Nonlinear regression model for predicting environmental traffic noise

Modelo
de regressão não linear para prever o ruído do tráfego ambiental

Alana Corsi

Mestranda em Engenharia de Produção.
Universidade Tecnológica Federal do Paraná (UTFPR) – Brasil.
[email-masked]

Franciely Velozo Aragão

Doutoranda em Engenharia de Produção.
[email-masked]

Daiane Chiroli

Doutora em Engenharia de Produção. Universidade
Tecnológica Federal do Paraná (UTFPR) – Brasil. [email-masked]

Márcia Santos

Graduada em Estatística. Universidade
Estadual de Maringá (UEM) – Brasil. [email-masked]

Eniuce Souza

Doutora em Estatística. Universidade
Estadual de Maringá (UEM) – Brasil. [email-masked]

Marcia Samed

Doutora em Engenharia de Produção.
Universidade Estadual de Maringá (UEM) – Brasil. [email-masked]

Paulo Soares

Doutor em Engenharia Civil. Universidade Estadual
de Maringá (UEM) – Brasil. [email-masked]

ABSTRACT

Transport is an essential
activity for urban life and for the economy, however, bad planning of the city
script causes some movement in some places, causing excessive noise levels
generated by road traffic. We aim to present a mathematical model that
represents the relationship between the equivalent level of sound and vehicle
volume quantities using the nonlinear logistic regression model in order to
facilitate decision-making in relation to urban planning. We collected the data
of sound pressure and vehicle volume for ten days during
five hours totaling a collection of 50 hours, with a total of 180 thousand data
of sound pressure level. The place of data collection is a highway that passes
through the city of Maringá, in Paraná, being an
intense traffic highway. The results show the performance of the proposed model
were differences between measured and predicted traffic noise levels ranged
from -0.3 dB (A) to +0.3 dB (A) and the mean difference was -0.006 dB (A). The
proposed road traffic noise forecasting model can be used as a decision support
tool in urban planning, considering the same boundary conditions as the road
study.

Keywords: Sound Equivalent Level. Traffic
noise. Mathematical Optimization
Model.

RESUMO

Muitos estudos sobre o impacto ambiental em áreas urbanas estão
relacionados ao ruído do tráfego rodoviário. O transporte é uma atividade
essencial à vida urbana e à economia, seja ele de pessoas ou bens de consumo,
os tipos de veículos para transporte são classificados em veículos leves ou
pesados. Entretanto, o mau planejamento da roteirização das cidades ocasiona
certa movimentação em demasia em alguns pontos, causando níveis excessivos de
ruído gerados pelo tráfego rodoviário. Este estudo tem como objetivo apresentar
um modelo matemático que represente a relação entre as grandezas Nível
Equivalente Sonoro e Volume Veicular, utilizando o modelo de regressão
logística não linear, a fim de facilitar a tomada de decisão em relação ao
planejamento urbano. Os dados de pressão sonora e volume veicular foram
coletados por dez dias durante cinco horas totalizando uma coleta de 50 horas,
com um total de 180 mil dados de nível de pressão sonora e 124.316 veículos. O
local de coleta de dados foi uma rodovia que passa pela cidade de Maringá, no
Paraná, sendo uma rodovia de tráfego intenso. Os resultados mostram que as
diferenças entre os níveis de ruído de tráfego medido e previsto variam de -0,3
dB (A) a +0,3 dB (A) e a diferença média foi de -0,006 dB (A). O modelo de
previsão de ruído de tráfego rodoviário proposto pode ser utilizado como
ferramenta de apoio à decisão no planejamento urbano, levando em consideração
as mesmas condições de contorno da rodovia estudada.

Palavras-chave:
Nível Equivalente Sonoro. Ruído de Tráfego. Modelo de Otimização Matemática.

