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Sound source visualization has been widely used in many scenarios such as aerospace, industrial production, and urban management. Sound source localization technology plays an essential role in the realization of sound source visualization. The imaging results and calculation cost are the primary considerations in the problem of sound source localization. This article proposes a subspace iteration integrated variational Bayesian (SVB) method to realize adaptive imaging of different sound sources. First, the proposed variational Bayesian (VB) method is based on total variation (TV) prior to balance the sparsity and smoothness of the imaging results. Second, the subspace optimization method in the probability measure space is integrated into the proposed SVB method to solve the involved ill-posed inverse problem. The proposed SVB method can significantly improve the calculation speed, especially for large-scale inverse problems. Finally, the speed and robustness of the proposed SVB method can be demonstrated according to the extensive results of simulation and experimental validation. [ABSTRACT FROM AUTHOR]

• The SBL algorithm is used for sound source localization and quantification. • The SBL and IBF algorithms are compared in terms of effectiveness and robustness. • Advantages of SBL at low SNRs, low frequency are validated through experiments. The localization accuracy and acoustic quantification are the leading indicators of acoustic localization. It is difficult to reconstruct the acoustic field completely as the number of sources is larger than the number of microphones. To solve this problem, the sparse acoustic holography under the Bayesian framework is applied to acquire the phase and amplitude distribution of the acoustic field to achieve acoustic source localization. In this paper, a Sparse Bayesian Learning (SBL) algorithm is improved, which can not only perform acoustic localization quickly and accurately, but also quantize the sound source to achieve sparse acoustic holography. To verify the efficiency and robustness of the improved method, simulations and experiments with different sound sources and noise disturbances are performed in this paper to verify the superior performance of the SBL algorithm at low frequencies and low signal-to-noise ratios (SNR). [ABSTRACT FROM AUTHOR]

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]

Beamforming technology is an essential method in acoustic imaging or reconstruction, which has been widely used in sound source localization and noise reduction. The beamforming algorithm can be described as all microphones in a plane simultaneously recording the source signal. The source position is then localized by maximizing the result of the beamformer. Evidence has shown that the accuracy of the sound source localization in a 2D plane can be improved by the non-synchronous measurements of moving the microphone array. In this paper, non-synchronous measurements are applied to 3D beamforming, in which the measurement array envelops the 3D sound source space to improve the resolution of the 3D space. The entire radiated object is covered better by a virtualized large or high-density microphone array, and the range of beamforming frequency is also expanded. The 3D imaging results are achieved in different ways: the conventional beamforming with a planar array, the non-synchronous measurements with orthogonal moving arrays, and the non-synchronous measurements with non-orthogonal moving arrays. The imaging results of the non-synchronous measurements are compared with the synchronous measurements and analyzed in detail. The number of microphones required for measurement is reduced compared with the synchronous measurement. The non-synchronous measurements with non-orthogonal moving arrays also have a good resolution in 3D source localization. The proposed approach is validated with a simulation and experiment. [ABSTRACT FROM AUTHOR]

Noise source localization is considered a key technology for the low-noise design of machinery and equipment. The spatial resolution of conventional beamforming localization methods is effectively improved by the fast iterative shrinkage thresholding algorithm(FISTA). The application of FISTA for sound source localization in reverberant environments is limited by the selection of reflection parameters. In this paper, FISTA extends to FISTA-Net and is proposed to solve the problem of adaptive fitting of reflection parameters to improve the performance of sound source localization in a reverberant environment. In FISTA-Net, the network model can be established by expanding and truncating the FISTA algorithm based on a fixed number of iterations. The parameter iteration steps, shrinkage thresholds and update operators are updated in the FISTA-Net model by training. A series of simulations are conducted for various frequencies, reverberation times, and signal-to-noise ratios and compared to several de-reverberation algorithms to evaluate the performance of the proposed algorithm. The loudspeaker source localization experiment was conducted in a closed room to verify the effectiveness of FISTA-Net in real-world scenarios. [ABSTRACT FROM AUTHOR]

• Non-synchronous measurements beamforming is investigated. • ALM and ADMM based fast implementation are presented. • Simulations and an industrial application are given. Acoustic beamforming is a technique to measure the sound field and then achieve the localization of the sound sources. It usually works at a high frequency because the size and density of the microphone array are limited. Differing from the traditional beamforming, non-synchronous measurements beamforming can widen the working frequency bandwidth with a movable microphone array. It generates a cross-spectral matrix of all the microphones in the sequential positions of measurements, and this matrix is incomplete due to the missing phase relationships between non-synchronous measurements. Thus the non-synchronous measurements beamforming can be regarded as a cross-spectral matrix completion problem. One application of the non-synchronous measurements beamforming is that it can immediately obtain a completed noise image by scanning a large sound source; then the primary sound sources are expected to be identified by the global image. However, it is still a challenge for the current non-synchronous measurements beamforming algorithm since the computation time is long when more numbers of measurements are involved. In this paper, two algorithms based on the augmented Lagrange multiplier method and alternating direction method of multipliers are proposed for achieving fast implementation. The proposed algorithms can improve the iteration speed of the non-synchronous measurements beamforming which is proved first in the simulation, and they are further applied in the on-site measurement of the vehicle engine compartment (the data missing cross-spectral matrix of 15 non-synchronous measurements for a given frequency can be completed only in a few seconds). This industrial application has shown the potential of the proposed methods to be further applied for the sound source imaging of large mechanical systems. [ABSTRACT FROM AUTHOR]

