Sparsity constrained deconvolution approaches for acoustic source mapping

Using microphone arrays for estimating source locations and strengths has become common practice in aeroacoustic applications. The classical delay-and-sum approach suffers from low resolution and high sidelobes and the resulting beamforming maps are difficult to interpret. The deconvolution approach for the mapping of acoustic sources (DAMAS) deconvolution algorithm recovers the actual source levels from the contaminated delay-and-sum results by defining an inverse problem that can be represented as a linear system of equations. In this paper, the deconvolution problem is carried onto the sparse signal representation area and a sparsity constrained deconvolution approach (SC-DAMAS) is presented for solving the DAMAS inverse problem. A sparsity preserving covariance matrix fitting approach (CMF) is also presented to overcome the drawbacks of the DAMAS inverse problem. The proposed algorithms are convex optimization problems. Our simulations show that CMF and SC-DAMAS outperform DAMAS and as the noise in the measurements increases, CMF works better than both DAMAS and SC-DAMAS. It is observed that the proposed algorithms converge faster than DAMAS. A modification to SC-DAMAS is also provided which makes it significantly faster than DAMAS and CMF. For the correlated source case, the CMF-C algorithm is proposed and compared with DAMAS-C. Improvements in performance are obtained similar to the uncorrelated case.     

Improving the resolution of three-dimensional acoustic imaging with planar phased arrays

This paper examines and compares two methods of improving the quality of three-dimensional beamforming with phased microphone arrays. The intended application is the detection of aerodynamic noise sources on wind turbines. Both methods employ Fourier based deconvolution. The first method involves a transformation of coordinates that tends to make the response to a point source, the point spread function, more shift invariant. The result is a significant improvement in sound source imaging in the transformed coordinate system. However, the inverse transformation to Cartesian coordinates introduces range dependent resolution limitations because of the irregular distribution of the focal points. The second method combines the transformation of coordinates with an alternative scanning technique. This method can be used in near field three-dimensional acoustic imaging to produce maps free of sidelobes and with constant resolution. The robustness of the proposed methods is validated both with computer simulations and experimentally.     

A fast signal subspace approach for the determination of absolute levels from phased microphone array measurements

Phased microphone arrays are used in a variety of applications for the estimation of acoustic source location and spectra. The popular conventional delay-and-sum beamforming methods used with such arrays suffer from inaccurate estimations of absolute source levels and in some cases also from low resolution. Deconvolution approaches such as DAMAS have better performance, but require high computational effort. A fast beamforming method is proposed that can be used in conjunction with a phased microphone array in applications with focus on the correct quantitative estimation of acoustic source spectra. This method bases on an eigenvalue decomposition of the cross spectral matrix of microphone signals and uses the eigenvalues from the signal subspace to estimate absolute source levels. The theoretical basis of the method is discussed together with an assessment of the quality of the estimation. Experimental tests using a loudspeaker setup and an airfoil trailing edge noise setup in an aeroacoustic wind tunnel show that the proposed method is robust and leads to reliable quantitative results.     

A covariance fitting approach for correlated acoustic source mapping

Microphone arrays are commonly used for noise source localization and power estimation in aeroacoustic measurements. The delay-and-sum (DAS) beamformer, which is the most widely used beamforming algorithm in practice, suffers from low resolution and high sidelobe level problems. Therefore, deconvolution approaches, such as the deconvolution approach for the mapping of acoustic sources (DAMAS), are often used for extracting the actual source powers from the contaminated DAS results. However, most deconvolution approaches assume that the sources are uncorrelated. Although deconvolution algorithms that can deal with correlated sources, such as DAMAS for correlated sources, do exist, these algorithms are computationally impractical even for small scanning grid sizes. This paper presents a covariance fitting approach for the mapping of acoustic correlated sources (MACS), which can work with uncorrelated, partially correlated or even coherent sources with a reasonably low computational complexity. MACS minimizes a quadratic cost function in a cyclic manner by making use of convex optimization and sparsity, and is guaranteed to converge at least locally. Simulations and experimental data acquired at the University of Florida Aeroacoustic Flow Facility with a 63-element logarithmic spiral microphone array in the absence of flow are used to demonstrate the performance of MACS.     

