A probabilistic approach to identifying duct acoustic modes through non-synchronous measurements using microphone arrays

Fan noise, comprising both tonal and broadband components, is a predominant source of noise in aero-engines. Calculating duct acoustic modes for random broadband noise is more complex than that for tonal noise. This paper proposes a probabilistic method for identifying duct acoustic modes based on non-synchronous measurements from microphone arrays. The method overcomes the challenge of acoustic mode aliasing and accurately identifies duct modes in the presence of broadband fan noise. By rotating a circular duct with a microphone array, the proposed method equivalently increases the number of non-synchronous microphone measurement points. The completion of the cross-spectral matrix is realized by the Fast Iterative Shrinkage Thresholding Algorithm (FISTA) to obtain the sound pressure signals from more measurement points. The mode coefficients are estimated using a hierarchical a priori probability method. The inverse problem of mode identification is represented by a Bayesian framework based on a Gaussian-scale mixture prior model. Simulations and experiments validate the method's effectiveness in suppressing mode aliasing, providing accurate results for duct mode identification with broadband noise, eliminating the influence of interfering modes on identification results, and offering improved observation of mode characteristics across a wide frequency and rotational speed range.