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Patch nearfield acoustic holography based on the equivalent source method

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Abstract

On the basis of nearfield acoustic holography (NAH) based on the equivalent source method (ESM), patch NAH based on the ESM is proposed. The method overcomes the shortcoming in the conventional NAH that the hologram surface should be larger than the source surface. It need not to discretize the whole source and its measurement need not to cover the whole source. The measurement may be performed over the region of interest, and the reconstruction can be done in the region directly. The method is flexible in applications, stable in computation, and very easy to implement. It has good potential applications in engineering. The numerical simulations show the invalidity of the conventional NAH based on the ESM and prove the validities of the proposed method for reconstructing a partial source and the regularization for reducing the error effect of the pressure measured on the hologram surface.

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References

  1. Williams E G, Maynard J D, Skudrzyk E. Sound source reconstruction using a microphone array. J Acoust Soc Am, 1980, 68(1): 340–344

    Article  Google Scholar 

  2. Veronesi W A, Maynard J D. Digital holographic reconstruction of source with arbitrarily shaped surfaces. J Acoust Soc Am, 1989, 85: 588–598

    Article  Google Scholar 

  3. Wang Z, Wu S F. Helmholtz Equation-Least Squares Method for Reconstructing the Acoustic Pressure Field. J Acoust Soc Am, 1997, 102(4): 2020–2032

    Article  Google Scholar 

  4. Williams E G. Continuation of acoustic near-fields. J Acoust Soc Am, 2003, 113(3): 1273–1281.

    Article  Google Scholar 

  5. Williams E G, Houston B H. Fast Fourier transform and singular value decomposition formulations for patch nearfield acoustical holography. J Acoust Soc Am, 2003, 114(3): 1322–1333

    Article  Google Scholar 

  6. Maynad J D, Williams E G, Lee Y. Nearfield acoustic holography I: Theory of generalized holography and development of NAH. J Acoust Soc Am, 1985, 78(4): 1395–1413

    Article  Google Scholar 

  7. Bai M R. Application of BEM (boundary element method)-based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries. J Acoust Soc Am, 1992, 92: 533–549

    Article  Google Scholar 

  8. Kim B K, Ih J G. On the reconstruction of the vibro-acoustic field over the surface enclosing an interior space using the boundary element method. J Acoust Soc Am, 1996, 100(5): 3003–3016

    Article  Google Scholar 

  9. Hald J. Patch near-field acoustical holography using a new statistically optimal method. Proc. INTER-NOISE 2003, 2003. 2203–2210

  10. Saijyou K, Uchida H. Data extrapolation method for boundary element method-based near-field acoustical holography. J Acoust Soc Am, 2004, 115(2): 785–796

    Article  Google Scholar 

  11. Lee M Y, Bolton J S. Patch near-field acoustical holography in cylindrical geometry. J Acoust Soc Am, 2005, 118(6): 3721–3732

    Article  Google Scholar 

  12. Saijyou K, Yoshikawa S. Reduction methods of the reconstruction error for large-scale implementation of near-field acoustical holography. J Acoust Soc Am, 2001, 110(4): 2007–2023

    Article  Google Scholar 

  13. Angie Sarkissian. Extension of measurement surface in near-field acoustic holography. J Acoust Soc Am, 2004, 115(4): 1593–1596

    Article  Google Scholar 

  14. Angie Sarkissian. Method of superposition applied to patch near-field acoustic holography. J Acoust Soc Am, 2005, 118(2): 671–678

    Article  Google Scholar 

  15. Koopmann G H, Song L, Fahnline J. A method for computing acoustic fields based on the principle of wave superposition. J Acoust Soc Am, 1989 86(5): 2433–2438

    Article  Google Scholar 

  16. Song L, Koopmann G H, Fahnline J. Numerical errors associated with the method of superposition for computing acoustic fields. J Acoust Soc Am, 1991, 89(6): 2625–2633

    Article  Google Scholar 

  17. Bi C X, Chen X Z, Zhou R, et al. Nearfield acoustic holography based on the equivalent source method. Sci China Ser E-Tech Sci, 2005, 48(3): 338–353

    Article  Google Scholar 

  18. Williams E G. Regularization methods for near-field acoustical holography. J Acoust Soc Am, 2001, 110(4): 1976–1988

    Article  Google Scholar 

  19. Williams E G, Houston B H. Interior near-field acoustical holography in flight. J Acoust Soc Am, 2000, 108(4): 1451–1463

    Article  Google Scholar 

  20. Landweber L. An iteration formula for Fredholm integral equations of the first kind. Am J Math, 1951, 73: 615–624

    Article  MATH  MathSciNet  Google Scholar 

  21. Tikhonov A N. Solution of incorrectly formulated problems and the regularization method. Soviet Math Dokl, 1963, 4: 1035–1038

    Google Scholar 

  22. Morozov V A. On regularization of Ill-posed problems and selection of regularization parameter. J Comp Math Phys, 1966, 6(1): 170–175

    Google Scholar 

  23. Hansen P C. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev, 1992, 34: 561–580

    Article  MATH  MathSciNet  Google Scholar 

  24. Golub G H, Heath M, Wahba G. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics, 1979, 21: 215–223

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Sound and Vibration Research, Hefei University of Technology, Hefei, 230009, China

    Bi ChuanXing, Chen XinZhao, Xu Liang & Chen Jian

Authors
  1. Bi ChuanXing
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  2. Chen XinZhao
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  3. Xu Liang
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  4. Chen Jian
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Corresponding author

Correspondence to Bi ChuanXing.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 10504006 and 50675056) and the Research Fund for the Doctoral Program of Higher Education (Grant No. 20060359003)

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Bi, C., Chen, X., Xu, L. et al. Patch nearfield acoustic holography based on the equivalent source method. Sci. China Ser. E-Technol. Sci. 51, 100–110 (2008). https://doi.org/10.1007/s11431-008-0001-4

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  • DOI: https://doi.org/10.1007/s11431-008-0001-4

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