Measurement of airborne sound insulation of building components by near-field acoustic holography Wei Xiong 1 School of Architecture, South China University of Technology 381 Wushan Road, Tianhe District, Guangzhou City, Guangdong Province, China Hongwei Wang 2 School of Architecture, South China University of Technology 381 Wushan Road, Tianhe District, Guangzhou City, Guangdong Province, China Guangyao Zhang 3 School of Architecture, South China University of Technology 381 Wushan Road, Tianhe District, Guangzhou City, Guangdong Province, China

ABSTRACT A new method of sound insulation measurement of building components based on near-field acoustic holography is proposed in the paper. First, multi-channel measurements are performed at the near- field position of the member using a microphone array, and the measured holographic surface complex sound pressure is reconstructed by a spatial sound field transformation algorithm to find the normal sound intensity distribution on the surface of the member. Then, a window function is applied in the wave number domain to separate the propagating and swift waves to obtain the normal sound intensity distribution of the propagating waves on the surface of the component, and then calculate the magnitude of the sound power radiated from the component to the receiving room; finally, the radiated sound power of the component is converted to the incident sound power of the source room to obtain the frequency characteristics of the airborne sound insulation of the component, and the sound insulation defects of the component are detected based on the acoustic image. The basic principle of the near-field acoustic holographic sound insulation measurement method is explained in the paper, and the accuracy and validity of the method are verified through experiments.

1. INTRODUCTION

Airborne sound insulation is an important parameter that reflects the ability and characteristics of building components to isolate noise transmission. Accurate field measurement of airborne sound insulation can be more scientifically, reasonably and intuitively evaluated for the actual application of the components, which is of great importance in noise control and acoustic design. The current widely used sound insulation measurement methods, such as those based on sound pressure

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measurement and sound intensity measurement, have been relatively mature and have formed relevant measurement standards [1-3]. However, the application of traditional sound insulation measurement methods in practical engineering is still subject to many limitations due to the complexity of sound radiation from on-site structural vibration, the instability of the test environment, and the increasing test requirements. How to quickly and accurately measure sound insulation in the field has been a hot issue for research in the field of building acoustics.

Near-field acoustic holography (NAH) is one of the sound field visualization techniques based on multichannel simultaneous measurement and processing, which can calculate acoustic quantities at arbitrary field points throughout space from holographic data (sound pressure or particle velocity) measured in the near field, as well as reconstruct the sound field distribution on the surface of the vibrating source [4-5]. Currently, the NAH technique has been widely used in the fields of noise source identification [6-7], mechanical fault diagnosis [8-9], and sound field visualization [10-11], but it has rarely been applied in the sound insulation measurement of building components. In recent years, some scholars have initially explored the feasibility of applying NAH technology to sound insulation measurements through experimental studies, and certain results have been achieved [12- 13]. According to the principle of sound insulation testing, the test member is excited by the diffuse sound field in the source chamber and vibrates, and then radiates sound energy to the receiving chamber and forms the corresponding sound field distribution in space. If the complex sound pressure distribution is measured in the near field of the component, and then the spatial sound field transformation algorithm of NAH is applied to the reconstruction of the radiated sound field of the component, then not only the magnitude of the sound power radiated to the receiving chamber by the component can be calculated from the reconstructed normal sound intensity, but also the comprehensive and subtle features related to sound leakage can be extracted from the acoustic image of the surface of the component, so that the sound insulation frequency characteristics and the location of sound insulation defects of the test component can be determined In addition, the NAH technique has the advantage of being multi-functional. In addition, NAH technology also has the advantages of multi-channel measurement, background noise suppression and sound field visualization. According to the above characteristics, NAH technology has a large application prospect in the field measurement of sound insulation. Therefore, it is necessary to conduct an in-depth study of this sound insulation test method.

This study proposes the application of NAH technique to measure the sound insulation characteristics of building components. Its main contributions are the application of the spatial sound field transformation algorithm of NAH to the reconstruction of radiated sound power in sound insulation measurement and the application of the spatial distribution information of the sound field to the detection of sound insulation defects, and a new method of airborne sound insulation measurement of building components based on NAH theory is systematically proposed. In this study, a 16-channel microphone line array is used to experimentally validate the method for measuring sound insulation and detecting sound insulation defects.

