# Parameter Estimation for Traffic Noise Models Using a Harmony Search Algorithm

Authors: Deok-Soon An; Young-Chan Suh; Sungho Mun; Byung-Sik Ohm
Journal: Journal of Applied Mathematics
 (2013)

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## Abstract

A technique has been developed for predicting road traffic noise for environmental assessment, taking into account traffic volume as well as road surface conditions. The ASJ model (ASJ Prediction Model for Road Traffic Noise, 1999), which is based on the sound power level of the noise emitted by the interaction between the road surface and tires, employs regression models for two road surface types: dense-graded asphalt (DGA) and permeable asphalt (PA). However, these models are not applicable to other types of road surfaces. Accordingly, this paper introduces a parameter estimation procedure for ASJ-based noise prediction models, utilizing a harmony search (HS) algorithm. Traffic noise measurement data for four different vehicle types were used in the algorithm to determine the regression parameters for several road surface types. The parameters of the traffic noise prediction models were evaluated using another measurement set, and good agreement was observed between the predicted and measured sound power levels.


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## Body

## 1. Introduction

It is important to evaluate the primary impact of traffic noise for several different road surfaces in order to predict the interactive noise between road surfaces and vehicle tires. A number of noise prediction models [1–6] have been developed for environmental estimation of traffic noise levels in terms of vehicle and pavement types. For example, the vehicle types in the ASJ model [1, 2] are large vehicles, medium vehicles, light trucks, and cars, and the pavement types are dense-graded asphalt (DGA) and permeable asphalt (PA). Thus, the ASJ traffic noise prediction model is restricted to four vehicle types, varying vehicle speeds, and two pavement types.In order to expand the applicability of the ASJ model, the present paper introduces a parameter estimation procedure based on a harmony search (HS) algorithm as follows: (a) the traffic noise for a targeted road surface is measured, (b) the parameters of the noise prediction model are estimated via the HS algorithm, and (c) the resulting coefficients are evaluated using another set of measurements (consisting of vehicle speeds and vehicle types) for a different traffic volume on the targeted road surface. To validate the proposed traffic noise prediction technique, traffic noise measurement sets from three different surface types were used in this study: stone mastic asphalt surfaces (SMA), 30 mm transversely tined Portland cement concrete surfaces (30 mm trans.), and 18 mm longitudinally tined Portland cement concrete surfaces (18 mm long.), as shown in Figure1. The measurement site is a 7.7 km long. 2-lane highway along the side of the south bound of Jungbu inland highway in South Korea. This measurement section includes both asphalt and Portland cement concrete pavements.Pavement surface types: (a) SMA, (b) 30 mm trans., and (c) 18 mm long.
(a)
(b)
(c)This paper is organized as follows. Section2 describes the ASJ model and vehicle characterization. Section 3 explains the application of the HS algorithm to estimate the parameters of ASJ-based noise prediction models, and Section 4 presents the conclusions of this research.


## 2. ASJ Model

The Acoustic Society of Japan (ASJ) published the ASJ model [1, 2] for calculating road traffic noise. The procedure involves calculating the noise level generated by traffic as well as the attenuation during noise propagation. The octave-band power spectrum for nominal midband frequencies (63 Hz to 8 kHz) can be generated according to the ISO 9613-2 standard [7]. The ASJ model classifies vehicles into four types listed in Table 1.Table 1
Vehicle types used in this study.
Type
Specification
Heavy vehicle
Large vehicle
(i) Trucks equipped with three or more axles, which aregreater than 8 tons or above 5-ton cargo trailers (ii) Buses providing 30 or more passengers (iii) Large special purpose vehicles
Medium vehicle
(i) Trucks equipped with two axles(ii) Buses providing less than 30 passengers
Light vehicle
Light truck
Light trucks equipped with 50 to 2000 cc engine
Car
Car designed for the transportation of less than and equal to 10 passenger.The A-weighted overall sound power levels (LWA) of the noise emitted by interactions between vehicles and pavement are listed in Table 2 for a dense-graded asphalt (DGA) surface. In terms of nominal midband frequencies, the individual A-weighted sound power level for each octave band (LWA,i) is calculated as follows:
(1)LWA,i=LWA+ΔLi+ΔLA,i+ΔLadj,
where LWA is the overall sound power level (dB) and ΔLi is the relative level (dB) at the ith nominal mid-band frequency given by
(2)ΔLi=-10log10{1+(fi2000)2}-2.5log10(fi1000).ΔLA,i is a factor of the standard A-weighting frequency given by the following equation:
(3)ΔLA,i=2.0+20log10×[(fi2+107.72)(fi2+737.92))-1(122002·fi4)×((fi2+107.72)(fi2+737.92)(fi2+20.62)(fi2+122002)×(fi2+107.72)(fi2+737.92))-1],
where fi is the nominal mid-band frequency. Finally, ΔLadj is the correction factor defined by
(4)ΔLadj=-10log10{∑i=18100.1(ΔLi+ΔLA,i)}.Table 2
A-weighted sound power levels (LWA) in dB for a dense-graded asphalt (DGA) surface.
Vehicle types
Steady traffic flow (40 km/h to 140 km/h)
Large vehicle
54.4
+
30
log
10
V
*
Medium vehicle
51.5
+
30
log
10
V
Light truck
47.6
+
30
log
10
V
Car
46.4
+
30
log
10
V
*
V is a velocity.


