Higher-Order Statistical Metrics for Characterizing Multirotor Acoustics

Several higher-order statistical metrics are used to evaluate the significance of waveform nonlinearities in the sound field of a laboratory-scale coaxial, corotating rotor in hover. These comprise the magnitude-squared coherence, skewness, and kurtosis of the pressure waveform and its time derivative, number of zero crossings per rotation, a wave steepening factor, and the quadrature spectral density and its integral. A unique feature of this rotor setup is the constructive and destructive interference of sound waves produced by neighboring blades, which are incubators for signal distortion effects. Waveform distortions are evaluated for changes to rotor index angle, the separation distance between the upper and lower rotors, as well as changes to rotor speed for different observer positions. Significant sensitivities in the kurtosis of the pressure waveform and its time derivative, the number of zero crossings, and the integral of the quadrature spectral density are shown for changes in rotor index angle, observer position, and rotor speed; stacking distance appears less important at affecting changes to these metrics. The trade space between these metrics and rotor figure of merit demonstrates how changes to the rotor index angle can invoke relatively small changes in rotor performance while generating large changes in acoustic waveform nonlinearities.