2. NAH-BASED SOUND INSULATION MEASUREMENT PRINCIPLE

The NAH-based sound insulation measurement method approximates the incident sound power by measuring the average sound pressure level in the indoor space of the source room, and the complex sound pressure distribution in the near field of the component using microphone arrays in the receiving room, then the normal sound intensity distribution on the surface of the component is reconstructed in the inverse direction by the spatial sound field transformation algorithm, and the sound power radiated from the component to the receiving room is further calculated to obtain the airborne sound insulation of the component.

The following is a brief description of the basic principles and processes of the NAH sound insulation measurement method:

(1) signal acquisition. The signal to be collected includes the holographic surface sound pressure signal and the reference sound pressure signal, both of which are recorded and sampled at the same time. The holographic surface time domain sound pressure signal ( ) H 1 2 P l ,l ,t is scanned and measured

by the microphone array set in the near field, while the reference time domain sound pressure signal

( ) H 0 0 P l ,l ,t is measured by a separate microphone, and the position of the reference microphone is kept constant during the whole sound field measurement process.

(2) Holographic surface complex sound pressure calculation. In the whole frequency range, the holographic surface complex sound pressure distribution ( ) H 1 2 , , P l l f can be expressed as

( ) ( )

1 2 ( , , ) H 1 2 H 1 2 | , , , , | j l l f P l l f P l l f e  = (1)

( ) H 1 2 , , P l l f and ( ) 1 2 , , l l f  are the amplitude and phase distributions of the complex sound pressure in

the holographic plane, respectively, and 1 2 l l n =

、 1，2，， represents the serial numbers of the holographic measurement points and the sound field reconstruction points in the real number field

x y 、 . ( ) 1 2 , , H P l l f is derived from the time domain sound pressure signal of each measurement point

in the holographic plane by self-spectroscopy.

In practical applications, since it is difficult to sample all holographic measurement points synchronously, the reference signal is used to obtain the phase information, and ( ) 1 2 , , l l f  is obtained

from the time domain sound pressure signal of each measurement point in the holographic plane and the reference signal by mutual spectroscopy ( ) ( ) H 1 2 x 1 2 | | , , , , P l l f S l l f = (2)

( ) ( ) ( )

        =          

Im , , , , arctan

S l l f l l f

xy 1 2 1 2

S l l f 

(3)

Re , ,

xy 1 2

Where "Re" and "Im" represent the complex function to take the real part and the imaginary part,

( ) x 1 2 , , S l l f is the unilateral self-power spectral density function of the sound pressure of each channel

of the holographic surface, ( ) xy 1 2 , , S l l f is the unilateral mutual power spectral density function of the

sound pressure of each channel and the reference sound pressure.

(3) Sound field reconstruction. According to the sound insulation measurement needs, the reconstructed sound field is divided into two categories, the first category is the normal sound intensity distribution ( ) S 1 2 , , I l l f  containing only propagating wave components, reflecting the

contribution of the energy radiated by the component after excitation to the sound field of the receiving room, used to calculate the amount of sound insulation of the component; the second category is the normal sound intensity distribution ( ) S 1 2 , , I l l f  containing swift waves and

propagating wave components, reflecting the real state of the component after excitation, its surface sound field distribution, used to detect the sound insulation of the component Defect location.

