Functional Beamforming Research Articles

Comparison and application of the far-field identification algorithms for multiple sound sources based on microphone array

Based on the conventional beamforming (CBF), some algorithms for far-field sound source identification have been proposed in the past few decades. Typically, the functional beamforming (FBF) and the deconvolution methods, such as CLEAN, CLEAN with source coherence (CLEAN-SC), CLEAN-SC with compressed grids (CLEAN-SC-CG), CLEAN with cross spectral matrix function (CLEAN-CSM), High-resolution CLEAN-SC (HR-CLEAN-SC), are frequently mentioned and their advantages are widely discussed in the previous literatures. To assess their efficacy and suitability in engineering applications, with a focus on spatial resolution, computational efficiency, and dynamic range, a comparative study by locating two types of sound sources is carried out. The first scenario represents the case where the distance between two sound sources is smaller than the Rayleigh limit, while the second scenario represents the situation involving multiple sound sources, such as four or more complex sound sources. The analysis demonstrates that CBF, CLEAN, and CLEAN-SC cannot surpass the Rayleigh limit. However, FBF, CLEAN-SC-CG, CLEAN-CSM, and HR-CLEAN-SC have the potential to overcome it. In FBF, the grid mismatch results in a compromise between its dynamic range and source strength estimation. Meanwhile, HR-CLEAN-SC requires prior knowledge of the number of sound sources, which is challenging in applications. Because of superiority in the fundamental acoustic image and searching strategy, CLEAN-CSM and CLEAN-SC-CG exhibits superior features compared to the others. By compressing the number of grids, the CLEAN-SC-CG can improve the computational efficiency up to at least 46%. By constructing the cross spectral matrix function related to the real source, CLEAN-CSM uses the power function to simultaneously enhance the spatial resolution, dynamic range and source strength estimation. The conclusions are further validated through sound-source identification experiments involving two loudspeakers and an engine. The findings presented in this paper serve to guide the selection of suitable approaches for multi-sound source identification in engineering applications.

Performance analysis of beamforming algorithm based on compressed sensing

The beamforming (BF) algorithm is widely used in sound source recognition due to its superior performance, but its main lobe is wide, side lobes are high, and its running speed is slow. Therefore, a method based on the compressed sensing beamforming method is proposed. The sound source measurement model is established, the compressed sensing reconstruction matrix is applied to the beamforming method, and propose a compressed sensing beamforming sound source recognition method. The sound source recognition performance of orthogonal matching pursuit (OMP), generalized orthogonal matching pursuit (gOMP), and regularized orthogonal matching pursuit (ROMP) is compared and analyzed through MATLAB simulation, and the OMP algorithm is selected to combine with the beamforming method. Further study the OMP-BF way and compare and analyze the recognition accuracy and running time of OMP-BF with functional beamforming (F-BF) and L1 minimum norm method beamforming (L1-BF). The results show that the OMP-BF method can accurately identify the sound source location, and the running time is much lower than L1-BF and F-BF. Finally, through experiments, the effectiveness of the algorithm is verified.

An improved functional beamforming algorithm for far-field multi-sound source localization based on Hilbert curve

In view of the mismatch problem between the sound sources and searching grid points (non-ideal case), an improved functional beamforming (FBF) algorithm based on the Hilbert curve, so-called HFBF, for far-field localization of multi-sound sources is presented in this paper. In contrast with the traditional FBF, the HFBF may generate the searching grids on a sound source plane and optimize them by reducing the searching plane size, adjusting the function order and the focusing vector direction, so as to improve the efficiency of grid searching and the estimation accuracy of sound source parameters. A computational procedure of the HFBF is proposed and applied to identify two independent sound sources. In terms of the locating error and the estimated error of sound pressure level (SPL), the performances of four algorithms are compared by simulations and experiments. The results suggest that the accuracies of the location coordinates and the estimated SPL values are significantly improved by the Hilbert-based grid searching. The conclusions can be drawn that, for multi-source localization, the HFBF can somewhat break through the Rayleigh limit. If the exponent value is selected properly, the estimated SPL error of the HFBF can be less than 0.1 dB. The HFBF has a larger range of available exponent values, which is negatively correlated with the frequency of a sound source. Generally speaking, in the non-ideal cases, the proposed HFBF is more accurate and effective than the FBF. It can be applied to a large-scale space, such as aircraft, train, traffic environment, etc., for far-field localization of multi-sound sources in engineering.

An alternating iterative algorithm for sound source identification based on equivalent source method

Near-field acoustical holography (NAH) based on equivalent source method (ESM) is an efficient technique for sound source identification. Conventional ESM with Tikhonov regularization (TRESM), ESM based on CVX MATLAB toolbox (CVX) and wideband acoustic holography (WBH) are commonly used methods for calculating equivalent source strengths. However, all of them have their respective limitations. To address some of these, an alternating iterative algorithm for sound source identification based on equivalent source method (AIESM) is proposed in this article, which is a combination of alternating direction method and a non-monotone line search technique. The method makes use of sparse regularization under the principle of compressive sensing (CS) to calculate equivalent source strengths. Moreover, inspired by the idea of functional beamforming (FB), AIESM with order n can yield an improved dynamic range when detecting the source location. Numerical simulations are carried out at different frequencies, and the results suggest that the computational efficiency of the proposed method is close to that of TRESM. In addition, AIESM has a better reconstruction accuracy than TRESM and WBH in a relatively wide frequency range. Compared with ESM based on CVX, AIESM is slightly better in reconstruction accuracy and has a higher computational efficiency. Meanwhile, AIESM with order n can provide more accurate source position and better resolution. The validity and practicality of the proposed method are further supported by experimental results.

