Estimation of insertion loss for a noise barrier with multichannel sound reproduction technology

Satoshi Hoshika 1 , Tetsuya Doi, Masaaki Hiroe Kobayasi Institute of Physical Research 3-20-41 Higashimotomachi, Kokubunji, Tokyo, 185-0022, Japan

Takahiro Iwami Kyushu University 4-9-1 Shiobaru, Minami-ku, Fukuoka, 815-8540, Japan

ABSTRACT A method based on the wave field synthesis is proposed to estimate the insertion loss of noise barriers under complex di ff racted sound fields owing to the characteristics of noise sources and transmitted sound through barriers. This method is equivalent to evaluating the acoustic insertion loss of noise barriers in a reproduced sound field. The proposed method has two main features. First, by storing the radiated sound data of various noise sources in advance, their insertion losses can be obtained. Second, the multipoint impulse responses can be measured by sequentially changing the position of one loudspeaker. Therefore, many loudspeakers are not required. To validate this method, a numerical simulation was performed considering a di ff racted sound field consisting of a point source and rigid barrier. Moreover, the insertion loss of wooden noise barriers for one loudspeaker was experimentally estimated under primary and synthesised sound field conditions. As a practical example, the insertion losses of these noise barriers for a moving automobile were estimated. The results demonstrate that the estimation error is within a few decibels in the frequency band where spatial aliasing does not occur.

1. INTRODUCTION

Installing noise barriers is a common noise reduction method for dampening railway and road tra ffi c noise. Numerical simulations [1, 2] and scaled acoustic model tests [3] are commonly performed to estimate the noise-reduction e ff ect. However, it is sometimes di ffi cult for these methods to consider conditions such as the directivity of sound sources, time variability, and detailed structure of noise barriers. The methods using actual barriers such as European standard [4], field test [5], and full-scale model experiment [6] are able to consider the structure of barriers but since they use one loudspeaker as a source, they can not take into account the characteristics of actual sound sources. In-situ tests [7, 8] are among the best approaches to consider the abovementioned conditions. However, these experimental processes are costly and time consuming. Therefore, a practical estimation method is

1 hoshikasatoshi@gmail.com

useful for considering the abovementioned conditions. In this study, we propose an insertion loss estimation based on the wave field synthesis [9], which is a sound field reproduction technique, as a method to obtain the insertion loss considering the characteristics of noise sources and transmitted sound through barriers. This method uses a transfer function between multiple points and is equivalent to physically evaluating the acoustic insertion loss of noise barriers within a reproduced sound field. Some techniques of physical acoustic measurements using sound field reproduction have been reported in the literature. For example, measuring the sound absorption coe ffi cient of materials in a reproduced sound field [10] reproduces random incident waves via boundary-surface control [11]. Moreover, the study reproduced the idling sound of an automobile from outside the car cabin [12] using higher-order ambisonics [13]. The sound field of the car cabin was evaluated by placing the actual car in the reproduced sound field. Although there are many examples of sound field reproduction technologies used for subjective evaluation experiments, there are few examples of their use for objective evaluation, except for the abovementioned investigations. In this study, to verify the validity of the proposed method, we have conducted numerical analysis and laboratory experiments on the di ff racted sound field of a point source with barriers. As an application example of the proposed method, we report the results of estimating the insertion loss of barriers for the drive-by noise an automobile created.

2. PRINCIPLES OF REPRODUCED AND SIMPLE DIFFRACTED SOUND FIELD Figure 1 shows a conceptual diagram of reproduced and di ff racted sound fields. The x-axis is the length direction, y-axis is the height direction, and z-axis is the normal direction of the noise barrier. As shown in Figure 1(a), when z = z S with boundary S and half-space V =

!

