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Enhancing the Reconstruction of Acoustic Source Field Using Wavelet Transformation  

Ko Byeongsik (Korea Simulation Technology Inc.)
Lee Seung-Yop (Department of Mechanical Engineering, Sogang University)
Publication Information
Journal of Mechanical Science and Technology / v.19, no.8, 2005 , pp. 1611-1620 More about this Journal
Abstract
This paper shows the use of wavelet transformation combined with inverse acoustics to reconstruct the surface velocity of a noise source. This approach uses the boundary element analysis based on the measured sound pressure at a set of field points, the Helmholtz integral equations and wavelet transformation for reconstructing the normal surface velocity field. The reconstructed field can be diverged due to the small measurement errors in the case of nearfield acoustic holography (NAH) using an inverse boundary element method. In order to avoid this instability in the inverse problem, the reconstruction process should include some form of regularization for enhancing the resolution of source images. The usual method of regularization has been the truncation of wave vectors associated with small singular values, although the order of an optimal truncation is difficult to determine. In this paper, a wavelet transformation is applied to reduce the computation time for inverse acoustics and to enhance the reconstructed vibration field. The computational speed-up is achieved, with solution time being reduced to $14.5\%$.
Keywords
Wavelet; Wavelet Transformation; Boundary Element Method (BEM); Nearfield Acoustic Holography (NAH); Acoustics;
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1 Veronesi, W. A. and Maynard, J. D., 1989, 'Digital Holographic Reconstruction of Source with Arbitrarily Shaped Surfaces,' J. Acoust. Soc. Am., Vol. 85, pp. 588-598   DOI
2 Williams, E. G., Houston, B. H. and Bucaro, J. A., 1989, 'Broadband Nearfield Acoustical Holography for Vibrating Cylinders,' J. Acoust. Soc. Am., Vol. 86, pp.674-679   DOI
3 Williams, E. G., Houston, B. H. and Herdic, P. C., 1996, 'Reconstruction of the Surface Velocity and Interior Acoustic Intensity from an Aircraft Fuselage Using Nearfield Acoustical Holography,' Proc. Noise-Con 96, Seattle, WA, pp. 193-198
4 Williams, E. G., 1999, 'An Overview of the Inverse problem for Sound Reconstruction in Interior Spaces,' J. Acoust. Soc. Am., Vol. 105, pp.968-000   DOI
5 Youcef Saad, and Martin H. Schultz, 1986, 'GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems,' SIAM Journal on Scientific and Statistical Computing, Vol. 7, No.3, pp. 856-869   DOI
6 Prasad, K. G., Kane, J. H., Keyes, D. E. and Balakrishna, C., 1994, 'Preconditioned Krylov Solvers for BEA,' Int. J. Num. Meth. Eng., Vol. 37, pp. 1651-1672   DOI   ScienceOn
7 Rokhlin, V., 1983, 'Rapid Solution of Integral Equations of Classical Potential Theory,' J. Comp. Phys., Vol. 60, pp. 187-207   DOI   ScienceOn
8 Said, A. and Pearlman, W. A., 1996, 'A New Fast and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees,' IEEE Trans. Circ. and Syst. Video Tech., Vol. 6, No.3, pp. 243-250   DOI   ScienceOn
9 Shao, X. and Cherkassky, V., 1998, 'Model Selection for Wavelet-based Signal Estimation,' Proc. IEEE IntI. Joint Conf. on Neural Networks, Vol. 2, pp. 843-848
10 Shapiro, J. M., 1993, 'Embedded Image Coding Using Zerotrees of Wavelet Coefficients,' IEEE Trans. Signal Processing, Vol. 41, pp. 3445-3462   DOI   ScienceOn