The acoustic imaging results in the diffuse field are seriously affected by reverberation. The acoustic source localization algorithms based on the free-field assumption will produce many artifacts in the reverberant environment. To achieve accurate acoustic source localization in a reverberant environment, a sound field morphological component analysis (SF-MCA) model and an enhanced alternating direction method of multipliers (ADMM) algorithm are proposed in this article. First, the solution of the inhomogeneous Helmholtz equation is analyzed to characterize the acoustic components. Second, Green’s function and plane-wave basis function serve as dictionaries for sparse representation of the acoustic signal in the frequency domain, and the corresponding decomposition coefficients are obtained by the enhanced ADMM algorithm. Finally, the accurate acoustic imaging results are realized in the reverberant chamber space with strong reverberation ($T_{20}=174.30\,\,\text {ms}$). Experiments demonstrate the validation of the proposed SF-MCA method. The acoustic imaging obtained by the proposed SF-MAC dereverberation model is far superior to the acoustic imaging that treats the reverberation as the general Gaussian noise. [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]

The Non-Synchronous Measurements is an efficient technique to improve the acoustic image of conventional beamforming for sound source localization. It is unable to quickly reveal the sound sources of the large machinery which requires a large synthetic array with many microphones to capture enough sound pressure data. In this paper, four Non-Synchronous Measurement algorithms with improved computational efficiency are demonstrated. They are implemented by combining the Alternative Direction Method of Multipliers (ADMM) method with different randomization-based acceleration strategies. The new algorithms are developed firstly by (1) using Randomized Singular Value Decomposition (RSVD) to construct the projection basis, and then by (2) migrating the computation platform from the Central Processing Unit to the Graphics Processing Unit for the Cross-Spectral Matrix completion steps, (3) accelerating the soft threshold shrinkage operator with RSVD, or (4) replacing the soft threshold shrinkage with RSVD-enhanced optimal shrinkage in the Cross-Spectral Matrix completion steps. Numerical simulations are carried out under different conditions, including the number of sequential measurement positions, the step length between two sequential measurement positions, the frequency of the sound sources, and the Signal-to-Noise Ratio of the sound pressure signals measured by the microphones. The sound source localization performance of the improved algorithms is assessed by examining their acoustic maps, and the computational performance of these algorithms is compared through their Cross-Spectral Matrix reconstruction errors and time consumption. • Four accelerated Non-Synchronous Measurement algorithms are proposed. • Proposed algorithms are based on the Randomized Singular Value Decomposition. • The matrix completion accuracy of the original algorithm are optimized. [ABSTRACT FROM AUTHOR]

• Oder domain beamforming is proposed for the localization of rotating machineries under variable speed conditions. • A steering vector of order domain beamforming is constructed. Rotating machinery is widely used in the modern industry, which undergoes huge amounts of variable speed working conditions. Localizing the sound sources of the rotating machinery on a specific order is significant to noise source identification and fault diagnosis. The order domain beamforming method (ODBF) is proposed in this paper to localize the source in the rotating machinery at a specific order. Firstly, the measured acoustic array signals are resampled into the angle domain via the key phase signal. Then, the fast Fourier transform is operated to obtain the acoustic pressure on a specific order. Finally, with the derivated steering vector in the order domain, the proposed order domain beamforming method can obtain the acoustic map on the scanning plane to localize the primary acoustic sources of the rotating machinery. The numerical simulation investigates the performance of the proposed ODBF under different cases. The industrial motor noise source identification experiment further verifies the effectiveness of the proposed ODBF. [ABSTRACT FROM AUTHOR]

This paper presents an experimental investigation of rotating source localization to identify the axial fan noise with high spatial resolution methods. It exploits the on time-domain de-Doppler, and sparsity-based inversion and the convolution model to approximate the power propagation model of the rotating source. This work is also an extension of the previous paper of authors. But the focus of this study is the experimental investigation and application of actual data. To evaluate the performance of the proposed algorithm, a vortex generator is attached to the fan blade, creating discontinuities in the blade to simulate axial fan blade defects (cracks, holes, dust accumulations, etc.). The experimental data are shared as a data benchmark to promote further studies in the field of rotating acoustic localization. Compared with the state-of-the-art rotating Beamforming method (ROSI), the acoustic imaging results at various working frequencies for three different axial fans with different rotating speeds (RPM) are accurately identified and sparsely distributed. In addition, the power propagation model derived in the previous paper can be interpreted by a convolutional approximation model in this paper, and this technique can help to reduce the computational costs of proposed methods for real applications. The accuracy of the aerodynamic noise positions estimated by the proposed method are further proved to match well with the aerodynamic mechanism. • A practical implementation for the rotating sound sources localization in industrial axial fans is presented. • Two types of vortex generators (VGs) are attached to the blade, simulating the blade defects. • An explanation for the power propagation model based on the convolutional approximation is presented. • A data benchmark is established for peers to compare various rotating sound source localization methods. [ABSTRACT FROM AUTHOR]

