Acoust. Sci. & Tech. 38, 6 (2017) PAPER #2017 The Acoustical Society of Japan Prediction of insertion loss of detached houses against road traffic noise using a point sound source model: Simplification of prediction formula F2012 Kazutoshi Fujimoto 1; and Ken Anai 2;y 1 Professor Emeritus of Kyushu University, Hakozaki 6 10 1, Higashi-ku, Fukuoka, 812 8581 Japan 2 Faculty of Engineering, Kyushu Institute of Technology, Sensuicho 1 1, Tobata-ku, Kitakyushu, 804 8550 Japan (Received 31 October 2016, Accepted for publication 3 March 2017) Abstract: In order to predict the equivalent continuous A-weighted sound pressure level (L Aeq )of road traffic noise in areas facing roads, knowledge of the insertion loss of buildings against road traffic noise is needed. The authors previously proposed formula F2012 for predicting the insertion loss of detached houses against road traffic noise using a point sound source model. F2012 is applicable to the evaluation of the Environmental Quality Standards for Noise in Japan (EQS). F2012 is composed of four factors: direct sound E dir, reflections E ref, first diffractions E dif,1, and others E dif,2. However, it is not easy to find the values of the parameters for E ref and E dif,1 in spite of their smaller sound energies than E dir and E dif,2. A simple calculation is essential for the evaluation of EQS. Therefore, a simplification of F2012 is examined and the simplified formula F2012 is proposed in this paper. In addition, a means of simplifying the computation of F2012 is examined. Keywords: Road traffic noise, Insertion loss of buildings, Environmental Quality Standards for Noise PACS number: 43.50.Lj, 43.50.Rq, 43.28.Fp, 43.28.Js [doi:10.1250/ast.38.287] 1. INTRODUCTION The Environmental Quality Standards for Noise in Japan (EQS) [1] state that the problem of environmental noise in areas facing roads should be evaluated by obtaining the numbers and proportions of buildings at which noise levels exceed the standard value. EQS allow the estimation of noise levels, instead of requiring actual measurements, in cases where taking the actual measurements would be difficult. In order to estimate noise levels, it is necessary to know the insertion loss of buildings in an evaluated area. With this background, the authors proposed an original method of predicting the insertion loss of detached houses against road traffic noise in an area facing a flat road, F2006 [2], and a banked road, F2006 þ [3]. F2006 and F2006 þ were adopted in ASJ RTN-Model 2008 [4], which is a standard prediction model for road traffic noise in Japan. Both formulas are based on a line sound source model and can only be applied to an area along a e-mail: fujimoto@arch.kyushu-u.ac.jp y e-mail: anai@civil.kyutech.ac.jp straight road. On the other hand, ASJ RTN-Model 2008 is based on a point sound source model, and consequently, it can predict the equivalent noise level L Aeq in areas along not only a straight road but also a curved road. With these points as the background, the authors proposed F2012 [5], which can predict the insertion loss of detached houses against road traffic noise using a point sound source model. F2012 can also be applied to an area along a curved road and was adopted in ASJ RTN-Model 2013 [6], which is the latest version of ASJ RTN-Model. F2012 is composed of four factors: direct sound E dir, reflections E ref, first diffractions E dif,1, and others E dif,2. However, it is not easy to find the values of the parameters for each factor. In particular, finding the values of the parameters for E ref and E dif,1 is very complicated even though their sound energies are small compared with E dir and E dif,2. Since the evaluation of EQS requires noise estimation for many houses, a simple calculation is essential for the evaluation of EQS. Therefore, in this paper, a simplification of the prediction formula F2012 is examined and a simplified prediction formula F2012 using only two factors, E dir and E dif,2, is presented. In addition, a 287
