基于BDRM理论的深海声场快速预报研究

深海存在深海声道和双轴声道两种典型环境，WKBZ简正波方法已实现了深海声道中声场的快速准确预报，而对于双轴海洋声道则存在一定的误差。本文在WKBZ本征函数的基础上，推导出了参考界面相位修正的一致表达式，并将浅海声传播的波束位移射线简正波（BDRM）理论应用于计算双轴海洋声道中的声场，进行了数值模拟并与传统简正波方法进行比较，结果表明应用BDRM理论计算的传播损失具有很高的精度和速度。     

Modification to first-order Born approximation for improved prediction of scattered sound from weakly scattering objects

When deriving the Fourier diffraction theorem based on the first-order Born approximation,the difference between wave number of the scattering object and that of the surrounding medium is ignored,causing substantial errors in sound scattering prediction.This paper modifies the Born approximation by taking into account the amplitude and phase changes between the scattering object and the water due to the wave number difference.By changing the radius and center position of the sampling circle in the Fourier domain,accuracy of the predicted sound scattering is improved.With the modified Born approximation,the computed far-field directional pattern of the scattered sound from a circular cylinder is in good agreement with the rigorous solution.Numerical calculations for several objects with different shapes are used to show applicability and effectiveness of the proposed method.     

修正一阶Born近似改进水中弱散射目标的散射声场预报

在推导Fourier衍射定理中运用一阶Born近似时忽略了弱散射体内外的波数差异,使散射声场方向特性的预报产生较大误差,针对这一问题,对一阶Born近似进行修正。考虑散射体内外波数差异引起的幅度和相位误差,通过调整频域采样圆弧半径并移动圆心位置得到了修正的一阶Born近似解。由于更准确地反映了目标与周围水介质的声学性质,有效提高了散射声场的预报精度。根据修正的Born近似计算了弱散射条件下无限长圆柱目标的散射远场指向性,结果与严格解相吻合,对其它形状截面的柱状目标也得到了合理的计算结果。     

混响环境下目标声场稀疏分解多域声场重放方法

对于封闭空间内的声场重放,传统的多点声压匹配方法 (Cov-PM)依据在目标声场测得的声压直接使用最小二乘来计算扬声器权重。然而这种方法要求较多的目标声场采样点以实现足够的精度。对于一类特殊的声场景,也就是目标声场是由少量声源辐射产生时,提出一种对目标声场稀疏分解的方法来进行混响环境下多域声场重放以降低对目标声场采样数量的要求。该文给出基于目标声场等效源稀疏分解多域重放方法(Sparse-ESM)理论推导,通过数值计算以及实验测试两种方式对比所提方法与最小二乘等效源分解方法以及Cov-PM的声场重放性能。数值结果表明,在600 Hz以上的频段,Sparse-ESM方法的重放误差性能提升明显。实验结果也得出了与数值计算相同的结论。同时,还通过数值计算和实验测试两种方法证明了当目标声场声源方向波动时,Sparse-ESM仍然可以保持与其余两类方法相近的声对比度,并且实现较高的亮区重放精度。     

Free-space Fresnel diffraction for the approximation of fractional Fourier transform

Fractional Fourier transformation of an object can be approximated by the object's free-space Fresnel diffraction pattern under some restricted conditions and plane wave illumination according to Hua's method. A better approximation is achieved under least-squared conditions developed in this paper. Simulation results verify that our theoretical development works for any fractional order a compared with the previous approach.     

基于衍射理论的无像散场曲的分析与处理

 基于衍射成像理论,用洛默尔函数得到仅有场曲的像点的光强分布积分式,进而得到像面对高斯面的偏离误差——场曲的解析式,结合模拟实验,探讨了无像散场曲和无像散像点的光强分布,分析它的三维形态图、斯特列尔比、逆滤波场曲校正等,所得结果有利于衍射成像理论与技术的应用。     

Dynamics of Rabi model under second-order Born Oppenheimer approximation

We apply the second-order Born–Oppenheimer(BO)approximation to investigate the dynamics of the Rabi model,which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approximation.By comparing with the numerical results,we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.     

