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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 acoustic vector sensor (AVS) has a wide application in the direction of arrival (DOA) estimation of sound sources including aircraft, underwater or on-land vehicles, search-and-rescue efforts, etc. The performance of only one acoustic vector sensor can compare favorably with a traditional acoustic array in DOA estimation. The anisotropic noise problem of the vector sensor has had a severe affective on the estimation accuracy and has caused little attention until now. In this paper, an AVS measurement system is designed, and an Anisotropic Sparse Bayesian Learning (SBL) method (the A-SBL method) is proposed to model and estimate the anisotropic noise of the AVS system. A high-resolution DOA estimation method is also introduced based on the noise estimation algorithm. The experimental results exhibit the necessity of modeling the anisotropic noise, and the estimation accuracy of the proposed A-SBL method based on the noise model is verified. The comparison of DOA methods shows the superiority of the proposed method, in which the DOA estimation error is not more than 1 °. The proposed method's utility may be found in applications for localization or tracking of targets with prominent acoustic characteristics when the environment is complicated. [ABSTRACT FROM AUTHOR]

Abstract The effects of dynamical load from acoustic waves to structural responses cannot be neglected for some cases such as a thin structure submerged in a heavy fluid. To deal with this kind of problem, a hybrid numerical method consisting of finite element method (FEM) and boundary element method (BEM) for the acoustic-structural coupling problems is proposed. The FEM is built on the first-order Reissner-Mindlin plate theory and the discrete shear gap (DSG) method is applied to construct a locking-free FEM. A collocation BEM with linear continuous element based on Burton-Miller formulation is adopted with an aim to produce a meshing conforming coupling method with the FEM not only on geometry but also on physical nodal quantities at the interface. In addition, analytical expressions of the singular integrals appeared in the Burton-Miller formulations are available to eliminate the numerical difficulties in the implementation of the BEM. Furthermore, the coupling matrix at the interface based on the conforming linear triangular mesh is obtained analytically to avoid the numerical quadrature. A solution scheme by absorbing the FEM equations to the BEM's is proposed to take the advantage of less memory cost of the linear BEM. Optimized algorithms are designed to reduce the memory cost while keep the accuracy of the coupling method during the absorption of the structure effects to the acoustic domain. Numerical examples are setup to validate the accuracy and demonstrate the potential capability of the proposed method. [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]

The water entry transient sound of a projectile can be used for early target detection in passive sonar. Two detectors for the transient sound with low Signal to Noise Ratios (SNRs) have been proposed depending on the spectrum matrix decomposition. One detector is the Robust Principal Component Analysis (RPCA)-based detector, and the other one is the Non-negative Matrix Factorization (NMF)-based detector. In the RPCA-based detector, the measured spectrogram is divided into a low-rank matrix and a sparse matrix, and the sparse matrix representing the transient sound is used to construct the detection function. In the NMF-based detector, the measured spectrogram is decomposed into a series of rank-1 matrices, and the temporal patterns with large kurtoses are used to construct the detection function. The detectors are data-driven approaches based on a single channel, and no prior information is needed. The performances of the proposed algorithms are determined, and the experimental results demonstrated that the proposed algorithms have good performance with more than 2 dB relative detection gain. [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]

