Modeling urban traffic noise indonesia
Applied Acoustics 74 (2013) 614–621
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Applied Acoustics
journal homepage: www.elsevier.com/locate/apacoust
Modeling urban traffic noise with stochastic and deterministic traffic models
Alberto Ramírez ⇑, Efraín Domínguez
Facultad de Estudios Ambientales y Rurales, Pontificia Universidad Javeriana, Transversal 4, No. 42-00, Piso 8, Bogotá, Colombia
a r t i c l e
i n f o
Article history:
Received 27 January 2012
Received in revised form 6 June 2012
Accepted 1 August 2012
Available online 3 September 2012
Keywords:
Noise pollution
Urban modeling
Traffic noise prediction model
Traffic dynamics
Urban noise monitoring
a b s t r a c t
This paper presents the development and evaluation of a stochastic dynamic traffic noise prediction
model based on noise curves for vehicle classes and their speed. The model was tested on urban two-lane
roads in the city of Bogotá and was established on the basis of the fit of single Li,17sec noise functions for
different types of vehicles. The model showed a slightly better fit than was found in four deterministic
models that are highly internationally recognized. Additionally, a deterministic model was derived contextualized to the city of Bogotá. The approach used is promising for further investigations of urban traffic
noise given the traffic conditions in these systems.
Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Urban noise pollution is causing increased health risks in the
population. This is due both to the fact that noise levels, particularly those associated with transport, have increased dramatically
since the mid-twentieth century and that a higher percentage of
the world population is now concentrated in urban systems [1,2].
This problem has also increased economic costs due to failing
health and reduced productivity of the population, affecting between 0.2% and 2% of gross domestic product in the US [3]. In
the European Union, the costs range between $13 billion and
$38 billion per year [4]. In addition, traffic noise causes the depreciation of properties exposed to high noise levels [5].
Studies on urban noise are becoming more numerous, reflecting
the growing importance of this pollutant, for which levels currently exceed those specified by regulations in Spain [6], Iran [7],
India [8], Egypt [9], China [10], Brazil [11] and Colombia [12,13],
among others.
Computer models are highly valued in developed countries for
assessing environmental problems, including sources of pollution,
their spreading in the environment, impacts on human populations
and associated regulatory processes, many of which follow the
guidelines of the USEPA [14]. Modeling of traffic noise represents
an example of this technique and has been implemented in the
context of environmental impact studies for transport projects
[15]. Additionally, this type of modeling has played an important
role in the analysis of mitigation measures during road construction [16,17] and in identifying the variables with the highest noise
⇑ Corresponding author. Tel.: +57 1 3208320x4819; fax: +57 1 3208320x4859.
E-mail address: alberto.ramirez@javeriana.edu.co (A. Ramírez).
0003-682X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.apacoust.2012.08.001
incidence [9,18]. Noise prediction also plays a prominent role in
planning and development of new urban projects and roads [16].
The traffic noise model plays an important role in the construction of noise maps, since they combine both observed and simulated records. These maps have been employed mainly for urban
planning, environmental risk assessment [19], identification of
hotspots, evaluation of the exposed population and simulation of
mitigation measures [20,21].
The simplest models have been designed based on relationships
between the logarithm of the number of vehicles and the level of
noise they generate [7,22–24]. The relationship between these
two variables is obvious, as the greater the number of vehicles that
are simultaneously on the road, the greater the number of emissions sources there will be. More elaborate models have also included the proportion of heavy vehicles and speed, and even
variables such as pavement type, width and inclination of the track
and height of buildings, among others [7,15,23,25–30].
These models are based on theoretical factors that are applicable based on statistical relationships and on macroscopic traffic
variables such as total flow and average speed. Their results have
been very good related to roads and highways where traffic prevails, and flow conditions are relatively homogeneous [9,16,17].
In contrast, these same models have rarely been applied to urban
roads where traffic volumes and speeds are not fixed due to the
start-stop and acceleration–deceleration situations that are typical
of these systems [5] and because of cycles in traffic and noise associated with traffic lights [13,31].
Nevertheless, research on urban intersections has achieved a
good fit between the continuous equivalent level, (Leq), and the
traffic volume, the number of heavy vehicles, the slope and the
type of pavement [32].
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A. Ramírez, E. Domínguez / Applied Acoustics 74 (2013) 614–621
Other mathematical approaches that have achieved good performance include neural networks [33,34], microscopic traffic
models [35,36] and models based on single traffic noise [37].
In Colombia, the problem of traffic noise has been largely overlooked by environmental authorities. Very few studies have involved modeling, and their results have been highly variable
[12,13,38,39]. This report presents the results of a study in which
a stochastic and dynamic microscopic model is developed, and
its performance is analyzed in the city of Bogotá based on the single noise generated by each vehicle during its passage in front of a
measurement point. Additionally, we compare the results of this
model with a deterministic model derived from it, as well as four
international deterministic models that are widely used.
iii. A collection point for the information, which receives the
instantaneous sound pressure of the two lanes every second
and calculates the continuous equivalent level (Eqs. (1) and
(2)). This descriptor is the constant sound level over a stated
period of time which is equivalent in total sound energy to
the time-varying sound level measured over the same period
of time and is used worldwide in traffic noise evaluation
[15,26]. The simulation and sampling time was 10 min,
which is a duration that was previously shown (presampling) to be sufficient for LAeq stabilization. This unit of time
was reported as suitable for such measurements [35].
Calculation of the continuous equivalent level for each lane was
determined as follows:
2. Methodology
Leq;10min ¼ 10log10
2.1. Single noise
This study was conducted in Bogota. As a starting point, vehicles
were classified into the following categories: motorcycles, cars
(including cars, trucks, small delivery vans and microbuses), buses,
mini-buses (small buses) and trucks (over 3 tons). Subsequently,
we conducted measurements of single noise on the streets of the
city (n = 533 vehicles), seeking to exclude the impact of other vehicles and other sources of noise. To this end, we used an integrated
Extech type II sound level meter (SLM) to evaluate the instantaneous sound level (Li,1sec) during the approach and passage of each
vehicle in front of the SLM on roads with 1 and 2 lanes. These measurements followed conventional techniques [15] and were conducted using a tripod and a windscreen at a height of 1.2 m at a
distance of 1 m from the road with A and slow weights. In parallel,
we measured the speed at which each vehicle was traveling using
manual Bushnell equipment. In all cases, the prevailing conditions
included flat, dry roads, wind speeds less than 4 km/h and a low
incidence of other noise sources.
For each type of vehicle, we conducted a regression analysis between the maximum noise level (when passing in front of the SLM)
and speed. Because this yielded low coefficients of determination,
we implemented classification trees to dissociate subgroups
depending on the speed of vehicles. Subsequently, we averaged all
noise levels recorded in each subgroup at time zero (passing in front
of the SLM) and during the approach at times 1 through 8 s in
time steps of 1 s. Using these values, we tested various models of linear and nonlinear regression and chose the model with the highest
coefficient of determination using SPSS v.15 (statistical software)
and Curve Expert v.1.3 (nonlinear regression). The noise level was
assumed to be symmetric for the approach and retreat of vehicles.
