Spatial correlation and coherence in reverberant acoustic fields: Extension to microphones with arbitrary first-order directivity

Spatial correlation and coherence functions in reverberant sound fields are relevant to the acoustics of enclosed spaces and related areas. Theoretical expressions for the spatial correlation and coherence functions between signals representing the pressure and/or the components of the particle velocity vector in a reverberant sound field are established in the literature and most of these have also been corroborated with measurements [F. Jacobsen, J. Acoust. Soc. Am. 108, 204-210 (2000)]. In the present paper, these expressions are generalized to microphones of first-order directivity, whereby the directivity can be expressed in terms of pressure and pressure gradient. It is shown that the resulting spatial correlation and coherence functions can be expressed in terms of the established spatial correlation and coherence functions. The derived theoretical expression for the spatial coherence function is validated with a modeled diffuse sound field. Further, it is compared with the experimental coherence obtained from the reverberant tails of room impulse responses measured with two common surround sound microphone setups in a concert and a lecture hall.     

A model for the spatial coherence of arbitrarily directive noise in the depth-stratified ocean

Though referred to as noise, the ambient ocean soundscape carries valuable information about the physical ocean environment. To study this information, Kuperman and Ingenito introduced a model for spatial coherence in a depth stratified ocean arising from the vertically directive diffuse acoustic noise produced by bubbles distributed throughout the surface. Here the model is adapted to incorporate horizontal directivity as well, making it possible to include additional noise contributions from directive features such as storms, biologics, shipping, and wave breaking. As an analytic approach, the model can serve as a computationally light complement to existing methods.     

Array gain for a conformal acoustic vector sensor array:An experimental study

An acoustic vector sensor can measure the components of particle velocity and the acoustic pressure at the same point simultaneously, which provides a larger array gain against the ambient noise and a higher angular resolution than the omnidirectional pressure sensor. This paper presents an experimental study of array gain for a conformal acoustic vector sensor array in a practical environment. First, the manifold vector is calculated using the real measured data so that the effects of array mismatches can be minimized. Second, an optimal beamformer with a specific spatial response on the basis of the stable directivity of the ambient noise is designed, which can effectively suppress the ambient noise.Experimental results show that this beamformer for the conformal acoustic vector sensor array provides good signal-tonoise ratio enhancement and is more advantageous than the delay-and-sum and minimum variance distortionless response beamformers.     

利用矢量海洋环境噪声提取声场格林函数

考虑到矢量水听器在垂直方向上具有8字形指向性,能够有效抑制远方非平稳噪声源的干扰,提出了一种矢量环境噪声相关函数(NCF)提取声场时域格林函数(TDGF)的方法。基于简正波理论建立了声压和垂直振速垂直相关性模型。在此基础上,给出了声压和垂直振速相关函数提取声场纵向格林函数的过程.数值仿真对比和实验数据分析表明,相对于声压提取方法,垂直振速提取方法能够有效消除直达波前出现的亮纹与亮区干扰。此外,对于同等时间长度噪声序列,声压提取方法只提取到直达波路径,而垂直振速提取方法还提取到了我们更为关心的海底反射路径。利用直达波与海底反射波到达时延差估计的海深与实测海深吻合较好。      

Imaging of directional distributed noise sources

This study relates to the acoustic imaging of noise sources that are distributed and strongly directional, such as in turbulent jets. The goal is to generate high-resolution noise source maps with self-consistency, i.e., their integration over the extent of the noise source region gives the far-field pressure auto-spectrum for a particular emission direction. Self-consistency is possible by including a directivity factor in the formulation of the source cross-spectral density. The resulting source distribution is based on the complex coherence, rather than the cross-spectrum, of the measured acoustic field. For jet noise, whose spectral nature changes with emission angle, it is necessary to conduct the measurements with a narrow-aperture array. Three coherence-based imaging methods were applied to a Mach 0.9 turbulent jet: delay-and-sum beamforming; deconvolution of the beamformer output; and direct spectral estimation that relies on minimizing the difference between the measured and modeled coherences of the acoustic field. The delay-and-sum beamforming generates noise source maps with strong spatial distortions and sidelobes. Deconvolution leads to a five-fold improvement in spatial resolution and significantly reduces the intensity of the sidelobes. The direct spectral estimation produces maps very similar to those obtained by deconvolution. The coherence-based noise source maps, obtained by deconvolution or direct spectral estimation, are similar at small and large observation angles relative to the jet axis.     

