Cutting the Double Loop: Theory and Algorithms for Reliability-Based Design Optimization with Statistical Uncertainty

TL;DR

This paper introduces a new approximation method for reliability-based design optimization under statistical uncertainty, replacing the computationally expensive double loop simulation with a more efficient approach, supported by a novel theoretical framework and practical examples.

Contribution

It presents a flexible approximation technique for RBDO that eliminates the need for double loop simulation, along with a new theory and metrics for reliability under uncertainty.

Findings

The approximation method effectively replaces double loop simulation.

New metrics for measuring RBDO strategy efficacy.

Demonstrated with open-source examples.

Abstract

Statistical uncertainties complicate engineering design -- confounding regulated design approaches, and degrading the performance of reliability efforts. The simplest means to tackle this uncertainty is double loop simulation; a nested Monte Carlo method that, for practical problems, is intractable. In this work, we introduce a flexible, general approximation technique that obviates the double loop. This approximation is constructed in the context of a novel theory of reliability design under statistical uncertainty: We introduce metrics for measuring the efficacy of RBDO strategies (effective margin and effective reliability), minimal conditions for controlling uncertain reliability (precision margin), and stricter conditions that guarantee the desired reliability at a designed confidence level. We provide a number of examples with open-source code to demonstrate our approaches in a reproducible fashion.