The steps of acoustic field reconstruction are as follows: firstly, the angular spectrum of the holographic surface complex acoustic pressure distribution is obtained by the two-dimensional Fourier transform after the 1-fold complementary zero of ( ) H 1 2 P l ,l , f , which is recorded as

( ) H 1 2 P k ,k , f ; then the angular spectrum of the complex acoustic pressure on the surface of the

component ( ) S 1 2 P k ,k , f is solved by the angular expression of Rayleigh's first integral, and the angular

component of the velocity spectrum in the z-direction is solved by the Euler equation after the two- dimensional Fourier transform, which is the normal velocity spectrum ( ) S 1 2 U k ,k , f on the surface of

the component; Finally, a two-dimensional Fourier inversion is performed on the angular spectrum to solve for the complex sound pressure ( ) S 1 2 P l ,l , f and velocity ( ) S 1 2 U l ,l , f in the spatial domain, and the normal sound intensity (time-averaged) distribution ( ) S 1 2 , , I l l f on the surface of the component

is obtained by associating the two. the expression of the sound field reconstruction calculation is

( ) ( )   ( )   S 1 2 H 1 2 1 2

− =

1 , , IDFT DFT , , , , P l l f P l l f k f G k

(4)

−   =        

0 , , IDFT DFT , , , , k U l l f P l l f k k f c k G 

1

( ) ( ) ( ) z S 1 2 H 1 2 1 2 0

(5)

( ) ( ) ( ) S 1 2 S 1 2 S 1 2 * 1 , , Re , , , , 2 I l l f P l l f U l l f •   =   (6)

The above equation 0  is the air density, 0 c is the sound velocity in air, z k is the normal component of the acoustic wave number,   • • DFT IDFT 、 represent the two-dimensional Fourier transform and the inverse transform, respectively,  “ ” represents the complex conjugate operator, and

− is the angular spectral expression of the Green's function. Since the holographic surface measures

1 G

− used for the sound field reconstruction is based on the

the complex sound pressure data, the 1 G

Green's function under the Dirichlet boundary condition, which is obtained by spatial sampling in the wave number domain

( ) ( ) ( )



d k k k k G k k f − − − 

2 2

exp

jd k k k k

1

r r

= (7)

exp , ,

2 2 2

1

 

−

r r

Where, d is the acoustic field reconstruction distance, k is the acoustic wave number, radiation

circle radius ( ) ( )

2 2 1 x 2 y r k k k k k =  +  , 1 2 k k 、 represents the sampling sequence number of the wave

number domain x y 、 direction, x y k k   、 is the sampling interval of the wave number domain upper

x y 、 direction, x y x y L L k k   =   = ， , where, x y L L 、 is the measurement aperture of the holographic surface x y 、 direction. In the reconstruction process of the first type of sound field, the window function ' W is used to remove the swift wave components outside the radiation circle and retain only the propagating waves located inside the radiation circle. The reconstruction of the second type of sound field uses the window function '' W proposed by H.S. Kwon and Y.H. Kim to filter the complex sound pressure angle spectrum in order to suppress the effect of high wave number errors on the reconstruction results [14]

k k k k W k k     = (8)

( ) 1 2 1

0 ' ,

r

r

( ) ( ) 1 2

− −         −        



1 0.5exp 1

k k k k



r c r c



z



h

0.5exp 1 '' ,

k k k k W k k

3

( )

= (9)

r c r c

      



1

k k k k



r c

z

0

h

3

r c

where c 0.6 x k  =  , x  is the sampling spacing, steepness factor  is 0.2, h z is the distance between the holographic surface and the sound source, and  is the wavelength of the sound wave

(4) Calculation of sound insulation volume and sound insulation defect detection. Firstly, the normal sound intensity distribution ( ) ( ) S 1 2 S 1 2 , , , , I l l f I l l f   、 of the two types of sound fields is obtained

from equation (6), and the 1/3 octave normal sound intensity ( ) ( ) S 1 2 m S 1 2 m , , , , I l l f I l l f   、 is calculated;

then the average normal sound intensity level ( ) S,1/3 m LI f  of the propagating waves on the surface of

the component is calculated from equation (10), and then the sound insulation amount ( ) m R f is

solved by the sound intensity insulation calculation equation (11); finally, ( ) S,1/3 1 2 m , , I l l f  is converted

into sound intensity level ( ) S,1/3 1 2 m , , LI l l f  and visualized, and the sound insulation defect location of

the component is located by the sound image map

      =         (10)

( ) 1 2

, , 1 10lg

I l l f LI f N N I = =

N N

S,1/3 1 2 m

( )