"

r ∈ R 3 | z ≥ z S

, the sound pressure at the sound receiving point r ∈ V is expressed by Rayleigh’s second integral using the sound pressure at s on S [14]

#

P ( s ) ∂ G ( s , r )

P ( r ) = − 2

∂ n d S , (1)

S

where G denotes Green’s function in three-dimensional free space and ∂ G ( s , r ) /∂ n represents the propagation from a dipole source oriented towards n to r at position s . n denotes the normal vector from S to V . The sound pressure P is expressed in the frequency domain; however, the frequency variable ω is omitted for simplicity. In the wave-field synthesis method based on Rayleigh’s second integral, dipole loudspeakers are discretely placed on S as secondary sound sources. The sound field is reproduced by playing back the sound pressure recorded in an original sound field. On the other hand, when an aperture S ′ and rigid barrier surface S ′′ are set at z = z S ′ and half-space V ′ =

!

"

, as shown in Figure 1(b), the sound pressure at r ∈ V ′ can also be expressed

r ∈ R 3 | z ≥ z S ′

(a) (b) (c)

Figure 1: Conceptual diagram of reproduced and di ff racted sound fields: (a)Reproduced field, (b)di ff racted

field, (c)di ff racted field in reproduced field.

by Rayleigh’s second integral according to the sound pressure in s ′ on S ′ . This is the expression of di ff racted fields through an analogy of optics [15], which corresponds to considering the slit for light as an aperture for sound.

#

S ′ P ( s ′ ) ∂ G ( s ′ , r )

∂ n d S ′ . (2)

P d ( r ) = − 2

From the above expression, a di ff racted sound field when a rigid barrier is placed in a reproduced sound field, as shown in Figure 1(c), can be expressed through equation (3) by substituting equation (1) with r = s ′ into equation (2)

#

#

P ( s ) ∂ G ( s , s ′ )

∂ G ( s ′ , r )

∂ n d S d S ′ . (3)

P d ( r ) = 4

∂ n

S ′

S

Therefore, the insertion loss IL d owing to a rigid barrier installed in a reproduced sound field can be expressed through equation (4) as the level of the sound pressure with and without the rigid barrier

$$$

$$$ $$$ 2

%

S P ( s ) ∂ G ( s , r )

∂ n d S

| P ( r ) | 2

IL d ( r ) = 10 log 10

| P d ( r ) | 2 = 20 log 10

∂ n d S d S ′ $$ $ . (4)

%

%

S P ( s ) ∂ G ( s , s ′ )

∂ G ( s ′ , r )

S ′

∂ n

Equation (4) does not represent only the insertion loss of a rigid barrier. The insertion loss can be calculated, if radiated sound pressure of noise sources in an original sound field can be measured on the plane S , by setting up a virtual rigid barrier installation plane S ′′ and an adjacent aperture S ′

in the region z ≥ z S . The actual sound barrier is not perfectly rigid; thus, some transmission and leakage noises from the gap may occur. In addition, the di ff racted sound field becomes more complex when equipment, such as di ff racting elements, are added. To express the insertion loss taking these e ff ects into account, we let S w = S ′ ∩ S ′′ and introduce the transmittance τ ( s w ), where s w on S w . Accordingly, equation (3) can be expressed as:

#

#

∂ G ( s w , r )

P ( s ) τ ( s w ) ∂ G ( s , s w )

P w ( r ) = 4

∂ n d S w d S . (5)

∂ n

S

S w

Equation (5) is equivalent to equation (3) after properly setting the open condition on S ′ and rigid barrier condition on S ′′ , i.e. τ ( s ′ ) = 1 , ∀ s ′ on S ′ and τ ( s ′′ ) = 0 , ∀ s ′′ on S ′′ .

3. ESTIMATION PROCEDURE OF INSERTION LOSS USING THE PROPOSED METHOD

Assuming that the reproduction space is a free field, the sound field when noise barriers are installed within the reproduction sound field can be expressed by equation (6) using the transfer function H w from the secondary dipole sound source to the acoustic evaluation point.

