Experimental results of Double Near-filed Holography method for a commercial product Masao Nagamatsu 1 Hokkaido University of Science 15-4-1, Maeda-7-jo, Teine, Sapporo, Hokkaido, 006-8585, JAPAN

ABSTRACT In my laboratory, a new noise localization method, ‘Double nearfield acoustic holography (DNAH) method’ is being developed. This method aims for mechanical noise source localization of the low frequency noise under 100Hz. Formerly, the experimental results of speaker tests in laboratory envi- ronment is presented (4)(6). It shows the better experimental results compared with the conventional near-field acoustic holography method as a low frequency noise sources localization method. In this paper, the experimental results of low frequency noise localization for a motor scooter using DNAH method are presented. As an example of mechanical product, a 50cc scooter’s low frequency noise are measured by DNAH method, and by conventional near-field acoustic holography (NAH) method. The experimental results are compared with the results of conventional holography method. By these experiments, it is proved that the developing DNAH method can detect the low frequency noise source location of mechanical products, even if the sound frequency is lower than 100Hz.

1. INTRODUCTION

Currently, as noise localization systems, many products are sold from many companies, and widely used in mechanical industry. Almost of these are based on the beamforming theory.

On the other hands, there is a modern type acoustic holography method, formally called ‘near-field acoustic holography (NAH) method.’ This method can include the evanescent sound wave in its an- alytical calculation, and said as it has better resolution than the classic type acoustic holography method.

All products in commerce regardless of the types, a beamforming type or a NAH type, has lower frequency limitation at around 500Hz. This limitation is caused by the theoretical fact that to measure low frequency sound, the holographic methods require the huge measurement plane, and it is not realistic. On the other hand, the acoustic intensity method can measure low frequency sound, but it does not have enough preciseness for fine sound localization.

To overcome this limitation, the new acoustic holographic method ‘double near-field acoustic ho- lography (DNAH) method’ is proposed. This method is a converted method of NAH method, and is aiming for low frequency sound localization with the available size measurement plane in a chamber. Formerly, the experimental results of speaker tests in laboratory environment is presented (4) . In that paper, the effectiveness of DNAH for low frequency sound localization is probed.

In this paper, the several experimental results for mechanical product (a 50cc scooter) about low frequency noise localization are explained. As a result, the images acquired by the proposing DNAH

1 nagamatu@hus.ac.jp

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method has better resolution than its of conventional NAH method. And it is said that by using the proposing DNAH method, the low frequency noise source of the mechanical product can be detected. • . 2. THE MEASUREMENT AND ANALYSIS OF PROPOSING DNAH METHOD

In this chapter, the proposing DNAH method is explained. In this chapter, the theory of proposing DNAH method is explained with comparison with the theory of conventional NAH method (1) .

2.1. Measurement configuration of DNAH method The figure 1 shows the configuration of conventional NAH method. The conventional NAH method has ‘single’ measurement plane. This plane is set at certain distance from the plane which is estimated as the sound source(s) is located (the machine surface).

On this measurement plane, the distribution of sound pressure in the sound field is measured. Therefore, the conventional NAH method can acquire the information of sound field on single plane.

Figure 1: The measurement configuration of conventional NAH method. The proposing DNAH method uses doubled measurement planes. Microphones of conventional NAH method measurement system and almost of beamforming’s array, are located on single plane in sound field. There is a former research (5) using doubled measurement planes, however the purpose of it is different from this method. In the proposing DNAH method, the front and rear measurement planes are set in the sound field. The figure 2 shows the measurement configuration of proposing DNAH method. The DNAH method measures the information of sound field on parallel two measurement planes.

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Rear Measurement Plane

Front Measurement Plane

Sound Source(s)

y

x

z

Distance between Planes

Figure 2: The measurement configuration of proposing DNAH method. 2.2. Analysis of DNAH method

Because proposing DNAH method has doubled measurement plane, the measured datum by DNAH method is doubled. Therefore, the computation of holographic back propagation analysis is also con- verted. In this section, the computation steps of conventional NAH method (1) and proposing DNAH method are explained. The conventional NAH method is measuring the sound pressure distribution on the single plane in sound field. The analysis steps of conventional NAH method is shown in figure 3. To the measured sound pressure distribution on the measurement plane, the time domain Fourier transformation is applied to pick up the certain frequency sound. The analysis of conventional NAH method is calculated for certain single frequency sound information. By this calculation, the distribu- tion of complex sound pressure on the measurement plane is calculated.