Stream ambient noise, spectrum and propagation of sounds in the goby Padogobius martensii: sound pressure and particle velocity

The most sensitive hearing and peak frequencies of courtship calls of the stream goby, Padogobius martensii, fall within a quiet window at around 100 Hz in the ambient noise spectrum. Acoustic pressure was previously measured although Padogobius likely responds to particle motion. In this study a combination pressure (p) and particle velocity (u) detector was utilized to describe ambient noise of the habitat, the characteristics of the goby's sounds and their attenuation with distance. The ambient noise (AN) spectrum is generally similar for p and u (including the quiet window at noisy locations), although the energy distribution of u spectrum is shifted up by 50-100 Hz. The energy distribution of the goby's sounds is similar for p and u spectra of the Tonal sound, whereas the pulse-train sound exhibits larger p-u differences. Transmission loss was high for sound p and u: energy decays 6-10 dB10 cm, and sound pu ratio does not change with distance from the source in the nearfield. The measurement of particle velocity of stream AN and P. martensii sounds indicates that this species is well adapted to communicate acoustically in a complex noisy shallow-water environment.     

一种矢量水听器基阵模拟器的设计

矢量水听器的每个阵元同时测量声场中声矢量和质点振速的3个分量,相对于声压水听器阵来说,矢量阵获取声场中更多的信息。利用矢量阵所获得速度场的信息可以去除目标方位估计中的 180°模糊。模拟器可以模拟实际海洋环境中目标的辐射特性和噪声特性,应用模拟器可以有效地缩短声纳的研制周期。本文提出一种矢量水听器基阵模拟器的设计方案,该方案解决了矢量阵中宽带信号的90°移相问题、时延精确控制问题和宽带噪声的谱状控制问题。     

噪声源非均匀分布海洋环境噪声水平声能流理论分析

研究水平非均匀分布噪声源所产生的各向异性海洋环境噪声场声能流。提出一种混合型非均匀分布噪声源模型,理论分析并数值计算了此模型情况下的环境噪声场水平声能流。结果表明:非均匀分布噪声源引起的海洋环境噪声场具有显著非零平均水平声能流;不同接收点的水平声能流明显不同;其幅度和方向取决于各个局部海域不等强度声源产生的合成噪声声能流矢量和。研究了两接收点间噪声的声压和振速水平分量、振速水平分量归一化相关系数随两接收点间距的关系,各量之间表现出较强相关性,为分析水下矢量声场目标探测技术性能提供理论依据。      

快速随机粒子网格法的气动噪声预测方法

耦合随机湍流速度生成模型与线化欧拉方程技术,形成了一套具备模拟噪声在非均匀流场中传播能力的气动噪声混合预测方法。该混合方法的随机湍流速度生成模型采用了快速随机粒子网格法,为声传播模拟提供了可靠的源项。而噪声的传播计算选用线化欧拉方程,其空间离散采用9点5阶的色散保持关系格式,时间推进选用了高精度大时间步长的6级4阶龙格库塔格式,远场边界应用了无分裂形式的理想匹配层边界条件。首先,选用高斯脉冲传播算例对线化欧拉方程的时空离散格式、远场无反射边界条件进行了验证分析。然后,计算分析各向同性湍流的空间相关性验证湍流速度生成模型的可靠性。最后,基于已搭建的气动噪声混合预测方法进行了30P30N三段翼缝翼噪声的计算分析。计算分析可知:监测点处功率谱密度曲线、噪声指向性等计算结果与参考文献结果取得了较好的一致性。数值计算结果表明所建立的气动噪声混合预测方法能有效预测二维复杂构型的气动噪声问题。      

Passive acoustic tomography of the ocean using arrays of unknown shape

It was recently established that ocean acoustic tomography based on an inversion of ray travel times can be implemented without use of any dedicated sound sources by cross-correlating the ambient noise recorded on two line arrays, the shapes of which are known. In contrast to active tomography, the amount of useful information from noise interferometry is proportional to the product of the numbers of receivers in the two arrays. In our study based on the 2D and 3D numerical experiments, we examine a hypothesis concerning the feasibility of simultaneous performance of a passive ray tomography and passive positioning of arrays through cross-correlation of ambient or shipping noise. The numerical experiments are conducted under conditions close to those of a field experiment on passive ocean tomography. It is demonstrated that, when using arrays of 20–40 hydrophones, the sound velocity profile and the array shape can be found from noise correlation to an accuracy adequate for oceanological and acoustic applications.     

Highly directional acoustic receivers

The theoretical directivity of a single combined acoustic receiver, a device that can measure many quantities of an acoustic field at a collocated point, is presented here. The formulation is developed using a Taylor series expansion of acoustic pressure about the origin of a Cartesian coordinate system. For example, the quantities measured by a second-order combined receiver, denoted a dyadic sensor, are acoustic pressure, the three orthogonal components of acoustic particle velocity, and the nine spatial gradients of the velocity vector. The power series expansion, which can be of any order, is cast into an expression that defines the directivity of a single receiving element. It is shown that a single highly directional dyadic sensor can have a directivity index of up to 9.5 dB. However, there is a price to pay with highly directive sensors; these sensors can be significantly more sensitive to nonacoustic noise sources.     