S,1/3 m

1 1 1 2 0

l l

1 2

( ) ( ) ( ) m m P,1/3 m S,1/3 m 10lg 6 S R f L f LI f S    = − + −    

(11)

where m f is the 1/3 octave center frequency, 1 2 N N 、 is the number of reconstruction points in the direction of the reconstruction surface x y 、 , the reference sound intensity 0 I =10 -12 W/m 2 , m S is the area of the reconstruction surface, and S is the area of the component. 3. EXPERIMENTAL

3.1. Experimental system and device

The NAH and ISO10140:2010 measurement methods were used to measure the airborne sound insulation of double-layer insulating glass curtain wall (size 2.9mx2.7m) respectively, and the sound pressure method measurement data were used as the benchmark to judge the accuracy of NAH sound insulation measurement. The experiments were done in the sound insulation room of the State Key Laboratory of Subtropical Building Science, South China University of Technology. the principle of the NAH measurement system is shown in Figure 1. Firstly, the white noise signal is generated by Audition software and amplified by power amplifier to excite the loudspeaker to emit sound; then the average sound pressure level of the source room is measured by point-by-point method; finally, the holographic surface sound pressure is measured by microphone array in the receiving room, and the sound field reconstruction and sound insulation calculation are completed by the developed LabVIEW system.

Figure 1: Hardware setting and measuring point distribution

The experimental setup is shown in Figure 2. Among them, QSC amplifier and BSWA OS003A non-directional loudspeaker are used for the sound generating device; B&K2270 sound level meter and 4189 microphone are used for the sound pressure level measurement in the source and receiver rooms; 16-channel line array of BSWA-MPA201 free-field microphone is used for the holographic signal acquisition in the receiver room, and GRAS-46AE standard microphone is used for the reference signal acquisition. The measurement system uses NI PXIe-1062Q chassis, PXIe-8102 embedded controller, and PXIe-4497 and PXI-4461 data acquisition cards. The experiment uses a line array to measure the holographic surface one by one, with a holographic surface aperture of 2.9mx2.7m, 0.045m from the surface of the component, and a sampling interval ∆x=∆y=0.045m.

reference Sound pressure microphone measuring point 4800 Microphone array Data Acquisition speaker

(a)

| Reference : [microphone Controllers and Pp Data Acquisition Microphone

(b)

(c)

(d) Figure 2: Experimental device. (a) Test equipment in the receiving room, (b) Test component, (c)

Microphone array, (d) Controller and Data acquisition card.

3.2. Application of NAH technique to measure airborne sound insulation

The measured sound insulation amounts of the two methods are compared below to verify the accuracy and validity of the NAH-based sound insulation measurement method. From the measurement principles in Section 2, it is clear that the NAH-based sound insulation measurement method reconstructs the sound intensity normal to the surface of the member to calculate the sound power radiated from the test member to the receiving chamber, including the sound power in the central region and the sound power in the boundary region. Since ISO10140:2010 measures the average sound pressure level in the central area of the receiving chamber to characterize the sound power, if the measurement results of the two measurement methods are compared, the sound insulation NAH R measured by NAH needs to be corrected by Waterhouse according to the following formula. The corrected sound insulation volume NAH,W R can be expressed as

b S L R R V V     = + + +    

2 2 NAH,W NAH 10lg 1 8 32π

(12)

where 2 b S is the total surface area of all boundary surfaces of the receiving chamber, and λ is the wavelength corresponding to the center frequency of the frequency band. the logarithmic part of equation is called the Waterhouse correction term.

The sound insulation frequency curves measured by the two measurement methods are given in Figure 3. Table 1 gives the deviation Δ R （ Δ R= NAH,W R R − ） of the sound insulation measured by the two methods. It can be seen that the deviation of sound insulation measured by the two measurement methods does not exceed 4 dB in the range of 100-3150 Hz and 1 dB in the range of 160-630 Hz. The sound insulation frequency curves are weighted to obtain the single value of sound insulation and the spectral correction ( ) tr ; W R C C . The final ( ) tr ; W R C C obtained by the two methods is the same, which is 41(-2; -6) dB.