2.2. Stochastic model
Based on this information, we built a dynamic model using the
Stella v.8 program (dynamic modeling software) consisting of 3
segments:
i. A stochastic Monte Carlo traffic simulator for each lane, with
sampling without replacement, which defines for each second whether or not a vehicle is present and the class to
which it belongs, along with its speed simulated from a normal distribution with estimated parameters (l, r2) for each
vehicle class and station. In this regard, the model follows
the guidelines given by the [5] regarding including specific
conditions for each lane.
ii. A time window of 17 s (8 . . . 0 . . . +8) for each lane, in
which the vehicle is moving and sends information about
instantaneous sound pressure (Li;1sec ) from the Weibull functions estimated from vehicle type and speed.
600
1 X
10Li;1s=10
600 i¼1
(
)
ð1Þ
For the two lanes:
L
Leq;10min lane 2
eq;10min lane 1
10
10
Leq;10min ¼ 10log10 10
þ 10
ð2Þ
The model is dynamic and is based on the physical principle of
the addition of sound pressure per vehicle and lane, along with
empirical equations for single noise based on speed and vehicle
type, which in this case, correspond to the Weibull function. The
model also incorporates randomness derived from the speed of each
vehicle, which is why the continuous equivalent level estimated at
each station was obtained from the average of 10 simulations.
The assumptions included in the model were as follows: (a)
conservation of vehicles during the 17-s window; (b) sound energy
conservation, but with divergence based on the distance between
the vehicle and the level meter, which is implied in the Weibull
function; (c) constant vehicle speed during passage through the
time window; (d) no vehicle passing any other vehicle or changing
lanes; (e) negligible effects of reflection due to walls, reflection and
shielding between vehicles and refraction and absorption by other
elements present in the acoustic field; (f) negligible impacts of
other noise sources compared to the sound pressure arising from
the vehicle; and (g) the climatic impact is considered negligible given the distance.
2.3. Deterministic models
For comparison purposes, we evaluated the German model
RLS90 – Richtlinien für den Lärmschutz an Straben [25]; the English model CoRTN – Calculation of road traffic noise [40]; the Nordic model Nordic prediction method for road traffic noise-statens
planverk 96 [25,41] and the Northamerican model TNM – Traffic
noise model V.2.5 [27]. Previous models estimate the Leq based
on traffic flow, speed and heavy vehicle proportion. They are static
and deterministic.
We also derived and evaluated a deterministic model based on
the TNM, but operating with the single noise levels measured in
Bogotá (Eq. (3)).
X
LAeq;17segðCars;sÞ
10
LAeq;10min ¼ 10 log
Q Cars;s 10
X
LAeq;17segðMotorcycles;sÞ
10
þ
Q Motorcycles;s 10
X
LAeq;17segðBuses;sÞ
10
þ
Q Buses;s 10
X
LAeq;17segðSmall Buses;sÞ
10
þ
Q Small Buses;s 10
X
LAeq;17segðTrucks;sÞ
10
þ
Q Trucks;s 10
ð3Þ
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A. Ramírez, E. Domínguez / Applied Acoustics 74 (2013) 614–621
where Qj,s is number of vehicles of type j, at speed s; LAeq,17seg,j,s is
17 s continuous equivalent level for vehicle j, at speed s.
2.4. Sampling stations
We studied 28 two-lane stations (one- and two-way streets) in
the city of Bogotá. These stations were chosen because they exhibited a low noise level associated with sources other than the vehicles being studied and were located in contexts that varied with
respect to volume, composition and vehicle speed. At each station,
the following descriptors were recorded: (a) continuous equivalent
level for 10 min (LAeq,10min.), measured with an integrated Extech
type II sound level meter at a height of 1.2 m, located 1 m of from
the lane and more than 4 m from any facades; (b) the number of
vehicles of each type in each lane, which were video recorded;
(c) the speed of as many vehicles as possible, recorded using a
Bushnell speedometer; and (d) the distance between the sound level meter and the middle of the lanes, to correct for the divergence
of the deterministic models (Fig. 1).
Sampling points were chosen more than 50 m away from traffic
lights to reduce stop-start effects during sampling but there were
numerous situations of detention.
2.5. Analysis
2.5.1. Deterministic models
The English, German and Nordic models were calculated using a
Java algorithm, while the US model of the Federal Highway Administration was computed from the Traffic Noise Model software V
2.5. The results were all corrected by adding background noise –
L90 – and adjusting distance of each lane to the sound level meter
(Eq. (4), for d = 1) [37]:
L ¼ LRef : 10log10
D
DRef :
d
ð4Þ
where L is sound pressure at a specific distance D; LRef. is sound
pressure at a reference distance DRef.
To evaluate the models performance, we divided the total sample into 2 groups: 20 samples for estimation and calibration and 8
samples for validation. Calibration was performed by adjusting the
parameters of the models up to 50% of its value, based on the function that minimizes the differences between observed and estimated results. This procedure was performed with the solver
function of Excel. A similar method was employed by Alimohammadi et al. [7] and by Calixto et al. [11].
2.5.2. Stochastic model
We estimated the continuous equivalent level through the Stella model for each station from the average of 10 simulations. In
addition, regression analysis between the background-noise and
mean error – ME – (Eq. (5)) was carried out to establish whether
there was incidence of the first variable in the second. This analysis
was necessary as background noise was not added explicitly in the
stochastic model as was done in the deterministic models. We did
not find, however, a relationship between them (p > 0.05).
1m
Sound meter
Speed meter
Video camera
Fig. 1. Information recorded in field: LAeq,10min, speed of different types of vehicles
in different lanes, video recording for vehicles count per lane.
The deterministic model derived from the stochastic model was
calibrated allowing variations up to 5% in the LAeq,17s of each type of
vehicle, following a similar procedure to that described previously
for the deterministic model (Table 1).
We studied the goodness of fit of the models using parameters
that relate the measured and estimated values, such as the mean
error (ME), the mean absolute error (MAE), the mean absolute relative error (MARE) and the coefficient of determination (r2) (Eqs.
(5)–(8)) [42].
ME ¼
n
1X
ðLAeq ^LAeq Þ
n i¼1
MAE ¼
ð5Þ
n
1X
jLAeq ^LAeq j
n i¼1
MARE ¼
ð6Þ
n
1X
jLAeq ^LAeq j
n i¼1
LAeq
ð7Þ
P
P
P
LAeqi ^LAeqi LAeqi ^LAeqi=n
r2 ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
P
2
2
P ^2
P 2
ð LAeq Þ
ð ^LAeq Þ
L
LAeq
Aeq
n
n
ð8Þ
Likewise, for the microscopic model, we conducted a sensitivity
analysis that evaluated the noise level at all stations under varying
traffic volumes. To this end, we rounded the maximum value of
each vehicle type and divided it into five equal units. Subsequently,
we simulated LAeq,10min for each station using the values given in
Table 2. Given the high sound pressure levels found in the city, this
analysis favored an approach that reduced the number of vehicles
and did not take into account variations in density and velocity referred to in the fundamental traffic diagram [43].