岛礁海域海洋环境噪声垂直分布和垂直指向性

依据岛礁海域复杂海底地形、海试期间航船分布和实测风速数据,应用射线声传播理论,建立岛礁海域海洋环境噪声三维模型。在海试岛礁海域深海声道条件下,采用射线3D算法,仿真计算了32元垂直测量阵所处265~885 m负声速梯度深度范围内1 kHz风关和50 Hz远处航船海洋环境噪声级垂直分布,以及50 Hz航船海洋环境噪声垂直指向性,并与实测分析进行比较。结果表明,仿真结果与海试实测数据一致性良好。在本例海底起伏、接收点周边存在众多岛礁和海底山的三维环境中,1 kHz风关海洋环境噪声级随深度分布较近于均匀;西南方向较远处航道区海域海底较平坦,航道区至接收阵为缓斜坡海底,50 Hz远处航船海洋环境噪声级随深度有所增加,其噪声垂直指向性无明显水平凹槽。文中建立的岛礁海域海洋环境噪声三维模型,可较好地表征本例岛礁复杂地形海底起伏海域的风关和航船海洋环境噪声级的垂直分布、及航船环境噪声的垂直指向性,实测和仿真的岛礁海域海洋环境噪声相关数据,可供实际应用及相关研究参考。      

Mapping of the ocean surface wind by ocean acoustic interferometers

Measurements of marine surface winds are crucial to understanding mechanical and thermodynamic forces on the ocean. Satellite measurements of surface winds provide global coverage but are problematic at high wind speeds. Acoustic techniques of wind speed retrieval, and even for tracking hurricanes, have been suggested as an alternative since wind is a strong source of ambient noise in the ocean. Such approaches involve near-local measurements with bottom-mounted hydrophones located close to the area of interest. This paper suggests a complementary approach: measuring directivity of low-frequency ambient noise in the horizontal plane. These measurements would employ long vertical line arrays (VLAs) spanning a significant portion of the ocean waveguide. Two VLAs separated by a distance of some tens of kilometers and coherently measuring acoustic pressure form a single ocean interferometer. By sampling the area of interest from different perspectives with at least two interferometers, marine surface winds might be mapped over horizontal scales of the order of 1000 km with about 10 km resolution (more specifically, the 10 km resolution here means that contribution from the basis functions representing surface wind field with the scale of spatial variations of the order of 10 km can be resolved; independent retrieval of the wind within 10(4) cells of a corresponding grid is hardly possible). An averaging time required to overcome statistical variability in the noise field is estimated to be about 3 h. Numerical simulations of propagation conditions typical for the North Atlantic Ocean are presented.     

射线理论下的浅海环境噪声场空间相干性分析及海底声学参数反演

基于射线理论,以简化海底模型为基础,获得了浅海噪声场空间相干性在频域上的表示方法,并用于海底声学参数反演。将风关海洋噪声看作分布在无限大平面上的点源,通过计算噪声场垂直方向上的能量分布,进一步获得空间两点噪声场频域相干性表达式。利用数值仿真验证了模型对于不同海底类型的敏感性。并结合噪声场空间两点的频域相干性海上实验数据,反演得到该处海域的底质类型,进一步获得海底声速、密度和声衰减系数。结果表明,反演得到的海底参数与实际情况符合较好,文中提出采用的这种计算方法能够有效的反映海底反射对于噪声场空间相干性的影响,并且可在一定程度上提高反演海底声学参数效率。      

Fast prediction of aerodynamic noise induced by the flow around a cylinder based on deep neural network

Accurate and fast prediction of aerodynamic noise has always been a research hotspot in fluid mechanics and aeroacoustics. The conventional prediction methods based on numerical simulation often demand huge computational resources, which are difficult to balance between accuracy and efficiency. Here, we present a data-driven deep neural network (DNN) method to realize fast aerodynamic noise prediction while maintaining accuracy. The proposed deep learning method can predict the spatial distributions of aerodynamic noise information under different working conditions. Based on the large eddy simulation turbulence model and the Ffowcs Williams-Hawkings acoustic analogy theory, a dataset composed of 1216 samples is established. With reference to the deep learning method, a DNN framework is proposed to map the relationship between spatial coordinates, inlet velocity and overall sound pressure level. The root-mean-square-errors of prediction are below 0.82 dB in the test dataset, and the directivity of aerodynamic noise predicted by the DNN framework are basically consistent with the numerical simulation. This work paves a novel way for fast prediction of aerodynamic noise with high accuracy and has application potential in acoustic field prediction.     