The above data show that the airborne sound insulation frequency characteristics measured by the method in the paper and ISO10140:2010 are basically consistent. Therefore, the accuracy and validity

of the method applied to the sound insulation measurement of building components are proved by the sound insulation room experiment. In addition, the uncertainty of the measurement results is only the standard deviation of the sound pressure levels at different measurement points in the source room, which is much smaller than the uncertainty of the sound insulation measured by the sound pressure method, and the measurement accuracy is basically not affected by the volume size of the receiving room and the diffusion degree of the sound field. Theoretically, the method in this paper is more suitable than the traditional method for application in field conditions where the measurement environment and room acoustic conditions are more complex.

60

ISO 10140: 2010 NAH

sound reduction index R /dB

50

40

30

125 200 315 500 800 1250 2000 3150 20

1/3 octave band center frequency /Hz

Figure 3: Sound Reduction Index of test members using NAH and ISO 10140:2010.

Table 1: Measurement error of sound reduction index for each 1/3 octave band within 100 ～ 3150Hz. [dB]

100 125 160 200 250 315 400 500 630 800 1000 1250 1600 2000 2500 3150

2.9 0.8 -0.9 0.6 0.8 -0.8 0.9 0.2 -0.6 -1.2 -1.2 -0.9 -2.3 -2.3 -3.2 -2.8

3.3. Application of NAH technique to measure airborne sound insulation

While measuring the sound insulation frequency characteristics of the building components, the method in the paper uses swift waves to reconstruct the normal sound intensity level distribution on the surface of the test components and to image the sound field. The obtained acoustic image not only contains the energy flow information of the radiated sound field on the surface of the component, but also the resolution of the image is not limited by the wavelength of the radiated acoustic wave, and is only related to the sampling spacing of the holographic surface. Figure 4 gives the distribution of the normal sound intensity levels at 250 Hz, 500 Hz, 1000 Hz and 2000 Hz on the surface of the test member. It can be seen that the acoustic image maps of different frequency bands have different characteristics of sound field distribution. The sound intensity values in the lower right corner of the 2000 Hz band are significantly larger than those in the other regions, indicating that the sound insulation defects in the 2000 Hz band are mainly located in the small right corner.

The traditional method based on single-channel measurement can only get local acoustic characteristics, when the location of the measurement point is not selected properly, the local acoustic characteristics are not sensitive to the leakage path of the sound insulation defect detection effect will be affected, based on the analysis of the single-channel acoustic signal can not fully and stably reflect the acoustic radiation characteristics of the test components, which largely affects the detection effect. The method in this paper is based on the spatial distribution of the acoustic field characteristics of simultaneous measurement of multi-channel acoustic signals on the holographic surface, and the application of NAH spatial acoustic field transformation algorithm to reconstruct the acoustic

information on the entire surface of the component, which is obviously much richer than the single channel, and the spatial distribution of the acoustic field characteristics extracted from it is inevitably more comprehensive and stable than the features extracted by the traditional sound insulation defect detection technology .

67 dB

86 dB

1.5

1.5

84

66

0.8

0.8

81

64

y /m

y /m

0

0

79

63

77

61

-0.8

-0.8

74

60

72

58

-1.5 -0.8 0 0.8 1.5 -1.5

-1.5 -0.8 0 0.8 1.5 -1.5

(a)

(b)

x /m

x /m

51 dB

37 dB

1.5

1.5

50

36

0.8

0.8

49

35

y /m

y /m

0

0

48

34

47

33

-0.8

-0.8

46

32

45

31

-1.5 -0.8 0 0.8 1.5 -1.5

-1.5 -0.8 0 0.8 1.5 -1.5

(c)

(d) Figure 4: Image of the normal sound intensity distribution on the surface of the tested component. (a)

x /m

x /m

Acoustic image of 250Hz, (b) Acoustic image of 500Hz, (c) Acoustic image of 500Hz, (d) Acoustic image of 2000Hz. 4. CONCLUSIONS

In this paper, a new NAH-based field measurement method for sound insulation of building components is proposed, the spatial sound field transformation algorithm of NAH is applied to the reconstruction of radiated sound power in sound insulation measurement, and the spatial distribution information of the sound field on the surface of the tested components is applied to the sound insulation defect detection, and the corresponding experimental studies are conducted. The main conclusions are as follows:

(1) The comparison between the results of the paper method and the sound pressure method in the sound insulation room shows that the application of the paper method to measure the sound insulation characteristics of building components not only has higher accuracy, but also the uncertainty of the measurement results is smaller than that of the traditional method, so it is more suitable for application in field conditions.

