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• The models, imaging algorithms, and applications are systematically compared, analyzed, and concluded in this paper to explore the differences between the PAD-DBF and FDD-DBF techniques and provide guidance on the application of the technology. • A large number of simulations are investigated to explore the imaging characteristics of two rotor aerodynamic dipole source imaging technologies under different testing conditions, including different analysis frequencies, axis directions, SNRs, and measured distances. • The two imaging techniques are applied to the semi-anechoic chamber test for rotating dipole sources and the actual BO105 rotor wind tunnel test, respectively, which is further used to compare and validate the imaging effectiveness and applicability of the two techniques. The acoustic imaging technology for rotating dipole sources has been one of the topics concerned. In recent years, two state-of-the-art imaging technologies for rotating dipole sources were proposed, including beamforming technologies based on the predefined axis direction (PAD-DBF) and frequency-domain deconvolution (FDD-DBF). However, a systematic comparison of these two imaging technologies does not currently exist. In this paper, the models and imaging algorithms are firstly systematically compared and analyzed to explore the differences between the two technologies and provide guidance on the application of the technology. Secondly, extensive simulations are investigated to analyze the performance of the two imaging technologies under different working conditions. Finally, the two imaging technologies are applied to the semi-anechoic chamber test for rotating dipole sources and the actual BO105 rotor wind tunnel test, respectively, which is further used to compare and validate the imaging effectiveness and applicability of the two technologies. The analysis shows that both technologies can effectively achieve rotating dipole source localization. The PAD-DBF technology can achieve a more accurate rotating dipole source location, higher imaging resolution at a lower time cost, and it can get more robust imaging results in the low signal-to-noise ratio (SNR) of the wind tunnel environment. In contrast, the FDD-DBF technology can get a more accurate sound source magnitude while effectively imaging the rotating dipole source. [ABSTRACT FROM AUTHOR]

• The propagation process of a randomly inhomogeneous medium is considered rather than based on the free field assumption. • The numerical solution of Green's function is used instead of the original analytical solution of Green's function. • The IBF algorithm based on the Bayesian framework is used to achieve acoustic imaging in the inhomogeneous propagation media. A random inhomogeneous sound propagation medium is considered in acoustic imaging, which is modeled by a random function of the spatial medium. The inhomogeneity of the sound propagation environment can cause large errors in the modeling and measurement of acoustic imaging. Since the wave equation contains random variables, Green's function no longer has a specific analytical solution. The main work of this paper is as follows: (1) The acoustic inverse problem is considered in the inhomogeneous sound field, which is expressed according to predefined statistical information; (2) Karhunen-Loève expansion is used to simplify the proposed inhomogeneous propagation sound field, and the numerical solution of Green's function is used instead of the original analytical solution; (3) A dual-driven (including data-driven and knowledge-driven) algorithm based on the Bayesian framework is developed to achieve acoustic imaging, which is implemented through the joint estimation of the aperture function and the sparse prior. Finally, the proposed model and algorithm are verified by a numerical simulation. The proposed algorithm is compared with conventional beamforming in terms of localization accuracy and sound power quantization. The simulation results show that the inhomogeneous sound field can be represented by a small number of random variables, and the proposed dual-drive algorithm can accurately achieve acoustic imaging in the inhomogeneous propagation environment. [ABSTRACT FROM AUTHOR]

The transformer discharge fault localization is important for the power supply reliability. The audible sound radiated by the transformer can reflect the extensive operation information. Thus, discharge faults can be localized by high spatial resolution acoustic imaging techniques to facilitate the inspection and maintenance of power equipment. In this paper, the grid-moving equivalent source method (GMESM) is proposed to visualize the discharge fault on a transformer, where the equivalent source grids can approach the discharge fault position adaptively. A probability framework is established in GMESM. The noise power can be firstly estimated by the Bayes rule to avoid an additional measurement of the background noise. Then, the expectation maximization algorithm is used to optimize the proposed model. Two experiment cases are used to validate the proposed method. It turns out that the proposed GMESM can visualize the discharge fault on the transformer with high spatial resolution and accuracy. • The transformer discharge fault is localized by audible acoustic array. • GMESM is proposed for high-resolution transformer discharge fault localization. • The background noise power is estimated to avoid an additional measurement. [ABSTRACT FROM AUTHOR]