### 2.1. Equivalent Sound Power Level for a Road

The A-weighted sound power level emitted by a specific type of vehicle moving along a road over a specified time period,LWAT, can be calculated via the following equation:
(5)LWAT=LWA+10log10(3.6ΔlV·N3600),
where LWA is the basic sound power level (dB) emitted by the vehicle (listed in Table 2), Δl is the length of the road segment (in meters), V is the mean speed for the vehicle type (in km/h), and N is the hourly traffic flow for the vehicle type (in vehicles/h). The equivalent sound power level, Leq(WA), emitted by all vehicles moving along the road can then be calculated as follows:
(6)Leq(WA)=10log10{∑i10LWAT,i/10},
where LWAT,i is the A-weighted sound power level for each vehicle type. Here, LWAT,1, LWAT,2, LWAT,3, and LWAT,4 are the A-weighted sound power levels for a large vehicle, a medium vehicle, a light truck, and a car, respectively, as listed in Table 2. Furthermore, the attenuation (e.g., geometrical divergence, atmospheric absorption, ground effect, and screening structures) was calculated based on ISO 9613-2 [7].


## 2.1. Equivalent Sound Power Level for a Road

The A-weighted sound power level emitted by a specific type of vehicle moving along a road over a specified time period,LWAT, can be calculated via the following equation:
(5)LWAT=LWA+10log10(3.6ΔlV·N3600),
where LWA is the basic sound power level (dB) emitted by the vehicle (listed in Table 2), Δl is the length of the road segment (in meters), V is the mean speed for the vehicle type (in km/h), and N is the hourly traffic flow for the vehicle type (in vehicles/h). The equivalent sound power level, Leq(WA), emitted by all vehicles moving along the road can then be calculated as follows:
(6)Leq(WA)=10log10{∑i10LWAT,i/10},
where LWAT,i is the A-weighted sound power level for each vehicle type. Here, LWAT,1, LWAT,2, LWAT,3, and LWAT,4 are the A-weighted sound power levels for a large vehicle, a medium vehicle, a light truck, and a car, respectively, as listed in Table 2. Furthermore, the attenuation (e.g., geometrical divergence, atmospheric absorption, ground effect, and screening structures) was calculated based on ISO 9613-2 [7].