The procedure of the research is summarized in Fig. 2.
3. Application and discussion
3.1. Traffic conditions
The traffic conditions for the 28 samples are presented in Table 3,
highlighting the dominance of cars over other types of vehicles.
3.2. Single noise
The number of vehicles tested in each class to obtain the single
sound level varied between 30 and 115 (n = 533 vehicles). The best
Table 1
Calibration of single LAeq,17sec for the stochastic model.
LAeq,17sec estimated
Lane
1
Motorcycles L1 6 47
Motorcycles L1 47–70
Motorcycles L1 > 70
Motorcycles L2 6 51
Motorcycles L2 > 51
Cars L1 6 50
Cars L1 > 50
Cars L2 6 49
Cars L2 49–63
Cars L2 > 63
Minibuses L1 6 54
Minibuses L1 > 54
Minibuses L2
Buses
Trucks
63.5
66.3
71.1
2
LAeq,17sec adjusted
1
62.7
67.3
63.7
66.9
65.7
65.5
62.2
63.7
61.8
65.5
68.7
70.3
71.9
74.9
75.6
2
66.7
69.7
71.1
62.0
62.7
68.7
70.4
68.7
71.9
74.2
74.8
75.3
74.7
72.2
77.3
75.2
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A. Ramírez, E. Domínguez / Applied Acoustics 74 (2013) 614–621
Table 2
Traffic flow used in the sensitivity analysis of the
stochastic model (observed maximum flow divided into
5 classes).
Type
Vehicles/h
Motorcycles
Cars
Minibuses
Buses
Trucks
40–80–120–160–180
300–600–900–1200–1500
20–40–60–80–100
20–40–60–80–100
16–32–48–64–80
Table 3
Range observed for the main traffic characteristics.
Motorcycles
Volume (No./10 min)
Lowest
3
Highest
36
Speed (km/h)
Lowest
20
Highest
60
function to describe the relationship between the average instantaneous sound pressure and the approach of the vehicle in a 9-s window was the Weibull function (Eq. (9)). For all types of vehicles, the
coefficient of determination was greater than 0.990 (n = 9,
p < 0.001), and function parameters varied as follows: a between
71.9 and 84.9, b between 44.8 and 123.6, c between 2 and 3.4
and d between 0.6 and 0.3 (Fig. 3).
ct d
Li;1s ¼ a be
ð9Þ
Similar plots were obtained by [37], who measured LAeq,10sec and
also found a weak relationship between the speed and the sound
pressure within each vehicle class, which indicates high variability
within the classes.
3.3. Modeling
The performance of the models across the different metrics is
shown in Table 4 and Figs. 4 and 5. From this, we extract the
following:
i. The stochastic model and the deterministic model derived
from it, showed better performance than the deterministic
models. The mean absolute error –MAE- of the stochastic
model was close to 1 dBA, while the MAE of the deterministic models is between 1.7 and 3.6 dBA.
ii. The mean error – ME – of the stochastic model is slightly
negative which indicates a small overestimation in the
model output, whereas it was positive for the deterministic
models. However, the ME was lower in the Nordic model,
which due to its value near zero, indicates a lack of bias.
iii. All of the adjusted deterministic models resulted in a better
fit than in the original models. However, there were no
significant differences in the average residuals (p > 0.05).
Cars
Minibuses
49
247
0
36
0
7
0
13
10
53
22
60
10
72
25
58
Monte Carlo simulation:
vehicle type, sample
without replacement
Average
speed and
standard
deviation
Normal distribution
simulation: speed (µ, σ)
The underestimation of LAeq by the macroscopic models could
be a sign that single noise in the city of Bogotá is higher than in
other countries.
The results of other studies show similar or slightly lower models performance than was obtained in this study. In Beirut, there
was an underestimation of 5 dBA using the FHWA model, which
could be caused by the impact of background noise, specific characteristics of different forms of transportation, the use of horns or
excessive acceleration or deceleration; however, with the adjusted
model, the differences were reduced to 0.7–1.2 dBA [27]. Furthermore, the FHWA model was tested previously in Bogota, where it
presented an underestimation of 7 dBA (close to 10%), which the
authors attributed to the possible effect of background noise
[39], although the results of the present study suggest that underestimation arises from the high level of noise produced by single
buses and minibuses.
The CoRTN model was applied in Tehran (Iran), where it exhibited an overestimation of L10, 1h of 1.46 dBA, which appeared to be
related to traffic fluctuations and differences between classes of
vehicles and types of surfaces [7]. In Dublin, with this same model,
there were errors of up to 3 dB and underestimations of up
to1.8 dB, amounts considered by the authors as adequate for mapping and simulate noise mitigation measures [20]. Likewise, in
Hong Kong there were errors of up to 3 dB for 90% of the simulated
Weibull function for vehicle type
Time window: 17 seconds
-8 -7 -6 -5 -4 -3 -2 -1 0 1
L1s
Leq
estimated
Leq
measured
R2 , a, b - ME - MAE - MARE
Leq
estimated
Trucks
iv. The goodness-of-fit statistics of all models in the first 20 stations (calibration) was better than in the last 8 stations (validation); the stochastic model adjustment back 0.5 dBA and
the deterministic models 1–2 dBA, nevertheless, stochastic
model performance remains high. The discrepancy possibly
occurred by significant changes in traffic conditions, because
in the last 8 seasons the average volume of buses and minibuses was double that of the first 20 stations and the speed
of the cars was 1.8 times higher.
Stochastic model
Volume and
composition
Buses
Deterministic
models
Fig. 2. Research methodology.
2 3 4 5 6 7
8
618
90
90
80
80
Li,1sec
Li,1sec
A. Ramírez, E. Domínguez / Applied Acoustics 74 (2013) 614–621
70
60
70
60
50
50
40
40
0
1
2
3
4
5
6
7
0
8
1
3
2
Time (sec.)
M/C L170
CARS L150
CARS L263
70
60
70
60
50
50
40
40
0
1
2
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
Time (sec.)
Time (sec.)
TRUCKS L1
BUS L1
BUS L2
BUSETAS L1 54
TRUCKS L2
BUSETAS L2
Fig. 3. Li,1sec. curves (Weibull function) for different vehicles subclasses at different speeds approach (M/C: Motorcycles; L: Lane; speed: km/h).
Table 4
Performance of all models under different metrics (St: stochastic; Det: deterministic
derived; : adjusted parameters).
St-model
Det-model
Det-model
German
German
English
English
Nordic
Nordic
FHWA
r2
ME
MAE
MARE
0.742
0.756
0.868
0.425
0.441
0.395
0.420
0.586
0.640
0.721
0.51
0.33
0.09
1.53
0.37
0.48
0.44
0.03
0.06
1.44
1.14
1.09
0.76
2.09
1.55
1.69
1.58
1.48
1.18
1.90
0.016
0.016
0.011
0.029
0.022
0.024
0.022
0.021
0.017
0.027
data [44]. The same model was used in Pereira (Colombia), where it
presented an average error of 1.62 dBA for L10,1h [38].