Acoust. Sci. & Tech. 38, 6 (2017) Fig. 1 Sound propagation from a sound source (S i )toa prediction point (P). procedure to omit the calculation of some parts of F2012 to simplify the computation is presented. 2. F2012: PREDICTION FORMULA OF THE INSERTION LOSS OF DETACHED HOUSES AGAINST ROAD TRAFFIC NOISE Firstly, F2012 is introduced. When detached houses are located in an area along a flat road, the A-weighted sound pressure level (L A;i ) at a point (Fig. 1) behind the houses from the ith point sound source on a road is calculated by L A;i ¼ L WA;i 8 20 log 10 r i þ L B ; where L WA;i is the A-weighted sound power level of the ith sound source [db], r i is the direct distance of the prediction point from the sound source [m], and L B is the insertion loss of the detached houses against road traffic noise [db]. L B is given by Eq. (2), which the authors proposed and gave the name of F2012 to, L B ¼ p L BB þ q p ¼ 0:017 ðh h p 8:8Þþ1 q ¼ 0:063 ðh h p 8:8Þ; where H and h p are the heights of the houses and the prediction point [m], respectively. L BB is the value when H is 10 m and h p is 1.2 m, and is given by L BB ¼ 10 log 10 a 0 þ a 1 þ a X i 2 i d road d ref;i þ a 3 1 X n 0:251 ð3þ n 1 þ 0:522 k¼1 k þ a 4 10 0:0904 d SP : Here, a 0 ¼ 0:0390, a 1 ¼ 1:16, a 2 ¼ 0:201, a 3 ¼ 0:346, and a 4 ¼ 0:288. The first item of Eq. (3) expresses the component of the direct sound from the ith point source to the prediction point. and are angles [rad] determined by the target road that is visible from the prediction point P, as shown in Fig. 2, when there are houses and no houses, respectively. The second item of Eq. (3) expresses the component of reflections. Only the first and second reflections by houses ð1þ ð2þ Fig. 2 Perspective angles ( and ) to a road from a prediction point when there are houses and no houses. are considered, assuming a simple model in which sound propagates as a ray based on geometrical acoustics, as shown in Fig. 3. Here, i is the angle [rad] determined by the target road that is visible from the mirror point P 0 of the prediction point P relative to the reflecting walls of houses, d ref;i is the perpendicular horizontal distance of P 0 from the road, and d road is the perpendicular horizontal distance of P from the road. P i means the summation of the first and second reflections, while third and subsequent reflections are ignored. The third item of Eq. (3) expresses the component of diffractions. Only a sound that diffracts only once at a point O and arrives at P after being emitted by a sound source S k, as shown in Fig. 4, is considered. k is the diffraction path difference (S k O þ OP S k P). Here, k denotes each point sound source and n is the number of diffraction paths. However, point sound sources that are visible from a prediction point are omitted from this calculation. The fourth item of Eq. (3) expresses the component representing other factors (direct sound, reflections, and diffractions). Here, d SP is the horizontal distance of the prediction point P from the sound source point S and is the house density in a rectangular area of width 15 m and length d SP, as shown in Fig. 5. F2012 was derived from experimental results. Because of the experimental conditions, F2012 is valid only when the distance of the prediction point from the road is between 20 m and 50 m, the covering percentage (total horizontal area of houses as a percentage of the whole of the target area) is between 16.8% and 34.4%, the height of the houses is less than 10 m, and the height of the prediction point is less than that of the houses. When houses with various heights are located in a target area, the average value can be applied as the height of the houses (H) for F2012 [7]. 288
