Uncertainty Quantification of Unsteady Loading Noise of a Hovering Rotor Using Polynomial Chaos Expansion

In this study, we employ the Polynomial Chaos Expansion (PCE) and Monte Carlo (MC) methods to quantify the uncertainty of unsteady loading noise generated by a hovering rotor under the presence of vertical gust. The unsteady loading noise is predicted using a frequency-domain approach combined with a quasi-steady Blade Element Momentum Theory, accounting for time-varying aerodynamic forces. A sinusoidal gust is modeled using two parameters: gust length and gust amplitude. Then, the uncertainty quantification (UQ) of the unsteady loading noise is performed using the PCE and MC with these two gust parameters. The UQ analyses show that the largest uncertainty in unsteady loading noise occurs at the rotor axis, and PCE and MC simulations show good agreement. The individual and combined effects of the gust parameters on the acoustic uncertainty are analyzed, and parallel coordinate plots are utilized to visualize combinations of the gust parameters that produce noise outliers. It is found that the gust length leads to larger uncertainty in the unsteady loading noise than does the gust amplitude, especially at fifth harmonic. Furthermore, low magnitude of high harmonic noise is produced even at high gust amplitudes when combined with wide gust lengths.