In the countries of origin of the Nordic model, it has shown errors near ±2 dBA at a distance of 200 m [41]. In Japan, it presented
differences of less than 1 dB in areas without buildings and up to
4 dBA in developed areas [17].
The German model was employed in the city of Curitiba (Brazil),
where it yielded a MARE between 2.2% and 2.9% [11], which represents approximately 1.6–2.1 dBA. This same model tested in the
city of Chungiu (Republic of Korea) gave a ME of 0.6 dB and an r2
of 0.50 [45].
In general, the reported errors meet the requirements of government regulations and road engineers [23], however, caution is
to be exercised since the presence of anomalous traffic noise
events can affect the results up to 4 dB [46].
For the previously reported European models, Arana et al. [25]
found that there are differences in the parameters that define the
sound pressure of heavy vehicles. The German model penalizes
these vehicles the most and the Nordic model the least. For example, in the German model, the sound pressure of a heavy vehicle is
equivalent to 20 times that of a light one. In contrast, in the English
model, it is between 4.5 and 14 times that of a light one, and in the
Nordic model, it is considered to be between 6 and 10 times that of
a light one, depending on the speed. However, this variable is likely
to not have played a relevant role in the present study because of
the low flow of these vehicles.
Compared to neural network technology, the results associated
with our model are not considerably different. Cammarata et al.
[33] accepted errors of up to 2.5 dBA during the training phase of
network implementation. Genaro et al. [34] incorporated 26 input
variables and achieved errors that were generally less than 5%,
with a prominent average error of 0.79 dBA.
For micromodels, Can et al. [35] believe that the incorporation
of simple macroscopic rules may be sufficient to achieve reasonable estimates of city traffic noise. They found that this noise is
more sensitive to traffic signals than to the driving conditions.
However, application of a micromodel in the city of Gentbrugge
(Belgium) showed errors of less than 3 dBA, with the greatest differences being observed under conditions of low traffic density
[36].
As noted previously, the fit of the stochastic model developed in
this study gives slightly better results than those obtained in other
studies, which is explained by the fact that our model considered
contextual information specific to Bogota, where buses and minibuses emit high levels of single noise. In this sense, from a physical
perspective, both the stochastic model and the deterministic model developed here are equivalent to the FHWA model, which is
based on combining single traffic noise. This bestows upon it a
619
LAeq,10min
A. Ramírez, E. Domínguez / Applied Acoustics 74 (2013) 614–621
and for the optimization of parameters. In this regard, traffic noise
prediction models can provide very different results depending on
where they are implemented due to the geographical and physiological characteristics of each city [47].
The stochastic model investigated in this study was confronted
with results derived from a multivariate step-wise regression analysis that included the abundance of each class of vehicle, their
speeds, the background noise and the width of the lane. The most
significant relationship of LAeq,10min was found with the number of
buses and mini-buses (log), which accounted for 78% of the explained variance (Eq. (10)).
76
74
72
70
68
66
64
62
60
0
5
10
15
20
25
Stations
Measured
German
English
Nordic
FHWA
LAeq;10min ¼ 67:35 þ 3:10 logðvol: busesÞ þ 3:71
logðvol: Mini-busesÞ
74
72
70
68
66
64
0
5
10
15
20
25
Stations
Measured
German*
English*
Nordic*
LAeq,10min
76
74
72
70
68
66
64
0
5
10
15
20
25
Stations
Measured
St-model
Det-model
Det-model*
Fig. 4. Performance of the models at each station ( adjusted models; St: stochastic;
Det: deterministic derived).
Det-model*
Det-model
St-model
Nordic
Nordic*
English
English*
FHWA
German
German*
ð10Þ
However, it is noteworthy that the regression analysis carried
out on roads with six lanes in the city of Bogotá only managed to
explain between 40% and 43% of the sound pressure in the vehicle
volume [13]. Additionally, estimates in the city of Madrid explained between 55% and 88% of this sound pressure [22], while
in Cáceres, 69% was explained, although Barrigón-Morillas et al.
[6] presented results of other studies explaining between 53%
and 96%. In Pamplona and Valencia, between 56% and 83% of the
sound pressure was explained when including the width of the
road and the percentage of heavy vehicles in addition to traffic flow
[31], and in Envigado (Colombia), 38% was explained, with an error
close to ±3 dBA [12]. Therefore, these records demonstrate that the
performance of this procedure is highly variable, despite the greater parsimony of the regressive model.
Micro and macroscopic models seek to generalize the estimation of traffic noise, a fact that is reflected even in the prediction
and design of noise mitigation measures on roads not built yet
[15]. Regression models show 2 problems: (1) they are obtained
only on existing roads and, (2) they are generally particular to each
pathway and its traffic conditions, so they generally cannot be generalized to different streets.
Additionally, the random effect included in the stochastic model
related to the speed of each class of vehicles showed differences
between the highest and lowest LAeq,10min per station, ranging between 0.1 and 1.1 dBA, with a mean value of 0.54 dBA. This value
has no net impact on the results, as reflected in the similarity between the stochastic model and the deterministic model derived
from it.
3.4. Analysis of sensitivity
Fig. 6 expresses the results for the sensitivity analysis performed on the 28 stations with respect to relative variations in
84
0.0
0.5
1.0
1.5
2.0
1 to 20
2.5
3.0
3.5
4.0
21 to 28
Fig. 5. Performance of the models through comparing MAE calibration (1–20) and
validation stations (21–28) (St: stochastic; Det: deterministic derived).
82
LAeq,10min
LAeq,10min
76
80
78
76
74
72
universal character, sharing the same principle employed by
Pamanikabud et al. [37]. However, it requires local measurements
of single noise levels.
In contrast, the European models are based on fixed equations
that were defined for their home countries. Thus, when these models are used in contexts that are different from those where they
were developed, there is often a period required for adjustment
0
0.25
0.5
0.75
1
Relative flow
Motorcycles
Cars
Buses
Trucks
Minvibuses
Fig. 6. Continuous equivalent level simulated with respect to a reduction in the
observed traffic flow.
620
A. Ramírez, E. Domínguez / Applied Acoustics 74 (2013) 614–621
Table 5
Regression analysis between the traffic flow (log) and the continuous equivalent level
(a: intercept; b: slope; r2: coefficient of determination; p-value: regression significance level).
Motorcycles
Cars
Minibuses
Buses
Trucks
a
b
r2
p-Value
75.80
78.73
78.68
81.60
81.24
1.593
0.813
2.218
2.657
2.608
0.859
0.939
0.881
0.898
0.896
0.024
0.006
0.018
0.014
0.015
traffic flow. Based on these curves, we estimated the regression
equation for a logarithmic model (log10) (Table 5).