K. FUJIMOTO and K. ANAI: SIMPLE PREDICTION OF INSERTION LOSS OF HOUSES Fig. 5 Horizontal distance from a sound source to a prediction point (d SP ), and house density in a rectangle (). (a) 1st reflections (b) 2nd reflections Fig. 3 Perpendicular horizontal distances (d road and d ref;i ) from a road to a prediction point and an image prediction point. 3. F2012 : SIMPLIFIED FORMULA OF F2012 3.1. Scale Model Experiment F2012 was derived from experimental results, and the simplification of F2012 is also examined on their basis. Therefore, the details of the experiment are not described in this paper. Please refer to Experiment I in the authors previous study [5]. 3.2. Simplification of Prediction Formula F2012 Equation (3) was derived from a multiple regression analysis whose objective variable was L BB obtained in the scale model experiment while the explanatory variables were the four items in Eq. (3): direct sound E dir, reflections E ref, first diffractions E dif,1, and others E dif,2. However, it is not easy to find the values of the parameters needed to calculate each item. In particular, finding the values of the parameters for E ref and E dif,1 is very complicated even though their sound energies are small compared with E dir and E dif,2. Since the evaluation of EQS requires the noise estimation for many houses, a simple calculation is essential for the evaluation of EQS. Therefore, a multiple regression analysis whose objective variable is L BB and whose explanatory variables are only two factors E dir and E dif,2, is carried out. As a result, Eq. (4) is obtained. The multiple correlation coefficient is 0.96, which is almost the same as that in F2012 (0.97). The authors call Eq. (4) F2012 hereafter. Fig. 4 5 m 5 m S S k Road O P Diffraction path difference of the first diffraction. L BB ¼ 10 log 10 b 0 þ b 1 þ b 2 10 0:0904 d SP ; where b 0 ¼ 0:0460, b 1 ¼ 1:01, and b 2 ¼ 0:554. Here, the constant b 0 is, in the same manner as for F2012, determined after a least-squares method is applied to the experimental data and data calculated using the equation. By comparing the coefficients of Eq. (4) with those of Eq. (3), it is found that the coefficient of E dir changes from ð4þ 289
Acoust. Sci. & Tech. 38, 6 (2017) [m] [m] [m] Fig. 6 Comparisons of L BB (unit patterns). 1.16 (a 1 : Eq. (3)) to 1.01 and the coefficient of E dif,2 changes from 0.288 (a 4 : Eq. (3)) to 0.554. This shows that E dif,2 contributes to L BB in F2012 more greately than in F2012. 4. EXAMINATION OF THE VALIDITY OF F2012 4.1. Unit Pattern In order to examine the validity of F2012, L BB calculated by F2012 is compared with that calculated by F2012. First, three examples from among all the 64 experimental arrangements, whose conditions were described in the authors previous study [5], are shown in Fig. 6. In each example, the left figure shows the arrangement of houses and the right one shows the fluctuation of L BB at a receiving point when a vehicle runs from a point where X ¼ 20 m to a point where X ¼ 80 m on a road. Scattered dots, thick and thin lines show the measured L BB, L BB predicted by F2012, and L BB predicted by F2012, respectively. The upper figure is an example where the values predicted by both F2012 and F2012 agree with the experimental ones well. In the middle example, considerable differences between the experimental and predicted values are found when X is greater than 55 m. Under such conditions, the parameters of E dir, E ref, and E dif,1 are all zero, and L BB predicted by F2012 converges to 13 db, compared with 14 db for F2012, and neither F2012 nor F2012 has good accuracy. In the lower example, both F2012 and F2012 give smaller values of L BB than the experimental ones. However, the differences are small. 4.2. Comparison of F2012 with F2012 All the experimental values of L BB are compared with the ones calculated by F2012 (left of Fig. 7) and F2012 (right of Fig. 7). The root mean square (RMS) of the differences and the maximum difference are 1.9 db and 7.3 db for F2012, compared with 1.6 db and 6.0 db for F2012, respectively. That is, the average prediction accuracy of F2012 is on average 0.3 db lower and at most 1.3 db lower than that of F2012. Figure 8 shows a comparison between the experimentally obtained and calculated L bldgs for the 64 arrangements of houses, where L bldgs is the average energy level of L BB when a vehicle runs from a point where X ¼ 20 m to a point where X ¼ 80 m on a road. The RMS of the differences and the maximum difference between the experimental and predicted values are 0.9 db and 2.3 db, 290
