A Data-driven Approach to Risk-aware Robust Design

TL;DR

The paper tackles robust design under data uncertainty by embracing scenario-based optimization that does not require full probabilistic models. It introduces risk-averse and risk-agnostic formulations, with and without moments, that leverage perturbed scenarios and outlier elimination to trade off objective value $J(\theta)$ against constraint satisfaction. It also provides computational-cost reduction techniques, notably adversarial perturbations and sequential design, and demonstrates the approach on aeroelastic-wing design to show meaningful gains in reliability and robustness with limited data. The work bridges verification and design by integrating Monte Carlo-style testing with data-driven optimization, offering scalable tools for simulation-based engineering under uncertainty.

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 the perturbed scenarios to violate the requirements with an acceptably small probability. For instance, we can seek a design that satisfies the requirements for as many perturbed scenarios as possible, or pursue a riskier design that attains a lower objective value in exchange for a few scenarios violating the requirements. These ideas are illustrated by considering the design of an aeroelastic wing.

Figures (6)

• Figure 1: Success (white) and failure (non-white) domains for $\theta_1^\star$ (top-left), $\theta_2^\star$ (top-right), $\theta_3^\star$ (bottom-left) and $\theta_4^\star$ (bottom right). The failure domain is shown in tones of gray: the darker the color the greater the number of constraint violations. The nominal scenarios are marked with a "$\times$" whereas the nominal scenarios falling into the failure domain are also marked with "$\circ$" (if any). The center $c_1$ is marked with a "${\square}$" whereas the center $c_2$ is marked with a "$\circ$".
• Figure 2: Success and failure domains for $\theta_5^\star$ (top-left), $\theta_6^\star$ (top-right), $\theta_7^\star$ (middle-left), $\theta_8^\star$ (middle-right), $\theta_9^\star$ (bottom-left) and $\theta_{10}^\star$ (bottom-right). The elements of $\delta_p^{(i)}$ corresponding to outliers are marked with a "$\boldsymbol{\cdot}$" (if any), inliers are marked with a "$\boldsymbol{\cdot}$", and sample points falling into the failure domain are marked with a "$\circ$" (if any).
• Figure 3: Success and failure domains for $\theta_A^\star$ (top-left), $\theta_B^\star$ (top-right), $\theta_C^\star$ (bottom-left) and $\theta_D^\star$ (bottom-right).
• Figure 4: Shape and sizing design variables for the aeroelastic wing.
• Figure 5: Optimal wing designs. The dashed black line indicates the baseline planform shape used for reference.