Recebido
em 29/07/2019.  Aprovado em 09/12/2019.
Avaliado pelo sistema double blind peer review. Publicado conforme normas da APA.

http://dx.doi.org/10.22279/navus.2020.v10.p01-12.1035

1 INTRODUCTION

Ever since the emergence of cities, man has
always sought ways to move around and move his goods. With its evolution and
with the industrialization, this need is even greater, for the movement of
goods and people at substantial distances, while a globalization has strongly
increased these flows (Molina and Molina, 2012). This has resulted in problems
with the construction of a supply system, as well as problems of congestion and
urban mobility (Cattaruzza et al., 2017).

Transportation systems, whether urban or
freight, cause damage to health, accidents and pollution, which may be due to
the emission of air pollutants, high noise, and contamination of soils and water,
in this sense the emission of these harmful agents must be minimized in order
to preserve the population at high levels of these pollutants. (Taniguchi et
al., 2014). Allied to this, the increasing use of motor vehicles has increased
the occurrence of environmental problems, besides the problems of flow in urban
roads (Who, 2009; Tadic et al., 2004; Hesse and Rodrigue,
2004; Melo, 2002; Smith, 2015; Goines and Hagler,
2007).

The development of countries is directly
related to problems such as congestion, accidents and environmental pollution (Jica, 2007), and together with the lack of planning of
cities, problems such as noise production occur (Marques, 2010), which
according to Zannin et al. (2003) and Nunes (1999),
is one of the most common and troublesome environmental problems that has
affected the world population (Suthanaya, 2015). Koç et al. (2016) mentions that such problems can be solved
through innovative mechanisms developed between public and private sector
partnerships.

From the above, it can be seen that urban
logistics is a very important tool, since it consists of a combination of
transportation planning and urban environment, contributing to the achievement
of economic and environmental objectives (Lidasan,
2001). Urban logistics is defined as the process of optimizing logistics and
transport activities by private companies in urban areas, considering traffic,
congestion and energy consumption (Taniguchi et al., 1999). Dutra (2014) shows
that the movement of goods in urban areas affects urban planning and causes
environmental and health problems. Based on the population's awareness in this
regard, and the integration between the precepts of urban logistics and the
concern with physical infrastructure logistics and road safety, resulted in City
logistics (Gwillian, 2012). City Logistics aims to
reduce traffic congestion, increase mobility, reduce pollution and noise levels
considerably (Ricciardi et al., 2003; YANG et al., 2016).

"Traffic noise is an undesirable
sound", the noise level, related to urban problems and noise pollution
generated by traffic, is one of the major problems of the lack of urban
planning, responsible for reducing the quality of life of the population, and
to cause degradation of acoustic comfort in urban areas. (Ow and Ghosh, 2017; Maijala et al., 2012; Debnath and Singh, 2018; Morillas et al., 2002, Lee, 2007). In this sense, it can be
affirmed that considering the problems caused by the movement of goods and
people in urban areas, evaluating the problems and the actions to control the
adverse effects are becoming a concern for the community, evidenced by the
great number of laws and regulations that limiting noise (Mansouri et al.,
2006). Ramírez and Domínguez (2013) report that studies on traffic noise have
been growing considerably, especially in countries where the maximum levels of
tolerance established by regulations are exceeded, notably Spain, India, China
and Brazil.

According to the World Health Organization
(Who, 2009), excess noise in urban areas causes problems in the health and
well-being of the inhabitants, generating diseases such as stress and
discomfort for noise up to 55 dB, and from 65 dB promotes degrative stress,
increases the risk of heart attack; stroke; infections, among others.

In a study carried out by Aragão
(2016), the Brazilian city of Maringá - Paraná, is
governed by law number 218/98, which provides limits of tolerance of noise
levels for each area of urban zoning. Also, the Brazilian Association of
Technical Standards (ABNT) defines the limits of acceptable noise levels for
each type of area, according to the period of the day, in decibels, as
described in NBR 10151:2000, which describes that in mixed areas, predominantly
residence, the acceptable noise level in daytime is 55 dB and in night time is
50 dB.

In addition, according to research by Calixto
et al. (2001), the noise that most annoys the population is the traffic
generated by vehicles. Therefore, according to Guarnaccia
(2013), the need to measure traffic noise in urban areas is evident, and
necessary for urban planning (Garg and Maji, 2014).

