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This paper investigates using an Iterated Bayesian Focusing Algorithm and out-duct array measurements to identify multiple broadband sources placed in a cylindrical duct. The problems of large main lobe and low resolution due to localization of sources using conventional methods are investigated in this paper. To solve these problems, an Iterated Bayesian Focusing (IBF) method is utilized to localize the broadband sources. To evaluate and confirm the efficacy of the method, simulation tests and experimental validation are performed. In our experiments, we used a 56-channel dobby spiral array for out-duct measurements and beamforming method, equivalent source method (ESM), deconvolution approach for the mapping of acoustic sources (DAMAS), and Iterated Bayesian Focusing (IBF) method to localize broadband sources inside the duct. Simulation and experimental results demonstrate that the Iterated Bayesian Focusing (IBF) method significantly reduces the main lobe width and minimizes the number of minor lobes. This leads to improved accuracy in localizing double sources. • Broadband localization of stationary sources in a cylindrical duct is investigated. • Investigated using an out-duct microphone array for localizing induct sound sources. • Localization of a single sound source versus two sources is investigated. • Iterated Bayesian Focusing (IBF) is applied to improve the resolution of the results from the conventional methods. [ABSTRACT FROM AUTHOR]

This article proposes a variational Bayesian (VB) inference based on the nonsynchronous array measurement (NAM) (VB-NAM) method in order to obtain the fast and robust localization of low-frequency acoustic sources. To enlarge the aperture size compared with the prototype array, the NAM is performed to measure the acoustic pressures with low-frequency based on the forward power propagation model. The implementation of the NAM can be reformulated into a cross-spectral matrix (CSM) completion problem. Then, to solve the inverse problem of the NAM power propagation model, the VB inference based on the Student-t priors and Kullback–Leibler (KL) divergence optimization is proposed. The advantages of the proposed VB-NAM benefit from the optimization of matrix inversion and adaptive estimation of regularization parameters. The contribution of the adaptive parameter evaluation is to reduce the impact of multiple interferences (such as additive noise and the matrix completion error) in NAM. Finally, both simulations at 800 Hz and experimental results at 1000 Hz are presented to show the validation of the proposed VB-NAM method, even under the anisotropic Gaussian noise conditions. Algorithm performance and iteration process are analyzed to demonstrate the efficiency and robustness. [ABSTRACT FROM AUTHOR]

The localization of cyclostationary sound sources is important for rotating machinery noise source identification and fault diagnosis. Cyclostationary sound sources are a special class of nonstationary sound sources, which exhibit periodic changes in statistics. Most of the conventional sound source identification methods are based on the stationary sound source assumption, which do not consider the cyclostationarity of the radiated sound field by rotating machinery. Thus, they are hard to localize the acoustic sources with different cyclic frequencies. In this paper, a novel technique of localizing the cyclostationary acoustic sources with different cyclic frequencies is proposed. First, the cyclostationary conventional beamforming (CSCBF) method is deviated. In CSCBF, the cyclic-cross-spectral matrix (CCSM) is defined considering all the cross cyclic spectral correlation (CSC) between different microphones in the array. The left steering vector and right steering vector are constructed to focus the CCSM on each scanning grid point at a given combination of cyclic frequency and spectral frequency. Then, the high resolution cyclostationary beamforming (HR-CSBF) is further developed to improve the spatial resolution of CSCBF. In HR-CSBF, two linear equations according to the property of CSC is established as the acoustic inverse problems. With the sparse distribution of the cyclostationary sources in the space as the prior knowledge, the iterated Bayesian focusing (IBF) is utilized to obtain a robust and sparse solution in HR-CSBF. Numerical simulations and experiments are conducted to validate the proposed methods. To explore the potential applications of the proposed methods, the localization of high pressure pump (HPP) and rolling bearing with outer-race failure are also used to evaluate the effectiveness of the proposed methods. It turns out that both CSCBF and HR-CSBF can localize the cyclostationary sources with different cyclic frequencies. Compared with CSCBF, HR-CSBF can achieve a higher spatial resolution in the obtained acoustic map. [ABSTRACT FROM AUTHOR]