A Data-driven Approach to Risk-aware Robust Design

Abstract: This paper proposes risk-averse and risk-agnostic formulations to robust design in which solutions that satisfy the system requirements for a set of scenarios are pursued. These scenarios, which correspond to realizations of uncertain parameters or varying operating conditions, can be obtained either experimentally or synthetically. The proposed designs are made robust to variations in the training data by considering perturbed scenarios. This practice allows accounting for error and uncertainty in the measurements, thereby preventing data overfitting. Furthermore, we use relaxation to trade-off a lower optimal objective value against lesser robustness to uncertainty. This is attained by eliminating a given number of optimally chosen outliers from the dataset, and by allowing for the perturbed scenarios to violate the requirements with an acceptably small probability. For instance, we can pursue a riskier design that attains a lower objective value in exchange for a few scenarios violating the requirements, or we might seek a more conservative design that satisfies the requirements for as many perturbed scenarios as possible. The design of a flexible wing subject to aeroelastic constraints is used for illustration.