The Modal Composition Beamforming (MCB) method can quickly achieve the localization of fast-rotating sound sources; however, its low resolution and unclear applied conditions severely limit its industrial application. This study aims to investigate the MCB-based high-resolution localization method for multiple rotating sound sources and apply it to the localization and identification of axial-fan blade-noise. In this paper, the Variational Bayesian Approximation (VBA) and the Subspace Variational Bayesian Approximation (SVB) methods are used to solve the MCB-based rotating sound power propagation (RSP) model, denoted as RSP-VBA and RSP-SVB, respectively. The effectiveness of the proposed RSP-VBA and RSP-SVB are experimentally validated for the first time. Compared to the conventional MCB method, the resolution is significantly improved, and the proposed high-resolution methods are even faster than the classical Rotating Source Identifier (ROSI) method in most conditions. More importantly, the applied condition of the MCB, RSP-VBA, and RSP-SVB methods is given and verified by using three evaluation indicators. Then a schematic of the applied condition with examples is provided. With the guide of the applied conditions, the RSP-VBA and RSP-SVB methods are applied to the blade-noise localization of various multiblade high-speed axial fans. [ABSTRACT FROM AUTHOR]

• Proposed methods localize rotating monopoles at high rotation speed and low SNR. • The rotation blur and Doppler effect is removed by the de-Doppler Beamforming. • The ill-posed inverse problem is solved with high resolution. • Aerodynamic sound sources can be localized in the industrial fan experiment. The rotating-acoustic source localization has played an important role in rotary machine fault diagnosis, engine noise reduction and propeller recognition etc. To achieve high-resolution localization of fast rotating sources, this paper proposes an improved power propagation forward model of rotating acoustic source based on the equivalent source hypothesis. Then the ill-posed inverse problem derived from the forward power model is solved robustly by proposed two sparsity-based methods: the Least Absolute Shrinkage and Select Operator for Rotating-acoustic Sources (LASSO-RS) and Least Angle Regression for Rotating-acoustic Sources (LAR-RS). The contributions of this paper are that, at one hand, the improved forward model is indeed time-invariant for the fast-rotating source owing to the time-domain de-Doppler technique; at the other hand, high-resolution acoustic maps can be obtained by proposed LASSO-RS and LAR-RS thanks to the sparsity-based regularization, even under very low signal-to-noise ratio (SNR). Moreover, the proposed LAR-RS is the data-driven method, rather than the parameter-dependent method such as the LASSO-RS with careful selection of regularization parameter. In simulations and experiments, the proposed methods can robustly localize rotating monopoles in the condition of 3000 RPM rotation speed (50 Hz), −5 dB SNR, and 2500 Hz working frequency. [ABSTRACT FROM AUTHOR]

• Non-stationary noise source localization of permanent magnet synchronous motors (PMSMs) is investigated. • Spatial acoustic maps of PMSMs at a characteristic order can be restored. • Physical insights into the non-stationary noise mechanism of the motors can be revealed. • Experimental results with two industrial PMSMs verify the efficacy of the proposed method. Noise source localization of rotating machinery plays an important role in machinery noise diagnosis and control. Various beamforming methods have been developed for stationary sound source localization. However, for rotating machinery working under time-varying speed conditions, the radiated acoustic signals are typically nonstationary. Under these conditions, characterizing and localizing nonstationary sound sources remains a challenge. Permanent magnet synchronous motors are one of the most widely used rotating machinery in modern industries and often work under variable speed conditions. Herein, the noise source localization problem of motors under time-varying speed conditions was studied. A nonstationary noise source localization method based on the Vold-Kalman filter and time-domain beamforming is proposed to restore the spatial acoustic maps of permanent magnet synchronous motors(PMSMs) at a characteristic order. First, the Vold-Kalman filter is adopted to extract acoustic signals at a characteristic order from the nonstationary measurements using a microphone array. Then, the filtered multichannel acoustic signals are fed into the time-domain beamforming algorithm to obtain the noise source localization result in a characteristic order. Combining Vold-Kalman filter with time-domain beamforming enables the characterization of non-stationary sound sources in the time, spatial, and order domains. The experimental results verify the effectiveness of the proposed method in noise source localization for motors under time-varying speed conditions. In addition, the experimental case with two motors further proves that the proposed method can simultaneously realize noise source separation at different characteristic orders. [ABSTRACT FROM AUTHOR]