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Figure 3.18: Demonstration in case of hg < hi or h3 > hi sources located in the direction of the central screening building become more rel- evant. Assuming that the source lies in the middle of the canyon W, and according to the simple ratio aWesOoWs = ae = 1,2,---, the relation between h and hy is: h = a0 hy, where h; = H,,-source height. When h = a8 hy > hs, the ath image source will become unavailable. Specifically, the relation actually is h = 1/3hy, 1/3h1, 3/5h1, 5/Thi-. 2 the total contribution becomes: Instead of 52°, |pa.o evant. Assuming that the source lies in the middle of the canyon W, and according

Figure 3 18: Demonstration in case of hg < hi or h3 > hi sources located in the direction of the central screening building become more rel- evant. Assuming that the source lies in the middle of the canyon W, and according to the simple ratio aWesOoWs = ae = 1,2,---, the relation between h and hy is: h = a0 hy, where h; = H,,-source height. When h = a8 hy > hs, the ath image source will become unavailable. Specifically, the relation actually is h = 1/3hy, 1/3h1, 3/5h1, 5/Thi-. 2 the total contribution becomes: Instead of 52°, |pa.o evant. Assuming that the source lies in the middle of the canyon W, and according

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Figure 2.1: Distribution(a) and cumulative probability(b) of the projected building and canyon width in the city of Ghent, Belgium. In the simulations, the widths of buildings and canyons are limited to 42 m.
Figure 2.1: Distribution(a) and cumulative probability(b) of the projected building and canyon width in the city of Ghent, Belgium. In the simulations, the widths of buildings and canyons are limited to 42 m.
Figure 2.2: A typical simulation configuration, where W;, W and W,, are the width of source canyon, intermediate building and receiver canyon; Hs, H; and H, are the height of the left, intermediate and right building; h; and hz are the distance from the source or receiver to the top of the building; 0, and 0, are the angle between the building fagade and the connecting line from the source or receiver to the diffraction edge; 3; and 8, are the outside angle of the building which equals 37/2 in this study. 2.3.1.1 Adar, fiat? rigid barrier with flat roof In most noise mapping methods (including CNOSSOS-EU), the [S096 13-2 diffrac- tion formula or similar is used to calculate Apar, fiat. By comparing with an in- situ long-term measurements [20] and FDTD simulations, it was found that using the ISO standard to calculate Apa, leads to large predicting errors. Therefore, a more accurate but still computational efficient approximation is needed. In a first step, ground reflection is ignored. According to the literature [21, 22, 23, 24], An... ¢1-4:0 can be expressed with high accuracy by equation (2.4):
Figure 2.2: A typical simulation configuration, where W;, W and W,, are the width of source canyon, intermediate building and receiver canyon; Hs, H; and H, are the height of the left, intermediate and right building; h; and hz are the distance from the source or receiver to the top of the building; 0, and 0, are the angle between the building fagade and the connecting line from the source or receiver to the diffraction edge; 3; and 8, are the outside angle of the building which equals 37/2 in this study. 2.3.1.1 Adar, fiat? rigid barrier with flat roof In most noise mapping methods (including CNOSSOS-EU), the [S096 13-2 diffrac- tion formula or similar is used to calculate Apar, fiat. By comparing with an in- situ long-term measurements [20] and FDTD simulations, it was found that using the ISO standard to calculate Apa, leads to large predicting errors. Therefore, a more accurate but still computational efficient approximation is needed. In a first step, ground reflection is ignored. According to the literature [21, 22, 23, 24], An... ¢1-4:0 can be expressed with high accuracy by equation (2.4):
Figure 2.3: Error estimation of f _ gv compared with the theoretical values. In this case, W =10A,rs =Trr = 10A, Bs = Br = at 0. = 4, 9, increases from 0 to m/2
Figure 2.3: Error estimation of f _ gv compared with the theoretical values. In this case, W =10A,rs =Trr = 10A, Bs = Br = at 0. = 4, 9, increases from 0 to m/2
