mathematical modeling of road traffic noise ... - Semantic Scholar

MATHEMATICAL MODELING OF ROAD TRAFFIC NOISE PREDICTION K. Kumar1, V. K. Katiyar1, M. Parida2, and K. Rawat1 1

2

Department of Mathematics, IIT Roorkee, India-247667. Centre for Transportation, Department of Civil Engineering, IIT Roorkee, India-247667. Email: [email protected] Received 17 September 2010; accepted 14 January 2011

ABSTRACT Noise is one of the environmental pollutant that is encountered in daily life. Noise pollution has become a major concern of communities living in the vicinity of major highway corridors. In view of the rapid development it is essential to study highway noise with respect to various causative factors. In the present paper a road traffic noise prediction model for Indian conditions is developed using regression analysis which is based on Calixto model. Data collected has been analyzed and compared with the values predicted by Calixto model. After comparison of results it was observed that Calixto Model could be satisfactorily applied for Indian conditions as they give accepted results with a good value. Keywords: Calixto model, traffic noise, weighting factor, traffic flow, percentage of heavy vehicles.

1 INTRODUCTION With urbanization and corresponding increase in number of vehicles in metropolitan cities, the pollution is increasing at an alarming rate. Main areas of concern are related to air and noise pollution. More than 70% of total noise in our environment is due to vehicular noise. Noise levels are showing an alarming rise and infact level exceeds the prescribed levels in most of the areas. Investigation in several countries in the past decades have shown that noise has adverse effect on human health, living in close proximity to busy road highways (Ohrstorm and Rylander 1990, Babisch et al 2001, Ljungberg and Neely 2007, Rylander 2004, Graham et al. 2009, Pirrera et al. 2010) The level of highway traffic noise depends mainly on the following factors: (i)

Volume of the traffic

(ii)

Speed of the traffic

Int. J. of Appl. Math and Mech. 7 (4): 21-28, 2011.

22

(iii)

K. Kumar et al.

Number of the heavy vehicles in the flow of traffic.

To create a healthy and noise pollution free environment a noise prediction model is needed so that the noise level along a busy highway can be predicted and investigated in advance during the planning and design process (Brown and Macdonald 2003). A mathematical model for road traffic noise in urban situation making use of grid coordinates in order to measure the noise due to direct propagation, diffraction and deflection was developed (Clayden et al. 1974). Bodsworth and Lawrence investigated the contribution of heavy vehicles such as trucks and buses on the noise profile of traffic stream to urban traffic noise by showing that number of heavy vehicles play a major role in road traffic noise (Bodsworth and Lawrence 1978). A computer model for predicting noise levels generated by urban road traffic under interrupted flow conditions was developed (Radwan and Oldham 1987). Applicability of autoregressive integrated moving averages (ARIMA) modeling, a special class of time series techniques for the development forecast models of road traffic noise was investigated by Kumar and Jain in Delhi city (Kumar and Jain 1999).Traffic composition is defined as the percentage of heavy vehicles with respect to the total number of vehicles by investigating the annoyance from road traffic noise (Ouis 2001). Filho et al. investigated the effect of traffic composition on the noise generated by Brazilian roads (Filho et al. 2004). A motor traffic noise model based on the perpendicular propagation analysis technique (direction perpendicular to the centerline of motorways carriageway) is found performed well in a statistical goodness of fit test against the field data (Tansatcha et al. 2005). A methodology through which the UK calculation of road traffic noise (CORTN) has been converted to the algorithms that are able to calculate hourly A-weighted equivalent sound pressure level for the Tehran’s roads was developed (Givargis and Mahmoodi 2008). A highway traffic noise prediction model making use of outdoor sound propagation method by considering various road surface types is developed (Cho and Mun 2008). Fyhri and Aasvang developed the relationship between road traffic noise and cardiovascular system (Fyhri and Aasvang 2010). Results of their analysis showed significant relationship between noise annoyance at night and sleeping problems. Their analysis showed no relationship between neither noise exposure nor response to noise and cardiovascular problems. A statistical model of road traffic noise in an urban setting which is based on the fact that percentage of heavy vehicles plays an important role over road traffic noise emission is developed (Calixto et al. 2003). Keeping this in mind in the present paper we calculated weighting factor that represents the weightage of presence of heavy vehicles over road traffic noise emission in Indian road conditions. Developed model is then checked for validation by value and found suitable for Indian road conditions.

2 METHODOLOGY Most of the countries, keeping in view the alarming increase in environmental noise pollution, have given the permissible noise standards. Ambient noise standards being followed in India for different types of areas are given in table 1. Calixto et al. (Calixto et al. 2003) presented a statistical model of road traffic noise in an urban setting. In this model, by claiming the fact that heavy vehicles generate stronger noise than a lighter vehicle, they introduced a new factor , called as weighting factor. Data on basic noise level which consists of traffic flow, average speed of traffic stream, percentage of heavy vehicles is measured at different hours


Mathematical Modeling Of Road Traffic Noise Prediction

23

and locations on NH-58 by using noise analyzer (B & K 2260 sound level meter) and is given in table 2.