• An FM-TPWM is proposed to reconstruct the non-stationary sound field in a uniformly flow medium. • The proposed FM-TPWM can provide a higher precision and more stable reconstruction result in the flow medium. • The superiorities of the proposed FM-TPWM are demonstrated under various parameter configurations by comparing with the F-RTNAH. A multistep time domain plane wave superposition method (M-TPWM) is expanded into a new environment that the medium is fluid, and an M-TPWM with flow medium (FM-TPWM) is proposed to reconstruct the non-stationary sound field in a uniformly flow medium. In the FM-TPWM, two situations that the flow directions of the medium are parallel to and perpendicular to the hologram plane are researched. The time-varying pressures on the hologram plane in these two situations are expressed as a superposition of time convolutions between the pressure time-wavenumber spectra of a virtual source plane and the corresponding new time domain propagation kernel derived in the flow medium. Subsequently, the discrete solving equations in the parallel and perpendicular situations at one time are established. The pressure time-wavenumber spectra at only this time can be solved by once solving inverse calculation. Then, these discrete solving equations in the flow medium at several times are combined for forming the larger solving matrix equations in the parallel and perpendicular situations, and by once multistep calculation, the pressure spectra at these times are acquired concurrently. Consequently, the time-varying pressures on the reconstruction plane in the flow medium are calculated by the corresponding acquired pressure time-wavenumber spectra. Numerical simulations with parallel and perpendicular situations are applied to examine the performance of the proposed FM-TPWM, in which two monopole sources in the flow medium are used to engender the non-stationary sound field. The simulation results prove that the proposed FM-TPWM can reconstruct the non-stationary sound field very well when the flow directions of the medium are parallel to and perpendicular to the hologram plane, respectively. Besides, several meaningful parameters are discussed in detail to prove the adaptability and robustness of the proposed FM-TPWM in the flow medium, and its reconstruction advantages are protruded in comparison to the real-time nearfield acoustic holography with the flow medium. [ABSTRACT FROM AUTHOR]

Fan noise, comprising both tonal and broadband components, is a predominant source of noise in aero-engines. Calculating duct acoustic modes for random broadband noise is more complex than that for tonal noise. This paper proposes a probabilistic method for identifying duct acoustic modes based on non-synchronous measurements from microphone arrays. The method overcomes the challenge of acoustic mode aliasing and accurately identifies duct modes in the presence of broadband fan noise. By rotating a circular duct with a microphone array, the proposed method equivalently increases the number of non-synchronous microphone measurement points. The completion of the cross-spectral matrix is realized by the Fast Iterative Shrinkage Thresholding Algorithm (FISTA) to obtain the sound pressure signals from more measurement points. The mode coefficients are estimated using a hierarchical a priori probability method. The inverse problem of mode identification is represented by a Bayesian framework based on a Gaussian-scale mixture prior model. Simulations and experiments validate the method's effectiveness in suppressing mode aliasing, providing accurate results for duct mode identification with broadband noise, eliminating the influence of interfering modes on identification results, and offering improved observation of mode characteristics across a wide frequency and rotational speed range. • The non-synchronous measurements technique is employed to increase the number of measurement points. • A probabilistic model with a hierarchical prior is utilized to characterize the sound field. • The iterative parameter adjustment process is adaptive. • Experiments were performed on an axial compressor test rig to validate the proposed method. [ABSTRACT FROM AUTHOR]

Accurate identification of in-duct acoustic modes is crucial for comprehending fan noise generation mechanisms, propagation characteristics, and control strategies. The number of fan noise modes increases with frequency, and using a sufficient number of microphones for higher-order mode identification becomes challenging due to cost considerations. A Bayesian compressive sensing method for mode identification is proposed in this paper to address the issue of insufficient microphones. The sensing matrix is constructed by randomizing the arrangement of a small number of microphones. The acoustic field is characterized using a Bayesian probabilistic model, and the inverse problem is formulated as the estimation of mode coefficients within the Bayesian compressed sensing framework. The proposed method accurately identifies acoustic modes in the presence of adaptive parameters and achieves more precise magnitude recovery than previous methods. The effectiveness and robustness of the proposed method under various parameters is demonstrated by comparing the simulation results of different mode identification methods. The effectiveness of proposed method is further substantiated by experimental validation using a 1.5-stage axial flow compressor, demonstrating accurate identification of target modes with fewer microphones. • A Bayesian compressive sensing method for identifying tonal modes is proposed to solve the problem of insufficient microphones. • Simulation and experiments proved the effectiveness and modes can be accurately identified with a small number of microphones. [ABSTRACT FROM AUTHOR]