Obtaining absolute acoustic spectra in an aerodynamic wind tunnel

Cost effective methods for identifying and reducing sources of noise have become essential in the design of many modern transport vehicles. Whilst closed-section wind tunnels can readily evaluate aerodynamic performance, obtaining accurate acoustic spectra is often a major challenge because of the poor signal to noise ratios available. In this paper, methods of obtaining absolute spectra from the non-acoustically treated Markham wind tunnel at the University of Cambridge are discussed. Initial measurements with a small monopole source compare well with simulations and show that it is possible to obtain similar spectra from two nested acoustic arrays. However, a series of further experiments with simplified landing gear models show very different spectra from each array. By comparing measurements with simulations, it is shown that negative side lobes affect beamforming source maps. Measurements of an ‘empty tunnel’ cross spectral matrix allow the removal of sidelobes, providing much greater consistency between spectra. Finally, a dipole beamforming vector is used to account for the directivity of the landing gear noise, leading to good agreement between absolute spectra from the differently sized arrays. This analysis demonstrates that data from a phased array in a hard-walled, aerodynamic wind tunnel can provide meaningful acoustic spectra from low-noise models.     

Spectral estimation method for noisy data using a noise reference

The development of array processing methods to extract the useful characteristics of acoustic sources such as their locations and absolute levels, starting from the measured sound field is one of the main issues in aero-acoustics. The conventional beamforming method is a very popular technique investigated to solve the power level estimation problem. It has the advantage of being robust, easy to implement and cheap in computation time. However, this technique is also known for having poor spatial resolution capabilities which prevents the correct source levels being obtained for numerous practical applications. Deconvolution techniques of the result computed with CBF, with the point spread function of the array manifold, may restore the power levels of the acoustic sources that would be observed in the absence of the array resolution effects. However, the accuracy of the results provided by deconvolution methods is very sensitive to background noise, always present in acoustic measurements. This process should be carried out after the additive noise has been suitably attenuated and, ideally, the deconvolution operator should amplify the noise as little as possible. Another approach is described in the article. It consists in using a noise reference and a new technique called spectral estimation method with additive noise to remove both the smearing effect produced by the array response and the background noise. The technique has been applied to computer and experimental simulations conducted both in an anechoic chamber and in the test section of an open wind tunnel involving acoustic sources radiating in a noisy environment. The levels of the sources were found with a good level of accuracy and the background noise greatly reduced, confirming the validity of the approach and the satisfactory performance of the method proposed.     

Observer-based beamforming algorithm for acoustic array signal processing

In the field of noise identification with microphone arrays, conventional delay-and-sum (DAS) beamforming is the most popular signal processing technique. However, acoustic imaging results that are generated by DAS beamforming are easily influenced by background noise, particularly for in situ wind tunnel tests. Even when arithmetic averaging is used to statistically remove the interference from the background noise, the results are far from perfect because the interference from the coherent background noise is still present. In addition, DAS beamforming based on arithmetic averaging fails to deliver real-time computational capability. An observer-based approach is introduced in this paper. This so-called observer-based beamforming method has a recursive form similar to the state observer in classical control theory, thus holds a real-time computational capability. In addition, coherent background noise can be gradually rejected in iterations. Theoretical derivations of the observer-based beamforming algorithm are carefully developed in this paper. Two numerical simulations demonstrate the good coherent background noise rejection and real-time computational capability of the observer-based beamforming, which therefore can be regarded as an attractive algorithm for acoustic array signal processing.     

