Cyclostationary modeling for the aerodynamically generated sound of helicopter rotors

Helicopter rotor aerodynamic noise research has become essential as helicopters’ reliability and comfort requirements have increased. Significant progress has been made in modeling the aerodynamically generated sound of helicopter rotors. The cyclostationary signal processing methods have been widely used for machine fault diagnosis, machinery system identification and mechanical source separation. However, the lack of a generally accepted formal definition of cyclostationarity based on the basic aerodynamic theory and wave propagation model limits cyclostationary methods’ application to the helicopter rotor aerodynamic noise. A formal cyclostationary modeling process to the helicopter rotor aerodynamic noise based on aerodynamic and wave propagation theory is proposed in this paper for subsequent cyclostationary signal processing. The rotor blade noise is mathematically formulated as a cyclostationary process by imposing the periodic Green's function based on the Wold–Cramer decomposition form of the Ffowcs Williams–Hawkings (FW–H) equation, and the formal definition of the rotor blade noise cyclostationary process is derived. Then, the cyclostationarity is defined for both the tonal noise and the broadband noise of rotor aerodynamic noise, respectively. Furthermore, a periodic amplitude modulation (PAM) signal model is proposed to approximate the measured rotor aerodynamic noise signal. The proposed signal model is validated by the measurement in the wind tunnel test.