In some European city centers, gabled roofs are very common. The sound waves propagating over an idea ized gabled roof may be diffracted once, twice or three times before reaching the observer. It should be noted that roofs may be more complicated and diffracti sound attenuation [26]. T position, the angle of the for Ghent (as a typical o on may result in a wid he effect of roof shape d ld European city), the and buildings is 12 m and e range of significantly different epends on the source and receiver roof and the building height. According to the statistics most common width of canyons 24 m respectively, and the mean height of the buildings is 10.9 m. If the height of the roof is assumed to be 4.5 m, then most of the sources and receivers below 4.5 m high would be located inside the shadow region where the sound wave has to diffract three times to reach the receiver at the other side of the building, as shown in figure 2.5. Under this condition, Abar,roof iS linearly correlated to Apar, fiat. To simplify the calculation of the roof, Agar,roof is rewritten as a linear function of Abar, fiat:
In some European city centers, gabled roofs are very common. The sound waves propagating over an idea ized gabled roof may be diffracted once, twice or three times before reaching the observer. It should be noted that roofs may be more complicated and diffracti sound attenuation [26]. T position, the angle of the for Ghent (as a typical o on may result in a wid he effect of roof shape d ld European city), the and buildings is 12 m and e range of significantly different epends on the source and receiver roof and the building height. According to the statistics most common width of canyons 24 m respectively, and the mean height of the buildings is 10.9 m. If the height of the roof is assumed to be 4.5 m, then most of the sources and receivers below 4.5 m high would be located inside the shadow region where the sound wave has to diffract three times to reach the receiver at the other side of the building, as shown in figure 2.5. Under this condition, Abar,roof iS linearly correlated to Apar, fiat. To simplify the calculation of the roof, Agar,roof is rewritten as a linear function of Abar, fiat:
Figure 2.6: Accuracy of the fitted and analytical curve. The curve labeled “W = 10m” indicates the exact values, while curve labeled “W = 10m fit” indicates the approximated values obtained using equation (2.13). The height of the building is 12 m. The source is 5 m to the facade and the distances from receivers to facade are 0.1, 0.5, 1, 2, 3, 5m respectively. age receiver would most probably lie outside the three-diffraction region, which
Figure 2.6: Accuracy of the fitted and analytical curve. The curve labeled “W = 10m” indicates the exact values, while curve labeled “W = 10m fit” indicates the approximated values obtained using equation (2.13). The height of the building is 12 m. The source is 5 m to the facade and the distances from receivers to facade are 0.1, 0.5, 1, 2, 3, 5m respectively. age receiver would most probably lie outside the three-diffraction region, which
(b) Case study 2 with H, = H, = W, = W, = 9.6m, W = 10m, and H; changes (a) Case study 1 with H; = H, = Ws = W; = 9.6m, W = 10m, and H, changes
(b) Case study 2 with H, = H, = W, = W, = 9.6m, W = 10m, and H; changes (a) Case study 1 with H; = H, = Ws = W; = 9.6m, W = 10m, and H, changes
Figure 2.10: Measurement positions of Ghent city, Belgium.
Figure 2.10: Measurement positions of Ghent city, Belgium.
Figure 2.12: Spectrum of position 6. Legend “Scatter” is calculated by the model in [10]; “Reflection” is calculated by equation (2.2); “Reflectiont+Scatter” is calculated by equation (2.1) with C? = 0.4K? /m?/3 and C? = 1.2m4/3 /s?. Cy and C; are the structure parameters of velocity and temperature fluctuations, respectively, describing their partial turbulence strengths. Figure 2.11: Comparison of predicted level and measurement. The legends “Measurement” indicates the measured Laay; “END” is the Laay calculated for the END map; “MR+T+END” uses the background noise mapping concept, including multiple reflections and the turbulence scattering model [10] applied to the END map predictions.
Figure 2.12: Spectrum of position 6. Legend “Scatter” is calculated by the model in [10]; “Reflection” is calculated by equation (2.2); “Reflectiont+Scatter” is calculated by equation (2.1) with C? = 0.4K? /m?/3 and C? = 1.2m4/3 /s?. Cy and C; are the structure parameters of velocity and temperature fluctuations, respectively, describing their partial turbulence strengths. Figure 2.11: Comparison of predicted level and measurement. The legends “Measurement” indicates the measured Laay; “END” is the Laay calculated for the END map; “MR+T+END” uses the background noise mapping concept, including multiple reflections and the turbulence scattering model [10] applied to the END map predictions.
Figure 2.14: Spectrum of position 9. Figure 2.13: Spectrum of position 8.