As the next step, the space domain 2 dimensional Fourier transformation is applied for complex sound pressure distribution on the measurement plane. By this transformation, the space domain spec- tra are calculated. In the next step, Back propagation computation is applied to these spectra. This computation is derived from the planer propagation theory of sound propagation. At last, by applying inverse Fourier transformation to the results of back propagation computation, the distribution of sound pressure on the reconstruction plane, which is estimated as sound source(s) is located, is cal- culated. The visualized image of this distribution is the reconstructed image which is used for detec- tion of the location of the sound source(s).

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Measured Sound Pressures

Time domain Fourier Transformation

Time domain Spectrums

Space domain Fourier Transformation

Wave number domain Spectrums on measurement plane

Back Propagation Computation

Wave number domain Spectrums on reconstruction plane

Space domain Inverse Fourier Transformation

Reconstructed images

Figure 3: The analysis steps of conventional NAH method. The analysis of proposing DNAH method is same with conventional NAH method without the back- propagation step. The proposing DNAH method measures the sound pressure information on two parallel measurement planes. Therefore, the DNAH method can obtain the actual planer propagation information in sound field from the difference of sound information on two measurement planes. The figure 4 is the explanation of analysis steps of proposing DNAH method.

Figure 4: The analysis steps of conventional NAH method.

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In these steps, the procedure of Fourier transformations and inverse Fourier transformation are same with conventional NAH method. In the conventional NAH method, the Green function using for back propagation computation is as follows.

2 2 2 ) , , (

− − =

y x k k k iz y x e z k k G

(1) In this equation, z is distance between the measurement plane and reconstruction plane, and k is the wave number of the sound of analyzing frequency. The k x and k y are the wave number frequency of corresponding direction on the measurement plane. By multiplying this Green function to the space domain spectra, the space domain spectra on the reconstruction plane is calculated.

In this equation, if the inner part of root computation is positive value, the absolute value and argument (phase value) of G is as follows.

(2)

1 = G

(3) In this case, the absolute value of G is 1, therefore the absolute values of spectra are not change. And phase of G is proportional with z.

2 2 2 ) arg( y x k k k z G − − =

And if the inner part of root computation is negative value, the absolute value and argument value of G is as follows.

2 2 2 k k k z y x e G

− + − =

(4)

0 ) arg( = G

(5) In this case, the absolute values of spectra are change, and phases of spectra are not changed. In both equations, in function (3) and (5), it is said that the argument value is proportional with distance z . In proposing DNAH method, the actual argument changes in sound space can be derived by compar- ing the arguments of the measured sound distributions on front and rear measurement planes, because of doubled measurement plane. In the analysis of DNAH method, because it is one of holography methods, the argument (phase) is thought important.

In the proposing DNAH method, equation (3) or (5) are converted. As stated former, the change of argument, phase of spatial spectra is proportional with z , the distance of the rectangular direction with the measurement planes. And about this phase change, equation (3) and (5) are the theoretical change of planer sound propagation which is led from physical law. In proposing DNAH method, the actual phase change of sound propagation can be acquired by comparing the datum on the two meas- urement planes. Instead of theoretical phase change of equation (3) or (5) in the conventional NAH method, in the proposing DNAH method, the actual phase change is used for back propagation cal- culation. Therefore, the proposing DNAH method uses function (6), instead of function (3) or (5) in conventional method.

( )     ) arg( ) arg( / ) arg( ) arg( ) arg( r f r f P P d

z d P P z G − = − =

(6)

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In this equation, d is the distance between the front and rear measurement planes, and P f and P r are the wave number domain spectra of front and rear measurement planes. Because phase change is important in holographic method, in calculation of absolute value, function (2) is always used. 3. EXPERIMENTS

In this paper, the experimental results of DNAH method for a mechanical product, a 50cc scooter is reported. In this chapter, the experimental configuration and results are explained.

