Sequential Bayesian optimal experimental design for structural reliability analysis

Abstract Structural reliability analysis is concerned with estimation of the probability a critical event taking place, described by $$P(g(\mathbf{X} ) \le 0)$$ P ( g X ) ≤ 0 for some n -dimensional random variable $$\mathbf{X} $$ and real-valued function g . In many applications practically unknown, as evaluation involves time consuming numerical simulation or other form experiment that expensive to perform. The problem we address in this paper how optimally design experiments, Bayesian decision theoretic fashion, when goal estimate using minimal amount resources. As opposed existing methods have been proposed purpose, consider general structural model given hierarchical form. We therefore introduce formulation experimental problem, where distinguish between uncertainty related any additional epistemic want reduce through experimentation. effectiveness strategy evaluated measure residual uncertainty, efficient approximation quantity crucial if apply algorithms search an optimal strategy. method propose based on importance sampling combined unscented transform propagation. implement myopic (one-step look ahead) alternative, demonstrate series experiments.