Spatial coherence and cross correlation of three-dimensional ambient noise fields in the ocean

Ambient acoustic noise fields in the ocean are generally three dimensional in that they exhibit vertical and horizontal directivity. A model of spatially homogeneous noise is introduced in which the directionality is treated as separable, that is, the overall directionality of the field is the product of the individual directivities in the horizontal and vertical. A uni-modal von Mises circular distribution from directional statistics is taken to represent the noise in the horizontal, whilst the vertical component is consistent with a surface distribution of vertical dipoles. An analysis of the coherence and cross correlation of the noise at two horizontally aligned sensors is developed. The coherence function involves a single integral over finite limits, whilst the cross-correlation function, derived on the assumption that the noise has been pre-whitened, is given by an integral with limits that depend on the correlation delay time. Although the cross-correlation function does not exhibit delta functions that could be identified with the Green's function for propagation between the two sensors in the field, it does drop abruptly to zero at numerical time delays equal to the travel time between the sensors. Hence the noise could be used to recover the sound speed in the medium.     

The effect of ocean wave on the vertical spatial correlation of ocean ambient noise

The effect of the correlation function of noise sources derived from the ocean wave spectrum on the vertical spatial correlation of ocean ambient noise is investigated. The spatial correlation models of ocean ambient noise usually assume that the surface noise sources are uncorrelated. This assumption can be used to explain some physical phenomena, but it is not consistent with the real situation. Considering the relation between the ocean wave motion and the ambient noise generated by wind, the spectrum of ocean wave is introduced to calculate the vertical correlation of ocean ambient noise as the correlation function of noise sources by using the Kuperman-Ingenito(K/I) noise model. The comparison of the simulations and the experimental data shows that the simulations of vertical correlation of ambient noise have some differences with the experimental data by assuming the noise sources are uncorrelated and the simulations of vertical correlation of ambient noise have a good agreement with the experimental data by using the correlation function of noise sources derived from the ocean wave spectrum under the situation of high wind speed.     

海面波浪对海洋环境噪声垂直空间相关性的影响

研究了由海浪谱导得的噪声源的相关函数对海洋环境噪声垂直空间相关性的影响。常用的海洋环境噪声空间相关性模型一般假设海面噪声源是非相关的,这种假设可以解释一些物理现象,但是与真实情况并不符合。考虑到风成噪声与海浪运动的相关性,引入海浪谱,得到噪声源的相关函数,利用Kuperman-Ingenito (K/I)噪声模型,计算海洋环境噪声的垂直相关性。通过仿真结果与实验数据对比可以看出,在高风速下,假设噪声源不相关时计算得到的噪声场垂直相关性与实验结果相差较大,而利用由海浪谱导得的噪声源的相关函数计算得到的噪声场的垂直相关性与实验结果符合较好。      

The effects of the ocean surface wave spectrum on low frequency ambient noise in deep water

An ocean surface wave spectrum which is used for low frequency ambient noise in deep water is proposed. It explains the mechanism of low frequency ambient noise from the theoretical relation between the spectrum of sound pressure and wave. Combining the surface wave spectrum and local wind speed in deep water, a theoretical expression of low frequency ambient noise is obtained with wave generated noise theory. Simulation results show that the wave spectrum is crucial to the intensity and the spectral slope of radiated noise spectrum,and the theoretical noise spectrum could be used to predict the ambient noise in deep water.The predicting results axe verified through the experimental data recorded by an ocean bottom seismometer that was deployed on the floor of deep water in April 2016. It is observed that the statistical noise levels from the experimental data for frequencies from 1 Hz to 100 Hz are larger than 70 dB, and the low frequency ambient noise spectrum follows the shape of inverted"N",the valley of noise spectrum is at 3-4 Hz, and the noise intensity is 70 dB. The peak of noise spectrum is at 50 Hz, and the noise intensity is 92 dB. The correlation coefficient is 0.95 between the model spectrum and measured data.     

深远海线性内波条件下声场时间相关性的空间分布

深海声场特定的干涉结构导致其时间相关性的空间起伏,研究这种空间特性可以为水声信号的探测与处理提供重要参考。利用抛物方程声场仿真模型,联合Monte-Carlo数值方法计算分析了深远海线性内波条件下声场时间相关性的空间分布特性。与现有的研究相比,给出了时间相关性的距离和深度起伏特征。结果表明,当接收达到一定距离,声场时间相关性的空间分布具有与声场干涉条纹类似的结构,声场干涉越强,时间相关性越好。此外,声源频率和声速标准差的变化会引起时间相关性空间分布规律的改变,且会聚区传播模式下的改变强于深海声道传播模式。