Robustness-based design optimization under data uncertainty

Abstract

This paper proposes formulations and algorithms for design optimization under both aleatory (i.e., natural or physical variability) and epistemic uncertainty (i.e., imprecise probabilistic information), from the perspective of system robustness. The proposed formulations deal with epistemic uncertainty arising from both sparse and interval data without any assumption about the probability distributions of the random variables. A decoupled approach is proposed in this paper to un-nest the robustness-based design from the analysis of non-design epistemic variables to achieve computational efficiency. The proposed methods are illustrated for the upper stage design problem of a two-stage-toorbit (TSTO) vehicle, where the information on the random design inputs are only available as sparse point and/or interval data. As collecting more data reduces uncertainty but increases cost, the effect of sample size on the optimality and robustness of the solution is also studied. A method is developed to determine the optimal sample size for sparse point data that leads to the solutions of the design problem that are least sensitive to variations in the input random variables.

Enhancing product robustness in reliability-based design optimization

“…Rangavajhala et al [13] examined the challenge of equality constraints in robust design optimization. Zaman et al [14] analyzed the impact of non-design epistemic variables on robustness-based design optimization. Tang [15] developed a feasible robustness index and integrated it into the RBDO formulation.…”

Optimal design of composite shells based on minimum weight and maximum feasibility robustness

“…Other perspective of RDO used in structural applications but not applied in composite structures is based on the optimization of mean performance commonly known as optimality, and the minimization of the variability of the performance function known as robustness (Huang and Du 2007;Zaman et al 2011;Ragavajhala and Mahadevan 2013). Nevertheless, another concept of robustness can be defined as the maximization size of the deviations from the target design that can be tolerated, whereby the product satisfies all requirements (Salazar and Rocco 2007).…”

Optimization Under Mixed Aleatory/Epistemic Uncertainty Using Derivatives

“…The ability to identify and catalog overly conservative design margins resulting from applying safety factors on top of other safety factors, for example, is an important application for robust design, which is being increasingly viewed as an enabling technology for design of aerospace, civil, and automotive structures subject to uncertainty. [27][28][29][30] The reliability-based methods, on the other hand, are predominantly used for risk analysis by computing the probability of failure of a system. Thus, reliability approaches concentrate on the rare events at the tails of the probability distribution.…”