Fast implementation of sparse iterative covariance-based estimation for source localization

Fast implementations of the sparse iterative covariance-based estimation (SPICE) algorithm are presented for source localization with a uniform linear array (ULA). SPICE is a robust, user parameter-free, high-resolution, iterative, and globally convergent estimation algorithm for array processing. SPICE offers superior resolution and lower sidelobe levels for source localization compared to the conventional delay-and-sum beamforming method; however, a traditional SPICE implementation has a higher computational complexity (which is exacerbated in higher dimensional data). It is shown that the computational complexity of the SPICE algorithm can be mitigated by exploiting the Toeplitz structure of the array output covariance matrix using Gohberg-Semencul factorization. The SPICE algorithm is also extended to the acoustic vector-sensor ULA scenario with a specific nonuniform white noise assumption, and the fast implementation is developed based on the block Toeplitz properties of the array output covariance matrix. Finally, numerical simulations illustrate the computational gains of the proposed methods.     

二维解卷积波束形成水下高分辨三维声成像

针对水下三维成像的空间分辨率难以提高,且具有较高旁瓣级的问题,提出了一种二维解卷积波束形成高分辨三维声成像算法,该算法首先完成任意距离切片的平面阵波束形成,近场情况下采用菲涅尔近似实现近场平面阵波束形成,然后通过二维解卷积技术对任意距离切片的二维波束形成结果进行解卷积处理,去除阵列指向性函数的影响,改善波束响应非理想冲击函数所造成波束形成主瓣宽及旁瓣级高的问题。通过计算机仿真分析,新算法可以有效的提高水下三维成像的空间分辨率,抑制旁瓣级,并能够在较宽频带和不同阵列孔径内保持与常规波束形成相当的稳定性。通过试验研究,新方法比常规波束形成实际目标成像分辨率提高一倍,最高旁瓣级下降20 dB,验证了该算法在实际系统中的有效性.      

Adaptive beamforming for array signal processing in aeroacoustic measurements

Phased microphone arrays have become an important tool in the localization of noise sources for aeroacoustic applications. In most practical aerospace cases the conventional beamforming algorithm of the delay-and-sum type has been adopted. Conventional beamforming cannot take advantage of knowledge of the noise field, and thus has poorer resolution in the presence of noise and interference. Adaptive beamforming has been used for more than three decades to address these issues and has already achieved various degrees of success in areas of communication and sonar. In this work an adaptive beamforming algorithm designed specifically for aeroacoustic applications is discussed and applied to practical experimental data. It shows that the adaptive beamforming method could save significant amounts of post-processing time for a deconvolution method. For example, the adaptive beamforming method is able to reduce the DAMAS computation time by at least 60% for the practical case considered in this work. Therefore, adaptive beamforming can be considered as a promising signal processing method for aeroacoustic measurements.     

A robust super-resolution approach with sparsity constraint in acoustic imaging

Acoustic imaging is a standard technique for mapping acoustic source powers and positions from limited observations on microphone sensors, which often causes an ill-conditioned inverse problem. In this article, we firstly improve the forward model of acoustic power propagation by considering background noises at the sensor array, and the propagation uncertainty caused by wind tunnel effects. We then propose a robust super-resolution approach via sparsity constraint for acoustic imaging in strong background noises. The sparsity parameter is adaptively derived from the sparse distribution of source powers. The proposed approach can jointly reconstruct source powers and positions, as well as the background noise power. Our approach is compared with the conventional beamforming, deconvolution and sparse regularization methods by simulated, wind tunnel data and hybrid data respectively. It is feasible to apply the proposed approach for effectively mapping monopole sources in wind tunnel tests.     