11 Simoncelli, E. P., 1999, 'Bayesian De-noising of Visual Images in the Wavelet Domain,' in Bayesian Inference in Wavelet Based Models, Muller and Vidakovic (eds.), Springer Verlag
12 Veronesi, W. D. and Maynard, J. D., 1987, 'Nearfield Acoustic Holography: II. Holographic Reconstruction Algorithms and Computer Algorithms,' J. Acoust. Soc. Am., Vol. 81, No.5, pp. 1307-1322   DOI
13 Mansur, W. J., Araujo, F. C. and Malaghini, J. E. B., 1992, 'Solution of BEM Systems of Equations Via Iterative Techniques,' Int. J. Num. Meth. Eng., Vol. 33, pp. 1823-1841   DOI
14 Nabors, K., Korsmeyer, F.T., Leighton, F. T. and White, J., 1994, 'Preconditioned, Adaptive, Multipole-accelerated Iterative Methods for Three-dimensional Potential Integral Equations of the First Kind,' SIAM J. Sci. Comp., Vol. 15, pp.713-735   DOI   ScienceOn
15 Maynard, J. D., Williams, E. G. and Lee, Y., 1985, 'Nearfield Acoustic Holography: I. Theory of Generalized Holography and the Development of NAH,' J. Acoust. Soc. Am., Vol. 78, No. 4, pp. 1395-1413   DOI
16 Meyer, Y., 1993, Wavelets: Algorithms and Applications, SIAM
17 Morlet, J., 1983, 'Sampling Theory and Wave Propagation,' in NATO ASI Series, Vol.1, Issues in Acoustic signal/Image processing and recognition, C. H. Chen, ed. Springer-Verlag, Berlin, pp.233-261
18 Kirkup, S. M., 1998, The Boundary Element Method in Acoustics, Integrated Sound Software
19 Lee, H. and Sullian, D. P., 1988, 'Fundamental Limitation of Resolution Enhancement by Wave-field Extrapolation,' J. Acoust. Soc. Am., Vol. 84, pp.611-617   DOI
20 Gyure, M. F. and Stalzer, M. A., 1998, 'A Prescription for the Multilevel Helmholtz FMM,' IEEE Computational Science & Engineering, Vol. 5, No.3, pp. 39-47   DOI   ScienceOn
21 Ih, J. -G. , Kang, S. -C., Kim, S. -J. and Kang, K. -S., 1998, 'Reconstruction of the Vibroacoustic Field on the Surface of the Refrigerator Compressor by Using the BEM-based Acoustic Holography,' in Proc. 1998 Int. Compressor Eng. Conference, Purdue, IN, pp. 525-529
22 Haar, A., 1910, 'Zur Theorie der Orthogonalen Funktionen Systeme,' Math. Ann., Vol. 69, pp. 331-371   DOI
23 Hackbusch, W., Nowak, Z. P., 1989, 'On the Fast Matrix Multiplication in the Boundary Element Method by Panel Clustering,' Numerische Mathematik, Vol. 54, pp.463-491   DOI
24 Ih, J. -G., Kim, J. -Yo and Kim, B. -K., 1993, 'Acoustic Field Prediction of Complex Radiators by Using Near-field Measurements and BEM,' in Proc. 11th IMAC, Orlando, FL, pp. 1396-1401
25 Kammer, D. C., 1992, 'Effect of Modal Error on Sensor Placement for on-orbit Modal Identification of Large Space Structures,' J. Guid. Control Dyn., Vol. 15, pp. 334-341   DOI
26 Kane, J. H., Keyes, D. E., Prasad, K. G., 1991, 'Iterative Equation Solution Techniques in Boundary Element Analysis,' Int. J. Num. Meth. Eng., Vol. 31, pp. 1511-1536   DOI
27 Kim, B. -K. and Ih, J. -G., 1996, 'On the Reconstruction of Vibro-acoustic Field Over the Surface Enclosing an Interior Space Using the Boundary Element Method,' J. Acoust. Soc. Am., Vol. 100, pp. 3003-3016   DOI   ScienceOn
28 Kirkup, S. M., 1994, 'Computational Solution of the Acoustic Field Surrounding a Baffled Panel by the Rayleigh Integral Method,' Applied Mathematical Modelling, Vol. 18, PP.403-407   DOI
29 Demoment, G., 1989, 'Image Reconstruction and Restoration: Overview of Common Estimation Structures and Problems,' IEEE Trans. Acoust., Speech, Signal Process., Vol. ASSP-37, pp.2024-2036   DOI   ScienceOn
