Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization

TL;DR

This paper develops a method to handle structural optimization problems with reliability constraints under uncertain input distributions by converting them into deterministic constraints, enabling the use of nonlinear semidefinite programming.

Contribution

It introduces a distributionally-robust reliability constraint framework that reduces to deterministic constraints, facilitating robust structural design optimization.

Findings

The method effectively bounds failure probability under distributional uncertainty.

Numerical examples demonstrate the relationship between optimal value, reliability targets, and uncertainty.

The approach enables deterministic optimization techniques to address probabilistic reliability constraints.

Abstract

This paper considers structural optimization under a reliability constraint, where the input distribution is only partially known. Specifically, when we only know that the expected value vector and the variance-covariance matrix of the input distribution belong to a given convex set, we require that, for any realization of the input distribution, the failure probability of a structure should be no greater than a specified target value. We show that this distributionally-robust reliability constraint can be reduced equivalently to deterministic constraints. By using this reduction, we can treat a reliability-based design optimization problem under the distributionally-robust reliability constraint within the framework of deterministic optimization, specifically, nonlinear semidefinite programming. Two numerical examples are solved to show relation between the optimal value and either the target reliability or the uncertainty magnitude.