#

P w ( r ) = − 2

P ( s ) H w ( s , r )d S . (6)

S

Because Green’s function is a solution of the inhomogeneous wave equation with the delta function, equation (6) corresponds to equation (4) when a rigid barrier used and equation (5) when the transmittance is known. Similarly, for a free sound field without a noise barrier, by setting ∂ G /∂ n mentioned in equation (1) as the transfer function H f , we can obtain the insertion loss IL as follows:

$$$

$$$ $$$

%

S P ( s ) H f ( s , r )d S

| P ( r ) | 2

IL ( r ) = 10 log 10

| P w ( r ) | 2 = 20 log 10

$$$ . (7)

%

S P ( s ) H w ( s , r )d S

For the sound field reproduction with a finite number of secondary sources, discretising Equation (7) with equal discretisation widths gives

$$$& N

$$$ $$$& N

n = 1 P ( s n ) H f ( s n , r )

IL ( r ) ≃ 20 log 10

$$$ , (8)

n = 1 P ( s n ) H w ( s n , r )

where N denotes the number of loudspeakers that are secondary sources. The product of the recorded sound pressure and transfer function provides the signal obtained at the receiver point by playing the recorded sound from the loudspeakers in the playback space. However, suppose that the transfer function, which denotes the impulse response in the time domain between the loudspeakers and the receiving point, can be measured. In this case, these signals can be obtained by multiplying them with the recorded sound in post-processing. The features of this method are as follows. The radiated sound data of noise sources can be stored as a database in advance. Then, a post-processing sequence can calculate the insertion loss for various noise sources. For example, it is possible to study the e ff ect of noise reduction for di ff erent noise sources, such as road tra ffi c and railway noise, in a series of transfer function measurements. In addition, because multipoint impulse responses can be measured by changing one loudspeaker position sequentially, multiple loudspeakers are not required. A conceptual diagram of the measurement procedure is depicted in Figure 2. The measurement procedure is as follows. First, the transfer functions between the multipoint loudspeaker and omnidirectional sound evaluation point are measured in each field with and without noise barriers in an anechoic chamber. Next, these transfer functions are multiplied with the recorded sound of the original sound field corresponding to each loudspeaker position s i in the frequency domain. Then, the insertion losses at the sound evaluation points are estimated by summing all the signals and obtaining a ratio for the presence and absence of noise barriers.

4. INSERTION LOSS ESTIMATION FOR A MONOPOLE SOURCE BY NUMERICAL ANALYSIS

‘Secondary source (Loudspeaker) ‘r:Evaluated point

4.1. Di ff racted sound field with monopole source and rigid barrier To validate the proposed method, the insertion losses of rigid barriers for monopole sources are considered. The sound wave radiated by a monopole source from a source point r s with wave source intensity A in a free sound field is expressed as

˜ P ( r ) = 4 π AG ( r s , r ) . (9)

Substituting equation (9) with r = s ′ into equation (2), the di ff racted sound field (Figure 1(b)) when a rigid barrier is placed within the radiated sound field can be expressed as

Figure 3: Analysis condition （ unit: m ）

Figure 2: Conceptual diagram of measurement

40.165 Secondary sources (82x32ch loudspeaker array) Rigid barrier ‘Monopole source 52

#

S ′ G ( r s , s ′ ) ∂ G ( s ′ , r )

˜ P d ( r ) = − 8 π A

∂ n d S ′ . (10)

Therefore, the insertion loss ˜ IL d ( r ) of the rigid barrier for a monopole source in the primary sound field can be expressed using equation (11) based on equations (9) and (10)

$$$ ˜ P ( r )

$$$ $$$ ˜ P d ( r )

| G ( r s , r ) | $$$ − 2

˜ IL d ( r ) = 20 log 10

$$$ = 20 log 10

∂ n d S ′ $$ $ . (11)

%

S ′ G ( r s , s ′ ) ∂ G ( s ′ , r )