Figure 2.14: Spectrum of position 9. Figure 2.13: Spectrum of position 8.
According to the diffraction theory, the factor B has to be multiplied with the small- est of the two X terms. Therefore we have a closer look at the ratio Xq,5/Xa,r which is iy / re oe Considering that the receiver is generally higher than the source and that all fagades of buildings have the same height, h1 > ha. In most cases it can be shown that this ratio is less than 1 after a few reflections, since Ya,s >> Tr is expected. For deducing an analytic form for Acan, fiat, all Xa,s are supposed to be less than X,. As aresult, X¢.1 = Xa,5B and Xq,2 = Xp. Let us now consider the second term in equation (2.16) which we call C, for convenience:
According to the diffraction theory, the factor B has to be multiplied with the small- est of the two X terms. Therefore we have a closer look at the ratio Xq,5/Xa,r which is iy / re oe Considering that the receiver is generally higher than the source and that all fagades of buildings have the same height, h1 > ha. In most cases it can be shown that this ratio is less than 1 after a few reflections, since Ya,s >> Tr is expected. For deducing an analytic form for Acan, fiat, all Xa,s are supposed to be less than X,. As aresult, X¢.1 = Xa,5B and Xq,2 = Xp. Let us now consider the second term in equation (2.16) which we call C, for convenience:
which becomes independent of a when it can be assumed that W + r¢.5 > Tr, which is the case for higher order reflections at least. The remaining part of equa-
which becomes independent of a when it can be assumed that W + r¢.5 > Tr, which is the case for higher order reflections at least. The remaining part of equa-
Figure 2.15: Demonstration of contributed image sources. After one more diffraction, the sound power decreases significantly, which can be
Figure 2.15: Demonstration of contributed image sources. After one more diffraction, the sound power decreases significantly, which can be
Similarly, when oe se < 1/3, the canyon effect is neglected and L;,,. is set to —00; when 1/3 < ae < 3/5, 21 [po,e|? = 107014e"#!2t. In a special case when H, = h,., the canyon effect is neglected as well. where F'(2) is the fitting coefficient, h, is the height of the receiver, p, is the aver- age reflection coefficient of the fagade in the receiver canyon and other parameters are as follows:
Similarly, when oe se < 1/3, the canyon effect is neglected and L;,,. is set to —00; when 1/3 < ae < 3/5, 21 [po,e|? = 107014e"#!2t. In a special case when H, = h,., the canyon effect is neglected as well. where F'(2) is the fitting coefficient, h, is the height of the receiver, p, is the aver- age reflection coefficient of the fagade in the receiver canyon and other parameters are as follows:
The asymmetry is caused by the above assumption. If we calculate the double sum from the receiver canyon, a similar form could be achieved only replacing “h,” by “ho”. To moderate this error, the average of the two calculations is used to approximate the double sum by:
The asymmetry is caused by the above assumption. If we calculate the double sum from the receiver canyon, a similar form could be achieved only replacing “h,” by “ho”. To moderate this error, the average of the two calculations is used to approximate the double sum by:
Although the Fresnel integrals can be solved rather easily nowadays, further sim- plification is still useful. If X >> 0, the Fresnel Integral can be simplified as C(X) *® 0.5+ —4 sin (4 X*) and $(X) » 0.5-—4 cos (4 X?), However, in real urban cases, x > 0 appears frequently, implying that S(X) * 0.5- cos (z ao 2) definition of the angles is shown in figure (3.1). Other parameters are:
Although the Fresnel integrals can be solved rather easily nowadays, further sim- plification is still useful. If X >> 0, the Fresnel Integral can be simplified as C(X) *® 0.5+ —4 sin (4 X*) and $(X) » 0.5-—4 cos (4 X?), However, in real urban cases, x > 0 appears frequently, implying that S(X) * 0.5- cos (z ao 2) definition of the angles is shown in figure (3.1). Other parameters are:
Figure 3.1: Geometry of single-wedge (a) and double-edge (b) diffraction. has a strong singularity point at _X = 0. The later means that this approximation can lead to big errors when X is close to 0. To avoid this singularity, the Fresnel Integrals are approximated by [15]:
Figure 3.1: Geometry of single-wedge (a) and double-edge (b) diffraction. has a strong singularity point at _X = 0. The later means that this approximation can lead to big errors when X is close to 0. To avoid this singularity, the Fresnel Integrals are approximated by [15]:
Figure 3.2: Distribution of X in two European cities. Xi+ and X;- are explained in Eq.(3.2). The X values shown in this figure follow a 2.5 D approach to noise mapping considering the typical vertical cross sections that occur during this process. Since strict but complicated formulas of single-wedge and double-edge diffrac- tion have been given in Pierce’s work, the simplified equations proposed in this work will be compared with Pierce’s theoretical solution. Figure (3.4) shows the amplitude difference,
Figure 3.2: Distribution of X in two European cities. Xi+ and X;- are explained in Eq.(3.2). The X values shown in this figure follow a 2.5 D approach to noise mapping considering the typical vertical cross sections that occur during this process. Since strict but complicated formulas of single-wedge and double-edge diffrac- tion have been given in Pierce’s work, the simplified equations proposed in this work will be compared with Pierce’s theoretical solution. Figure (3.4) shows the amplitude difference,
Figure 3.3: Comparison of the approximation accuracy of Fresnel Integral C(x) and S(2).