The regression analyses were significant in all cases (p < 0.05)
and explained nearly 90% of the continuous equivalent level. One
of the most relevant results was that the sound pressure associated
with the car flow becomes saturated at 600 veh/h, so increases in
the car volume do not increase the level of traffic noise. In contrast,
for other types of vehicles, monotonic growth was observed, which
was likely due to the lower flows assessed (
Contents lists available at SciVerse ScienceDirect
Applied Acoustics
journal homepage: www.elsevier.com/locate/apacoust
Modeling urban traffic noise with stochastic and deterministic traffic models
Alberto Ramírez ⇑, Efraín Domínguez
Facultad de Estudios Ambientales y Rurales, Pontificia Universidad Javeriana, Transversal 4, No. 42-00, Piso 8, Bogotá, Colombia
a r t i c l e
i n f o
Article history:
Received 27 January 2012
Received in revised form 6 June 2012
Accepted 1 August 2012
Available online 3 September 2012
Keywords:
Noise pollution
Urban modeling
Traffic noise prediction model
Traffic dynamics
Urban noise monitoring
a b s t r a c t
This paper presents the development and evaluation of a stochastic dynamic traffic noise prediction
model based on noise curves for vehicle classes and their speed. The model was tested on urban two-lane
roads in the city of Bogotá and was established on the basis of the fit of single Li,17sec noise functions for
different types of vehicles. The model showed a slightly better fit than was found in four deterministic
models that are highly internationally recognized. Additionally, a deterministic model was derived contextualized to the city of Bogotá. The approach used is promising for further investigations of urban traffic
noise given the traffic conditions in these systems.
Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Urban noise pollution is causing increased health risks in the
population. This is due both to the fact that noise levels, particularly those associated with transport, have increased dramatically
since the mid-twentieth century and that a higher percentage of
the world population is now concentrated in urban systems [1,2].
This problem has also increased economic costs due to failing
health and reduced productivity of the population, affecting between 0.2% and 2% of gross domestic product in the US [3]. In
the European Union, the costs range between $13 billion and
$38 billion per year [4]. In addition, traffic noise causes the depreciation of properties exposed to high noise levels [5].
Studies on urban noise are becoming more numerous, reflecting
the growing importance of this pollutant, for which levels currently exceed those specified by regulations in Spain [6], Iran [7],
India [8], Egypt [9], China [10], Brazil [11] and Colombia [12,13],
among others.
Computer models are highly valued in developed countries for
assessing environmental problems, including sources of pollution,
their spreading in the environment, impacts on human populations
and associated regulatory processes, many of which follow the
guidelines of the USEPA [14]. Modeling of traffic noise represents
an example of this technique and has been implemented in the
context of environmental impact studies for transport projects
[15]. Additionally, this type of modeling has played an important
role in the analysis of mitigation measures during road construction [16,17] and in identifying the variables with the highest noise
⇑ Corresponding author. Tel.: +57 1 3208320x4819; fax: +57 1 3208320x4859.
E-mail address: alberto.ramirez@javeriana.edu.co (A. Ramírez).
0003-682X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.apacoust.2012.08.001
incidence [9,18]. Noise prediction also plays a prominent role in
planning and development of new urban projects and roads [16].
The traffic noise model plays an important role in the construction of noise maps, since they combine both observed and simulated records. These maps have been employed mainly for urban
planning, environmental risk assessment [19], identification of
hotspots, evaluation of the exposed population and simulation of
mitigation measures [20,21].
The simplest models have been designed based on relationships
between the logarithm of the number of vehicles and the level of
noise they generate [7,22–24]. The relationship between these
two variables is obvious, as the greater the number of vehicles that
are simultaneously on the road, the greater the number of emissions sources there will be. More elaborate models have also included the proportion of heavy vehicles and speed, and even
variables such as pavement type, width and inclination of the track
and height of buildings, among others [7,15,23,25–30].
These models are based on theoretical factors that are applicable based on statistical relationships and on macroscopic traffic
variables such as total flow and average speed. Their results have
been very good related to roads and highways where traffic prevails, and flow conditions are relatively homogeneous [9,16,17].
In contrast, these same models have rarely been applied to urban
roads where traffic volumes and speeds are not fixed due to the
start-stop and acceleration–deceleration situations that are typical
of these systems [5] and because of cycles in traffic and noise associated with traffic lights [13,31].
Nevertheless, research on urban intersections has achieved a
good fit between the continuous equivalent level, (Leq), and the
traffic volume, the number of heavy vehicles, the slope and the
type of pavement [32].
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A. Ramírez, E. Domínguez / Applied Acoustics 74 (2013) 614–621
Other mathematical approaches that have achieved good performance include neural networks [33,34], microscopic traffic
models [35,36] and models based on single traffic noise [37].
In Colombia, the problem of traffic noise has been largely overlooked by environmental authorities. Very few studies have involved modeling, and their results have been highly variable
[12,13,38,39]. This report presents the results of a study in which
a stochastic and dynamic microscopic model is developed, and
its performance is analyzed in the city of Bogotá based on the single noise generated by each vehicle during its passage in front of a
measurement point. Additionally, we compare the results of this
model with a deterministic model derived from it, as well as four
international deterministic models that are widely used.
iii. A collection point for the information, which receives the
instantaneous sound pressure of the two lanes every second
and calculates the continuous equivalent level (Eqs. (1) and
(2)). This descriptor is the constant sound level over a stated
period of time which is equivalent in total sound energy to
the time-varying sound level measured over the same period
of time and is used worldwide in traffic noise evaluation
[15,26]. The simulation and sampling time was 10 min,
which is a duration that was previously shown (presampling) to be sufficient for LAeq stabilization. This unit of time
was reported as suitable for such measurements [35].
Calculation of the continuous equivalent level for each lane was
determined as follows:
2. Methodology
Leq;10min ¼ 10log10
2.1. Single noise
This study was conducted in Bogota. As a starting point, vehicles
were classified into the following categories: motorcycles, cars
(including cars, trucks, small delivery vans and microbuses), buses,
mini-buses (small buses) and trucks (over 3 tons). Subsequently,
we conducted measurements of single noise on the streets of the
city (n = 533 vehicles), seeking to exclude the impact of other vehicles and other sources of noise. To this end, we used an integrated
Extech type II sound level meter (SLM) to evaluate the instantaneous sound level (Li,1sec) during the approach and passage of each
vehicle in front of the SLM on roads with 1 and 2 lanes. These measurements followed conventional techniques [15] and were conducted using a tripod and a windscreen at a height of 1.2 m at a
distance of 1 m from the road with A and slow weights. In parallel,
we measured the speed at which each vehicle was traveling using
manual Bushnell equipment. In all cases, the prevailing conditions
included flat, dry roads, wind speeds less than 4 km/h and a low
incidence of other noise sources.
For each type of vehicle, we conducted a regression analysis between the maximum noise level (when passing in front of the SLM)
and speed. Because this yielded low coefficients of determination,
we implemented classification trees to dissociate subgroups
depending on the speed of vehicles. Subsequently, we averaged all
noise levels recorded in each subgroup at time zero (passing in front
of the SLM) and during the approach at times 1 through 8 s in
time steps of 1 s. Using these values, we tested various models of linear and nonlinear regression and chose the model with the highest
coefficient of determination using SPSS v.15 (statistical software)
and Curve Expert v.1.3 (nonlinear regression). The noise level was
assumed to be symmetric for the approach and retreat of vehicles.
