英汉双语.docx

1、英汉双语原文第2820页Optimized vector sound intensity measurements with a tetrahedral arrangement of microphones in a spherical shell利用在球面内切正四面体顶点布置传声器的方法优化声强的测量技术Thomas Sondergaard and Morten Wille托马斯桑德迦，莫滕威尔G.R.A.S. Sound and Vibration, Skovlytoften 33, 2840 Holte, Denmark丹麦，霍尔特市，斯扣维特分，G.R.A.S. 声音与振动公司Rece

2、ived 7 November 2014; revised 14 July 2015; accepted 6 October 2015; published online 5 November 20152014年11月7日收到论文；2015年7月14日修订完成；2015年10月6日接受此论文；2015年11月在线发表。AbstractRecent times have seen the introduction of small spherical arrays whose usefulness as sound intensity probes is the focus of this pa

3、per.1 The presented probe consists of a spherical shell, 30 mm in diameter, housing four 1/4 in. microphones arranged in a regular tetrahedral configuration. Classical formulae may be used to estimate the sound intensity vector, as may methods based on spherical harmonics decomposition. Results are

4、shown to be comparable to those obtained from classical sound intensity probes. The existence of an analytical model for a plane waves diffraction about a sphere provides a means for adopting common optimization techniques for potentially improving the intensity vector estimate, however. 2This paper

5、 examines the validity of non-linear least squares optimization in conjunction with the proposed spherical sound intensity probe when placed in the following sound fields: (1) a simple plane wave; (2) a plane wave corrupted by noise; and (3) multiple incident plane waves. Under certain conditions, t

6、he probe is shown to greatly extend the operational frequency range of classical sound intensity probes. The optimization algorithm is found to lack robustness against deviations from plane wave conditions, however.2015 Acoustical Society of America. http:/dx.doi.org/10.1121/1.4934347MS Pages: 28202

7、828摘要最近研究的以小型球阵列布置传声器作为声强探头的介绍是本文的重点。1(这里使用倒译法，主要是将“介绍”的定语前置，使译文更加符合汉语的表达习惯)探测器由一个直径为30毫米的球组成，四个传声器分布在常规的四面体顶点上，即每个传声器各占1/4。用于估计声强矢量的传统公式，是基于球面的谐波分解。根据公式来制作那些传统的声强探头。然而，存在一个平面波的衍射的分析模型提供了一种方法可能改善强度矢量的估计，这种方法被使用到常见的优化技术领域。2(这里使用增译法，增加了“然而”，“这种方法”等连词，这样使译文具有连贯性。)本文探讨了非线性最小二乘的有效性及优化，结合球形声强探头放置在以下声场的情况：

8、(1)一个简单的平面波；(2)一个平面噪声波；和(3)多个入射平面波。在一定条件下，该探测器的操作频率范围比传统声强探头大的多。但是却该发现优化算法在平面波条件下缺乏鲁棒性。2015年美国声学学会 网址http:/dx.doi.org/10.1121/1.4934347 页码：2820-2828I. INTRODUCTIONVector sound intensity measurements are today an integral tool for many an acoustician. Among its applications are(1) sound power measure

9、ments;13 (2) sound source localization; and (3) vector sound field mapping.4,5 Traditionally, sound intensity probes have consisted of pairs of measurement microphones arranged uni-axially or tri-axially in accordance with the Cartesian coordinate system.3 So, too, is the configuration advocated by

10、the existing International Electrotechnical Commission standard.6 This paper instead investigates the benefits drawn from arranging four 1/4 in. microphones at the vertices of a regular tetrahedron in an 30 mm spherical shell. 41. 引言目前矢量声强测量是许多声学专家不可或缺的工具。它的应用领域有以下几个方面：（1）声压的测量；1-3(2)声源的定位；（3）矢量声场的绘

11、制。4,5传统的声强测量探头由非轴向的或依据三维迪卡尔坐标系的双传声组成。3（这里使用音译法，将“Cartesian coordinate system”译为“笛卡尔坐标系”）并且依据国际电力学会的标准进行校准。6本文主要介绍的是一种新的声强探头，该探测器由一个直径为30毫米的球组成，四个传声器分布在常规的四面体顶点上，即每个传声器各占1/4。4(这里使用分译法，将原文的长句译成一个个独立成分的小短句，使译文通顺，简洁，易懂)Large spherical arrays both transparent and rigid are increasingly adopted for beamfo