Figure 3.3: Comparison of the approximation accuracy of Fresnel Integral C(x) and S(2).
Figure 3.5: Comparison of calculation efficiency between Pierce’s solution (labelled by “theory” ) and the simplified method presented in this work. The results are based on running the algorithms 10000 times. The algorithm used for calculating the Fresnel Integral is based on [19], using 12 terms in the Taylor series expansion. the second part of the double-edge diffraction: path 1 > 2 > R, Xp, = Xp_. Based on the above analysis, the diffraction function of a double connected edge then reads:
Figure 3.5: Comparison of calculation efficiency between Pierce’s solution (labelled by “theory” ) and the simplified method presented in this work. The results are based on running the algorithms 10000 times. The algorithm used for calculating the Fresnel Integral is based on [19], using 12 terms in the Taylor series expansion. the second part of the double-edge diffraction: path 1 > 2 > R, Xp, = Xp_. Based on the above analysis, the diffraction function of a double connected edge then reads:
Figure 3.6: Schematic diagram of multiple diffraction. 3.2.3 Generalization to multiple diffraction
Figure 3.6: Schematic diagram of multiple diffraction. 3.2.3 Generalization to multiple diffraction
Figure 3.7: Geometries considered to validate multiple diffraction in absence of a source and receiver canyon.
Figure 3.7: Geometries considered to validate multiple diffraction in absence of a source and receiver canyon.
Figure 3.8: Contour plots showing the sound pressure level difference between the presented method and Pierce’s method (Lsimplified — L Pierce) in the receiver zone as defined in Fig. 3.7, for geometrical configuration (a). Calculations were performed for 250 Hz and 2000 Hz.
Figure 3.8: Contour plots showing the sound pressure level difference between the presented method and Pierce’s method (Lsimplified — L Pierce) in the receiver zone as defined in Fig. 3.7, for geometrical configuration (a). Calculations were performed for 250 Hz and 2000 Hz.
Figure 3.9: Contour plots showing the sound pressure level difference (Lsimplified — L Pierce) in the receiver zone as defined in Fig. 3.7, for configuration (b).
Figure 3.9: Contour plots showing the sound pressure level difference (Lsimplified — L Pierce) in the receiver zone as defined in Fig. 3.7, for configuration (b).
Figure 3.10: Contour plots showing the sound pressure level difference Lsimplified — LPierce) in the receiver zone as defined in Fig. 3.7, for configuration (c)
Figure 3.10: Contour plots showing the sound pressure level difference Lsimplified — LPierce) in the receiver zone as defined in Fig. 3.7, for configuration (c)
Figure 3.11: Contour plots showing the sound pressure level difference simplified — L Pierce) in the receiver zone as defined in Fig. 3.7, for configuration (d)
Figure 3.11: Contour plots showing the sound pressure level difference simplified — L Pierce) in the receiver zone as defined in Fig. 3.7, for configuration (d)
Figure 3.12: Demonstration of image sources and image receivers. Reflections from ground are not considered here. Circles are image sources and triangles are image receivers.
Figure 3.12: Demonstration of image sources and image receivers. Reflections from ground are not considered here. Circles are image sources and triangles are image receivers.
