Efficient Uncertainty Quantification for Aircraft Conceptual Design Using Polynomial Chaos Expansion

Early-stage aircraft conceptual design must accommodate substantial epistemic and aleatoric uncertainties while remaining computationally tractable. This study demonstrates an efficient framework for propagating those uncertainties through key performance metrics - maximum range, endurance, takeoff and landing distances, and their associated velocities - using non-intrusive polynomial chaos expansion (PCE). Random inputs representing aerodynamic, propulsion, weight and operating parameters are modeled as uniform random variables and fed into a vortex lattice-based aerodynamic solver to find relevant aerodynamic parameters. Then, basic analytical formulae are used to calculate the aircraft design performance. A sparse PCE expansion is constructed with coefficients determined via least-squares linear regression with ��1-regularization for each performance metric. For the single-engine jet aircraft design case analyzed, the mean and variance of all quantities of interest converge by third-order expansion of the PCE, yielding accurate probability density functions that are substantially similar to those created via 2��4 Monte Carlo simulations, but using only 910 model evaluations. The PCE model accuracy was found to agree well with two classical metamodel techniques: response surface model (RSM) and Gaussian process regression (GPR). Furthermore, the converged PCE was used to perform exact (analytical) global sensitivity analysis (GSA) by calculating various Sobol indices to identify influential random inputs without additional function evaluations, a feature that the RSM and GPR models can only achieve via MCS sampling (which induces sampling noise and computational expense). The Sobol indices reveal fuel weight as the dominant driver of range and endurance variance, whereas lift coefficients and total aircraft weight govern takeoff and landing dispersion. Using this information, a basic uncertainty reduction workflow is presented that uses the analytical PCE metamodel, along with information from the Sobol indices, to systematically reduce uncertainty in aircraft design with no additional function evaluations. The proposed workflow therefore delivers rapid stochastic performance assessment and global sensitivity insight suitable for iterative design optimization during the conceptual design stage, enabling designers to improve early decision-making and reduce downstream program risk.