4.2. Numerical simulation procedure To consider insertion loss in the synthesised and primary sound fields, the sound pressure P ( s ) = 4 π AG ( r s , s ) at the secondary source point s was substituted into equations (1), (3), and (4) to obtain numerical comparisons between the synthesised and primary sound fields. The analysis conditions are illustrated in Figure 3, where the analysis range was 0-5.2 m in the x , y , z directions. The source point was set at ( x , y , z ) = (2.6 m, 1 m, 0 m), the rigid barrier was set at (2.5 m), the aperture was set at z = 2 m, and the secondary source plane was set at z = 1 m. The sound pressure was calculated at 0.05 m intervals for a 500 Hz pure tone radiated from the source point. The discrete width of the secondary sources was set to 0.165 m, with ( x , y , z ) = (0 m, 0 m, 2 m) as the starting point; 32 × 32 of them were placed on the secondary source plane. To suppress errors due to spatially truncated secondary sources, 10% of the secondary source edges were multiplied with the spatial Tukey window.

4.3. Numerical simulation result Figures 4(a)-(d) show the results of the free and di ff racted fields with the rigid barrier placed in the primary and synthesised sound fields. The results consider a cross-section of x = 2.6 m and are normalised at the centre of the space. The sound pressure distributions in the primary and synthesised sound fields agree well under both the free-field and di ff racted-field conditions. Figures 5(a) and (b) show the results of insertion loss for the primary and synthesised sound fields, respectively, calculated using the sound pressure before normalisation for the free-field and di ff raction sound field conditions shown in Figure 4. Figure 5(c) shows the insertion loss errors between the primary and synthesised sound fields. The error is within ± 1 dB through nearly the entire analysis range but tends to increase near the edge of the secondary source.

5. INSERTION LOSS ESTIMATION FOR A LOUDSPEAKER SOURCE BY EXPERIMENTAL STUDY

To validate the proposed method, the insertion loss of wooden barriers was measured for a loudspeaker source in a semi-anechoic room. By playing a swept-sine signal (2 18 sample, 20 Hz-24 kHz) using a single loudspeaker, the sound field corresponding to the radiation of a pulse from the loudspeaker position was considered as the primary sound field. The di ff erence between the insertion loss obtained by installing barriers in the reference field and synthesised field obtained using the proposed method based on equation (8) was investigated, using a sampling frequency of 48 kHz. All the measured swept-sine response signals were converted into transfer functions (impulse responses in the time domain) by multiplying the inverse signal in the frequency domain.

5.1. Experimental procedure Experimental conditions are shown in Figure 6. The test conditions and measurement equipment series are shown in Figure 7. Secondary source loudspeakers and microphones were installed in the

(a) (b) (c) (d)

Figure 4: Numerically calculated sound pressure at 500 Hz: (a)Primary free field, (b) synthesised free field,

and (c)primary di ff racted field, (d)synthesised di ff racted field.

(a) (b) (c) Figure 5: Numerical calculated insertion loss at 500 Hz: (a)Primary field, (b)synthesised field, and (c)error.

vertical direction with 24 channels, with an interval width of 0.165 m. The size of a barrier was approximately 1.8 m x 0.9 m x 0.06 m; eight barriers were lined up to create an installation length of approximately 7.2 m. Radiated sounds from a single loudspeaker (sound pressure at 1 m away) P ( s i ) were recorded (Figure 6(a)) to be used for the proposed method. The transfer function H f of the evaluation points 1.5 m away from the loudspeaker array was measured. In addition, the barriers were placed 1 m away from the loudspeaker array and then transfer function H w was measured (Figure 6(b)). To measure the transfer function of the planar loudspeaker array using the line loudspeaker array, the sound evaluation point usually needs to be fixed and sound measurements must be taken by changing the line loudspeaker array position sequentially along with the horizontal direction. However, in this experiment, the loudspeaker array was fixed for ease of operation and microphone array position was changed sequentially along the horizontal direction instead. Only the measurement lines l = 0 to 11 shown in Figures 6(a) and (b) were measured; for l = − 11 to − 1, the corresponding measurements were spatially inverted around l = 0, assuming the sound field was symmetric, and substituted. Using the measured H f , H w , and recorded sound from a single loudspeaker P ( s i ), the insertion loss was estimated using equation (8). 10% of the secondary source edge was multiplied by the spatial Tukey window to suppress errors due to spatially truncated secondary sources. Under the reference sound field conditions (Figure 6(c)), the signal was played from a single loudspeaker only. Subsequently, the transfer function was measured at the evaluation point sequence 2.5 m away from the sound source. The reference insertion loss was determined by calculating the level di ff erence of the transfer function between setups with and without barriers placed 2 m from the sound source.

