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Journal of Sound and Vibration
Article . 2010 . Peer-reviewed
License: Elsevier TDM
Data sources: Crossref
https://doi.org/10.2514/6.2009...
Article . 2009 . Peer-reviewed
Data sources: Crossref
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Uncertainty analysis of the standard delay-and-sum beamformer and array calibration

Authors: Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA ( host institution ); Yardibi, T.; Bahr, C.; Zawodny, N.; Liu, F.; Cattafesta III, L.N.; Li, J.;

Uncertainty analysis of the standard delay-and-sum beamformer and array calibration

Abstract

Beamforming has become an ubiquitous task in aeroacoustic noise measurements for source localization and power estimation. The standard delay-and-sum (DAS) beamformer is the most commonly used beamforming algorithm due to its simplicity and robustness and also serves as the basis for more sophisticated algorithms, such as the deconvolution approach for the mapping of acoustic sources (DAMAS). The DAS data reduction equation is a function of many parameters including the microphone locations, microphone transfer functions, temperature and the cross spectral matrix (CSM), where each one of these parameters has a unique uncertainty associated with it. This paper provides a systematic uncertainty analysis of the DAS beamformer and Dougherty’s widely used calibration procedure under the assumption that the underlying mathematical model of incoherent, monopole sources is correct. An analytical multivariate method based on a flrst-order Taylor series expansion and a numerical Monte-Carlo method based on assumed uncertainty distributions for the input variables are considered. The uncertainty of calibration is analyzed using the Monte-Carlo method, whereas the uncertainty of the DAS beamformer is analyzed using both the complex multivariate and the Monte-Carlo methods. It is shown that the multivariate uncertainty analysis method fails when the perturbations are relatively large and/or the output distribution is non-Gaussian, and therefore the Monte-Carlo analysis should be used in the general case. The calibration procedure is shown to greatly reduce the uncertainties in the DAS power estimates. In particular, 95% confldence intervals for the DAS power estimates are presented with simulated data for various scenarios. Moreover, the 95% confldence intervals for the integrated DAS levels at difierent frequencies are computed using experimental data. It is shown that with experimental data, the 95% confldence intervals for the integrated power levels are within §1 dB of the mean levels when the component uncertainties are set at low but achievable values.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
37
Top 10%
Top 10%
Top 10%
Green