## 3. Application of the Harmony Search Algorithm

### 3.1. Harmony Search Algorithm

This section describes the procedure for estimating the parameters of noise prediction models, using a harmony search (HS) algorithm that employs a heuristic algorithm based on an analogy with natural phenomena [8–12]. The detailed procedure for applying a harmony search consists of four steps as follows.(1)
The algorithm parameters are specified. These include the harmony memory size (HMS), initialized as the number of solution vectors in the harmony memory (HM), the harmony memory consideration rate (HMCR, between 0 and 1), the pitch adjustment rate (PAR, between 0 and 1), and the maximum number of improvisations (or stopping criterion), which terminates the HS program. The optimization problem is specified as follows:(7)Minimizef(X)subjecttoxi∈Xi=1,2,…,N,wheref(X) is the objective function, X is the set of decision variables xi, N is the number of decision variables, and Xi is the possible range of values for the ith decision variable; that is, XLi≤Xi≤XUi, where XLi and XUi are the respective lower and upper bounds for the ith decision variable. To estimate the parameters of a noise prediction model, the following minimization function can be used:
(8)Minimize|LP_eq(WA)-LM_eq(WA)|subjecttoxi∈Xi=1,2,…,N,whereLP_eq(WA) is the predicted equivalent sound power level of (5), which can be calculated as follows:
(9)LP_eq(WA)=10log10[100.1{LWAT,1+LWAT,2+LWAT,3+LWAT,4}],whereLWAT,1, LWAT,2, LWAT,3, and LWAT,4 are the A-weighted sound power levels for a large vehicle, a medium vehicle, a light truck, and a car, respectively. LM_eq(WA) is the measured equivalent sound power level obtained from previous research [13, 14]. In this optimization problem, the A-weighted sound power levels can be defined as given in Table 3. Thus, the coefficients of x1, x2, x3, and x4 must be determined via the HS algorithm. The slope is fixed in the ASJ models for both surface types (DGA and PA); therefore, the slope given in Table 3 is fixed at 30.(2)
The HM matrix is initially filled with randomly generated solution vectors up to the HMS, together with the corresponding function values of the random vectorsf(X):
(10)HM=[x11x21x31x41x12x22x32x42⋮⋮⋯⋮x1HMSx2HMSx3HMSx4HMS|f(X1)f(X2)⋮f(XHMS)].(3)
A column vector of the newly generated harmony,X′=(x1′x2′x3′x4′), is improvised utilizing the following three mechanisms: (a) random selection, (b) memory consideration, and (c) pitch adjustment. In the random selection, the value of each decision variable, xi′, in the column vector is randomly chosen within the range of values with a probability of (1-HMCR). HMCR (which is between 0 and 1) is the rate at which a single value is chosen from the historical values stored in the HM. The value of each decision variable selected by memory consideration is examined in terms of pitch adjustment. This operation uses the PAR parameter (which is the rate of the necessary pitch adjustment according to the neighboring pitches) with a probability of HMCR × PAR. Pitch adjustment is applied to each variable as follows:
(11)xi′⟵{xi′+rand×bw,withaprobabilityofHMCR×PAR×0.5xi′-rand×bw,withaprobabilityofHMCR×PAR×0.5xi′,withaprobabilityofHMCR×(1-PAR).If the newly generated column vector is better than the worst harmony in the HM, based on evaluation of the objective function, the newly generated column vector is included in the HM, and the existing worst harmony is excluded from the HM.(4)
If the stopping criterion (or maximum number of improvisations) is satisfied, the computation is terminated. Otherwise, Steps 3 and 4 are repeated.Table 3
A-weighted sound power levels (LWA) in dB for the different surface types.
Vehicle types
Steady traffic flow (40 km/h to 140 km/h)
Large vehicle
x
1
+
30
log
10
V
*
Medium vehicle
x
2
+
30
log
10
V
Light truck
x
3
+
30
log
10
V
Car
x
4
+
30
log
10
V
*
V is a velocity.


### 3.2. Application to Parameter Estimation for Noise Prediction Models

In order to estimate the parameters of noise prediction models based on the objective function of (8), noise measurements for three different road surfaces were obtained from previous research, which was conducted on a test track [13, 14]. The vehicle velocities and hourly traffic flows are listed in Table 4.Table 4
Vehicle velocities and hourly traffic flows.
Vehicle types
Average velocities
Hourly traffic flows
Large vehicle
90 km/h
48 vehicles/h
Medium vehicle
95 km/h
40 vehicles/h
Light truck
97 km/h
96 vehicles/h
Car
101 km/h
208 vehicles/hTo apply the HS algorithm to parameter estimation for the noise prediction models, the four coefficients were determined for each road surface type (stone mastic asphalt (SMA) surface, 30 mm transversely tined Portland cement concrete surface (30 mm trans.), and 18-mm longitudinally tined Portland cement concrete surface (18 mm long.)), as shown in Figure2 and Table 5, based on the training data from Table 4. In this way, the coefficients of the noise prediction models, which are dependent on the road surface type, can be updated via the HS algorithm. As a result, noise prediction models can be provided for various surface types by using the HS algorithm to update the ASJ model equations.Table 5
Determination of the model coefficients via the HS algorithm.
Surface types
Large vehicle (x1 in Table 3)
Medium vehicle (x2 in Table 3)
Light truck (x3 in Table 3)
Car (x4 in Table 3)
SMA
58.050
53.693
48.456
45.787
30 mm trans.
61.669
58.473
51.246
46.020
18 mm long.
60.097
54.428
50.095
45.360Figure 2
Minimizing the error function of (8) through the HS algorithm.Another set of testing data (given in Table6) was used to evaluate whether or not the updated noise prediction models (with the four coefficients estimated by the HS algorithm) provided results consistent with measured noise levels. The predictions and measurements are compared in Table 7; good agreement was noted for all three surface types. Using the original ASJ model, the prediction value is resulted in a same noise level regardless of surface types and in bad agreement when compared with the measured noise levels.Table 6
Vehicle velocities and hourly traffic flows used as evaluation data.
Vehicle types
Average velocities
Hourly traffic flows
Large vehicle
85 km/h
35 vehicles/h
Medium vehicle
90 km/h
58 vehicles/h
Light truck
95 km/h
87 vehicles/h
Car
103 km/h
198 vehicles/hTable 7
Comparison of predicted and measured traffic noise levels.
Surface types
Predicted levels
Measured levels
ASJ model prediction
SMA
96.1 dB
96.2 dB
94.4 dB
30 mm trans.
99.5 dB
99.7 dB
94.4 dB
18 mm long.
97.3 dB
97.6 dB
94.4 dBFinally, the A-weighted sound power levels for the individual octave bands were estimated for the SMA, 30 mm trans., and 18 mm long. surface types, utilizing the parameters estimated via the HS algorithm and (1). For example, Figure 3 shows the A-weighted sound power levels for the octave bands for the three different surface types in the case of the large vehicle speeding at 80 km/h.Figure 3
Octave band frequency versus noise level.