2.2. Stochastic model
Based on this information, we built a dynamic model using the
Stella v.8 program (dynamic modeling software) consisting of 3
segments:
i. A stochastic Monte Carlo traffic simulator for each lane, with
sampling without replacement, which defines for each second whether or not a vehicle is present and the class to
which it belongs, along with its speed simulated from a normal distribution with estimated parameters (l, r2) for each
vehicle class and station. In this regard, the model follows
the guidelines given by the [5] regarding including specific
conditions for each lane.
ii. A time window of 17 s (8 . . . 0 . . . +8) for each lane, in
which the vehicle is moving and sends information about
instantaneous sound pressure (Li;1sec ) from the Weibull functions estimated from vehicle type and speed.
600
1 X
10Li;1s=10
600 i¼1
(
)
ð1Þ
For the two lanes:
L
Leq;10min lane 2
eq;10min lane 1
10
10
Leq;10min ¼ 10log10 10
þ 10
ð2Þ
The model is dynamic and is based on the physical principle of
the addition of sound pressure per vehicle and lane, along with
empirical equations for single noise based on speed and vehicle
type, which in this case, correspond to the Weibull function. The
model also incorporates randomness derived from the speed of each
vehicle, which is why the continuous equivalent level estimated at
each station was obtained from the average of 10 simulations.
The assumptions included in the model were as follows: (a)
conservation of vehicles during the 17-s window; (b) sound energy
conservation, but with divergence based on the distance between
the vehicle and the level meter, which is implied in the Weibull
function; (c) constant vehicle speed during passage through the
time window; (d) no vehicle passing any other vehicle or changing
lanes; (e) negligible effects of reflection due to walls, reflection and
shielding between vehicles and refraction and absorption by other
elements present in the acoustic field; (f) negligible impacts of
other noise sources compared to the sound pressure arising from
the vehicle; and (g) the climatic impact is considered negligible given the distance.
2.3. Deterministic models
For comparison purposes, we evaluated the German model
RLS90 – Richtlinien für den Lärmschutz an Straben [25]; the English model CoRTN – Calculation of road traffic noise [40]; the Nordic model Nordic prediction method for road traffic noise-statens
planverk 96 [25,41] and the Northamerican model TNM – Traffic
noise model V.2.5 [27]. Previous models estimate the Leq based
on traffic flow, speed and heavy vehicle proportion. They are static
and deterministic.
We also derived and evaluated a deterministic model based on
the TNM, but operating with the single noise levels measured in
Bogotá (Eq. (3)).
X
LAeq;17segðCars;sÞ
10
LAeq;10min ¼ 10 log
Q Cars;s 10
X
LAeq;17segðMotorcycles;sÞ
10
þ
Q Motorcycles;s 10
X
LAeq;17segðBuses;sÞ
10
þ
Q Buses;s 10
X
LAeq;17segðSmall Buses;sÞ
10
þ
Q Small Buses;s 10
X
LAeq;17segðTrucks;sÞ
10
þ
Q Trucks;s 10
ð3Þ
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A. Ramírez, E. Domínguez / Applied Acoustics 74 (2013) 614–621
where Qj,s is number of vehicles of type j, at speed s; LAeq,17seg,j,s is
17 s continuous equivalent level for vehicle j, at speed s.
2.4. Sampling stations
We studied 28 two-lane stations (one- and two-way streets) in
the city of Bogotá. These stations were chosen because they exhibited a low noise level associated with sources other than the vehicles being studied and were located in contexts that varied with
respect to volume, composition and vehicle speed. At each station,
the following descriptors were recorded: (a) continuous equivalent
level for 10 min (LAeq,10min.), measured with an integrated Extech
type II sound level meter at a height of 1.2 m, located 1 m of from
the lane and more than 4 m from any facades; (b) the number of
vehicles of each type in each lane, which were video recorded;
(c) the speed of as many vehicles as possible, recorded using a
Bushnell speedometer; and (d) the distance between the sound level meter and the middle of the lanes, to correct for the divergence
of the deterministic models (Fig. 1).
Sampling points were chosen more than 50 m away from traffic
lights to reduce stop-start effects during sampling but there were
numerous situations of detention.
2.5. Analysis
2.5.1. Deterministic models
The English, German and Nordic models were calculated using a
Java algorithm, while the US model of the Federal Highway Administration was computed from the Traffic Noise Model software V
2.5. The results were all corrected by adding background noise –
L90 – and adjusting distance of each lane to the sound level meter
(Eq. (4), for d = 1) [37]:
L ¼ LRef : 10log10
D
DRef :
d
ð4Þ
where L is sound pressure at a specific distance D; LRef. is sound
pressure at a reference distance DRef.
To evaluate the models performance, we divided the total sample into 2 groups: 20 samples for estimation and calibration and 8
samples for validation. Calibration was performed by adjusting the
parameters of the models up to 50% of its value, based on the function that minimizes the differences between observed and estimated results. This procedure was performed with the solver
function of Excel. A similar method was employed by Alimohammadi et al. [7] and by Calixto et al. [11].
2.5.2. Stochastic model
We estimated the continuous equivalent level through the Stella model for each station from the average of 10 simulations. In
addition, regression analysis between the background-noise and
mean error – ME – (Eq. (5)) was carried out to establish whether
there was incidence of the first variable in the second. This analysis
was necessary as background noise was not added explicitly in the
stochastic model as was done in the deterministic models. We did
not find, however, a relationship between them (p > 0.05).
1m
Sound meter
Speed meter
Video camera
Fig. 1. Information recorded in field: LAeq,10min, speed of different types of vehicles
in different lanes, video recording for vehicles count per lane.
The deterministic model derived from the stochastic model was
calibrated allowing variations up to 5% in the LAeq,17s of each type of
vehicle, following a similar procedure to that described previously
for the deterministic model (Table 1).
We studied the goodness of fit of the models using parameters
that relate the measured and estimated values, such as the mean
error (ME), the mean absolute error (MAE), the mean absolute relative error (MARE) and the coefficient of determination (r2) (Eqs.
(5)–(8)) [42].
ME ¼
n
1X
ðLAeq ^LAeq Þ
n i¼1
MAE ¼
ð5Þ
n
1X
jLAeq ^LAeq j
n i¼1
MARE ¼
ð6Þ
n
1X
jLAeq ^LAeq j
n i¼1
LAeq
ð7Þ
P
P
P
LAeqi ^LAeqi LAeqi ^LAeqi=n
r2 ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
P
2
2
P ^2
P 2
ð LAeq Þ
ð ^LAeq Þ
L
LAeq
Aeq
n
n
ð8Þ
Likewise, for the microscopic model, we conducted a sensitivity
analysis that evaluated the noise level at all stations under varying
traffic volumes. To this end, we rounded the maximum value of
each vehicle type and divided it into five equal units. Subsequently,
we simulated LAeq,10min for each station using the values given in
Table 2. Given the high sound pressure levels found in the city, this
analysis favored an approach that reduced the number of vehicles
and did not take into account variations in density and velocity referred to in the fundamental traffic diagram [43].