K. FUJIMOTO and K. ANAI: SIMPLE PREDICTION OF INSERTION LOSS OF HOUSES Fig. 7 Comparisons of L BB (all data). Fig. 8 Comparisons of L bldgs. respectively, for F2012. They are nearly equal to the values for F2012 (0.7 db and 1.6 db, respectively). The above results show that F2012 has almost the same accuracy of L bldgs as F2012, although the precision of L BB of F2012 is less than that of F2012 under some conditions. 5. SIMPLIFYING THE COMPUTATION OF F2012 The main use of F2012 is expected to be the evaluation of EQS in areas facing roads. Although the formula of F2012 is already simple, further simplification is needed for the evaluation of EQS because it requires numerous noise estimations as well as many point sources on a target road. Therefore, a means of simplifying the computation is examined in this section. F2012 is, as shown in Eq. (4), expressed as a sum of three factors: a constant b 0, a direct sound E dir, and other factors E dif,2. As the values of E dif,2 are smaller than those of E dir, it is proposed that the accuracy of F2012 can be maintained even if the calculation of E dif,2 is omitted. From this standpoint, the effect of omitting the calculation of E dif,2 is investigated under the condition that the error of L BB is maintained under 0.5 db. 5.1. Relationship between L BB and d SP d SP, which is a parameter of E dif,2, is the horizontal distance between a sound source point S and a prediction point P. It is suggested that E dif,2 does not contribute to L BB when d SP is very large (S is far from P). On the basis of this idea, the relationship between L BB and d SP is investigated. Some examples are shown in Fig. 9 (S is visible from P) and Fig. 10 (invisible), where solid curves show the relationship between L BB and d SP. In Fig. 9, (a) and (b) show the cases when is larger than 0:9 and when is between 0:4 and 0:5, respectively. It is found in both figures that L BB converges to the value drawn by a dotted line as d SP increases. It is thought that this is because the value of E dif,2 approaches zero and therefore does not contribute to L BB when d SP becomes very large. This indicates that the value of E dif,2 can be set to zero once the distance from S to P exceeds a certain value. In this paper, this value is set to each convergence value plus 0.5 db, illustrated by a broken line, in each figure. Hereafter, d SP determined by the above condition is expressed by dsp. Considering the formula for E dif,2, it is clear that dsp increases as decreases. The smallest is 0.028 among all the data in the experiment carried out to derive F2012. Hence, dsp is searched for under the condition that is greater than 0.028. The experimental L BB coinciding with the calculated values in each figure among all 7,744 experimental L BB are plotted by circles in Figs. 9 and 10, where solid curves 291
Acoust. Sci. & Tech. 38, 6 (2017) Table 1 Summary of, minimum, =, and d SP. (a) 0.9Φ < a φ 1.0Φ [rad] Number of data Minimum [ ] = [ ] d SP [m] 0:0 5,297 0.10 0.00 219.8 0:0 0:1 270 0.099 0.10 167.4 0:1 0:2 314 0.090 0.20 156.4 0:2 0:3 294 0.082 0.29 152.9 0:3 0:4 290 0.074 0.39 153.6 0:4 0:5 214 0.066 0.49 157.3 0:5 0:6 190 0.058 0.59 165.1 0:6 0:7 202 0.050 0.69 174.9 0:7 0:8 156 0.039 0.80 207.2 0:8 0:9 148 0.034 0.89 221.5 0:9 1:0 369 0.028 1.0 253.1 Fig. 9 Fig. 10 (b) 0.4Φ < a φ 0.5Φ Relationship between L BB and d SP (>0:0 ). show the relationship between L BB and d SP when is smallest (dsp is largest). The experimental L BB are classified into categories of width 0:1, and the minimum in each category is listed in Table 1, where = and dsp are also listed. It is found in the table that decreases as increases, and consequently, dsp changes greatly. The maximum d SP is 253.1 m, which occurs when = is 1.0. Thus, the calculation of E dif,2 can be omitted when dsp exceeds 254 m, irrespective of the value of. A regression analysis is performed using the data in Table 1, and as a result, the following equation is obtained: dsp ¼ 234 3 þ 659 2 386 þ 220: ð5þ This formula enables us to conclude that the calculation of E dif,2 can be omitted when the point sound sources is less than 254 m from the prediction point. However, note that [m] Relationship between L BB and d SP ( ¼ 0:0 ). the value of dsp obtained by Eq. (5) occasionally exceeds 254 when = is 1.0, because the coefficients of Eq. (5) have been adjusted to avoid obtaining greater values than those in Table 1. 