## 3.1. Harmony Search Algorithm

This section describes the procedure for estimating the parameters of noise prediction models, using a harmony search (HS) algorithm that employs a heuristic algorithm based on an analogy with natural phenomena [8–12]. The detailed procedure for applying a harmony search consists of four steps as follows.(1)
The algorithm parameters are specified. These include the harmony memory size (HMS), initialized as the number of solution vectors in the harmony memory (HM), the harmony memory consideration rate (HMCR, between 0 and 1), the pitch adjustment rate (PAR, between 0 and 1), and the maximum number of improvisations (or stopping criterion), which terminates the HS program. The optimization problem is specified as follows:(7)Minimizef(X)subjecttoxi∈Xi=1,2,…,N,wheref(X) is the objective function, X is the set of decision variables xi, N is the number of decision variables, and Xi is the possible range of values for the ith decision variable; that is, XLi≤Xi≤XUi, where XLi and XUi are the respective lower and upper bounds for the ith decision variable. To estimate the parameters of a noise prediction model, the following minimization function can be used:
(8)Minimize|LP_eq(WA)-LM_eq(WA)|subjecttoxi∈Xi=1,2,…,N,whereLP_eq(WA) is the predicted equivalent sound power level of (5), which can be calculated as follows:
(9)LP_eq(WA)=10log10[100.1{LWAT,1+LWAT,2+LWAT,3+LWAT,4}],whereLWAT,1, LWAT,2, LWAT,3, and LWAT,4 are the A-weighted sound power levels for a large vehicle, a medium vehicle, a light truck, and a car, respectively. LM_eq(WA) is the measured equivalent sound power level obtained from previous research [13, 14]. In this optimization problem, the A-weighted sound power levels can be defined as given in Table 3. Thus, the coefficients of x1, x2, x3, and x4 must be determined via the HS algorithm. The slope is fixed in the ASJ models for both surface types (DGA and PA); therefore, the slope given in Table 3 is fixed at 30.(2)
The HM matrix is initially filled with randomly generated solution vectors up to the HMS, together with the corresponding function values of the random vectorsf(X):
(10)HM=[x11x21x31x41x12x22x32x42⋮⋮⋯⋮x1HMSx2HMSx3HMSx4HMS|f(X1)f(X2)⋮f(XHMS)].(3)
A column vector of the newly generated harmony,X′=(x1′x2′x3′x4′), is improvised utilizing the following three mechanisms: (a) random selection, (b) memory consideration, and (c) pitch adjustment. In the random selection, the value of each decision variable, xi′, in the column vector is randomly chosen within the range of values with a probability of (1-HMCR). HMCR (which is between 0 and 1) is the rate at which a single value is chosen from the historical values stored in the HM. The value of each decision variable selected by memory consideration is examined in terms of pitch adjustment. This operation uses the PAR parameter (which is the rate of the necessary pitch adjustment according to the neighboring pitches) with a probability of HMCR × PAR. Pitch adjustment is applied to each variable as follows:
(11)xi′⟵{xi′+rand×bw,withaprobabilityofHMCR×PAR×0.5xi′-rand×bw,withaprobabilityofHMCR×PAR×0.5xi′,withaprobabilityofHMCR×(1-PAR).If the newly generated column vector is better than the worst harmony in the HM, based on evaluation of the objective function, the newly generated column vector is included in the HM, and the existing worst harmony is excluded from the HM.(4)
If the stopping criterion (or maximum number of improvisations) is satisfied, the computation is terminated. Otherwise, Steps 3 and 4 are repeated.Table 3
A-weighted sound power levels (LWA) in dB for the different surface types.
Vehicle types
Steady traffic flow (40 km/h to 140 km/h)
Large vehicle
x
1
+
30
log
10
V
*
Medium vehicle
x
2
+
30
log
10
V
Light truck
x
3
+
30
log
10
V
Car
x
4
+
30
log
10
V
*
V is a velocity.


