Helmholtz equation-least-squares method for reconstructing the acoustic pressure field

A method using spherical wave expansion theory to reconstruct acoustic pressure field from a vibrating object is developed. The radiated acoustic pressures are obtained by means of an expansion of independent functions generated by the Gram–Schmidt orthonormalization with respect to the particular solutions to the Helmholtz equation on the vibrating surface under consideration. The coefficients associated with these independent functions are determined by requiring the assumed form of solution to satisfy the pressure boundary condition at the measurement points. The errors incurred in this process are minimized by the least-squares method. Once these coefficients are specified, the acoustic pressure at any point, including the source surface, is completely determined. In this paper, this method is used to reconstruct the surface acoustic pressures based on the measured acoustic pressure signals in the field. It is shown that this method can be applied to both separable and nonseparable geometries, and the...

[1]  Joel Franklin,et al.  Well-posed stochastic extensions of ill-posed linear problems☆ , 1970 .

[2]  J. D. Maynard,et al.  Nearfield acoustic holography: I. Theory of generalized holography and the development of NAH , 1985 .

[3]  L. Landweber.  An iteration formula for Fredholm integral equations of the first kind , 1951 .

[4]  A. Sarkissian.  Reconstruction of the surface acoustic field on radiating structures , 1992 .

[5]  R. J. Bernhard,et al.  A noise source identification technique using an inverse Helmholtz integral equation method , 1988 .

[6]  Earl G. Williams,et al.  Generalized nearfield acoustical holography for cylindrical geometry : theory and experiment , 1987 .

[7]  Julian D. Maynard,et al.  Sound source reconstructions using a microphone array , 1980 .

[8]  Earl G. Williams,et al.  Conformal generalized near‐field acoustic holography for axisymmetric geometries , 1990 .

[9]  H. A. Schenck.  Improved Integral Formulation for Acoustic Radiation Problems , 1968 .

[10]  Valentin F. Turchin,et al.  The use of mathematical-statistics methods in the solution of incorrectly posed problems , 1971 .

[11]  Mingsian R. Bai,et al.  Application of BEM (boundary element method)‐based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries , 1992 .

[12]  Y. Chao.  An implicit least‐square method for the inverse problem of acoustic radiation , 1987 .

[13]  Bo-Ha Lee,et al.  3-D sound source reconstruction and field reprediction using the Helmholtz integral equation , 1990 .

[14]  A. Sarkissian.  Acoustic radiation from finite structures , 1991 .

[15]  S. Twomey,et al.  On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature , 1963, JACM.

[16]  Brian H. Houston,et al.  Broadband nearfield acoustical holography for vibrating cylinders , 1989 .

[17]  Angie Sarkissian.  Near‐field acoustic holography for an axisymmetric geometry: A new formulation , 1990 .

[18]  Jean-Claude Pascal,et al.  Broadband acoustic holography reconstruction from acoustic intensity measurements. I: Principle of the method , 1988 .

[19]  Julian D. Maynard,et al.  Nearfield acoustic holography (NAH) II. Holographic reconstruction algorithms and computer implementation , 1987 .

[20]  David L. Phillips,et al.  A Technique for the Numerical Solution of Certain Integral Equations of the First Kind , 1962, JACM.

[21]  David S. Burnett,et al.  A three‐dimensional acoustic infinite element based on a prolate spheroidal multipole expansion , 1994 .

[22]  Julian D. Maynard,et al.  Digital holographic reconstruction of sources with arbitrarily shaped surfaces , 1989 .