Various implementation issues of the FDNESI technique have been investigated in this paper. A virtual microphone technique is suggested for minimizing edge effects using extrapolation and for improving resolution using interpolation.
Although the FDNESI is by far the most efficient method among all inverse filtering approaches, it can yield a noise source mapping with slightly larger spreading than the NESI. The FDNESI technique proved effective in identifying broadband and non-stationary sources produced by these sources.
Sound field imaging using microphone array by FDNESI algorithm are capable to reconstruct the sound field effectively which is suggested in the thesis by noise source identification and non-destructive mode shape evaluations. From the loudspeaker experiment and the compressor experiment, the six algorithms are compared on the point of resolution and performance. Both Fourier NAH and FDNESI have good performance while FDNESI is more robust than Fourier NAH for it can reconstruct the sound field from the source of arbitrary shape. As expected, the high resolution methods such as MVDR and MUSIC can obtain greater results than DAS and TR in localizing the source position. Although the resolution of MVDR and MUSIC are better than Fourier NAH and FDNESI but the performance of Fourier NAH and FDNESI are better. Most important of all, Fourier NAH and FDNESI can reconstruct the acoustic variables such as sound pressure, particle velocity and active intensity.
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Table 1. Comparison of computational complexity in terms of OPS of three multichannels filtering methods for three array configurations. The block size of FFT
i 512 N
. The numbers of microphones and focal points are assumed to be equal, i.e., m j. The DC method is used for benchmarking (100% in parenthesis).
Domain Method 4 4 URA 5 6 URA 8 8 URA Time DC 65,536 (100%) 230,400 (100%) 1,048,576 (100%) Frequency FDOA 544 (0.83%) 1440 (0.63%) 5248 (0.5%)
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Table 2. Experimentally Determined Relative Frequencies for a completely free square brass plate; =1/3
m/n +
Relative frequency for values of m/n minus-
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
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Fig. 1. Top view of the experiment arrangement using a 5 6 URA.
Focal surface Microphone
d
L
Lr
Focal point
Array surface
Source surface and Reconstruction surface
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(c)
Fig. 2. Illustration of the Overlap and add method. (a) The pressure data p( )n , (b) Decomposition of p n( ) into non-overlapping sections of length L, (c) Result of convolving each section with the inverse filter
P-1
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Fig. 3. The idea of the FDNESI with virtual microphone technique. The symbol“ ” indicates an interpolated microphone position. The symbol“ ” indicates an
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extrapolated microphone position. A The pressure data picked up by the microphones, B Reconstructed source strength at the focal points, C The pressure data interpolated at the virtual microphones, D Reconstructed source strength at the virtual focal points.
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(a)
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(b)
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(c)
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(d)
Fig. 5. The numerical simulation of NESI/FDNESI using the 4 4 URA and the virtual microphone technique. (a) The unprocessed sound pressure image received at the microphones, (b) the reconstructed active intensity image by 4 4 URA, (c) the reconstructed active intensity image using the virtual microphone technique in time domain processing, (d) the reconstructed active intensity image using the virtual microphone technique in frequency domain processing. The symbol“ ” indicates the microphones. The symbol“” indicates the focal points. The symbol“◇” indicates the noise sources.
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(a)
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(b)
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(c)
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(d)
Fig. 6. The numerical simulation result of vibrating plate by FDNESI using the 5 6 URA. (a) The reconstructed particle velocity with m=1, n=1 and f = 16.50 Hz, (b) the reconstructed particle velocity with m=2, n=1 and f = 33.57 Hz, (c) the reconstructed particle velocity with m=2, n=2 and f = 65.98 Hz, (d) the reconstructed
particle velocity with m=3, n=2 and f = 97.45Hz. The blue points are the microphones at the array surface and, black crosses are the simulated point sources at the source surface and the black lines are the nodal lines.
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(a)
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(b)
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(c)
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(d)
Fig. 7. The numerical simulation of vibrating plate using the 5 6 URA and the virtual microphone technique. (a) The unprocessed sound pressure image received at the microphones, (b) the real part of particle velocity in frequency domain image, (c) the real part of particle velocity in frequency domain using the virtual microphone technique image, (d) the nodal pattern with m=0, n=2 and f = 48.78 Hz. The symbol“” indicates the microphones. The symbol“” indicates the virtual point sources.
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Fig. 8. The experimental arrangement for a wooden box with a loudspeaker fitted inside ,the URA, and a 30-channel random array optimized for farfield imaging are also shown in the picture.
Array
URA
Random array
PXI /NI system
PXI 8106 controller
PXI 4496 DAQ
LabVIEW
Sound map Computer
Wooden box with a loudspeaker fitted inside
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(a)
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(b)
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(c)
Fig. 9. The results of run-up experiment obtained using FDNESI with the 4 4 URA.
The scooter engine was accelerated from 1500 rpm to 7500 rpm within ten seconds. (a) The unprocessed sound pressure image received at the microphones, (b) the reconstructed active intensity image, (c) the reconstructed active intensity image using the virtual microphone technique. The symbol“” indicates the focal points.
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(a)
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(b)
Fig. 10. The results of a wooden box with a loudspeaker fitted inside. The noise map is within the band 200 Hz ~ 1.6k Hz. (a) The unprocessed sound pressure image received at the microphones by 5 6 URA, (b) the particle velocity image reconstructed using FDNESI by the 5 6 URA. The symbol“” indicates the focal points.
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(a)
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(b)
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(c)
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(d)
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(e)
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(f)
Fig. 11. The results of Loudspeaker experiment obtained using the 5 6 URA. The loudspeakers are situated at (0.1m, 0.1m) and (0.4m, 0.2m) on the source surface that produce random noise band-limited to 1.7 kHz. The observed frequencies in the algorithms are chosen to be 1.2 kHz. (a) The reconstructed sound pressure image by Fourier NAH, (b) the reconstructed sound pressure image by FDNESI, (c) the source image obtained by using DAS, (d) the source image obtained by using TR, (e) the source image obtained by using MVDR, (f) the source image obtained by using MUSIC.
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(a)
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(b)
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(c)
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(d)
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(e)
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(f)
Fig. 12. The results of compressor experiment obtained using the 5 6 URA. The major noise is at the air intake position situated at (0.2m, 0.3m). The observed frequencies in the algorithms are chosen to be 1.2 kHz. (a) The reconstructed sound pressure image by Fourier NAH, (b) the reconstructed sound pressure image by FDNESI, (c) the source image obtained by using DAS, (d) the source image obtained by using TR, (e) the source image obtained by using MVDR, (f) the source image obtained by using MUSIC.
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Fig. 13. The experimental arrangement for a square aluminum plate driven from the center with a shaker, the shaker is mounted on a desk.
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(a)
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(b)
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(c)
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(d)
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(e)
Fig. 14. The results of vibrating plate experiment obtained using FDNESI with the 5 6 URA. (a) The real part of particle velocity in frequency domain image at 204Hz, (b) the real part of particle velocity in frequency domain image at 226Hz, (c) the real part of particle velocity in frequency domain image at 595Hz, (d) real part of particle velocity in frequency domain using the virtual microphone technique image at 204Hz, (e) real part of particle velocity in frequency domain using the virtual microphone technique image at 595Hz. The symbol“” indicates the focal points.