A comparative study of uncertainty quantification methods in gust response analysis of a Lift-Plus-Cruise eVTOL aircraft wing

TL;DR

This study addresses how uncertainties in gust and flight conditions propagate through the aeroelastic response of a Lift-Plus-Cruise (LPC) eVTOL wing. It employs a time-dependent, one-way-coupled framework combining a panel-method aerodynamic solver with a Reissner-Mindlin shell structural solver to predict two QoIs: $q_{\max}=\max(\text{tip displacement})$ and $q_E=\text{average strain energy}$. Five non-intrusive UQ methods—non-intrusive polynomial chaos (NIPC), kriging, Monte Carlo, univariate dimension reduction (UDR), and gradient-enhanced univariate dimension reduction (GUDR)—are evaluated for mean, standard deviation, and 95th percentile risk measures, with ground-truth reference from Kriging using $500$ samples. The results reveal substantial output variability and show method-dependent performance tied to the QoI and statistical metric, offering practical guidance on method selection for gust-load assessment in eVTOL design and certification.

Abstract

Wind gusts, being inherently stochastic, can significantly influence the safety and performance of aircraft. This study investigates a three-dimensional uncertainty quantification (UQ) problem to explore how uncertainties in gust and flight conditions affect the structural response of a Lift-Plus-Cruise eVTOL aircraft wing. The analysis employs an unsteady aeroelastic model with a one-way coupling between a panel method aerodynamic solver and a shell analysis structural solver to predict the wing's response under varying conditions. Additionally, this paper presents a comparative evaluation of commonly used non-intrusive UQ methods, including non-intrusive polynomial chaos, kriging, Monte Carlo, univariate dimension reduction, and gradient-enhanced univariate dimension reduction. These methods are assessed based on their effectiveness in estimating various risk measures-mean, standard deviation, and 95th percentile-of critical structural response outputs such as maximum tip displacement and average strain energy. The numerical results reveal significant variability in the structural response outputs, even under relatively small ranges of uncertain inputs. This highlights the sensitivity of the system to uncertainties in gust and flight conditions. Furthermore, the performance of the implemented UQ methods varies significantly depending on the specific risk measures and the quantity of interest being analyzed.

Figures (7)

• Figure 1: Lift-Plus-Cruise eVTOL aircraft concept
• Figure 2: Lift-Plus-Cruise eVTOL aircraft geometry
• Figure 3: LPC aircraft wing structure and the shell mesh used for structural analysis
• Figure 4: Gust profile and the numerical results of the aeroelastic simulation
• Figure 5: Probability density distributions of the QoIs (maximum tip displacement and average strain energy)