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Regularization methods for near-field acoustical holography.

E G Williams1

  • 1Naval Research Laboratory, Washington, DC 20375-5350, USA. williams@genah.nrl.navy.mil

The Journal of the Acoustical Society of America
|October 30, 2001
PubMed
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Near-field acoustical holography (NAH) reconstructs vibrating structure data using regularization methods to solve ill-posed inverse problems. This study presents four robust regularization techniques, enhancing automated NAH algorithm performance for various geometries.

Area of Science:

  • Acoustics
  • Signal Processing
  • Computational Physics

Background:

  • Near-field acoustical holography (NAH) reconstructs surface velocity and pressure from acoustic measurements.
  • NAH is a linear, ill-posed inverse problem due to evanescent waves, hindering accurate data reconstruction.
  • Existing methods require robust regularization to overcome ill-posedness.

Purpose of the Study:

  • To present and evaluate robust regularization methods for NAH.
  • To automate the NAH algorithm for improved performance and broader applicability.
  • To investigate parameter selection procedures crucial for regularization success.

Main Methods:

  • Four regularization techniques are presented: Tikhonov (standard and improved), Landweber iteration, and conjugate gradient.

Related Experiment Videos

  • The methods are applicable to planar, cylindrical, spherical, and conformal NAH geometries.
  • Parameter selection is addressed using Morozov discrepancy principle and generalized cross validation.

    • Main Results:

    • The study focuses on planar and cylindrical NAH due to their computational efficiency via discrete Fourier transform.
    • Reformulating NAH equations into an eigenvalue problem facilitates the integration of regularization theory.
    • The proposed methods demonstrate robustness and can be incorporated with minimal computational overhead.

    Conclusions:

    • Automated NAH algorithms incorporating regularization theory overcome significant hurdles in data reconstruction.
    • The presented regularization techniques enhance the accuracy and applicability of NAH for both separable and nonseparable geometries.
    • This work advances the practical implementation of NAH for analyzing vibrating structures.