5.2. When a Point Sound Source is Invisible from a Prediction Point When a point sound source is invisible from a prediction point, the minimum value of becomes relatively large, and the contribution of E dif,2 to the value of L BB decreases. Consequently, it is suggested that d SP becomes smaller. The chain line in Fig. 10 shows the relationship between L BB and d SP when is 0.30. It shows that L BB converges rapidly as increases from 0.10 to 0.30 and that L BB quickly reaches the convergent value of d SP, which is approximately 80 m, when is 0.30. These results suggest that d SP is a better index for judging whether the calculation of E dif,2 can be omitted or not. That is, E dif,2 can be set to zero when d SP exceeds a certain value in the case that the point sound source is invisible from the prediction point. Figure 10 indicates that E dif,2 can be set to zero when d SP is over 22.1 (the area below the dashed line in Fig. 10). This judgment can be applied to areas where buildings are uniformly distributed when the point sound sources used for noise calculation are selected in order of increasing distance from the prediction point. 5.3. Judgment Procedure for Omitting the Calculation of E dif,2 The judgment procedure for omitting the calculation of E dif,2 mentioned above is summarized as follows: (1) When the distance from the point sound source to the prediction point d SP exceeds 254 m, E dif,2 can be set to zero, (2) When d SP exceeds d SP obtained by Eq. (5), E dif,2 can be set to zero, 292
K. FUJIMOTO and K. ANAI: SIMPLE PREDICTION OF INSERTION LOSS OF HOUSES Fig. 11 Graph showing the area in which the calculation of the other component (E dif,2 ) can be omitted when is 0:0. (3) When houses are uniformly distributed and is zero, point sound sources are selected in order of increasing distance from the prediction point and used to calculate d SP. Once d SP exceeds 22.1, E dif,2 can be set to zero for the sound source point and subsequent points. 5.4. Verification of Omitting the Calculation of E dif,2 The validity of the proposed conditions under which E dif,2 can be set to zero presented in Sect. 5.3 is examined. First, the target road is assumed to be straight. An example when is 0:0 is presented pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi in Fig. 11, which shows the relationship between dsp 2 l2=l and. Here, l is the minimum horizontal distance from the sound source to the prediction point [m], and curved lines present the relationship when p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d SP is 22.1 and l is 20, 30, 40, and 50. It is found that dsp 2 l2=l decreases as increases. The range where the calculation of E dif,2 can be omitted is the area above each curved line. For example, when l is 20 m, E dif,2 can be set to zero for sound sources whose d SP exceeds 12:7 l. The results shown in Fig. 11 are also valid when is greater than 0:0 because the calculation of E dif,2 can be omitted while d SP is over 254. These threshold values of d SP are equivalent to about 34% of the value of 20 l recommended by ASJ RTN-Model 2013. Moreover, if the judgment based on d SP is applied when is zero, the result produces a greater reduction of the calculated value, that is, E dif,2 can be set to zero for sound sources whose d SP exceeds 9:2 l when l is 20 m and is greater than 0.12. There are about half the number of point sound sources recommended by ASJ RTN-Model 2013 within 9:2 l of d SP. When l is 20 m and is greater than 0.30, the calculation of E dif,2 can be omitted when d SP for the sound point source exceeds 3:5 l, which is equivalent to 78% to the value recommended by ASJ RTN- Model 2013. As mentioned above, omitting the calculation of E dif,2 is effective for simplifying the computation when a target road is straight. When a road is curved, a similar simplification is also expected, even though it is difficult to determine the effectiveness quantitatively because the shape of curved roads cannot be expressed in principle. 