Active learning-based structural design optimization under constraints on first-passage probability

Abstract

In efforts to manage the risk of unexpected failures caused by stochastic loads, the first-passage probability, i.e., the probability that the maximum structural response over a given time interval exceeds a prescribed threshold, often needs to be evaluated. With the growing complexity of modern engineering systems, it is essential to estimate the first-passage probability with low computational costs in structural design and performance assessment processes. This paper presents a new surrogate-based method to incorporate constraints on the first-passage probability into reliability-bassed design optimization (RBDO). The mixture-based alternative formulation of the first-passage probability is utilized to handle the high-dimensional sequences of stochastic excitations during the optimization. This procedure employs a Gaussian-process-based surrogate model with heteroscedastic noises to capture the variability stemming from the stochastic excitation sequences and to reduce the high computational costs in the first-passage probability estimation. The proposed active learning scheme guides the computational simulations to the near-optimal regions from the RBDO viewpoint. In addition, a sampling-based design parameter sensitivity of the first-passage probability is introduced to facilitate a gradient-based optimizer in the RBDO iterations. Thus, the proposed method can identify the optimal solutions satisfying reliability constraints efficiently and accurately by combining the adaptive training process of surrogate models with the design optimization procedure guided by the design parameter sensitivities. Several numerical examples are investigated to demonstrate the accuracy and efficiency of the proposed method. The results confirm that the method enables convergence toward the optimal designs satisfying reliability constraints through significantly fewer structural performance evaluations and can deal with high-fidelity computational simulations.