逆向傅里叶衍射定理快速预报水下目标三维声散射指向分布

提出逆向运用傅里叶衍射定理预报水下弱散射目标三维声散射指向分布的快速计算方法。依据目标形状、周围介质的密度和声速构建三维声场图像模型,建立散射远场积分结果与图像频域幅值的关系式,提取频域中半径为水中波数k;的球型表面上的幅值,获得精细化的宽带、全方位散射声压指向特性。数值计算表明:将傅里叶衍射定理逆向运用于解决声学正问题,适用于分层的、不均匀的、非规则及多体弱散射目标散射声场的求解。通过插值提取频域样本获得远场声压的方法,避免了有限元法(3D-FEM)所必须的大规模的网格划分和迭代运算,可以有效地减少计算成本并拓展散射频率响应的带宽。在水池中完成两种具有不同声学参数和形状目标指向性测试实验,得到散射声压指向性幅度函数与理论预报相一致。     

基于快速傅里叶变换的衍射现象的数值仿真

根据夫琅禾费衍射与傅里叶变换的关系,通过构建数值遮光屏,并利用快速傅里叶变换,可以获得夫琅禾费衍射图样的二维仿真及其相对光强的三维分布图．利用Matlab实现了对单缝、圆孔及多缝的衍射现象的仿真．结果显示,该方法思路清晰,结果准确可靠,可作为教学中分析夫琅禾费衍射现象的另一种有效方法．     

基于声线跟踪法对闭空间声场预测的接收球半径计算

接收球半径是采用声线跟踪法进行声场预测的一个重要参数。以前所用到的接收球半径一般是通过经验估计得到的,缺乏详细的理论分析。本文从声波传播机理角度分析了根据声线密度来确定接收球半径的原因,并推导了矩形闭空间中声线密度和接收球半径的计算方法。声线密度可以通过原始声线数目,声场空间体积与形状,边界吸声系数来确定。在一给定闭空间里,声线密度可看作是均匀分布的,所以接收球半径与空间位置无关,可看作是一个常数。但对不同的声场空间来说,由于空间体积、形状和吸声系数的变化,声线密度是不同的,因此接收球半径也会不同。声线密度越大,接收球半径越小;声线密度越小,接收球半径越大。实验表明,所提出的接收球模型能用来较准确地预测闭空间里的声压级和混响时间等声学参数。     

A computational method of evaluating noncompact sound based on vortex sound theory

A numerical investigation is made of the production of sound by turbulence interacting with a noncompact body. The problem is formulated in the frequency domain by extending the theory of vortex sound proposed by Howe. The anomalous "numerical" generation of sound by the sudden termination of Lighthill's stress tensor at the outer boundary of a finite computational domain is avoided by identification of "scattered" sound sources that generate sound principally by interaction with the solid surface. It is argued that the boundary element method is the most efficient means of computing the aeroacoustic Green's function for the problem, because it requires a minimum of CPU time, is not prone to numerical errors such as dispersion and dissipation during propagation, and the radiation condition is easily applied at the outer boundary. The method is applied to the problem of sound generation by high Reynolds number flow past a circular cylinder. The "scattered" sources are shown to be confined to the vicinity of the cylinder surface. At low frequencies the radiation has a dipole-like directivity in agreement with the compact approximation. However, the directivity is quite different at high frequencies, where our noncompact method predicts a more complicated "leaf-like" radiation pattern.     

基于单次傅里叶变换的分段衍射算法

针对单次傅里叶变换算法(S-FFT算法)受到采样定理的约束,衍射面画幅尺寸和有效内容像素数无法灵活控制,很容易出现衍射面画幅尺寸大小与衍射距离不匹配的情况,本文提出了一种分段衍射算法。首先,在采样数、光的波长、初始衍射面大小确定的情况下,利用拆分的衍射距离比控制最终衍射面画幅尺寸。然后,对单次衍射计算结果与分段衍射计算结果进行了图像相似度对比。实验表明,分段衍射算法可在画面强度分布不变的情况下,提高有效像素数目,数据量增加了2~3个数量级。此外,文章分析了造成误差的一个主要原因来自有效数据分辨率提高后,细节分布与低分辨率像素值之间的差别。在图像细节较丰富时,其差别较大。因此这种差别应视为优于直接计算的一种结果。本算法能够获得更加清晰的图像细节,灵活调整衍射面画幅尺寸,使得S-FFT算法在大衍射距离问题计算中能发挥其算法优势。     

一致性绕射理论求解球面反射点的快速方法

射线寻迹是应用一致性几何绕射理论分析电大尺寸目标电磁辐射和散射特性的关键,它的精度和速度对场值求解结果影响很大。根据反射定律,推导得出了球面反射点的参量必须满足的一元四次方程,通过求解方程得到球面反射点。给出了应用此方法得到的部分球面反射点,并给出了球柱模型附近半波振子天线的远场方向图。一致性绕射理论结果与FEKO仿真结果吻合较好。     