The procedure of the research is summarized in Fig. 2.
3. Application and discussion
3.1. Traffic conditions
The traffic conditions for the 28 samples are presented in Table 3,
highlighting the dominance of cars over other types of vehicles.
3.2. Single noise
The number of vehicles tested in each class to obtain the single
sound level varied between 30 and 115 (n = 533 vehicles). The best
Table 1
Calibration of single LAeq,17sec for the stochastic model.
LAeq,17sec estimated
Lane
1
Motorcycles L1 6 47
Motorcycles L1 47–70
Motorcycles L1 > 70
Motorcycles L2 6 51
Motorcycles L2 > 51
Cars L1 6 50
Cars L1 > 50
Cars L2 6 49
Cars L2 49–63
Cars L2 > 63
Minibuses L1 6 54
Minibuses L1 > 54
Minibuses L2
Buses
Trucks
63.5
66.3
71.1
2
LAeq,17sec adjusted
1
62.7
67.3
63.7
66.9
65.7
65.5
62.2
63.7
61.8
65.5
68.7
70.3
71.9
74.9
75.6
2
66.7
69.7
71.1
62.0
62.7
68.7
70.4
68.7
71.9
74.2
74.8
75.3
74.7
72.2
77.3
75.2
617
A. Ramírez, E. Domínguez / Applied Acoustics 74 (2013) 614–621
Table 2
Traffic flow used in the sensitivity analysis of the
stochastic model (observed maximum flow divided into
5 classes).
Type
Vehicles/h
Motorcycles
Cars
Minibuses
Buses
Trucks
40–80–120–160–180
300–600–900–1200–1500
20–40–60–80–100
20–40–60–80–100
16–32–48–64–80
Table 3
Range observed for the main traffic characteristics.
Motorcycles
Volume (No./10 min)
Lowest
3
Highest
36
Speed (km/h)
Lowest
20
Highest
60
function to describe the relationship between the average instantaneous sound pressure and the approach of the vehicle in a 9-s window was the Weibull function (Eq. (9)). For all types of vehicles, the
coefficient of determination was greater than 0.990 (n = 9,
p < 0.001), and function parameters varied as follows: a between
71.9 and 84.9, b between 44.8 and 123.6, c between 2 and 3.4
and d between 0.6 and 0.3 (Fig. 3).
ct d
Li;1s ¼ a be
ð9Þ
Similar plots were obtained by [37], who measured LAeq,10sec and
also found a weak relationship between the speed and the sound
pressure within each vehicle class, which indicates high variability
within the classes.
3.3. Modeling
The performance of the models across the different metrics is
shown in Table 4 and Figs. 4 and 5. From this, we extract the
following:
i. The stochastic model and the deterministic model derived
from it, showed better performance than the deterministic
models. The mean absolute error –MAE- of the stochastic
model was close to 1 dBA, while the MAE of the deterministic models is between 1.7 and 3.6 dBA.
ii. The mean error – ME – of the stochastic model is slightly
negative which indicates a small overestimation in the
model output, whereas it was positive for the deterministic
models. However, the ME was lower in the Nordic model,
which due to its value near zero, indicates a lack of bias.
iii. All of the adjusted deterministic models resulted in a better
fit than in the original models. However, there were no
significant differences in the average residuals (p > 0.05).
Cars
Minibuses
49
247
0
36
0
7
0
13
10
53
22
60
10
72
25
58
Monte Carlo simulation:
vehicle type, sample
without replacement
Average
speed and
standard
deviation
Normal distribution
simulation: speed (µ, σ)
The underestimation of LAeq by the macroscopic models could
be a sign that single noise in the city of Bogotá is higher than in
other countries.
The results of other studies show similar or slightly lower models performance than was obtained in this study. In Beirut, there
was an underestimation of 5 dBA using the FHWA model, which
could be caused by the impact of background noise, specific characteristics of different forms of transportation, the use of horns or
excessive acceleration or deceleration; however, with the adjusted
model, the differences were reduced to 0.7–1.2 dBA [27]. Furthermore, the FHWA model was tested previously in Bogota, where it
presented an underestimation of 7 dBA (close to 10%), which the
authors attributed to the possible effect of background noise
[39], although the results of the present study suggest that underestimation arises from the high level of noise produced by single
buses and minibuses.
The CoRTN model was applied in Tehran (Iran), where it exhibited an overestimation of L10, 1h of 1.46 dBA, which appeared to be
related to traffic fluctuations and differences between classes of
vehicles and types of surfaces [7]. In Dublin, with this same model,
there were errors of up to 3 dB and underestimations of up
to1.8 dB, amounts considered by the authors as adequate for mapping and simulate noise mitigation measures [20]. Likewise, in
Hong Kong there were errors of up to 3 dB for 90% of the simulated
Weibull function for vehicle type
Time window: 17 seconds
-8 -7 -6 -5 -4 -3 -2 -1 0 1
L1s
Leq
estimated
Leq
measured
R2 , a, b - ME - MAE - MARE
Leq
estimated
Trucks
iv. The goodness-of-fit statistics of all models in the first 20 stations (calibration) was better than in the last 8 stations (validation); the stochastic model adjustment back 0.5 dBA and
the deterministic models 1–2 dBA, nevertheless, stochastic
model performance remains high. The discrepancy possibly
occurred by significant changes in traffic conditions, because
in the last 8 seasons the average volume of buses and minibuses was double that of the first 20 stations and the speed
of the cars was 1.8 times higher.
Stochastic model
Volume and
composition
Buses
Deterministic
models
Fig. 2. Research methodology.
2 3 4 5 6 7
8
618
90
90
80
80
Li,1sec
Li,1sec
A. Ramírez, E. Domínguez / Applied Acoustics 74 (2013) 614–621
70
60
70
60
50
50
40
40
0
1
2
3
4
5
6
7
0
8
1
3
2
Time (sec.)
M/C L170
CARS L150
CARS L263
70
60
70
60
50
50
40
40
0
1
2
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
Time (sec.)
Time (sec.)
TRUCKS L1
BUS L1
BUS L2
BUSETAS L1 54
TRUCKS L2
BUSETAS L2
Fig. 3. Li,1sec. curves (Weibull function) for different vehicles subclasses at different speeds approach (M/C: Motorcycles; L: Lane; speed: km/h).
Table 4
Performance of all models under different metrics (St: stochastic; Det: deterministic
derived; : adjusted parameters).
St-model
Det-model
Det-model
German
German
English
English
Nordic
Nordic
FHWA
r2
ME
MAE
MARE
0.742
0.756
0.868
0.425
0.441
0.395
0.420
0.586
0.640
0.721
0.51
0.33
0.09
1.53
0.37
0.48
0.44
0.03
0.06
1.44
1.14
1.09
0.76
2.09
1.55
1.69
1.58
1.48
1.18
1.90
0.016
0.016
0.011
0.029
0.022
0.024
0.022
0.021
0.017
0.027
data [44]. The same model was used in Pereira (Colombia), where it
presented an average error of 1.62 dBA for L10,1h [38].
