Mitigating Surrogate Model Bias in Kriging Accelerated Subset Simulation: Empirical Insights and Advancements

Sampling-based probability estimation methods, such as Subset Simulation, are integral components of reliability-based design optimization methodologies, in which design requirements are specified as inequalities using maximum admissible failure probabilities. In practice, to further decrease the computational cost of the probability estimation, Subset Simulation is frequently combined with metamodeling techniques to reduce the number of necessary calls to computationally expensive computer simulations. Although the majority of the proposed algorithms offer significant advantages in terms of computational efficiency, the impact of the surrogate model error on the accuracy of the estimators often remains unclear. Given the substantial emphasis on safety and reliability in the field of aerospace engineering, this paper empirically analyzes the systematic error of a state-of-the-art Kriging metamodel accelerated Subset Simulation algorithm designed for rare event estimation. The results demonstrate that the use of the surrogate model in the Markov Chain Monte Carlo stage of the Subset Simulation algorithm can lead to a significant bias of the estimator. Importantly, this remains true, even if active learning strategies are used to train the metamodel in every subset level. In response, the paper proposes to extend the surrogate model refinement into the Markov Chain Monte Carlo-based conditional sampling stage of the algorithm. As demonstrated in multiple numerical examples, this extension significantly reduces the error of the estimator, thereby representing an advantageous modification for applications in aerospace engineering.