Duct modal identification considering statistical dependency via the Boltzmann machine

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.