Cutting the double loop: Theory and algorithms for reliability‐based design optimization with parametric uncertainty

Abstract

Summary Parametric 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 parametric uncertainty: we introduce metrics for measuring the efficacy of reliability‐based design optimization strategies (epistemic design gap 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.

Application and Safety Performance of Nanomaterials in Clothing Design Engineering

“…It introduces metrics to measure the effectiveness of RBDO strategies (effective margin and effective reliability), a minimum condition to control uncertainty reliability (accuracy margin), and tighter conditions to ensure that all desired required reliability. Numerous open-source code examples are provided to demonstrate our approach in a reproducible manner [1]. Xiaojing reported a robust porous superhydrophobic composite (PSC) based on a multiwalled carbon nanotube network and a poly (ethylene-vinyl acetate) matrix for recoverable shape reconfiguration and underwater vibration detection.…”

When Are Allowables Conservative?

“…This work is motivated by the question "When are allowables conservative?" To illustrate this question and introduce the relevant concepts, we review a trivial structural design problem that highlights salient features [8]. Ultimately, we will find that the question posed requires some refinement, which points toward the sections to follow.…”

“…To evaluate and compare the performance of design strategies, we evaluate the designs in terms of effective reliability [8]. This is the reliability of the design evaluated under the assumed "truth" parameter values, given by R eff;g d ≡ P X gd; X > 0 (10)…”

“…Very recent works have pursued computational approaches to developing allowables using simulation and uncertainty propagation to reduce physical test requirements [5][6][7]. However, previous investigations have found that the use of allowables in design can lead either to cases of overdesign (weight penalties) or to cases of noncompliance (insufficient reliability) [8][9][10]. This is not to say that allowables and other deterministic design approaches are incapable of safe design; Villanueva et al [11] have shown that current design practices can be used safely by carefully tuning design criteria.…”