For Suthanaya (2015);
Giraldo and Fernandez (2011) and Guarnaccia
(2013), the development of models and methodologies that monitor the
environmental noise is necessary to know the critical points, to map sensitive
areas and to apply the measures of reduction of the sound levels. Kumar et al.
(2014) used an artificial neural network model to predict traffic noise, Li et
al. (2016) used the Monte Carlo simulation to develop a statistical model of
probability to predict traffic noise, and all studies take into account the
contour characteristics of each location using known mathematical techniques to
predict noise from traffic.

The development and use of mathematical
modeling to monitor the Sound Pressure Level (SPL) of vehicle traffic
represents a gain for the study of the noise pollution problem and for urban
planning of existing and under way roadways (Calixto et al., 2001). Silva and
Mendes (2012) elaborated an index of environmental quality for cities, which
considers indicators of air pollution and noise pollution, in its application,
it was efficient in the combination of only one technique that could help urban
planning in decisions strategies. Cai et al. (2015) carried out a study on road
traffic noise mapping through the creation of a regional noise calculation
algorithm for the Guangzhou region of China. Maijala
et al. (2012) proposed a concept of SPL monitoring by means of an algorithm,
which classifies the sound sources by means of a wire sensor.

According to Regazzi
and Silva (2004), the study between a dependent variable and one or more
independent variables can be performed using the nonlinear regression model,
and also, according to Mazucheli et al. (2011)
nonlinear regression models are formulated based on the theoretical knowledge
inherent to the object of study, being the method used in this article.

Thus, we aim to develop a mathematical model,
which represents the relationship between vehicular volume and the sound
equivalent level, allowing control and support to the application of control
measures of the pathway under study, also, to compare noise levels measured at
the site with the limits acceptable by NBR 10151: 2000 and by the levels
acceptable by the World Health Organization, classifying the acoustic quality
of this area. For this, we collected the data on a highway in Maringá, Paraná, characterized by intense traffic of light
and heavy vehicles. In addition, the highway passes through the middle of the
city, in mixed areas, predominantly residential.

2 MATERIALS AND METHODS

In this section, we described the
methodological procedures of the research, starting from the characterization
of the studied area, and later the method of collection and processing data, as
follows.

2.1 Characterization of The Studied Area

The area of evaluation of this work is situated
in the city of Maringá, located in the northwest of
Paraná - Brazil, being the third largest city of the State, positioned in the
geographical coordinates: Latitude 23 º 25 '31' 'S and Longitude 51 º 56' 19 '
'W, cut by the Tropic of Capricorn, having an altitude of 555 meters.

The acoustic monitoring points are located at
Colombo Avenue (Federal Highway BR-376), which is characterized as an Urban
Crossing, being described as an intense traffic and long
distance road composed of heavy vehicles, light vehicles, motorcycles
and bicycles. BR-376 is a Diagonal Highway connecting the cities of Garuva / SC and Dourados / MS,
crossing the State of Paraná, with an extension of approximately 958,3 Km.

The highway under study has intersections with
streets of local traffic and viaducts to access the collecting traffic ways.
The track section is variable, depending on the presence of central beds,
however, the width of the tracks is constant, being 3.1 m each lane. As the
highway is inserted in the city, the maximum speed allowed is 60 km h -1. In
addition, the sites of the collection point are characterized by having, apart
from intense traffic, trade spots and is predominantly residential.

2.2 Method of collecting and processing Data

Firstly, we performed the acoustic monitoring
in the study sites where the Sound Pressure Levels were captured, according to
equation 1, and the volume of vehicles passing through the site. In order to do
it, a portable sonometer, model DL4200, of ICEL, with 1.4 dB precision, in
addition to a Sony camcorder, model DCR-SX21, was used for the purpose of
recording the flow of vehicles during the monitoring period.

The SPL is all acoustic energy emitted by a
particular source. In sound monitoring the SPL varies during a given time
interval (T), where the average one represents the Equivalent Sound Pressure
Level (Leq) reports Bistafa,
(2011). The SPL is defined by ISO 1996/1 (1987), having as unit the decibels
(dB), according to equation 1.