In the countries of origin of the Nordic model, it has shown errors near ±2 dBA at a distance of 200 m [41]. In Japan, it presented
differences of less than 1 dB in areas without buildings and up to
4 dBA in developed areas [17].
The German model was employed in the city of Curitiba (Brazil),
where it yielded a MARE between 2.2% and 2.9% [11], which represents approximately 1.6–2.1 dBA. This same model tested in the
city of Chungiu (Republic of Korea) gave a ME of 0.6 dB and an r2
of 0.50 [45].
In general, the reported errors meet the requirements of government regulations and road engineers [23], however, caution is
to be exercised since the presence of anomalous traffic noise
events can affect the results up to 4 dB [46].
For the previously reported European models, Arana et al. [25]
found that there are differences in the parameters that define the
sound pressure of heavy vehicles. The German model penalizes
these vehicles the most and the Nordic model the least. For example, in the German model, the sound pressure of a heavy vehicle is
equivalent to 20 times that of a light one. In contrast, in the English
model, it is between 4.5 and 14 times that of a light one, and in the
Nordic model, it is considered to be between 6 and 10 times that of
a light one, depending on the speed. However, this variable is likely
to not have played a relevant role in the present study because of
the low flow of these vehicles.
Compared to neural network technology, the results associated
with our model are not considerably different. Cammarata et al.
[33] accepted errors of up to 2.5 dBA during the training phase of
network implementation. Genaro et al. [34] incorporated 26 input
variables and achieved errors that were generally less than 5%,
with a prominent average error of 0.79 dBA.
For micromodels, Can et al. [35] believe that the incorporation
of simple macroscopic rules may be sufficient to achieve reasonable estimates of city traffic noise. They found that this noise is
more sensitive to traffic signals than to the driving conditions.
However, application of a micromodel in the city of Gentbrugge
(Belgium) showed errors of less than 3 dBA, with the greatest differences being observed under conditions of low traffic density
[36].
As noted previously, the fit of the stochastic model developed in
this study gives slightly better results than those obtained in other
studies, which is explained by the fact that our model considered
contextual information specific to Bogota, where buses and minibuses emit high levels of single noise. In this sense, from a physical
perspective, both the stochastic model and the deterministic model developed here are equivalent to the FHWA model, which is
based on combining single traffic noise. This bestows upon it a
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LAeq,10min
A. Ramírez, E. Domínguez / Applied Acoustics 74 (2013) 614–621
and for the optimization of parameters. In this regard, traffic noise
prediction models can provide very different results depending on
where they are implemented due to the geographical and physiological characteristics of each city [47].
The stochastic model investigated in this study was confronted
with results derived from a multivariate step-wise regression analysis that included the abundance of each class of vehicle, their
speeds, the background noise and the width of the lane. The most
significant relationship of LAeq,10min was found with the number of
buses and mini-buses (log), which accounted for 78% of the explained variance (Eq. (10)).
76
74
72
70
68
66
64
62
60
0
5
10
15
20
25
Stations
Measured
German
English
Nordic
FHWA
LAeq;10min ¼ 67:35 þ 3:10 logðvol: busesÞ þ 3:71
logðvol: Mini-busesÞ
74
72
70
68
66
64
0
5
10
15
20
25
Stations
Measured
German*
English*
Nordic*
LAeq,10min
76
74
72
70
68
66
64
0
5
10
15
20
25
Stations
Measured
St-model
Det-model
Det-model*
Fig. 4. Performance of the models at each station ( adjusted models; St: stochastic;
Det: deterministic derived).
Det-model*
Det-model
St-model
Nordic
Nordic*
English
English*
FHWA
German
German*
ð10Þ
However, it is noteworthy that the regression analysis carried
out on roads with six lanes in the city of Bogotá only managed to
explain between 40% and 43% of the sound pressure in the vehicle
volume [13]. Additionally, estimates in the city of Madrid explained between 55% and 88% of this sound pressure [22], while
in Cáceres, 69% was explained, although Barrigón-Morillas et al.
[6] presented results of other studies explaining between 53%
and 96%. In Pamplona and Valencia, between 56% and 83% of the
sound pressure was explained when including the width of the
road and the percentage of heavy vehicles in addition to traffic flow
[31], and in Envigado (Colombia), 38% was explained, with an error
close to ±3 dBA [12]. Therefore, these records demonstrate that the
performance of this procedure is highly variable, despite the greater parsimony of the regressive model.
Micro and macroscopic models seek to generalize the estimation of traffic noise, a fact that is reflected even in the prediction
and design of noise mitigation measures on roads not built yet
[15]. Regression models show 2 problems: (1) they are obtained
only on existing roads and, (2) they are generally particular to each
pathway and its traffic conditions, so they generally cannot be generalized to different streets.
Additionally, the random effect included in the stochastic model
related to the speed of each class of vehicles showed differences
between the highest and lowest LAeq,10min per station, ranging between 0.1 and 1.1 dBA, with a mean value of 0.54 dBA. This value
has no net impact on the results, as reflected in the similarity between the stochastic model and the deterministic model derived
from it.
3.4. Analysis of sensitivity
Fig. 6 expresses the results for the sensitivity analysis performed on the 28 stations with respect to relative variations in
84
0.0
0.5
1.0
1.5
2.0
1 to 20
2.5
3.0
3.5
4.0
21 to 28
Fig. 5. Performance of the models through comparing MAE calibration (1–20) and
validation stations (21–28) (St: stochastic; Det: deterministic derived).
82
LAeq,10min
LAeq,10min
76
80
78
76
74
72
universal character, sharing the same principle employed by
Pamanikabud et al. [37]. However, it requires local measurements
of single noise levels.
In contrast, the European models are based on fixed equations
that were defined for their home countries. Thus, when these models are used in contexts that are different from those where they
were developed, there is often a period required for adjustment
0
0.25
0.5
0.75
1
Relative flow
Motorcycles
Cars
Buses
Trucks
Minvibuses
Fig. 6. Continuous equivalent level simulated with respect to a reduction in the
observed traffic flow.
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A. Ramírez, E. Domínguez / Applied Acoustics 74 (2013) 614–621
Table 5
Regression analysis between the traffic flow (log) and the continuous equivalent level
(a: intercept; b: slope; r2: coefficient of determination; p-value: regression significance level).
Motorcycles
Cars
Minibuses
Buses
Trucks
a
b
r2
p-Value
75.80
78.73
78.68
81.60
81.24
1.593
0.813
2.218
2.657
2.608
0.859
0.939
0.881
0.898
0.896
0.024
0.006
0.018
0.014
0.015
traffic flow. Based on these curves, we estimated the regression
equation for a logarithmic model (log10) (Table 5).
The regression analyses were significant in all cases (p < 0.05)
and explained nearly 90% of the continuous equivalent level. One
of the most relevant results was that the sound pressure associated
with the car flow becomes saturated at 600 veh/h, so increases in
the car volume do not increase the level of traffic noise. In contrast,
for other types of vehicles, monotonic growth was observed, which
was likely due to the lower flows assessed (