Extraction of second-order cyclostationary signal from acoustic array measurements using a time-varying periodic variance model with variational Bayesian inference

Acoustic array measurements are widely employed for noise analysis, noise control, and consequently for low-noise design of product. In the presence of rotating machinery (e.g., rotors), acoustic signals typically include a mix of tonal and broadband components as well as background noise. The broadband components characterized by their periodic modulation can be effectively modeled as a second-order cyclostationary (CS2) signal. In recent years, the extraction of tonal components from acoustic array measurements has been extensively studied by many researchers. However, the extraction of the CS2 components from the acoustic array measurements presents a significant challenge, especially in wind tunnel tests. This paper presents a novel approach that constructs a time-varying periodic variance model to characterize the CS2 signal and a time-invariant variance model to characterize the background noise to address this issue. The distribution of the parameters in the model is estimated using variational Bayesian (VB) inference to construct a time-varying periodic filter. Importantly, a special processing in this paper is employed to enable the simultaneous extraction of the CS2 signal from multi-channel acoustic array measurements. The proposed method is evaluated through extensive simulations. Finally, the efficiency and applicability of the proposed method are validated through a helicopter rotor model and a twin-rotor helicopter model in wind tunnel tests.