High-resolution deconvolved beamforming for three-dimensional imaging sonars

Three-dimensional(3D) imaging sonars based on the conventional beamforming(CBF) suffers from relatively wide main-lobes and high sidelobe level.To improve the spatial resolution of 3D imaging sonars,a deconvolved beamforming method is proposed with the iterative Richardson-Lucy algorithm in this paper.At first,each distance slice can be processed to obtain images by the CBF.For the near field,the Fresnel approximation is used.Then,the deconvolution technique is applied to the CBF outputs to obtain high-resolution images and suppress the sidelobe level.The simulations demonstrate that the proposed algorithm is able to improve the spatial resolution significantly and suppress the sidelobes for 3D imaging sonars.Meanwhile,the algorithm shows similar robustness with the CBF in the case of wideband and sparse array.The priority of the proposed algorithm is also validated by the tank experiment data.The presented results indicate that the spatial resolution is increased by one time and the average sidelobe level is reduced by 20 dB.     

Wideband RELAX and wideband CLEAN for aeroacoustic imaging

Microphone arrays can be used for acoustic source localization and characterization in wind tunnel testing. In this paper, the wideband RELAX (WB-RELAX) and the wideband CLEAN (WB-CLEAN) algorithms are presented for aeroacoustic imaging using an acoustic array. WB-RELAX is a parametric approach that can be used efficiently for point source imaging without the sidelobe problems suffered by the delay-and-sum beamforming approaches. WB-CLEAN does not have sidelobe problems either, but it behaves more like a nonparametric approach and can be used for both point source and distributed source imaging. Moreover, neither of the algorithms suffers from the severe performance degradations encountered by the adaptive beamforming methods when the number of snapshots is small and/or the sources are highly correlated or coherent with each other. A two-step optimization procedure is used to implement the WB-RELAX and WB-CLEAN algorithms efficiently. The performance of WB-RELAX and WB-CLEAN is demonstrated by applying them to measured data obtained at the NASA Langley Quiet Flow Facility using a small aperture directional array (SADA). Somewhat surprisingly, using these approaches, not only were the parameters of the dominant source accurately determined, but a highly correlated multipath of the dominant source was also discovered.     

Turbulence and heat excited noise sources in single and coaxial jets

The generation of noise in subsonic high Reynolds number single and coaxial turbulent jets is analyzed by a hybrid method. The computational approach is based on large-eddy simulations (LES) and solutions of the acoustic perturbation equations (APE). The method is used to investigate the acoustic fields of one isothermal single stream jet at a Mach number 0.9 and a Reynolds number 400,000 based on the nozzle diameter and two coaxial jets whose Mach number and Reynolds number based on the secondary jet match the values of the single jet. One coaxial jet configuration possesses a cold primary flow, whereas the other configuration has a hot primary jet. Thus, the configurations allow in a first step the analysis of the relationship of the flow and acoustic fields of a single and a cold coaxial jet and in a second step the investigation of the differences of the fluid mechanics and aeroacoustics of cold and hot coaxial jets. For the isothermal single jet the present hybrid acoustic computation shows convincing agreement with the direct acoustic simulation based on large-eddy simulations. The analysis of the acoustic field of the coaxial jets focuses on two noise sources, the Lamb vector fluctuations and the entropy sources of the APE equations. The power spectral density (PSD) distributions evidence the Lamb vector fluctuations to represent the major acoustic sources of the isothermal jet. Especially the typical downstream and sideline acoustic generations occur on a cone-like surface being wrapped around the end of the potential core. Furthermore, when the coaxial jet possesses a hot primary jet, the acoustic core being characterized by the entropy source terms increases the low frequency acoustics by up to 5 dB, i.e., the sideline acoustics is enhanced by the pronounced temperature gradient.     

