A new data extrapolation method based on the modified Helmholtz equation least-squares method
A new data extrapolation method based on the modified Helmholtz equation least-squares method
复制标题
基于修正亥姆霍兹方程最小二乘法的新数据外推方法
DOI：
10.1177/0954406212458385
复制
发表时间：
2013-06
期刊：
影响因子：
--
通讯作者：
Dong, G. M.
中科院分区：
文献类型：
--
作者：
Wang, R.;Chen, J.;Dong, G. M.
基于快速傅立叶变换的近场声全息术要求测量孔径完全包围声源，这对于大规模声源来说是不切实际的。与基于快速傅里叶变换的近场声全息术相比，亥姆霍兹方程最小二乘法可以用更少的测量来重建声场。然而，它不适合重建来自多个源或由多个独立部分组成的复杂源的声辐射。为了克服这一困难并提高重建精度，提出了一种基于修正亥姆霍兹方程最小二乘法的新数据外推方法。该数据外推方法的基础是改进的亥姆霍兹方程最小二乘法，该方法将复杂源的声场表示为来自其所有分离部分的声辐射的叠加。使用改进的亥姆霍兹方程最小二乘法重建的声压，通过迭代过程扩展测量表面。同时，利用Tikhonov正则化方法和广义交叉验证参数选择方法来处理重建中的不适定问题。最后，将推断的压力作为输入数据，可以更精确地重建声场。数值模拟和实验结果表明，该方法可以显着提高重建精度和效率。
Fast Fourier transform-based near-field acoustic holography requires that the measurement aperture should completely enclose the source, which is impractical for large-scale sound sources. Helmholtz equation least-squares method can reconstruct the acoustic field with fewer measurements than fast Fourier transform-based near-field acoustic holography. However, it is not suitable for reconstructing acoustic radiation from multiple sources or a complicated source which consists of several separated parts. To circumvent this difficulty and enhance the reconstruction accuracy, a new data extrapolation method based on the modified Helmholtz equation least-squares method is proposed. The base of this data extrapolation method is a modified Helmholtz equation least-squares method which expresses the acoustic field of a complicated source as the superposition of the acoustic radiation from all of its separated parts. Using the acoustic pressures reconstructed with the modified Helmholtz equation least-squares method, the measurement surface is extended through an iterative procedure. Meanwhile, Tikhonov regularization method together with generalized cross-validation parameter choice method is utilized to treat the ill-posed problem in reconstructions. In the end, taking the extrapolated pressures as input data, the acoustic field can be reconstructed more precisely. Numerical simulation and experimental results demonstrate that this method can significantly enhance the reconstruction accuracy and efficiency.
登录
查看更多内容
修正波叠加算法重构复杂声源振动声场的研究
DOI：
10.1243/09544062jmes1052
发表时间：
2009-02
影响因子：
2
作者：
Huang, Z. Y.;Zhang, H. B.;Wan, Q.;Jiang, W. K.
通讯作者：
Jiang, W. K.
DOI：
10.1121/1.1528173
发表时间：
2003-02
期刊：
The Journal of the Acoustical Society of America
影响因子：
--
作者：
E. Williams
通讯作者：
E. Williams
DOI：
10.1121/1.1841591
发表时间：
2005-01
期刊：
The Journal of the Acoustical Society of America
影响因子：
--
作者：
T. Semenova;Sean F. Wu
通讯作者：
T. Semenova;Sean F. Wu
DOI：
10.1121/1.1361059
发表时间：
2001-06
期刊：
The Journal of the Acoustical Society of America
影响因子：
--
作者：
S. Wu;N. Rayess;X. Zhao
通讯作者：
S. Wu;N. Rayess;X. Zhao
DOI：
10.1016/0041-5553(66)90046-2
发表时间：
1966
期刊：
Ussr Computational Mathematics and Mathematical Physics
影响因子：
--
作者：
V. Morozov
通讯作者：
V. Morozov