Robust Design in the Presence of Aleatoric and Epistemic Uncertainty

TL;DR

This paper develops a comprehensive framework for designing systems under both aleatoric and epistemic uncertainties, introducing chance-constrained formulations and a sequential data update approach for improved robustness.

Contribution

It introduces novel chance-constrained formulations and an efficient sequential design method that accounts for both types of uncertainty in system design.

Findings

Risk-aware designs improve system robustness.

Sequential data updates enhance design efficiency.

Robustness evaluated effectively using Monte Carlo and Scenario Theory.

Abstract

This paper proposes strategies for designing a system whose computational model is subject to aleatory and epistemic uncertainty. Aleatory variables, which are caused by randomness in physical parameters, are draws from a possibly unknown distribution; whereas epistemic variables, which are caused by ignorance in the value of fixed parameters, are free to take any value in a bounded set. Chance-constrained formulations enforcing the system requirements at a finite number of realizations of the uncertain parameters are proposed. These formulations trade off a lower objective value against a reduced robustness by eliminating an optimally chosen subset of such realizations. Risk-aware designs are obtained by accounting for the severity of the requirement violations resulting from this elimination process. Furthermore, we propose a computationally efficient design approach in which the training dataset is sequentially updated according to the results of high-fidelity reliability analyses of suboptimal designs. Robustness is evaluated by using Monte Carlo analysis and Robust Scenario Theory, with the latter approach accounting for the infinitely many values that the epistemic variables can take.