where only a dataset of simulation results is available.