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The Non-Synchronous Measurements is particularly effective at expanding the operating frequency range of a single microphone array. The completed cross-spectral matrix of the synthetic array, when combined with high-resolution imaging algorithms, can yield accurate sound source identification results. However, when matrix completion algorithms are applied to large synthetic arrays, their computational complexity increases significantly. Furthermore, existing integrations with high-resolution imaging algorithms often encounter difficulties in the presence of coherent sound sources. To address this problem, this paper introduces the accelerated gradient descent algorithm for the covariance matrix fitting by orthogonal least squares. The matrix completion model for non-synchronous measurements is initially simplified through matrix decomposition, thereby enabling the rapid completion of the cross-spectral matrix using the accelerated gradient descent algorithm. This is then followed by the application of the covariance matrix fitting by orthogonal least squares to achieve quick and precise identification of coherent sound sources employing the completed cross-spectral matrix. The performance of the algorithm is evaluated using numerical simulations and validated through loudspeaker experiments in an anechoic chamber. The results from these simulations and experiments reveal that the proposed algorithm not only improves matrix completion performance on large synthetic arrays but also accurately identifies the locations and correlation coefficients of coherent sound sources. [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]

• 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 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]

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]

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]

• 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]