Assessment of the accuracy of microphone array methods for aeroacoustic measurements

In this paper, the performance of four acoustic imaging methods: conventional frequency domain beamforming (CFDBF), functional beamforming (FUNBF), enhanced high resolution CLEAN–SC (EHR–CLEAN–SC) and generalized inverse beamforming (GIBF), is investigated in terms of accuracy and variability. Three experimental test cases are considered: 1) a single speaker emitting synthetic broadband noise, 2) two speakers emitting incoherent synthetic broadband noise, and 3) trailing–edge noise generated by a tripped NACA 0018 airfoil. All the measurements were performed in the anechoic wind tunnel of Delft University of Technology. Overall, GIBF and EHR–CLEAN–SC offer the most accurate results when point sources (speakers) are present. They even achieve super–resolution by separating sound sources beyond the Rayleigh resolution limit. Repeating the measurements indicates a standard deviation in the results of less than 1 dB. When analyzing distributed sound sources, such as trailing–edge noise, CFDBF and FUNBF provide the best performance. This indicates that the acoustic imaging method needs to be selected based on the expected sound source configuration.

A Compressed Equivalent Source Method Based on Equivalent Redundant Dictionary for Sound Field Reconstruction

The equivalent source method (ESM) based on compressive sensing (CS) requires that the source has a sparse or approximately sparse representation in a suitable basis or dictionary. However, in practical applications, it is not easy to find the appropriate basis or dictionary due to the indeterminate characteristics of the source. To solve this problem, an equivalent redundant dictionary is constructed, which contains two core parts: one is the equivalent dictionary used in the CS-based ESMs under the sparse assumption, and the other one is the orthogonal basis obtained by the singular value decomposition (SVD). On this foundation, a method named compressed ESM based on the equivalent redundant dictionary (ERDCESM) is proposed to enhance the performances of source field reconstruction for different types of sources. Moreover, inspired by the idea of functional beamforming (FB), ERDCESM with order v (ERDCESM- v ) can possess a high dynamic range when detecting the source location. The numerical simulations are carried out at different frequencies to evaluate the performance of the proposed method, and the results suggest that the proposed method performs well both for sparse and even spatially extended sources. The validity and practicality of the proposed method are also verified by the experimental results.

Functional delay and sum beamforming for three-dimensional acoustic source identification with solid spherical arrays

Solid spherical arrays have become particularly attractive tools for doing acoustic sources identification in cabin environments. Spherical harmonics beamforming (SHB) is the popular conventional algorithm. Regrettably, its results suffer from severe sidelobe contaminations and the existing solutions are incapable of removing these contaminations both significantly and efficiently. This paper focuses on conquering these problems by creating a novel functional delay and sum (FDAS) algorithm. First and foremost, a new delay and sum (DAS) algorithm is established, and for which, the point spread function (PSF) is derived, the determination principle of the truncated upper limit of the spherical harmonics degree is explored, and the performance is examined as well as compared with that of SHB. Next, the FDAS algorithm is created by combining DAS and the functional beamforming (FB) approach initially suggested for planar arrays, and its merits are demonstrated. Additionally, performances of DAS and FDAS are probed into under the situation that the source is not at the focus point. Several interesting results have emerged: (1) the truncated upper limit of the spherical harmonics degree, capable of making DAS meet FB׳s requirement, exists and its minimum value depends only on the wave number and the array radius. (2) DAS can accurately locate and quantify the single source and the incoherent or coherent sources, and its comprehensive performance is not inferior to that of SHB. (3) For single source or incoherent sources, FDAS can not only accurately locate and quantify the source, but also significantly and efficiently attenuate sidelobes, effectively detect weak sources and acquire somewhat better spatial resolution. In contrast to that, for coherent sources, FDAS is not available. (4) DAS can invariably quantify the source accurately, irrespectively of the focus distance, whereas FDAS is burdened with a quantification deviation growing with the increase of the exponent parameter, when the focus distance is unequal to the distance from the source to the array center or the focus directions do not embrace the source direction. Fortunately, the deviation can be commendably compensated for by the introduced scale-and-integrate method. This study will be of great significance to the accurate and quick localization and quantification of acoustic sources in cabin environments.

An Improved Algorithm for Noise Source Localization Based on Equivalent Source Method

Near-field acoustical holography (NAH) based on the equivalent source method (ESM) is an efficient method applied for noise source identification. Asl2-norm-based regularization cannot produce a satisfactory solution of the ill-conditioned problem in high frequency, the conventional ESM is restricted to relatively low frequency, and the resolution of conventional ESM in middle to high frequency remains a limitation open to investigation. This article presents an algorithm known as improved functional equivalent source method (IFESM), designed to enhance the resolution of conventional ESM. This method is developed in the framework of wideband acoustical holography (WBH) combining with functional beamforming (FB). Through numerical simulations, it is proved that the proposed method can localize noise with higher resolution compared with WBH and conventional ESM, and the ghosts on noise source map can be suppressed effectively. The validity and the feasibility of the proposed method are manifested by experiments including single-source and coherent-source localization.