Table 1: Ambient Noise Standards in India S.N.

Area

1 2 3 4

Industrial Area Commercial Area Residential Area Silence Zone

Day Time 75 65 55 50

Night Time 70 55 45 40

3 MATHEMATICAL MODEL FOR BASIC NOISE EMISSION LEVEL Since heavy vehicle is responsible for stronger noise than a light vehicle, a factor has been taken into account for such vehicles. In Calixto model by considering as real hourly vehicle flow, as the percentage of heavy vehicles and as weighting factor, is given by following equation (1) and the term

will be transformed into (2)

Weighting factor is calculated by using largest correlation coefficient between observed values given in table 2 and the factor given by equation (2) and found (3) Using the observed data, a new model with weighting factor has been developed by calibrating Calixto model. Microsoft excel spread sheet has been used for estimating the values using equation (3). The estimated values were then compared with observed values (as given in table 2) to get the regression equation as follows (4)


24

K. Kumar et al.

Table 2: Measurement of noise level (dB A) and traffic parameters

S.NO. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.

Total No. of Vehicles/hour (Q) 1022 1024 1030 1036 1036 1036 1038 1111 1123 1130 1134 1139 1139 1146 1153 1170 1172 1174 1188 1202 1204 1205 1207 1213 1221 1223 1223 1225 1228 1229 1231 1232 1232 1232 1239 1248 1258 1267 1272

No. of heavy vehicles (HV) 124 125 125 128 131 132 134 144 149 150 153 156 157 160 162 165 167 168 170 173 173 177 177 179 185 185 185 186 187 187 189 189 189 191 192 194 197 198 200


Percentage of Heavy Vehicles (VP) 12.1 12.2 12.1 12.3 12.6 12.7 12.9 12.9 13.2 13.2 13.4 13.6 13.7 13.9 14.0 14.1 14.2 14.3 14.3 14.3 14.3 14.6 14.6 14.7 15.1 15.1 15.1 15.1 15.2 15.2 15.3 15.3 15.3 15.5 15.4 15.5 15.6 15.6 15.7

Observed

Calculated

78.4 78.7 79.2 80.2 80.2 80.4 80.4 80.4 80.6 80.7 80.7 80.7 80.8 81.0 81.0 81.2 81.6 81.7 81.7 81.7 81.7 81.7 81.8 82.1 82.1 82.2 82.2 82.2 82.2 82.2 82.2 82.4 82.4 82.4 82.4 82.6 82.7 82.7 82.7

79.4 79.4 79.4 79.6 79.7 79.7 79.8 80.4 80.6 80.7 80.8 80.9 80.9 81.1 81.1 81.3 81.4 81.4 81.5 81.6 81.6 81.7 81.8 81.8 82.0 82.0 82.0 82.1 82.1 82.1 82.2 82.2 82.2 82.2 82.3 82.3 82.5 82.5 82.6


40. 41. 42. 43. 44.

1295 1328 1328 1331 1352

206 211 217 220 227

15.9 15.8 16.3 16.5 16.7

82.8 82.8 82.9 83.0 83.0

25

82.8 83.0 83.1 83.2 83.4

84

Calculated L(dB A)

83

82

81

80

79

78 78

79

80

81

82

83

Obsvered L (dB A)

Figure 1: Observed

dB (A) against calculated

dB (A) for equation (4)

4 MODEL VALIDATION For the validity of new developed road traffic noise prediction model given by equation (4), calculated by equation (4) is then compared with observed values given in table 2. Scatter plot for model validation is shown in figure 1. Coefficient of determination of the 450 line is 0.92738.Thus the equation (4) for estimating the traffic noise levels for Indian condition need to be calibrated. value of 1.0 is considered to be the best fit, where as any value above 0.7 is considered to be good. The value of is used to test whether the deviations of two processes are significant or not. It is also used to test how well a set of observations fit a given distribution. It therefore, provides a test of goodness of fit. To test the significance of discrepancy between observed and calculated noise levels we have applied test of goodness of fit. It enables us whether deviation of measured from calculated is not by chance but due to inadequacy of the theory to fit measured data.


26

K. Kumar et al.

at 99% level of significance at 43 degrees of freedom= 22.859 at 97% level of significance at 43 degrees of freedom= 26.785 at 5% level of significance at 43 degrees of freedom= 59.304 Since our value is too small to tabulated value, therefore and values are in good agreement at 43 degrees of freedom and at 99, 97 and 5% significance level.

