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The measurements of aero-engine fan noise are crucial to engine-noise reduction and silent-turbofan design. The duct mode identification is adpoted to decompose inner duct noises into spinning modes from acoustic pressure measured by a microphone array. However, modes identification of the aero-engine fan are difficult cause the number of modes is usually much larger than the number of microphones and leading to an ill-posed problem during the inverse process. A mode identification method based on Iterative Bayesian Focusing is used to solve this problem. The in-duct sound field is described by a statistical model, and the inverse problem of mode identification is expressed in a Bayesian framework. The sparsity of the target acoustic modes is applied as a priori condition, and a Mode Aperture Function (MAF) is developed. The aperture width of the MAFis automatically updated and contracted through iterations, after which mode coefficients are contracted to a sparsest solution. The used mode identification method is firstly validated through numerical simulations, and the effects of the number of microphones and SNR on mode identification results are discussed. Then the Iterative Bayesian Focusing-based mode identification method is experimentally verified through a well designed Spinning Mode Synthesizer. Both numerical and experimentalresults indicate that target modes can be accurately identified when the number of microphones are much less than the number of all propagating modes. [ABSTRACT FROM AUTHOR]

The fan noise is the primary component of aero-engine noise. Duct acoustic modal identification is essential for analyzing the mechanism of fan noise generation and propagation. The acoustic modal in the duct can be identified by the measurement of the microphone array mounted on the duct wall. It is generally assumed in the conventional modal identification methods that the modal coefficients are independent of each other. However, the realistic duct acoustic modal coefficients exhibit significant statistical dependence. A Boltzmann machine(BM) model considering the statistical dependence between modal coefficients is proposed for recovering the modal coefficients in this paper. The modal coefficients are estimated using a block coordinate optimization method in a Bayesian framework. Moreover, the modal Boltzmann parameters can be learned iteratively by the BM. The effectiveness of the proposed method is verified by numerical simulations and experimental tests. It turns out that the modal coefficients can be accurately identified by the proposed method, and a more significant sparsity is shown by the results. In addition, the statistical dependence between the modal coefficients can be captured by the BM. • A Boltzmann machine modeling method that considers the statistical dependence between the modal coefficients is proposed. • The modal coefficients and the modal Boltzmann parameters can be estimated adaptively and iteratively. • The accuracy and robustness of the modal identification results are analyzed. • The proposed method is evaluated in Spinning Mode Synthesizer experiments. [ABSTRACT FROM AUTHOR]