• Space-snapshot representation for acoustic imaging in a complex, noisy environment is investigated. • Low rank and Mixture of Gaussian modeling are proposed to achieve significant denoising performance. • Comparisons with other methods are made in simulations and experiments to verify the effect of the state-of-the-art methods. The microphone array can simultaneously obtain the multi-dimensional information (space-time-frequency) of sound sources, which is recognized as a fundamental and powerful tool in acoustic imaging. Acoustic Beamforming is one of the widely used methods in acoustic imaging. However, most of the applications of beamforming are based on the Gaussian noise assumption, which is not always accurate in on-site measurements. For example, shock noise with a skewed probability density function (PDF) may appear on the signal record when the turbulent eddies are not controlled. Thus, in this paper, the conventional Gaussian noise model is extended to a Gaussian mixture noise model, which can approximate any probability distribution of the noise in theory. The space-snapshot representation of microphone array measurements is further modeled as a combination of the low-rank matrix part (measurements from the sound sources) and a Gaussian mixture matrix part (measurement noise). The signal from the sources of interest is finally recovered by the Expectation–maximization algorithm, which iterates between the low-rank approximation of the sound sources and the estimation of the parameter of the Gaussian mixture model. The proposed method is further investigated with simulations and compared with robust principal component analysis (RPCA) and Gaussian-based probabilistic factor analysis (PFA). It is concluded that the proposed method outperforms the state-of-the-art denoising methods. [ABSTRACT FROM AUTHOR]

• Acoustic inverse problems in the framework of ADMM are investigated. • The iteration algorithms of ADMM in the complex domain have been derived. • ADMM has been systematically compared with the sparse holography. • Both simulation and experimentation have verified the performance of ADMM. Acoustic imaging is an important technique for sound source identification which is widely used in noise control and fault detection. It can be described as a method for reconstructing the amplitude and phase distribution of an acoustic field in a given plane. When the size of radiating object is huge and measurement environment is noisy, accuracy and efficiency of acoustic imaging algorithm deteriorate easily. In this paper, a novel computational framework is investigated to simplify the algorithm and balance computation speed with accuracy. It converts acoustic imaging into an inverse problem and then divides this problem into two parts including forward model and denoising model. This computation framework is based on the alternating direction method of multipliers, which makes parallel implementation and distributed optimization possible, especially for large scale measurements. It is assumed that the acoustic field is composed of a cluster of monopole sources and the equivalent source method is taken to solve the acoustic inverse problem. Both L 2 -norm penalization based on the minimal energy assumption and L p -norm (0 < p ⩽ 1) penalization based on the sparsity hypothesis are taken in this framework. Thus, the regularization parameter in the algorithm, which balances the standard least square error and the norm of the source solution, can be coupled with some pre-existing methods incluing L-curve, GCV and Bayesian strategies. Different regularization parameters are proposed and the comparison is made in this paper. The proposed method provides a general and convenient method for different type of sound source priors and it is validated with an experiment. [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]

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]

It is valuable to improve the resolution and speed of acoustic beamforming in real-time measurement, especially fault location, noise mapping, and so on. However, multiplication of the power transfer matrix takes much time in the iteration of the deconvolution algorithm. This article proposes a novel method based on the convolution approximation and GPU platform to obtain acoustic imaging with a high resolution quickly. First, the power propagation matrix is approximated by a symmetric Toeplitz block Toeplitz (STBT) matrix, which can transform the product of matrix and vector into the convolution of two smaller patterns. Three different convolution kernels are derived for the convolution operation, including 2-D variant convolution kernel, 2-D invariant convolution kernel, and 1-D separable invariant convolution kernel. Then, the regularization deconvolution algorithm with the convolution kernel is derived. Besides, the relation between approximation error, time cost, and setting parameters is discussed. The results show that the separable invariant convolution kernel can obtain the fastest imaging and relatively accurate localization, while the time consumption of the variant kernel is the highest. Simulations and experiments are operated on the CPU and GPU to make a comparison, which validates that our proposed deconvolution-GPU implementation can significantly improve the computation speed for the matrix on a large scale. [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]