5 SUMMARY AND CONCLUSION Noise prediction is an integral part of environmental impact assessment of highway projects. The model developed in the present paper can be used for noise prediction for an existing busy highway or a proposed new highway. Inputs of the model are: (i)

Traffic flow

(ii)

Percentage of heavy vehicles

Using Calixto model a weighting factor is calculated that represents weightage of heavy vehicles over average noise emission level and using regression analysis to correlate the different traffic parameters a new road transportation noise prediction model is developed for Indian conditions. The value for observed versus calculated by new developed model is 0.92738. So calibration of model was needed for Indian conditions. Using the survey data, given in table 2, a calibrated model has been checked for validation by value and test, which have given good results. Hence calibrated model can be used for noise prediction for Indian conditions. Present study reveals that using road transportation noise prediction model developed so far traffic noise level can be reduced and so health problems of people living close proximity to busy road highways.

6 ACKNOWLEDGEMENTS Financial support by grant in aid from Council of Scientific and Industrial Research is gratefully acknowledged.

REFERENCES Babisch W, Fromme H, Beyer A, and Ising H (2001). Increased catecholamine levels in urine in subjects exposed to road traffic noise: The role of stress hormones in noise research. Environment International, 26 (7-8), pp. 475-481. Banerjee D, Chakraborty SK, Bhattacharyya S, and Gangopadhyay A (2008). Modelling of road traffic noise in the industrial town of Asansol, India. Transportation research part D 13 (8), pp. 539-541. Int. J. of Appl. Math and Mech. 7 (4): 21-28, 2011.


27

Bodsworth B and Lawrence A (1978). The contribution of heavy vehicles to urban traffic noise. Applied Acoustics 11(1), pp. 11-57. Brown AL and Macdonald GT (2003). From environmental impact assessment to environmental design and planning. Australian Journal of Environmental Management 2, pp. 65-77. Calixto A, Diniz FB, and Zannin PHT (2003). The statistical modeling of road traffic noise in an urban setting. Cities 20 (1), pp. 23-29. Cho D S and Mun S (2008). Development of a highway traffic noise prediction model that considers various road surface types. Applied Acoustics 69 (11), pp. 1120-1128. Clayden AD, Culley RWD, and Marsh PS (1975). Modeling traffic noise mathematically: Applied Acoustics 8 (1), pp. 1-12. El-Fadel M, Shazbak S, Baaj MH, and Saliby E (2002). Parametric sensitivity analysis of noise impact of multihighways in urban areas. Environmental Impact Assessment Review 22 (2), pp. 145-162. Filho JMA, Lenzi A, and Zannin PHT (2004). Effects of traffic composition on road noise: a case study.Transportation research part D 9(1), pp. 75-80. Fyhri A and Aasvang GM (2010). Noise sleep and poor health: Modeling the relationship between road traffic noise and cardiovascular problems. Science of total environment 408 (21), pp. 4935-4942 Givargis SH and Mahmoodi M (2008). Converting the UK calculation of road traffic noise (CORTN) to model capable of calculating Leq,1h for the Tehran’s road. Applied Acoustics 69 (11), pp. 1108-1113. Graham JMA , Janssen SA, Vos H, and Miedema HME (2009). Habitual traffic noise at home reduces cardiac parasympathetic tone during sleep. International Journal of Psychophysiology 72 (2), pp. 179-186. Kumar K and Jain VK (1999). Autoregressive integrated moving averages (ARIMA) modeling of a traffic noise time series. Applies Acoustics 58 (3), pp. 283-294. Kuttruff H (1982). A mathematical model for noise propagation between buildings. Journal of Sound and Vibration 85 (1), pp. 115-128. Ljungberg JK and Neely G (2007). Stress, subjective experience and cognitive performance during exposure to noise and vibration. Journal of Environmental Psychology 27 (1), pp. 4454. Ohrstrom E and Rylander R (1990). Sleep disturbance by road traffic noise-A laboratory study on number of noise events. Journal of Sound and Vibration 143 (1), pp. 93-101.


28

K. Kumar et al.

Ouis D (2001).Annoyance from road traffic noise: A review. Journal of Environmental Psychology 21 (1), pp. 101-120. Pirreera S, Valck ED, and Cluydts R (2010). Nocturnal road traffic noise: A review on its assessment and consequences on sleep and health. Environment International 36 (5), pp. 492498. Radwan MM and Oldham DJ (1987). The prediction of noise from urban traffic under interrupted flow conditions. Applied Acoustics 21 (2), pp. 163-185. Rawat K, Katiyar VK and Pratibha (2009). Modeling of single lane traffic flow using Cellular Automata. International Journal of Applied Mathematics and Mechanics 6(5), pp. 46-57. Rylander R (2004). Physiological aspects of noise- induced stress and annoyance. Journal of Sound and Vibration 277 (3), pp. 471-478. Tansatcha M,Pamanikabud P, Brown AL, and Affum JK ( 2005). Motorway noise modeling based on perpendicular propagation analysis of traffic noise. Applied Acoustics 66 (10), pp. 1135-1150.