12、rming7,8 and near-field acoustic holography (NAH),4,5,9 5usually with numerous benefits to follow. Their primary advantage, when rigid, is their ability to partially compensate for effects due to diffraction.5 Of equal attraction, however, is their inherent rotational symmetry.10 Their large size an

13、d microphone count unwarrent them as sound intensity probes in practice, however. 目前波束成型技术和近场声全息技术（NAH）4，5,9领域逐渐采用大型的严格排列的球面阵列。5( 这里使用倒译法，主要是将定语前置，使译文更加符合汉语的表达习惯)他们的主要优势在于它的稳定性，这使他们能够部分地补偿由于衍射效应带来的误差。5相同的条件下他们固有的旋转频率与尺寸是成正比例的。10然而，在实际情况中，大尺寸的声强探测器是无法计算并且测量它的声强的。The past few years have seen the intro

14、duction of significantly smaller spherical arrays.11,12 Advances in transducer technology, with a focus on miniaturization, have allowed both microphones and preamplifiers to remain housed within the shell of the probe.6 As with large arrays, this eliminates freely suspended cables and other obstruc

15、ting geometries otherwise common to classical intensity probes. What results is a well-defined shape highly suitable for analysis.7在前几年主要研究更小的小型球阵列布置传声器对于测量声强的有效性。11,12目前传感器的发展技术更加专注于微型化的设计，将传声器和前置放大器连接在一起。6(这里使用直译法，译文与原文完全一致)对于大的阵列，它消除自由悬挂的数据线和几何尺寸等方面对于传统声强探头测量的影响。这种比较规则的模型也非常适合分析。7(这里使用替代法，译文将“Wha

16、t results”替代为“这种比较规则的模型”，使译文前后连接更加紧密，逻辑更强)In this paper, we outline methods for calculating the three-dimensional sound intensity vector with the spherical probe previously described. Two methods for doing so are outlined in Sec. II. Of particular interest, however, is the use of non-linear least sq

17、uares optimization techniques for extending the probes operational frequency range. 8We explore this approach in Sec. III, when restricting the soundfield to be plane. Section IV validates the algorithm via simulation, while Sec. V exposes the algorithm to more complex soundfields: Sec. VA, a plane

18、wave corrupted by noise; and Sec. VB, multiple incident plane waves. The former test case is supported by measurements. In Sec. VI, we give our concluding remarks and highlight ideas for future work.在文章中，主要描述球面分布的声强探头测量三维矢量声强及其计算方法。我们将在第二章介绍两种方法。并且,特别感兴趣的是使用非线性最小二乘优化技术扩大声强探头的测量频率范围。8(这里使用意译法，译文根据原文需

19、要表达的意义和精神进行翻译的，使译文符合汉语文化的表达习惯)我们将在第三章研究在平面声场中声强计算的近似算法。在第四章通过仿真验证该算法，并且进一步研究比第三章更复杂的声场情况下声强的计算方法：第四章A是加载了噪声的平面波的声场；第四章B是多种类型平面波的声场。在第五章，将给出我们的结论和对未来工作的想法。II. SPHERICAL PROBEFour measurement microphones are arranged in a regular tetrahedral configuration with two microphones forwardfacing and two rea

20、rward-facing (see Fig. 1). 9Since the four microphones span a three-dimensional space, appropriate mathematical operations allow the determination of the full sound intensity vector. In what follows, we present two methods for doing so.2. 球面分布的探测器如图1所示，四个传声器分布在正四面体的四个顶点，其中两个探头，两个探头向后。9（这里使用重复法，译文重复使

21、用“两个探头”，使译文通顺，易懂）这四个传声器分布在一个三维空间内，通过适当的数学运算便可以算出正四面体中心的声强。接下来，我们将提出两种如上所述的方法。A. Calculating sound intensity by classical formulaeBy joining midpoints of oppositely-facing microphonepairs a local orthogonal coordinate system arises whose origin coincides with the center of the sphere. 10 This is the

22、point at which the sound intensity vector is estimated. Figure 2 visualizes this local Cartesian coordinate system in relation to the positions of the four microphones. The pressures at the aforementioned midpoints may be approximated by anappropriate average of the two microphones making up the giv