Figure 3.13: Effect of reflections without ground effect. The geometries are shown in figure (3.14). In (a), Ws = 22 m; hy = 10m; r- = 7m; W; = 22 m; Bs = Gr = 1.57; wave length= 0.68(500 Hz);source is in the middle of the canyon;. In (b), rr, Wi, Bs, Br are the same as (a), but the W; and hy varies in a urban setting range and the reflection coefficient is fixed as 0.97. Level difference is the increase between 50 image sources and one image source.
Figure 3.13: Effect of reflections without ground effect. The geometries are shown in figure (3.14). In (a), Ws = 22 m; hy = 10m; r- = 7m; W; = 22 m; Bs = Gr = 1.57; wave length= 0.68(500 Hz);source is in the middle of the canyon;. In (b), rr, Wi, Bs, Br are the same as (a), but the W; and hy varies in a urban setting range and the reflection coefficient is fixed as 0.97. Level difference is the increase between 50 image sources and one image source.
Figure 3.14: Geometry considered to evaluate the simplified strategy to include multiple reflections in between opposing parallel building facades. 3.3.2 Generalize the reflections combined with multiple diffrac- tion
Figure 3.14: Geometry considered to evaluate the simplified strategy to include multiple reflections in between opposing parallel building facades. 3.3.2 Generalize the reflections combined with multiple diffrac- tion
Figure 3.16: Geometry of a typical generalized case including reflections and multiple diffraction.
Figure 3.16: Geometry of a typical generalized case including reflections and multiple diffraction.
Figure 3.17: Contour plot of the level difference between the generalized model and the FDTD simulations for the geometry as in figure (3.16).
Figure 3.17: Contour plot of the level difference between the generalized model and the FDTD simulations for the geometry as in figure (3.16).
Figure 3.19: Geometry to check the generalized model with different facades heights: hg <hy
Figure 3.19: Geometry to check the generalized model with different facades heights: hg <hy
Where |pa,o|”;|4a,0|7»|d4,,0|° and |q/v |” are used to distinguish sound pressure diffracted by different paths. |pa.o|* is path a‘"image > 2 > 3 > R, |qa,ol”, is path a‘"image > 1 > R, |q/,o/° is path a’"image > 1 > 3 > R and {qo is path a‘"image > 2 1 3 R. Ci,9,2 and C3,g,.2 can be calculated from the generalized form Eq.(3.27) and Eq.(3.29). The indexes x of C192 and C3 g,x is only used to distinguish different C,,, and C’3,,. M is the image source number from which the diffraction path changes from a‘’image > 1 > R to
Where |pa,o|”;|4a,0|7»|d4,,0|° and |q/v |” are used to distinguish sound pressure diffracted by different paths. |pa.o|* is path a‘"image > 2 > 3 > R, |qa,ol”, is path a‘"image > 1 > R, |q/,o/° is path a’"image > 1 > 3 > R and {qo is path a‘"image > 2 1 3 R. Ci,9,2 and C3,g,.2 can be calculated from the generalized form Eq.(3.27) and Eq.(3.29). The indexes x of C192 and C3 g,x is only used to distinguish different C,,, and C’3,,. M is the image source number from which the diffraction path changes from a‘’image > 1 > R to
Figure 3.21: Geometry to check the generalized model with different facades heights: Hs > Am
Figure 3.21: Geometry to check the generalized model with different facades heights: Hs > Am
Figure 3.23: Special cases influencing the results.
Figure 3.23: Special cases influencing the results.
According to equation (4.9) and (4.13), the correction term 6 for a specified source The LMS method is also used to calculate Onn n Similar procedure is applied as when formulating the ¢!,. Also note that the corrections for different propaga- tion paths are independent, meaning that the derivatives to paths other than n will vanish. The derivative can be simplified to: when formulating the «),,. Also note that the corrections for different propaga- 4.3.2 Calculate propagation correction 6
According to equation (4.9) and (4.13), the correction term 6 for a specified source The LMS method is also used to calculate Onn n Similar procedure is applied as when formulating the ¢!,. Also note that the corrections for different propaga- tion paths are independent, meaning that the derivatives to paths other than n will vanish. The derivative can be simplified to: when formulating the «),,. Also note that the corrections for different propaga- 4.3.2 Calculate propagation correction 6
Figure 4.1: Implementation flow of the model.
