A sampling-based RBDO algorithm with local refinement and efficient gradient estimation

This article describes a two stage Reliability-Based Design Optimization (RBDO) algorithm. The first stage consists of solving an approximated RBDO problem using meta-models. In order to use gradient-based techniques, the sensitivity of failure probabilities are derived with respect to hyperparameters of random variables as well as, and this is a novelty, deterministic variables. The second stage focuses on the local refinement of the meta-models around the first stage solution using generalized “max-min” samples. The approach is demonstrated on three examples including a crashworthiness problem with 11 random variables and 10 probabilistic constraints.