30 Donoho, D. L., 1992, 'Wavelet Thresholding and W. V. D. : A 10-minute Tour,' IntI. Conf. on Wavelets and Applications, Toulouse, France, June
31 Donoho, D. L. and Johnstone, I. M., 1993, 'Adaptating to Unknown Smoothness by Wavelet Shrinkage,' Technical Report, Department of Statistics, Stanford University
32 Donoho, D. L. and Johnstone, I. M., 1994, 'Ideal Spatial Adaptation via Wavelet Thresholding,' Biometrika, Vol. 81, pp.425-455   DOI
33 Donoho, D. L., 1995, 'De-Noising by Soft-Threshholding,' IEEE Trans. Info. Theory, Vol. 41, No.3, pp. 613-627   DOI   ScienceOn
34 Dumbacher, S. M., Brown, D. L., Blough, J. R. and Bono, R. W., 2000, 'Practical Aspects of Making NAH Measurements,' SAE Transaction, Vol. 108, No.6, Part 2., pp. 3081-3090
35 Fleischer, H. and Axelrad, V., 1986, 'Restoring an Acoustic Source from Pressure Data Using Wiener Filtering,' Acustica, Vol. 60, pp.172-175
36 Gardner, K. and Bernhard, R. J., 1988, 'A Noise Source Identification Technique Using an Inverse Helmholtz Integral Equation Method,' ASME J. Vib., Acoust., Stress, Reliab. Des., Vol. 110, pp. 84-90   DOI   ScienceOn
37 Gonzalez, P., Cabaleiro, J. C. and Pena, T. F., 2000, 'Parallel Iterative Scheme for Solving BEM Systems Using Fast Wavelet Transforms,' Developments in Engineering Computational Technology, Civil-Comp Press, Edinburgh
38 Goodman, W., 1968, Introduction to Fourier Optics, McGraw-Hill
39 Beylkin, G., Coifman, R. and Rokhlin, V., 1991, 'Fast Wavelet Transforms and Numerical Algorithms,' Comm. Pure and Applied Math., Vol. 44, pp. 141-183   DOI
40 Bernhard, R. J., Gardner, B. K., Mollo, C. G. and Kipp, C. R., 1987, 'Prediction of Sound Fields in Cavities Using Boundary-Element Methods,' AIAA Journal, Vol. 25, pp.1176-1183   DOI
41 Biemond, J., Lagendijk, R. L. and Mersereau, R. M., 1990, 'Iterative Methods for Image Deblurring,' Proc. IEEE, Vol. 78, pp. 856-883   DOI   ScienceOn
42 Borgiotti, G., Sarkissian, A., Williams, E. G. and Schuetz, L., 1990, 'Conformal Generalized Near-Field Acoustic Holography for Axisymmetric Geometries,' J. Acoust. Soc. Am., Vol. 88, pp. 199-209   DOI
43 Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C., 1984, Boundary Element Techniques, Springer-Verlag, Berlin
44 Chambolle, A., DeVore, R. A., Lee, N. Y. and Lucier, B. J., 1998, 'Nonlinear Wavelet Image Processing: Variational Problems, Compression and Noise Removal through Wavelet Shrinkage,' IEEE Trans. Image Proc., Vol. 7, pp.319-335   DOI   ScienceOn
45 Chang, S. G. and Vetterli, M., 1997, 'Spatial Adaptive Wavelet Thresholding for Image Denoising,' Proc of IEEE Intl Conf on Image Processing, pp. 374- 377
46 Chui, C. K., 1992, An Introduction to Wavelets, Academic Press, New York
47 Coifman, R. R. and Donoho, D. L., 1995, Ideal Translation Invariant De-noising, Springer Verlag
48 Daubechies, I., 1992, Ten Lectures on Wavelets, SIAM, Philadelphia
49 Bai, M. R., 1995, 'Acoustical Source Characterization by Using Recursive Wiener Filtering,' J. Acoust. Soc. Am., Vol. 97, pp. 2657-2663   DOI   ScienceOn
50 Bai, M.R., 1992, 'Application of BEM (Boundary Element Method) based Acoustic Holography to Radiation Analysis of Sound Sources with Arbitrarily Shaped Geometries,' J. Acoust. Soc. Am., Vol. 92, pp. 533-548   DOI
51 Barra, L. P. S., Coutinho, A. L. G. A., Mansur, W. J. and Telles, J. C. F, 1994, 'Iterative Solution of BEM Equations by GMRES,' Computers and Structures, Vol. 111, pp. 335-355