Figure 4.1: Implementation flow of the model.
Figure 4.4: Adapting curve of the categorized traffic sources. C1, C2, C'3 and C'4 indicates the category number.
Figure 4.4: Adapting curve of the categorized traffic sources. C1, C2, C'3 and C'4 indicates the category number.
Figure 4.5: Adapting curve of the propagation term 6 for the traffic sources category 1. “direct” indicates the propagation correction for the direct sound path; “diffraction” indicates the diffraction path and “scattered” indicates the turbulence scattering path.
Figure 4.5: Adapting curve of the propagation term 6 for the traffic sources category 1. “direct” indicates the propagation correction for the direct sound path; “diffraction” indicates the diffraction path and “scattered” indicates the turbulence scattering path.
Figure 4.6: Adapting curve of the propagation term 6 for the traffic sources category 2.
Figure 4.6: Adapting curve of the propagation term 6 for the traffic sources category 2.
Figure 4.8: Adapting curve of the propagation term 6 for the traffic sources category 4.
Figure 4.8: Adapting curve of the propagation term 6 for the traffic sources category 4.
Figure 4.9: Adapting curve of the propagation term 6 for the industry sources category.
Figure 4.9: Adapting curve of the propagation term 6 for the industry sources category.
Figure 4.10: Density function and cumulative probability function of the improvement on the predicted L Aeq. Negative values indicate that predictions become worse and positive values indicate the prediction is improved after correcting. 206 and 220 are the two validating positions.
Figure 4.10: Density function and cumulative probability function of the improvement on the predicted L Aeq. Negative values indicate that predictions become worse and positive values indicate the prediction is improved after correcting. 206 and 220 are the two validating positions.
Figure 4.11: Density function and accumulative probability function of the improvement on the predicted Lo.
Figure 4.11: Density function and accumulative probability function of the improvement on the predicted Lo.
Figure 4.12: Density function and accumulative probability function of the improvement on the predicted Lgo.
Figure 4.12: Density function and accumulative probability function of the improvement on the predicted Lgo.
Figure 4.13: Original and adapted predictions of L109. Circle positions indicate the predicted errors; the circle radii indicate the number of predictions with this accuracy.
Figure 4.13: Original and adapted predictions of L109. Circle positions indicate the predicted errors; the circle radii indicate the number of predictions with this accuracy.
Figure 4.14: Noise map at 5:00 am.
Figure 4.14: Noise map at 5:00 am.
Figure 4.16: Noise map at 7:00 am. Figure 4.15: Noise map at 6:00 am.
Figure 4.16: Noise map at 7:00 am. Figure 4.15: Noise map at 6:00 am.
Figure 4.17: Comparison of LAeq between updating only sources and sources & propagations
Figure 4.17: Comparison of LAeq between updating only sources and sources & propagations
Figure 4.18: Comparison of L109 between updating only sources and sources & propagations
Figure 4.18: Comparison of L109 between updating only sources and sources & propagations
Figure 4.19: Comparison of L99 between updating only sources and sources & propagations
Figure 4.19: Comparison of L99 between updating only sources and sources & propagations
Figure A.2: Propulsion noise of the default condition.
Figure A.2: Propulsion noise of the default condition.
Figure A.3: Ar of category m =, light vehicles.
Figure A.3: Ar of category m =, light vehicles.
Figure A.7: Ar of category m = 2, medium heavy vehicles.
Figure A.7: Ar of category m = 2, medium heavy vehicles.
Figure A.12: Br of category m = 3. Figure A.11: Ar of category m = 3, heavy vehicles.
Figure A.12: Br of category m = 3. Figure A.11: Ar of category m = 3, heavy vehicles.
Figure A.15: Configuration of the comparison. call this model as “QSIDE” model. The corresponding attenuation of a double diffraction is:
Figure A.15: Configuration of the comparison. call this model as “QSIDE” model. The corresponding attenuation of a double diffraction is:
Figure A.18: Percentage of different H,, H;, and H,.
Figure A.18: Percentage of different H,, H;, and H,.
Figure A.19: Percentage of different W;, W; and W,.
Figure A.19: Percentage of different W;, W; and W,.
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