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Interior sound field control using generalized singular value decomposition in the frequency domain.

Yann Pasco1, Philippe-Aubert Gauthier1, Alain Berry1

  • 1GAUS, Groupe d'Acoustique de l'Université de Sherbrooke, Université de Sherbrooke, 2500 boul. de l'Université, Sherbrooke J1K 2R1, Canada.

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Summary

This study uses Generalized Singular Value Decomposition (GSVD) to simplify acoustic control systems. GSVD effectively cancels interior sound fields while preserving the exterior sound field, reducing controller complexity.

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Area of Science:

  • Acoustics
  • Signal Processing
  • Control Theory

Background:

  • Controlling sound fields within enclosed regions using acoustic sources is challenging.
  • The Kirchhoff-Helmholtz integral offers a theoretical basis but leads to complex implementations with numerous sources and sensors in 3D.
  • Approximating sources as monopole and radial dipole transducers is key to avoiding external field modification.

Purpose of the Study:

  • To investigate the use of Generalized Singular Value Decomposition (GSVD) for reducing controller complexity in acoustic field control.
  • To separate the influence of control sources on interior versus exterior sound fields.
  • To demonstrate effective interior sound field cancellation while maintaining the integrity of the exterior sound field.

Main Methods:

  • Application of Generalized Singular Value Decomposition (GSVD) to the acoustic control problem.
  • Truncation of the singular basis derived from the GSVD factorization.
  • Simulations in free field (circular arrays) and reflective environments (square arrays) to validate the approach.

Main Results:

  • GSVD significantly reduces controller complexity compared to direct Kirchhoff-Helmholtz integral implementations.
  • Proper truncation of the GSVD basis enables effective cancellation of the interior sound field.
  • The exterior sound field remains largely unaffected by the control sources below the spatial Nyquist frequency.

Conclusions:

  • GSVD is a powerful tool for simplifying complex acoustic control systems.
  • The method allows for targeted control of interior sound fields without perturbing the external environment.
  • Simulations confirm the efficacy of GSVD in both free field and reflective scenarios.