Spinning Mode Synthesizer is an effective engine noise test rig for aero-engine noise propagation and radiation research. Spinning mode generation is realized through amplitude modulation and phase shift between individual loudspeakers. The target spinning mode is not the primary mode. It is even submerged in the undesired modes due to the system error of artificial source generators, especially the magnitude and phase mismatch of loudspeakers. In this paper, a global calibration factor is used to minimize the effect of loudspeaker nonuniformity in mode generation. The mode generation process of the calibrated system is mainly divided into two steps. The first step is to identify the calibration factors of individual loudspeakers with an optimized microphone array, which is used primarily for mode analysis. No particular error sensor or additional devices is used in the measurement. The theoretical complex source strengths are multiplied by the calibration factor to calibrate artificial source generators. The second step is to carry out mode generation experiments using the calibrated system, and Radial Mode Analysis is used to analyze the mode components in the duct. A spinning mode synthesizer with three axially spaced rows of loudspeakers is introduced, and each row consists of 12 excitation units. The maximum controllable circumferential mode order is m = 9, and the maximum controllable radial mode order is n = 2. It has been proven that the calibrated system can generate the target mode more precisely, and the mode coefficient signal-to-noise ratio ( SNR A) of any propagable mode is greater than 10 dB in the operating frequency range. [ABSTRACT FROM AUTHOR]

The Non-synchronous Measurements (NSM) was proposed to enhance the accuracy of reconstruction and reduce the measurement cost. However, the investigated object of conventional NSM are only sparsely distributed sound sources, and little emphasis placed on the reconstructed accuracy of the spatially extended sound source. In this article, the traditional NSM is further investigated in the spatially extended sound source, and the sound pressure information is reconstructed by Bayesian compressive sensing algorithm (BCS). Firstly, the spatially extended sound source is scanned by moving the rectangular microphone array, and the measurement effects of the array with large aperture and high density are approximately obtained by using NSM technique. Then, BCS is applied to reconstruct sound field by the NSM of sound pressure. The results of numerical simulations provide evidence for the feasibility of applying the proposed investigation to the spatially extended sound source. NSM has advantages in reconstruction accuracy compared with the single measurement. At the same time, the reconstructed sound pressure under NSM can replace the simultaneous measurement (SM) results of multi-array, which avoids the limitation of using reference microphone in increasing the number of channels and spatial layout. The experimental results of the driven steel plate provide additional evidence to support the effectiveness and feasibility of the investigation. • The application problem of the NSM in the spatially extended sound source like the driven steel plate is investigated. • The NSM increases the number of microphones and avoids the limitation of using reference microphone in increasing the number of channels and spatial layout. • The traditional NSM is further investigated in the spatially extended sound source, and the sound pressure is reconstructed by BCS. [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]

• A cascade filter is proposed to separate the main and tail rotors' aerodynamic noise. • The Vold-Kalman filter is proposed to separate the rotors' tonal noise. • The cyclic Wiener filter is proposed to separate the rotors' broadband noise. • The method is validated in both simulation and wind tunnel test measurements. The noise issue has become an important factor limiting the massive application of helicopters as the requirements for helicopter reliability and comfort continue to increase. As the primary noise source of helicopters, the main and tail rotor aerodynamic noise should be separated for individual noise reduction investigations. According to the frequency domain characteristics, the rotor aerodynamic noise can be divided into tonal noise and broadband noise. A cascade filtering method with Vold-Kalman filter and cyclic Wiener filter is proposed in this paper to separate the tonal and modulated broadband noise of the main and tail rotors, respectively. The classical method only considers the periodic characteristics of the main and tail rotor aerodynamic noise for harmonic separation. The broadband noise is not considered within the separation of interest due to its randomness, which leads to the inaccuracy of the conventional method for the aerodynamic noise separation of the main and tail rotors. The broadband noise exhibits a second-order cyclostationarity due to the periodic modulation of the rotational motion of the rotor. According to its cyclostationarity, while considering the periodicity of tonal noise for harmonic separation, the proposed cascade filtering method also performs the separation of broadband noise. More precise separations of the main and tail rotor can be obtained by this method. The efficacy of the proposed cascade filtering method is demonstrated in both the simulation and wind tunnel noise measurement. [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]

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]