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Journal of the Acoustical Society of America / Volume 122 / Issue 3 / AEROACOUSTICS, ATMOSPHERIC SOUND [28]

Proper orthogonal decomposition and cluster weighted modeling for sensitivity analysis of sound propagation in the atmospheric surface layer

J. Acoust. Soc. Am. Volume 122, Issue 3, pp. 1374-1390 (2007); (17 pages)

Chris L. Pettit1 and D. Keith Wilson2

1Aerospace Engineering Department, United States Naval Academy, 590 Holloway Road, MS 11-B, Annapolis, Maryland 21402, USA
2U.S. Army Cold Regions Research and Engineering Laboratory, 72 Lyme Road, Hanover, New Hampshire 03755-1290, USA

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Outdoor sound propagation predictions are compromised by uncertainty and error in the atmosphere and terrain representations, and sometimes also by simplified or incorrect physics. A model’s predictive power, i.e., its accurate representation of the sound propagation, cannot be assessed without first quantifying the ensemble sound pressure variability and sensitivity to uncertainties in the model’s governing parameters. This paper describes fundamental steps toward this goal for a single-frequency point source. The atmospheric surface layer is represented through Monin-Obukhov similarity theory and the acoustic ground properties with a relaxation model. Sound propagation is predicted with the parabolic equation method. Governing parameters are modeled as independent random variables across physically reasonable ranges. Latin hypercube sampling and proper orthogonal decomposition (POD) are employed in conjunction with cluster-weighted models to develop compact representations of the sound pressure random field. Full-field sensitivity of the sound pressure field is computed via the sensitivities of the POD mode coefficients to the system parameters. Ensemble statistics of the full-field sensitivities are computed to illustrate their relative importance at every down range location. The central role of sensitivity analysis in uncertainty quantification of outdoor sound propagation is discussed and pitfalls of sampling-based sensitivity analysis for outdoor sound propagation are described.

© 2007 Acoustical Society of America

ACKNOWLEDGMENTS

Funding for this project was provided by the U.S. Army Engineer Research and Development Center. The constructive comments by the anonymous reviewers were valuable in revising the manuscript. The authors thank the reviewers for contributing their time and effort.

Article Outline

  1. INTRODUCTION
    1. Uncertainty quantification and validation of computational acoustics models
    2. Sensitivity analysis of sound propagation
  2. CONSTRUCTION OF REDUCED ORDER MODELS FOR SOUND PRESSURE FIELDS
    1. Physics model
    2. Latin hypercube sampling
    3. Proper orthogonal decomposition of the sound pressure field
    4. Reduced order models from cluster weighted approximations
  3. SOUND PRESSURE REALIZATIONS
    1. Sampling the sound pressure in parameter space
    2. POD modes of the sound pressure
  4. SENSITIVITY ANALYSIS OF REDUCED ORDER MODELS FOR SOUND PRESSURE FIELDS
    1. Sensitivities from Latin hypercube samples
    2. Empirical observations from scatter plots of POD coefficients
    3. Models for interpolating POD coefficients
    4. Sensitivity of the sound pressure field
      1. General observations
      2. Effects of upwind and downwind propagation on sensitivities
      3. Estimation of extreme sensitivities
      4. Errors caused by poor local sampling of parameters in the original ensemble
      5. Possible importance of parameter correlation
  5. SUMMARY AND CONCLUSIONS

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KEYWORDS and PACS

Keywords

acoustic wave propagation, atmospheric acoustics, parabolic equations

PACS

  • 43.28.Gq

    Outdoor sound propagation and scattering in a turbulent atmosphere, and in non-uniform flow fields

  • 43.28.Lv

    Statistical characteristics of sound fields and propagation parameters

ARTICLE DATA

History
Received 16 Jan 2007
Accepted 13 Jun 2007
Revised 04 Jun 2007
Digital Object Identifier
http://dx.doi.org/10.1121/1.2756176

PUBLICATION DATA

ISSN

0001-4966 (print)  

Publisher

$abstract.society.value is a Member of CrossRef Acoustical Society of America

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