|
|
|
| Construction and selection of nonconformal near-field acoustic holography wave function based on wave superposition method |
| XIANG Yu1， SHI Ziyu1,2， LU Jing1,2， WU Wenjun1,2 |
1.Key Laboratory of Automobile Componentand Vehicle Technology in Guangxi，Guangxi University of Science and Technology， Liuzhou 545006， China;
2.School of Mechanical and Traffic Engineering，Guangxi University of Science and Technology， Liuzhou 545006， China |
|
|
|
Abstract In traditional wave superposition method for near-field acoustic holography,its integral kernel function usually adopts the single-layer potential wave function or double-layer potential wave function. When the holographic plane and the equivalent source plane are non-conformal, this kind of wave function can easily lead to the enhancement of the linear correlation and the aggravation of the ill-conditioned state of the system matrix.Most studies focused on the regularization of ill-conditioned matrices to obtain better results.Firstly, the reason of ill-conditioned system caused by traditional single-layer potential wave function or double-layer potential wave function was analyzed theoretically. Then, a series of ray wave functions with strong directivity were constructed by calculating derivatives of the Green's function.By replacing the single-layer potential or double-layer potential wave function used in the traditional wave superposition method with the ray wave functions, the resulting system matrix can be principal diagonal dominant and approximate symmetrical form, so the results can be more accurate and stable without using the regularization method.In this paper, the numerical simulation of the conventional pulsating sphere and swing sphere source and the general ball source which can be superimposed as the external sound field of any sound source is carried out. The results show that the superposition method of high order wave function proposed in this paper can significantly reduce the condition number of system matrix and make the system matrix tend to be well-formed under the condition that the system matrix of traditional wave superposition method is ill-conditioned and cannot obtain satisfactory results without Tikhonov regularization.Therefore, in this sense, this method is also a regularization means to improve the stability of reconstruction.It was also found that, weather the traditional single-layer potential wave function and double-layer potential wave function, or the ray wave function constructed in this paper, each had itsapplication scope, advantages and disadvantages. Therefore, different wave functions should be selected according to different situations to improve the computational stability and efficiency.
|
|
Received: 08 January 2019
Published: 28 July 2020
|
|
|
|
[1] WILLIAMS E G, MAYNARD J D, SKUDRZYK E. Sound source reconstructions using a microphone array[J]. Journal of the Acoustical Society of America, 1998, 68(1):340-344.
[2] VERONESI W A, MAYNARD J D. Digital holographic reconstruction of sources with arbitrarily shaped surfaces[J]. Journal of the Acoustical Society of America, 1989, 85(2):588-598.
[3] BAI M R. Application of BEM (boundary element method)-based acoustic holography to radiation analysis of sound sources with arbitrarity shaped geometries[J].Journal of the Acoustical Society of America, 1992, 92(1):533-549.
[4] CUNEFARE K A , KOOPMANN G , BROD K. A boundary element method for acoustic radiation valid for all wavenumbers[J]. Journal of the Acoustical Society of America, 1989, 85(1):39-48.
[5] IH J G , KIM B K. On the use of the BEM-based NAH for the vibro-acoustic source imaging on the nonregular exterior surfaces[J]. Monthly Notices of the Royal Astronomical Society, 1998, 421(4):3277–3285.
[6] IH J G , KIM B. On the reconstruction of the vibro-acoustic field over the surface enclosing an interior space using the boundary element method[J]. Journal of the Acoustical Society of America, 1996, 100(5):3003-3016.
[7] KOOPMANN G H , SONG L , FAHNLINE J B. A method for computing acoustic fields based on the principle of wave superposition[J]. Journal of the Acoustical Society of America, 1989, 86(6):2433-2438.
[8] JEANS, R. The wave superposition method as a robust technique for computing acoustic fields[J]. The Journal of the Acoustical Society of America, 1992, 92(2):1156-1166.
[9] 于飞，陈剑，李卫兵，等. 一种稳健的全波数声场重构技术[J]. 中国科学:技术科学, 2004, 34(9):1069-1080.
YU Fei, CHEN Jian, LI Weibing, et al.A robust sound field reconstrction technique in full wave number domain[J]. Science China Technological Sciences, 2004, 34(9):1069-1080.
[10] 向宇，黄玉盈. 基于复数矢径的波叠加法解声辐射问题[J]. 固体力学学报, 2004, 25(01):35-41.
XIANG Yu, HUANG Yuying. Wave superposition method based on virtual source boundary with complex radius vector for solving acoustic radiation problems[J]. Acta Mechanic solida sinica, 2004, 25(01):35-41.
[11] 夏雪宝，向阳. 基于附加源波叠加法的声辐射计算研究[J]. 振动与冲击, 2015, 34(01):104-109+144.
XIA Xuebao, XIANG Yang. Acoustic radiation calculation based on additional sources wave superposition method[J]. Journal of vibration and shock, 2015, 34(01):104-109+144.
[12] BAO G , LIN J , TRIKI F.A multi-frequency inverse source problem[J]. Journal of Differential Equations, 2010, 249(12):3443-3465.
[13] CHENG J, ISAKOV V, LU S. Increasing stability in the inverse source problem with many frequencies[J]. Journal of Differential Equations, 2016, 260(5):4786-4804.
[14] LI P , YUAN G. Stability on the Inverse Random Source Scattering Problem for the One-Dimensional Helmholtz Equation[J]. Journal of Mathematical Analysis & Applications, 2017, 450(2):872-887.
[15] SONG L, KOOPMANN G H, FAHNLINE J B. Numerical errors associated with the method of superposition for computing acoustic fields[J]. Journal of the Acoustical Society of America, 1991, 89(6):2625-2633.
[16] 李加庆, 陈进, 杨超,等. 波叠加声场重构精度的影响因素分析[J]. 物理学报, 2008, 57(7):4258-4264.
LI Jiaqing, CHEN Jin, YANG Chao, et al.Analysis of the impact factors on the accuracy of sound field reconstruction based on wave superposition[J]. Acta Physica Sinica, 2008, 57(7):4258-4264.
[17] CHIEN C C, RAJIYAH H, ATLURI S N. An effective method for solving the hyper-singular integral equations in 3-D acoustics[J]. Journal of the Acoustical Society of America, 1998, 88(2):918-937.
[18] 陆静,向宇,黄玉盈.求解轴旋转空穴三维声辐射问题的复数矢径虚拟边界谱方法[J].声学学报,2011,36(03):308-317.
LU Jing, XIANG Yu, HUANG Yuying. A virtual boundary spectral method with complex radius vector for acousticradiation problem of 3-Dimension axisymetric cavity[J].Acta Acustica, 2011,36(03):308-317.
|
|
|
|
