On the choice of expansion functions in the Helmholtz equation least-squares method.
On the choice of expansion functions in the Helmholtz equation least-squares method.
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DOI：
10.1121/1.1841591
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发表时间：
2005-01
期刊：
影响因子：
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通讯作者：
T. Semenova;Sean F. Wu
中科院分区：
文献类型：
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作者：
T. Semenova;Sean F. Wu
研究了Helmholtz方程最小二乘（Helmholtz equation least-squares，HELS）方法在同一组测量数据下，分别采用局域球面波（localized spherical wave，LSW）、分布球面波（distributed spherical wave，DSW）和分布点源（distributed pointer sources，DPS）三种不同展开形式重建任意声源声辐射的性能。重建的声压验证对基准数据测量在相同的位置作为重建点的频率高达3275 Hz。重建是通过使用Tikhonov正则化或其修改与无误差的参数选择方法选择的正则化参数。研究了不同展开函数下测量点数量对重建精度的影响。结果表明，DSW导致一个更好的条件下的传递矩阵，产生更准确的重建比LSW和DPS，并不受测量点的变化。此外，通过采取独立的测量层，可以获得DSW、LSW和DPS的辅助源的最佳位置。使用这些辅助源和正则化和无误差的参数选择方法的最佳组合，可以产生一个令人满意的重建的源表面上的声学量，以及在该领域中的最具成本效益的方式。
This paper examines the performance of Helmholtz equation least-squares (HELS) method in reconstructing acoustic radiation from an arbitrary source by using three different expansions, namely, localized spherical waves (LSW), distributed spherical waves (DSW), and distributed point sources (DPS), under the same set of measurements. The reconstructed acoustic pressures are validated against the benchmark data measured at the same locations as reconstruction points for frequencies up to 3275 Hz. Reconstruction is obtained by using Tikhonov regularization or its modification with the regularization parameter selected by error-free parameter-choice methods. The impact of the number of measurement points on the resultant reconstruction accuracy under different expansion functions is investigated. Results demonstrate that DSW leads to a better-conditioned transfer matrix, yields more accurate reconstruction than both LSW and DPS, and is not affected as much by the change in measurement points. Also, it is possible to obtain optimal locations of the auxiliary sources for DSW, LSW, and DPS by taking an independent layer of measurements. Use of these auxiliary sources and an optimal combination of regularization and error-free parameter choice methods can yield a satisfactory reconstruction of acoustic quantities on the source surfaces as well as in the field in the most cost-effective manner.