3.1. Experimental configuration To prove that the low frequency noise sources of mechanical products can be detected by this method, the experiments for a small mechanical product, a 50cc scooter, are carried out. The picture of the experiment is shown in figure 5. The engine of the scooter is working (idling) and exhaust gas is exhaled from the muffler during experiments. The largeness of measurement plane is 1m x 1m. The rear portion of scooter, where there are the engine and the muffler, is measured.

The measurement distance is 10cm from most projected surface of the rearward of the scooter. The two scanning microphones and one reference microphone are used for measurement. These two scan- ning microphones, shown in figure 6, are attached to microphone traverse mechanism, and move vertically and horizontally. In analysis by conventional NAH method, the datum only from front scanning microphones is used. In analysis by proposing DNAH method, the datum from both of front and rear scanning microphones are used.

The gap between the front and the rear scanning microphones (=distance between 2 measurement planes) is 8cm. The measurement points (actually measured points) number is 11 x 11.

Figure 5: The overview of experiments site.

Figure 6: The scanning microphones setting of DNAH method.

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3.2. Experimental results The figure 7 shows the noise spectrum acquired from one of the reference signal datum.

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0.6

Voltage [V]

0.5

0.4

0.3

0.2

0.1

0

10.01 34.42 58.84 83.25 107.67 132.08 156.49 180.91

Frequency [Hz]

Figure 7: The frequency spectrums (10-200Hz) of the reference microphone signal. In this research, the lower two peak frequencies (31.01Hz and 62.01Hz) are analyzed.

The figure 8 shows the experimental results at 31.01Hz. In all figures, the red indicates the highest level in each image. The yellow indicates -5dB from the top, the green indicates -10dB, the blue indicates -15dB or lower. (a) The experimental result at 31.01Hz, (b)The experimental result at 31.01Hz,

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analyzing by conventional NAH method. analyzing by proposing DNAH method.

Figure 8: The experimental results at 31.01Hz. Comparing these images, the holographic image analyzed by the proposing DNAH method shows the sharper image than the image by the conventional NAH method. In the image by conventional NAH method, the large source image is shown near the muffler. However, from the image by pro- posing DNAH method, it is clearly indicated that the noise radiated from downside of muffler.

The figure 9 shows the experimental results at 62.01Hz. (b) The experimental result at 62.01Hz, (b)The experimental result at 62.01Hz,

analyzing by conventional NAH method. analyzing by proposing DNAH method.

Figure 9: The experimental results at 62.01Hz. Comparing these images, the holographic image analyzed by the proposing DNAH method also shows the sharper image than the image analyzed by the conventional NAH method. The image by proposing method, it is clearly indicated that the noise radiated from exhaust gas and the body beneath the seat. On the other hands, the image by conventional NAH method is blurry and it does not have enough resolution to detect noise sources.

4. CONCLUSIONS

In this paper, the experimental results of sound localization in low frequency for the mechanical product is reported. The proposing DNAH method made sharp holographic images, which has enough resolution to detect noise sources. The images by proposing DNAH method is sharper than images by conventional NAH method. As a result, the low frequency noise localization for mechanical prod- uct succeeded by using proposing DNAH method. 5. REFERENCES

1. Williams, W. G., Fourier Acoustics. Academic press , 1999. 2. Nagamatsu, M., Experimental Results of Converted NAH Method. JSME international Journal

Series C Vol49 . No.3, 2006. 3. Nagamatsu, M., A Research about Converted Nearfield Acoustic Holography Method. SAE Tech-

nical Paper 2005-01-2536, 2005. 4. Nagamatsu, M., Noise Source Localization by Double NAH method. SAE Technical Paper 2015-

01-2247, 2015. 5. Tamura, M., Spatial Fourier transformation method of measuring reflection coefficients at

oblique incidence. I: Theory and numerical examples. J. Acoust. Soc. Am. , 88(5) 2259-2264, 1990. 6. Nagamatsu, M., Experimental Results of Double Nearfield Acoustic Holography Method with

Variable Measurement Distance. S AE Technical Paper 2017-01-1872.

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