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Research Papers

Application of Inverse Patch Transfer Functions Method With Wideband Holography Algorithm to Sparsely Distributed Sources Identification

[+] Author and Article Information
Yansong He

School of Automotive Engineering,
Chongqing University,
Chongqing 400044, China
e-mail: hys68@cqu.edu.cn

Chong Liu

School of Automotive Engineering,
Chongqing University,
Chongqing 400044, China
e-mail: liuchong_cqu@cqu.edu.cn

Zhongming Xu

School of Automotive Engineering,
Chongqing University,
Chongqing 400044, China
e-mail: xuzm@cqu.edu.cn

Zhifei Zhang

School of Automotive Engineering,
Chongqing University,
Chongqing 400044, China
e-mail: z.zhang@cqu.edu.cn

Shu Li

School of Automotive Engineering,
Chongqing University,
Chongqing 400044, China
e-mail: leeshu@cqu.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 22, 2016; final manuscript received June 27, 2017; published online September 7, 2017. Assoc. Editor: Sheryl M. Grace.

J. Vib. Acoust 140(1), 011008 (Sep 07, 2017) (10 pages) Paper No: VIB-16-1556; doi: 10.1115/1.4037471 History: Received November 22, 2016; Revised June 27, 2017

Inverse patch transfer functions (iPTF) method has been developed to reconstruct the sound field of irregularly shaped sources in a noisy environment. The iPTF method, which uses classic regularization methods to solve the ill-posed problems generally, would incur some sidelobes ghosting in the process of identifying sparse sources. In view of the fact that the algorithm in wideband holography (WBH) can promote sparsity of results, a technique combining iPTF method with WBH algorithm is proposed to identify sparsely distributed sources in the present work. In the proposed technique, double layer pressure measurements are used to replace the measurements of the pressure and normal velocity which uses costly p-u probes. A gradient descent algorithm and a filtering process are applied to solve the minimization problem of identifying the normal velocities of target sources, which can suppress ghosting sources rapidly by an iterative process. In simulations, the field reconstruction results of two antiphase square piston sources show good sparsity and accuracy by employing the technique, nearly without ghosting sources. At different distances and frequencies of the two sources, the technique still performs well. Experimental validations at 200 Hz and 400 Hz are carried out in the end. The results of experiments are also coinciding with those of simulations.

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Figures

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Fig. 1

Definition of the closed virtual cavity Ω and its boundary surfaces

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Fig. 2

Schematic diagram of double layer pressure measurements

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Fig. 3

Definition of (a) two baffled piston sources in antiphase and (b) patches meshed on the virtual surfaces around sources

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Fig. 4

All hologram surfaces required for double layer pressure measurements

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Fig. 5

The condition number of patch impedance matrices for maximal order of modes extracted up to (-) 9 × 9 × 1, (--) 13 × 13 × 5, (•••) 15 × 15 × 7, and (-•) 18 × 18 × 10

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Fig. 6

The pressure distributions of patches on the virtual surface S0 at 400 Hz: (a) without a disturbing source and (b) with a disturbing source

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Fig. 7

Source velocities distribution at 400 Hz of (a) theoretical values and reconstructed results obtained using (b) WBH algorithm (ζ = 4.15%) and (c) Tikhonov regularization (ζ = 11.86%)

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Fig. 8

Source velocities distribution at 400 Hz with 15 dB SNR noise of (a) reconstructed results obtained using WBH algorithm (ζ = 5.97%) and (b) Tikhonov regularization (ζ = 26.0%)

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Fig. 9

Performance of the iPTF method with WBH algorithm ((a) and (c)) and Tikhonov regularization ((b) and (d)) at different distances between the two sources at 400 Hz

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Fig. 10

CSNRs of the target sources to a disturbing source on virtual surfaces within a frequency band range

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Fig. 11

Relative errors of the source velocities reconstructed by (–) the iPTF method with Tikhonov regularization and (-) the iPTF method with WBH algorithm with both the disturbing sources and 15 dB SNR noise

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Fig. 12

RVAC computed between the reference source velocity field identified by (-) the iPTF method with WBH algorithm and (–) the iPTF method with Tikhonov regularization adding both the disturbing source and 15 dB SNR noise

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Fig. 13

Experiment setup and measurements: (a) two baffled loudspeakers, a thick wooden, a phase preference microphone, and three measurement microphones and (b) diagram of measurements on side hologram surfaces

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Fig. 14

Comparison of source velocities distribution results obtained by the iPTF method with Tikhonov regularization and the iPTF method with WBH algorithm, respectively, at 200 Hz ((a) and (b)) and at 400 Hz ((c) and (d))

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