23、en point. For instance, for the z-direction we have (adopting an arithmetic average):11A. 利用传统的方法计算声强将传声器两两面对面布置在直角坐标系正交的方向，连接传声器，其交点便是球体的球心，也是直角坐标系的原点。10( 这里使用分译法，将原文的长句译成一个个独立成分的小短句，使译文通顺，简洁，易懂)图2表示的是在笛卡尔坐标系下四个传声器的位置关系。两两传声器连线的中点的声压可以被近似计算出来。因此这个点的声强就可以估算出来。举个例子，在Z方向上我们有（取算数平均）：11(这里使用重组法，译文采用逻辑顺序

24、进行重组，译文简洁清楚，逻辑清晰，符合汉语表达习惯)原文第2821页 （1）and并且 （2）Where Pi(w) is the pressure recorded by microphone i at rotational frequency w. With this, the calculation of the sound intensity vector (projected onto the z-direction) proceeds as per classical sound intensity probes14这里的Pi(w)表示传声器i在频率w下的声压值。利用这种方法，可以

25、使用传统的声强探头14计算每个方向的声强（比如可以计算投影在z方向的声强）。 (3)where is the imaginary part of the crosspower spectrum between signals pz1 and pz2; is the equivalent spacer distance between points z1 and z2; and is the unit vector in the z-direction. An analogous procedure exists for the directions defined by and. 12Meth

26、ods notably exist for approximating 15 but will not be commented on here. 表示pz1和 pz2 两个声压信号互谱声强的虚部值；表示z1 和 z2 两个点之间的距离；表示Z方向的单位向量。以此类推， 和分别表示X,Y方向的单位向量12。（这里使用转译法，译文中“以此类推”便是转译的，这样使译文更加具有逻辑性）很明显15是一个近似值，但是在这里不做评论。FIG. 1. The constructed probe, 30 mm in diameter, houses four 1 4 in. microphones at th

27、e vertices of a regular tetrahedron. Both microphones and preamplifiers are contained within the spherical shell, eliminating freely suspended cables and other obstructing geometries.图1.这是声强探头的结构图，该球体直径为30毫米，在内切的正四面体四个顶点各分布一个传声器。传声器和前置放大器连接在一起，消除了悬浮的数据线和其他几何尺寸的影响。FIG. 2. An illustration of the ortho

28、gonal coordinate system (x-y-z) that arises by joining midpoints of oppositely facing microphone-pairs. (Ref. 13) We note, however, that the illustrated microphones do not represent the probe under examination as the spherical shell is absent.图2. 示意图为正交坐标系（X-Y-Z），声压值为通过面对面的传声器连线的中点的声压。（公式13）我们注意到，然而

29、，可以看出该传声器的位置分布并不代表测量时没有球面外壳。B. Calculating intensity by spherical harmonics decompositionAlternatively, we may calculate the sound intensity vector by drawing on methods based on spherical harmonics decomposition. We write the soundfield as the linear combination of an incident and scattered field,1

30、6B. 通过球面调和变换计算声强另外，我们可以通过对基于球面调和分解法绘制计算矢量声强。本文所采用的是声场为入射场和散射场的线性组合场。16 (4)and expand the two in terms of spherical harmonics:并且分为如下两类球面调和函数： (5) (6)Where在这里 (7)We note that jn(kr) is the nth order spherical Bessel function; hn(kr) is the nth order spherical Hankel function of the second kind; P (x)

31、is the associated Legendre function of degree n and order m; k is the wave number; and a is the radius of the sphere. We further note that , using italics to differentiate it from the spherical Bessel function, j(x).13需要注意其中jn(kr)表示第n阶球面贝塞尔方程；hn(kr)表示第n阶第二类球面汉克方程；P (x)表示n次m阶勒让德方程；k表示平面波数；a表示球体的半径；注意

32、，需要区分它和球面贝塞尔方程j(x)是不同的。13(这里采用顺译法，译文按照原文的语序进行翻译，最大限度的再现了原文的内容和风格)Applying boundary conditions on the particle velocity in the radial direction on the surface of the sphere, we arrive at the following expression for the total soundfield:9粒子速度施加的边界条件，在球体的表面上的径向方向，可以获得总声场下的表达式，如下所示：9 (8)where we have adopted the shorthand notation , and similarly for.在这里，为了书写方便，令，类似。原文第2822页 By orthogonality o