(2) The reconstructed acoustic image can identify the local radiated sound power in each region of the test member, and the image resolution is not limited by the wavelength of the radiated wave, so the detection accuracy is greatly improved compared with the traditional method, which can provide an effective solution for improving the sound insulation characteristics of the member .

5. ACKNOWLEDGEMENTS

This work was supported by the National Natural Science Foundation of China [grant numbers 52078218]. 6. REFERENCES

1. International Organization for Standardization ISO 10140, Acoustics. Laboratory Measurement

of Sound Insulation of Building Elements – Part 2: Measurement of Airborne Sound Insulation , SC.2 2010 Edition. 2. International Organization for Standardization ISO 15186, Measurement of sound insulation in

buildings and of building elements using sound intensity – Part 1: Laboratory measurements , SC.2 2000 Edition. 3. International Organization for Standardization ISO 15186, Measurement of sound insulation in

buildings and of building elements using sound intensity – Part 2: Field measurements , SC.2 2003 Edition. 4. Lee, Y. & Williams, E.G. Nearfield acoustic holography: I. Theory of generalized holography

and the development of NAH. Journal of the Acoustical Society of America , 78(4) , 1395–1413 (1985). 5. Veronesi, W.A. & Maynard, J.D. Nearfield acoustic holography (NAH) II. Holographic

reconstruction algorithms and computer implementation. Journal of the Acoustical Society of America , 81(5) , 1307–1322 (1987). 6. Zhang, H., Guo, W. & Han, J, et al. Source localization in reverberation environment based on

improved equivalent sound source near-field acoustic holography algorithm. Journal of Vibroengineering , 21(8) , 2260–2272(2019). 7. Valdivia, N.P., Williams, E.G. & Herdic, P.C. Equivalent sources method for supersonic intensity

of arbitrarily shaped geometries. Journal of Sound and Vibration , 347 , 46–62 (2015). 8. Lu, W., Jiang, W. & Wu, H, et al. A fault diagnosis scheme of rolling element bearing based on

near-field acoustic holography and gray level co-occurrence matrix. Journal of Sound and Vibration , 331(15) , 3663–3674(2012). 9. Lu, W., Jiang, W. & Yuan, G, et al. A gearbox fault diagnosis scheme based on near-field acoustic

holography and spatial distribution features of sound field. Journal of Sound and Vibration , 332(10) , 2593–2610(2013). 10. Yang, D., Wang, Z. & Li, B., et al. Quantitative measurement of pass-by noise radiated by

vehicles running at high speeds. Journal of Sound and Vibration , 330(7) , 1352–1364(2011). 11. Moondra, M.S., & Wu, S.F. Visualization of vehicle interior sound field using Nearfield

Acoustical Holography based on the Helmholtz-Equation Least-Squares (HELS) method. Noise Control Engineering Journal , 53(4) , 145–154(2005). 12. Williams, E.G., Valdivia, N. & Herdic, P., et al. Determination of transmission loss of materials

from array measurements using nearfield acoustical holography/inverse boundary element methods in a transmission loss facility. Journal of the Acoustical Society of America , 118(3) , 1209-1216(2005). 13. Jacobsen, F. & Tiana-Roig, E. Measurement of the sound power incident on the walls of a

reverberation room with near field acoustic holography. Acta Acustica United with Acustica , 96(1) , 76–81(2010). 14. Kwon, H.S. & Kim, Y.H. Minimization of bias error due to windows in planar acoustic

holography using a minimum error window. Journal of the Acoustical Society of America , 98(4) , 2104–2111(1995).