## 3.2. Application to Parameter Estimation for Noise Prediction Models

In order to estimate the parameters of noise prediction models based on the objective function of (8), noise measurements for three different road surfaces were obtained from previous research, which was conducted on a test track [13, 14]. The vehicle velocities and hourly traffic flows are listed in Table 4.Table 4
Vehicle velocities and hourly traffic flows.
Vehicle types
Average velocities
Hourly traffic flows
Large vehicle
90 km/h
48 vehicles/h
Medium vehicle
95 km/h
40 vehicles/h
Light truck
97 km/h
96 vehicles/h
Car
101 km/h
208 vehicles/hTo apply the HS algorithm to parameter estimation for the noise prediction models, the four coefficients were determined for each road surface type (stone mastic asphalt (SMA) surface, 30 mm transversely tined Portland cement concrete surface (30 mm trans.), and 18-mm longitudinally tined Portland cement concrete surface (18 mm long.)), as shown in Figure2 and Table 5, based on the training data from Table 4. In this way, the coefficients of the noise prediction models, which are dependent on the road surface type, can be updated via the HS algorithm. As a result, noise prediction models can be provided for various surface types by using the HS algorithm to update the ASJ model equations.Table 5
Determination of the model coefficients via the HS algorithm.
Surface types
Large vehicle (x1 in Table 3)
Medium vehicle (x2 in Table 3)
Light truck (x3 in Table 3)
Car (x4 in Table 3)
SMA
58.050
53.693
48.456
45.787
30 mm trans.
61.669
58.473
51.246
46.020
18 mm long.
60.097
54.428
50.095
45.360Figure 2
Minimizing the error function of (8) through the HS algorithm.Another set of testing data (given in Table6) was used to evaluate whether or not the updated noise prediction models (with the four coefficients estimated by the HS algorithm) provided results consistent with measured noise levels. The predictions and measurements are compared in Table 7; good agreement was noted for all three surface types. Using the original ASJ model, the prediction value is resulted in a same noise level regardless of surface types and in bad agreement when compared with the measured noise levels.Table 6
Vehicle velocities and hourly traffic flows used as evaluation data.
Vehicle types
Average velocities
Hourly traffic flows
Large vehicle
85 km/h
35 vehicles/h
Medium vehicle
90 km/h
58 vehicles/h
Light truck
95 km/h
87 vehicles/h
Car
103 km/h
198 vehicles/hTable 7
Comparison of predicted and measured traffic noise levels.
Surface types
Predicted levels
Measured levels
ASJ model prediction
SMA
96.1 dB
96.2 dB
94.4 dB
30 mm trans.
99.5 dB
99.7 dB
94.4 dB
18 mm long.
97.3 dB
97.6 dB
94.4 dBFinally, the A-weighted sound power levels for the individual octave bands were estimated for the SMA, 30 mm trans., and 18 mm long. surface types, utilizing the parameters estimated via the HS algorithm and (1). For example, Figure 3 shows the A-weighted sound power levels for the octave bands for the three different surface types in the case of the large vehicle speeding at 80 km/h.Figure 3
Octave band frequency versus noise level.


## 4. Conclusions

In this study, it was shown that the optimization problem related to updating the noise prediction models for several surface types could be solved using an HS algorithm process. The process involves (a) obtaining measurements for different road surfaces, (b) estimating the coefficients of the noise prediction models using this measurement set as training data, and (c) evaluating the estimated coefficients using another measurement set as testing data. When this procedure was utilized, an evaluation of the parameters of the traffic noise prediction model yielded good agreement between predicted and measured sound power levels.



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*Source: 953641-2013-11-06.xml*