一致性绕射理论求解球面反射点的快速方法

射线寻迹是应用一致性几何绕射理论分析电大尺寸目标电磁辐射和散射特性的关键,它的精度和速度对场值求解结果影响很大。根据反射定律,推导得出了球面反射点的参量必须满足的一元四次方程,通过求解方程得到球面反射点。给出了应用此方法得到的部分球面反射点,并给出了球柱模型附近半波振子天线的远场方向图。一致性绕射理论结果与FEKO仿真结果吻合较好。     

Correlation reception of a diffraction sound field in an oceanic waveguide

Intensity matched processing is considered for a diffracted signal when the object is detected by the main lobe of the shadow scattered sound field. The consideration is based on the few-parameter model that adequately describes the characteristics of the desired signal. It is shown that, in the absence of noise and fluctuations in the parameters of the medium, the proposed algorithm provides the determination of the exact parameters of the signal and the moving object.     

非均匀流体介质内部散射声场重建的逐层计算方法*

入射声波激励下非均匀流体介质内部散射声场的重建方法对超声层析成像具有重要意义。以往采用矩量法求解,但该方法全域离散形成的复数满秩矩阵规模随着分辨率与计算精度的提高而急剧增大,对算力具有很高的要求,一定程度上限制了其在实际中的应用。为克服上述缺陷,本文以逐层离散、逐层计算为核心思想,以声散射基本公式与近场声全息理论为基础,推导出逐层计算非均匀流体介质内部散射声场的理论公式并给出对应的几何离散模型。为验证该方法的可行性,以矩量法为参照,对同样的介质模型进行介质内部声场重构仿真。结果表明,逐层算法不仅可以有效地重建非均匀流体介质内部散射声场,且大幅度减小了求解规模。     

基于声场重建的材料吸声系数测量方法

针对现有方法对材料吸声系数进行现场测量时存在低频测量误差大的问题,本文提出了一种利用扬声器线阵列对材料吸声系数进行现场测量的新方法。该方法使用基于能量比值约束的最小二乘法在待测材料表面进行平面波声场重建并结合双传声器传递函数法对材料的吸声系数进行测量。数值仿真表明在100～1600 Hz频率范围内,新方法在未加约束时能够对材料的吸声系数进行准确测量。在半消声室中利用新方法测量了三聚氰胺泡沫的吸声系数,分析了能量比值约束值对测量结果的影响,并和阻抗管以及其它两种现场测量方法的测量结果进行了对比。结果表明该方法能够对吸声材料在160～1600 Hz频段内的吸声系数进行准确测量,并且相较于现存的现场测量方法,新方法具有更低的测量频率下限。     

有限长导管声场预报的一种边界元方法

为了研究介质流动情况下有限长导管中点声源产生的声场,提出了一种以源势密度作为未知数的间接边界元方法。首先将整个求解空间划分为管内和管外两个相互独立的封闭域,然后利用压力和速度在开口处的连续条件和壁面边界条件将内外域的声场方程联立为一个矩阵方程,求解出源势密度后由源势密度计算出任意位置的声场。与Myers的基准数据比较表明本文所得计算结果与之相符。该方法简化了过去声场边界积分方程的形式和数值积分奇性的解决过程,稍加变换便可应用于任意形状导管和复杂声源。     

Numerical calculation of the correlation moments of the sound field scattered by a rough surface

Numerically calculated two-dimensional correlation moments of the surface-scattered sound field are presented in the form of correlation surfaces and analyzed. The models of three-dimensional anisotropic and two-dimensional quasi-harmonic surface waves are considered. Data are presented on the angular dependence of the space-time correlation domains of the scattered sound field for receivers spaced across the propagation path in both horizontal and vertical directions, as well as on the shapes of the time-frequency and space-frequency correlation domains.     

Measuring the optical rotation based on the Fast Fourier Transform

Based on the structure of polarizer–Faraday modulator–analyzer, a method of measuring the optical rotation is proposed by using Fast Fourier Transform to analyze the output signal of optical material. The output signal detected by a photodetector comprises two AC components, which angular frequencies are ω and 2ω, respectively. So, the amplitude ratio of different frequency signals can be obtained by using the Fast Fourier Transform. According to the relationship between the amplitude ratio and optical rotation, the optical rotation of material can be detected. Furthermore, the experiment results show that the correlation coefficient between the measured optical rotation and the sugar solution concentration is found to be 0.99979.