Identifying acoustic sources with high spatial resolution and precision is significant for machinery noise control. Off-grid compressive beamforming is an effective method for creating acoustic maps with a high spatial resolution. In this study, a two-dimensional off-grid compressive beamforming method via weighted block ℓ 1 norm regularization (WBS-OCSBF) is proposed. The weighted ℓ 1 norm offers a more uniform sparsity penalty compared to the ℓ 1 norm. This method can enhance the performance of off-grid compressive beamforming. Additionally, it is easily implemented on mature linear programming solvers and converges with only a few iterations. Numerical simulations are conducted to analyze the effects of several major parameters on the performance of the proposed method. The simulation results demonstrate the superiority of the proposed method over some traditional methods. The proposed method is then validated using a loudspeaker noises localization experiment. A gearbox transmission system and a transformer are used as two specific objects to explore the industrial application value. The proposed method can effectively localize the gear meshing noise and transformer discharge faults with a high spatial resolution. • Compressive beamforming via weighted Block L1 Norm is proposed in this paper. It enhances the spatial sparsity of the reconstruction results. • Simulation and speaker positioning experiments verify the effectiveness of the method. • Two industrial application experiments proved the potential industrial application value of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

• The non-synchronous measurements in the large-aspect-ratio cabin is investigated. • Non-synchronous measurements is applied to suppress reverberation interference. • The optimal spherical array measurement scheme and basis functions are determined. The resolution of conventional acoustic imaging methods in a large-aspect-ratio cabin is reduced seriously by array parameters limitation and reverberation. The non-synchronous measurements technique breaks through the limitation of array shape and the number of microphones. This method can approximate the result of synthetic large-aperture array acoustic imaging. The increase in the number of microphones and low-rank constraint assumption in non-synchronous measurements suppress the reverberation interference. The low-rank constraint filters out the eigenvalues of the reverberation sound other than the main noise sources, which is acted as an eigenvalue filter. It has been demonstrated that non-synchronous measurements with 3D beamforming can improve the resolution of acoustic imaging in cubic space, but the related research on the large-aspect-ratio cabin is still missing. The non-synchronous measurements method is applied to achieve high-resolution acoustic imaging in a large-aspect-ratio cabin in this paper. The array measurement scheme is investigated comprehensively, including the number of non-synchronous measurements, the array step distance and appropriate spatial basis functions. The experimental results show that the non-synchronous measurements can achieve high-resolution 3D acoustic imaging in the cabin of an urban rail vehicle. [ABSTRACT FROM AUTHOR]

Acoustic imaging from non-synchronous measurements is a powerful method that can achieve excellent performance of a densely sampled large array by using an arbitrary prototype array. It has attracted significant interest recently since it is beyond the fundamental limitation of the working frequency determined by the size and microphone spacing of an array. One basic assumption of the non-synchronous measurements theory is the spatial continuity of the acoustic field, which is implemented by introducing the spatial basis function. Nevertheless, a comprehensive investigation of spatial basis function in the context of non-synchronous measurements is still missing. Two kinds of methods are proposed to construct spatial basis functions based on the homogeneous Helmholtz equation solution in this paper. One is the generalized harmonic polynomials (GHPs) and the other is the plane wave expansion (the quasi-uniform plane wave and the non-uniform plane wave). Comparisons of their spectral matrix completion errors show that the proposed construction methods of spatial bases can both yield low errors. Moreover, the construction of the proposed bases is simple to be implemented with only one dimension parameter to be chosen and suitable for the complex sound field. The effectiveness of the proposed bases in the non-synchronous measurements is also validated with simulations and an experiment. [ABSTRACT FROM AUTHOR]