Inverse problem with beamforming regularization matrix applied to sound source localization in closed wind-tunnel using microphone array

Microphone arrays have become a standard technique to localize and quantify source in aeroacoustics. The simplest approach is the beamforming that provides noise source maps with large main lobe and strong side lobes at low frequency. Since a decade, the focus is set on deconvolution techniques such as DAMAS or Clean-SC. While the source map is clearly improved, these methods require a large computation time. In this paper, we propose a sound source localization technique based on an inverse problem with beamforming regularization matrix called Hybrid Method. With synthetic data, we show that the side lobes are removed and the main lobe is narrower. Moreover, if the sound noise source map provided by this method is used as input in the DAMAS process, the number of DAMAS iterations is highly reduced. The Hybrid Method is applied to experimental data obtained in a closed wind-tunnel. In both cases of acoustic or aeroacoustic data, the source is correctly detected. The proposed Hybrid Method is found simple to implement and the computation time is low if the number of scan points is reasonable.     

逆波束形成的旁瓣抑制

为了降低普通逆波束形成旁瓣,提出了一种新的旁瓣抵消技术。该技术利用指向性函数中的旁瓣部分去估计声场的响应,然后从基阵估计的声场减去这部分指向性函数旁瓣估计的声场,从而得到最终的声场估计。由于较多的旁瓣响应被估计的声场扣除,最终估计的声场中的旁瓣大大降低。利用该技术可有效地抑制干扰,同时又可保持普通逆波束形成的方位高分辨力。湖试结果显示了该技术的有效性和可行性。     

Acoustic imaging of objects buried in soil

In this study, we demonstrate an acoustic system for high-resolution imaging of objects buried in soil. Our goal is to image cultural artifacts in order to assess in a rapid manner the historical significance of a potential construction site. We describe the imaging system and present preliminary images produced from data collected from a soil phantom. A mathematical model and associated computer software are developed in order to simulate the signals acquired by the system. We have built the imaging system, which incorporates a single element source transducer and a receiver array. The source and receiver array are moved together along a linear path to collect data. Using this system, we have obtained B-mode images of several targets by using delay-and-sum beamforming, and we have also applied synthetic aperture theory to this problem.     

用于心脏电活动成像的空间滤波器输出噪声抑制方法

利用人体表面测量的心脏磁场数据无创成像心脏电活动,需要解决的关键问题是提高其重建分布电流源偶极矩强度的分辨率.本文在最小方差波束成形(MVB)方法的基础上,提出了一种可抑制空间滤波器输出噪声功率增益(SONG)的波束成形方法,目的是通过构造一种新的滤波器权矩阵,约束空间滤波器的输出噪声功率增益,提高重建分布电流源偶极矩强度的分辨率,即分布电流源空间谱估计的源分辨能力,从而增强心脏电活动磁成像的分辨率.文中给出了电流源重建的理论分析和仿真结果;比较了该方法与MVB方法的差别;并给出了两个健康人36通道心脏磁场数据的电活动成像.结果表明,SONG方法分辨电流源的能力较强,能够观察到心脏电磁场信号R峰时刻健康人的心室电活动较强,心房电活动较弱等特征.     

Spectral shaping to improve the point spread function in optical coherence tomography

We demonstrate inhibition of the sidelobes of the axial point spread function in optical coherence tomography by shaping the power spectrum of the light source with a remaining power of 4.54 mW. A broadband amplified spontaneous emission source radiating at 1565 +/- 40 nm is employed in a free-space optical coherence tomography system. The axial point spread functions before and after optical spectral shaping are presented. Results show that spectral shaping of the source can inhibit sidelobes of the point spread function up to 12.9 dB, with an associated small increase of 2.2 dB in noise floor in the far field. The effect of spectral shaping on axial resolution is demonstrated according to three metrics. Image quality improvement is also illustrated with optical coherence tomography images of an onion before and after spectral shaping.     

Identifying turbulent jet sound sources

Theoretical models of the formation of the acoustic field of a nonisothermal turbulent flow are analyzed. The paper presents possible methods of constructing solutions to the convective wave equation for a shear parallel nonisothermal turbulent flow. A simplified mathematical model of noise sources in the field of a nonisothermal shear turbulent flow is considered, based on real physical notions on the processes occurring in the jet mixing range, making it possible to approximately estimate the spectral noise characteristics.