5.2. Experimental result As an example of the results, Figures 8(a) and (b) show the 1 / 3-octave band level results of the insertion loss measured at over the evaluation point height range from 1.54 to 2.70 m in the reference and estimated sound fields, respectively. In the reference field, the insertion loss tended to increase

(a) (b) (c) Figure 6: Sketch of measurement layout: (a)Recording of radiated sound, (b)measurement of transfer functions, and (c)measurement of insertion loss(reference).

(a) (b) (c) Figure 7: Transfer function measurement of (a)setup without barriers, (b)setup with barriers, and (c)used

equipment.

as the microphone position decreased, where the di ff raction angle of the sound source by the barriers became deeper; a similar trend was observed in the estimated sound field. In this experiment, the frequency limit where spatial aliasing occurs, determined by the discrete width of the secondary sound source, was approximately 1 kHz (dotted red line in Figure 8). The insertion loss error between the reference and estimated sound fields shown in Figure 8(c) was within approximately ± 5 dB in the band below the limit frequency, whereas it tended to increase in the higher band and was within approximately ± 10 dB. As one of the error factors, it is possible that the loudspeaker used does not have the perfect dipole directivity required for a secondary sound source in wave-field synthesis.

6. INSERTION LOSS ESTIMATION FOR A MOVING AUTOMOBILE

As an application example of the proposed method, the sound field of a moving automobile was recorded; then, the insertion loss of the noise barrier was estimated using H w and H f measured in a semi-anechoic chamber in section 5. The reference insertion loss was calculated based on the di ff erence in the sound pressure level between the presence and absence of barriers in the actual sound field; subsequently, the estimation error was examined.

Lovin, Meeone rose s924 seers

(a) (b) (c) Figure 8: Insertion loss for a single loudspeaker in 1 / 3 Oct. band level: (a)Reference field, (b)estimated field,

and (c)error.

6.1. Experimental procedure-1: measurement of radiated sound The radiated sound field of an automobile moving at approximately 30 km / h was recorded at Kobayasi Institute of Physical Research. The measurement conditions and status are shown in Figures 9(a) and 10(a). The measurement equipment used was the same as that used in section 5. A 24-channel microphone array with an element spacing of 0.165 m was installed vertically 1 m from the nearest surface of the automobile. The recorded sound signals were used as function P in equation (8). Strictly speaking, P requires sound signals recorded by the planar microphone array. However, in this experiment, for the convenience of measurement, the signals recorded by the linear microphone array installed towards the vertical direction were directly used on di ff erent vertical lines and treated as signals recorded by the pseudo-planar microphone array.

6.2. Insertion loss estimation by the proposed method Using H w and H f measured in a semi-anechoic room in section 5 and radiated sound P recorded in section 6.1, where the automobile was driven between x = − 4 . 5 to 4 . 5 m, the insertion loss of the barriers is estimated using equation (8).

6.3. Experimental procedure-2: measurement of SPL with / without barriers in the reference sound field As shown in Figures 9(c) and 10(b), the wooden barrier was installed at a distance of 2 m from the nearest surface of the automobile. Ten barriers were lined up to provide an installation length of 9.0 m. A 24-channel microphone array was installed 2.5 m from the automobile’s nearest surface, using which the sound pressure at each sound evaluation point was measured. As shown in Figure 9(b), a similar measurement was conducted when the barriers were not installed. The insertion loss was calculated based on the di ff erence in the sound pressure levels between setups with and without barriers in the actual field. The sound pressure exposure level was calculated in the time interval when the car passed through the section x = − 4 . 5 to 4 . 5 m. Subsequently, the di ff erence between the levels with and without the barriers was used as the insertion loss. However, as it is di ffi cult to maintain the same automobile conditions of speed and position when driving with and without barriers, ten measurements were conducted both with and without barriers. Then, the di ff erence in average levels was used as the representative value of insertion loss in the reference sound field.

