指数分布モデルに基づく道路交通騒音の研究

抄録

In a previous paper, we investigated the statistical properties of road traffic noise based on a model of traffic flow, in which vehicles of the same acoustic power are distributed on a road of infinite length so that the spacing between successive vehicles has a probability density function (pdf) of a negative exponential form. In this paper, the outline of the results of the previous work is described introductorily, since the results are closely related with the subjects of the present investigation. It was found out that the cumulant generating function, K(u), of acoustic intensity at an observation point given in equation (4) can be well approximated by the function, K_1(u), given in equation (10), where S is the average spacing between successive vehicles and d is the perpendicular distance from an observation point to the road. This K_1(u) satisfies the conditions that K_1(u)=K(u) at d=0 and d→∞, and I^^-_1=I^^-, where I^^-_1 and I^^- are means of acoustic intensity determined by K_1(u) and K(u) respectively. From this approximated K_1(u), the pdf, mean and variance of sound pressure level (SPL) are derived as equations (16), (20), and (21). The correspondences between the results of simulated calculations and the values obtained from above equations are given in Fig. 2, Fig. 3, and Fig. 4. In the present study, an exponentially distributed model with the same acoustic power is modulated into a more realistic model. First, we introduce an exponentially distributed model in which two kinds of vehicles with different power levels are distributed independently on a road. The cumulant generating function of sound intensity I^^- is expressed by equation (28), and the mean and variance are given by equations (29) and (30). When d is 0, K(u) is expressed as shown in equation (31). In this case, one can find an exact expression for the probability density function (pdf) of sound intensity and of sound pressure level (SPL). As an approximate expression for K(u) , K_1(u) as shown in equation (32) is adopted, where S_0 and d_0 are given by equations (33) and (34) respectively. K_1(u) satisfies the conditions that K_1(u)=K(u) at d=0, and I^^-_1=I^^- for all the values of S_0 and d_0. Then the mean of SPL can be calculated from equation (20) by using S_0 and d_0 instead of S and d in equation (20). The correspondences between calculated values and the results of simulated calculation by means of the Monte Calro method are given in Fig. 6 and Fig. 7. In the next step, we deal with a model in which the power level of each vehicle is assumed to be a random variable having a pdf of normal distribution. The cumulant generating function of sound intensity is expressed as equation (46), where σ is a standard deviation in dB of power level. The mean and the variance of sound intensity are given in equations (48) and (49) respectively, where A is defined by equation (47). When d is zero, K(u) is given by equation (50) and in this case we can obtain an exact pdf of sound intensity and of SPL. K_1(u) in equation (51) is used as approximate expression for K(u) in equation (46). This K_1(u) satisfies the same conditions as are shown previously. Then the mean of SPL is given by equation (54). Fig. 8 shows the correspondence between the results of simulated calculation and the values from equation (54). In Figs. 9, the values of "mean of SPL minus energy mean level" are indicated as a function of d/S for the cases where σis 0, 5, and 10 dB.