6. CONCLUSIONS A simplification of F2012, which predicts the insertion loss of detached houses against road traffic noise using a point sound source model, was examined and a simplified formula, F2012, was proposed. F2012 leads to a small error in cases where the energy of the direct sound is small and that of the reflections and first diffractions, which correspond to the locations of a point sound source (a vehicle), houses, and a prediction point, is not negligible. Hence, it is necessary to be aware of arrangements of houses when predicting L BB under such conditions using F2012. However, F2012 provides almost the same value of L bldgs as F2012 and the parameters used in F2012 are easy to obtain. Therefore, F2012 is useful for the evaluation of EQS. In addition, a procedure to omit the calculation of some parts of F2012 to further simplify the computation is presented. The error in L BB caused by this omission of the calculation is under 0.5 db when about 30% to 70% of the point sources recommended by ASJ RTN-Model 2013 are omitted from the calculation. F2012 and the procedure for simplifying the computation proposed in this paper enable us to predict the insertion loss of detached houses against road traffic noise using a point sound source model more easily. ACKNOWLEDGEMENTS This work was supported by JSPS KAKENHI Number 24560715. The authors wish to thank Mr. Kengo Morita for his help with the analysis. REFERENCES [1] Environmental Quality Standards for Noise, Notification No. 64 of the Environmental Agency in Japan (1998). [2] K. Fujimoto, K. Yamaguchi, T. Nakanishi and K. Anai, Prediction of insertion loss of road traffic noise caused by detached houses in an area facing a plane road, J. Acoust. Soc. Jpn. (J), 63, 309 317 (2007) (in Japanese). [3] K. Yamaguchi, K. Fujimoto, K. Anai and Y. Hiraguri, Prediction of insertion loss of road traffic noise caused by detached houses in an area facing an embanked road, J. INCE/ J, 33, 153 161 (2009) (in Japanese). [4] K. Yamamoto, Road traffic noise prediction model ASJ RTN- Model 2008 : Report of the Research Committee on Road Traffic Noise, Acoust. Sci. & Tech., 31, 2 55 (2010). [5] K. Fujimoto, K. Tsuji, T. Tominaga and K. Morita, Prediction of insertion loss of detached houses against road traffic noise using a point sound source model, Acoust. Sci. & Tech., 36, 109 119 (2015). [6] S. Sakamoto, Road traffic noise prediction model ASJ RTN- 293
Model 2013 : Report of the Research Committee on Road Traffic Noise, Acoust. Sci. & Tech., 36, 49 108 (2015). [7] K. Fujimoto, K. Anai, K. Isogai and D. Sekito, ASJ Tech. Rep. of Noise & Vib., N-2003-64, pp. 1 7 (2003) (in Japanese). Kazutoshi Fujimoto graduated from Kyushu University in Japan in 1972 and received his Dr. Eng. degree in 1986. He is currently a Professor Emeritus of Kyushu University. His research interests include the prediction and evaluation of road traffic noise and the development of sound-absorbing panels applying Helmholtz resonators. He is a member of ASJ, AIJ (Architectural Institute of Japan), and INCE/J (Institute of Noise Control Engineering of Japan). AIJ, and INCE/J. Acoust. Sci. & Tech. 38, 6 (2017) Ken Anai received his BE, ME, and D. Eng. degrees from Kyushu University in 1995, 1997, and 2000, respectively. Currently he is an Associate Professor in the Department of Engineering, Kyushu Institute of Technology, Japan. His main research interests are road traffic noise prediction, active noise control on building façades, and sound absorption with microperforated panels. He is a member of ASJ, 294