(a) (b) (c) Figure 9: Sketch of the experimental layout: (a)Recording of radiated sound, (b)reference field without barriers

, and (c)reference field with barriers.

(a) (b) Figure 10: Measurement conditions: (a)Without barriers and (b)with barriers.

6.4. Estimation result As an example of the measurement results, Figures 11(a) and (b) show the 1 / 3-octave band level results for the insertion loss calculated at sound evaluation point height range from 1.54 to 2.70 m in the reference and estimated sound fields, respectively. Based on the signal-to-noise ratio of the recorded sound pressure, the frequency range from 200 to 2000 Hz was considered a meaningful frequency band. In the reference sound field, the insertion loss tends to increase as the di ff raction angle of the sound source by the barriers increases with a lower sound-receiving point height. A similar trend is approximately observed in the estimated sound field but with lower values. The insertion loss error shown in Figure 11(c) is approximately -2 to + 7 dB; the estimated results tend to be smaller than the reference values. A-weighted sound pressure exposure levels were calculated for each sound evaluation point with and without barriers. Then, the insertion loss was calculated from the level di ff erence as shown in Figure 12. The maximum error was approximately 5 dB at a height of 1.71 m. The insertion loss for both the reference sound field and estimated sound field decreased as the height of the sound evaluation point increased. The estimation error is detected because, as mentioned in section 5.3, the used loudspeaker is not a perfect dipole source required for a secondary source in the wave field synthesis. Moreover, the sound recorded by the linear microphone array is used instead of the originally required sound recorded by the planar microphone array, which results in a pseudo-planar sound. It is also possible that the estimated sound field does not consider the ground reflections and multiple reflections between the vehicle body and barriers.

(a) (b) (c) Figure 11: Insertion loss for the automobile in 1 / 3 Oct. band level: (a)Reference field, (b)estimated field, and

(c)error.

[ASS | ees (A “POPOPPOEEES "PIPPEPOEEOD "PBPPEPEEGED

Figure 12: Insertion loss for the automobile (A-weighted).

7. CONCLUSIONS

We have proposed a novel method for estimating the insertion loss of noise barriers using a multi- channel sound field reproduction technology. The estimation accuracy for a stationary point source was obtained through numerical calculations and experimental tests. As an application example of the proposed method, the insertion loss of wooden noise barriers against sound radiated from a moving automobile was estimated. The results showed that the proposed method had estimation errors of only a few decibels in the frequency band where spatial aliasing does not occur. In principle, this method enables us to estimate the insertion loss of barriers as e ff ectively as an in-situ experiment, which can be considered to treat not only the transmitted sound through the noise barrier and leakage sound from the gap but also the directivity and time variability of actual sound sources. In addition, there are two good features of the proposed method. First, the insertion loss of arbitrary noise barriers for their noise sources can be estimated by storing the radiated sound of various noise sources in advance. Second, multiple-position impulse responses can be measured by changing one loudspeaker position sequentially; thus, many loudspeakers are not required. However, the proposed method is strictly valid in only the field there are no obstacles except barriers. Therefore it is also possible that the estimated sound field does not consider the ground reflections and multiple reflections between the vehicle body and barriers. The handling of these problems and spatial aliasing should be considered as well. In future studies, it may be possible to target noise sources with faster moving speeds, such as automobiles at highway speeds and trains. This method can experimentally handle arbitrary sound fields that are currently simulated in numerical analysis and perform intermediate studies between

15 Insertion Loss [4BA] . . 2 3 4 Evaluation point height [m] —e-Primary —e-Synthosized —s—Error(Syn.-Prt)

actual measurements and numerical simulations. As a future research direction, we would like to study not only the evaluation of noise barriers but also other applications.

ACKNOWLEDGEMENTS

We would like to thank everyone at our institute and those who had meaningful discussions at the conference in Japan.

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