Uncertainty Quantification of Hovering Rotor Noise Due to Gust-Induced Unsteady Loading Using Polynomial Chaos Expansion

This study presents a polynomial chaos expansion (PCE) based uncertainty quantification framework for predicting un-steady loading noise of a hovering rotor subjected to vertical gust disturbances. A sinusoidal gust model, characterized by gust amplitude and gust length, is introduced to represent realistic inflow variability arising from environmental effects or rotor–airframe interactions. Unsteady loading noise is predicted using a frequency-domain acoustic formulation coupled with two aerodynamic models: a quasi-steady blade element momentum theory and an indicial response method to capture aerodynamic memory effects. The PCE approach is employed to efficiently propagate gust-induced uncertainties through the aeroacoustic model and is systematically validated against Monte Carlo simulations, demonstrating excellent agreement while requiring substantially fewer model evaluations. The results show that the largest uncertainty in unsteady loading noise consistently occurs along the rotor axis, with uncertainty levels varying across blade-passing frequency harmonics. Gust length is found to be the dominant contributor to acoustic uncertainty at higher harmonics, whereas gust amplitude more strongly influences mid-harmonic noise levels. Incorporating unsteady aerodynamic effects reduces the mean sound pressure levels at all harmonics but does not significantly alter the overall uncertainty bounds. The proposed framework provides an efficient and physically interpretable tool for assessing rotor noise robustness under realistic inflow disturbances and supports the development of low-noise rotor designs for advanced air mobility applications.