Patch near-field acoustic holography: Regularized extension and statistically optimized methods

Pascal, Jean‐Claude; Paillasseur, Sébastien; Thomas, Jean‐Hugh; Li, Jing-Fang

doi:10.1121/1.3192349

Cited by 10 publications

(3 citation statements)

References 18 publications

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“…Therefore, regularization methods are often used to overcome ill-posed problems in NAH and the regularization parameter choice is also important. Pascal et al [22] used the Morozov difference principle to compute the regularization parameter in SONAH improving the reconstruction accuracy. Gomes and Hansen [23] compared three generally used regularization parameter choice methods in NAH: generalized cross validation (GCV), L-curve and normalized cumulative periodogram.…”

Section: Introductionmentioning

confidence: 99%

A combined sound field reconstruction method for large cylindrical surfaces using non-conformal plane measurement

Cheng¹,

Han²,

Song³

et al. 2021

Meas. Sci. Technol.

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In practical acoustic measurement for large cylindrical surfaces, it is difficult to keep conformal and coaxial between the holographic surface and the reconstruction surface. To overcome this problem, a combined sound field reconstruction method using non-conformal plane measurement is proposed in this paper. Based on the sound pressure measured on the holographic plane, the combined method first reconstructs the sound field on the cylindrical conformal surface using statistically optimal planar near-field acoustic holography, and then reconstructs the sound field on the cylindrical reconstruction surface using statistically optimal cylindrical near-field acoustic holography. And a least square optimization method is proposed to determine the optimal position of the conformal surface. In addition, to overcome ill-posed problems, an error reduction method combining truncated singular value decomposition and Tikhonov regularization is proposed. Finally, the proposed method is applied to a test bed, and the accuracy and robustness of the sound field reconstruction for large cylindrical surfaces are obviously improved, which can provide reliable evidences for noise monitoring and control of mechanical systems.

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Section: Introductionmentioning

confidence: 99%

A combined sound field reconstruction method for large cylindrical surfaces using non-conformal plane measurement

Cheng¹,

Han²,

Song³

et al. 2021

Meas. Sci. Technol.

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show abstract

“…Saijyou [28] proposed an estimation method of appropriate regularization filter for applying the K-space data extrapolation method to solve the problem of the measured pressure contaminated by noise. Pascal [29] determined the regularization parameter using the Morozov discrepancy principle in SONAH and made significant improvements to the standard NAH. Gomes [30] compared the three regularization parameter choice methods (PCMs) used in NAH: GCV, L-curve and Normalized Cumulative Periodogram (NCP).…”

Section: Introductionmentioning

confidence: 99%

Conical Statistical Optimal Near-Field Acoustic Holography with Combined Regularization

Cheng

Song

et al. 2021

Sensors

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For the sound field reconstruction of large conical surfaces, current statistical optimal near-field acoustic holography (SONAH) methods have relatively poor applicability and low accuracy. To overcome this problem, conical SONAH based on cylindrical SONAH is proposed in this paper. Firstly, elementary cylindrical waves are transformed into those suitable for the radiated sound field of the conical surface through cylinder-cone coordinates transformation, which forms the matrix of characteristic elementary waves in the conical spatial domain. Secondly, the sound pressure is expressed as the superposition of those characteristic elementary waves, and the superposition coefficients are solved according to the principle of superposition of wave field. Finally, the reconstructed conical pressure is expressed as a linear superposition of the holographic conical pressure. Furthermore, to overcome ill-posed problems, a regularization method combining truncated singular value decomposition (TSVD) and Tikhonov regularization is proposed. Large singular values before the truncation point of TSVD are not processed and remaining small singular values representing high-frequency noise are modified by Tikhonov regularization. Numerical and experimental case studies are carried out to validate the effectiveness of the proposed conical SONAH and the combined regularization method, which can provide reliable evidence for noise monitoring and control of mechanical systems.

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“…Two ways have been investigated in recent years to improve the array size and microphone density. One way is based on the interpretation or extrapolation of a band-limited signal [26], [27], which is named as the patch method [28]- [30] in the sound source reconstruction. In the patch method, a microphone array is used for the measurements of the sound field information, and the acoustic field that is not measured are interpolated and extrapolated from the measured data.…”

Section: Introductionmentioning

confidence: 99%

Low Complexity Modeling of Cross-Spectral Matrix and Its Application in the Non-Synchronous Measurements of Microphones Array

Fan

Chu

et al. 2021

IEEE Access

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The resolution related with the image quality of acoustic imaging using a microphone array is limited by the size and density of the array. However, non-synchronous measurements can exceed the constraints defined by measurements with a single fixed array. The non-synchronous measurements can achieve a larger and denser aperture array by moving the single array. The key problem of archiving the non-synchronous measurements of a microphone array is the matrix completion of a block diagonal spectral matrix. A comprehensive investigation of the block diagonal spectral matrix completion is still missing in the microphone array signal processing literature since it is usually considered as a difficult problem if without the integrated physical information of the sound field. In this paper, the mathematical relation between the max-norm and the nuclear-norm is pointed out, and the max-norm minimization of the spectral matrix is discussed, which is an effective model with integrated spatial representation of the sound field for the spectral matrix completion. First, the max-norm is utilized for the low complexity modeling and the corresponding Proximal-Point method for Max-norm based Spectral matrix completion (PPMSMC) is proposed; Second, the rank, nuclear-norm and max-norm have been investigated as complexity measures in the context of spectral matrix completion, and their performances are compared. The proposed low-rank methods have constructed a concrete theorem foundation for the non-synchronous measurements of the microphone array.INDEX TERMS Acoustic measurements, low complexity model, max-norm minimization.

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Patch near-field acoustic holography: Regularized extension and statistically optimized methods

Cited by 10 publications

References 18 publications

A combined sound field reconstruction method for large cylindrical surfaces using non-conformal plane measurement

A combined sound field reconstruction method for large cylindrical surfaces using non-conformal plane measurement

Conical Statistical Optimal Near-Field Acoustic Holography with Combined Regularization

Low Complexity Modeling of Cross-Spectral Matrix and Its Application in the Non-Synchronous Measurements of Microphones Array

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