(1)

Where P: Sound pressure in pascal;

: Reference Sound Pressure.

Leq is also defined according to ISO 1996/1
(1987), having as unit the dB, according to equation 2.

(2)

Where T: Total time in hours; Li: Sound Intensity Level in dB; Ti:
Partial time in hours.

The data samples, vehicle volume and SPL, were
collected on different days of the week and in the afternoon period with a
duration of five hours, thus, being in accordance with ISO 11819-1, Acoustics -
Measurement of the influence of road surfaces on traffic noise - Part 1:
Statistical Pass-By method, which provides that the monitoring for the
calculation of Leq can vary between 1 and 4 hours of measurement during the day
in the rush hour.

Regarding the meteorological conditions, the
monitoring was carried out on days with conditions considered normal, with
clear skies, without rain or any meteorological interference that could compromise
the reliability of the data.

After tabulating the vehicle volume and sound
pressure data, a regression analysis was performed, which consisted of
investigating and modeling the dependence relation between a random variable
and the possible explanatory causes of its variability, represented by one or
more predictor variables. In this study, the noise level was considered as the
random variable Y and the number of vehicles that as the predictor variable X.
Firstly, we performed the study of the relation between the variables X and Y,
looking for a mathematical function of X that explains Y. However, since this
relation is not perfect, for the observed values would not be perfectly situated
on a function that related X and Y, the type of function adopted was suggested
by empirical evidence, that is, based on the observations of the variables. One
can evaluate the behavior of the relation approaching a line or any other
curve. After the study of the relation between the variables, we tested the regression
models that represent the behavior of these variables, in order to find the
model that best represents the parameters. To choose the best model, we used the
criterion of the lowest AIC (Akaike Criterion Information). To apply such
models to the data, we used the gcFitModel command belonging to the R software
grofit package.

3 RESULTS AND DISCUSSION

After the collection stage, we organized the
data on the amount of light and heavy vehicles per hour traveling in the
studied road, and the value of Sound Equivalent Level (Leq), calculated from
the monitored SPL, in Table 1. A collection of information on the noise level
caused by light and heavy vehicular traffic on Colombo Avenue occurred during
ten days, with five hours a day and on different days of the week, excluding
holidays or days that could cause changes in normal traffic conditions.

Data

Period

Light Vehicle Volume (Light Vehicle / h)

Heavy Vehicle Volume (Heavy Vehicle / h)

Leq measured period (dBA)

Beginning

End

1

13:00:00

14:00:00

2609

249

74,1

2

14:00:00

15:00:00

2658

291

74,3

3

15:00:00

16:00:00

2981

299

74,5

4

16:00:00

17:00:00

2271

237

74,0

5

17:00:00

18:00:00

2140

220

73,9

6

13:00:00

14:00:00

2306

287

74,3

7

14:00:00

15:00:00

2445

253

74,3

8

15:00:00

16:00:00

2308

238

74,1

9

16:00:00

17:00:00

2240

229

74,1

10

17:00:00

18:00:00

2357

273

74,2

11

13:00:00

14:00:00

2948

269

74,5

12

14:00:00

15:00:00

2514

272

74,1

13

15:00:00

16:00:00

2148

252

74,0

14

16:00:00

17:00:00

2105

207

73,6

15

17:00:00

18:00:00

1878

200

73,3

16

13:00:00

14:00:00

3228

332

74,6

17

14:00:00

15:00:00

2431

230

74,1

18

15:00:00

16:00:00

1960

201

73,8

19

16:00:00

17:00:00

2532

245

74,2

20

17:00:00

18:00:00

1938

193

73,5

21

13:00:00

14:00:00

2072

254

74,1

22

14:00:00

15:00:00

2218

236

74,2

23

15:00:00

16:00:00

2630

267

74,3

24

16:00:00

17:00:00

2807

257

74,4

25

17:00:00

18:00:00

2367

250

74,3

26

13:00:00

14:00:00

2174

224

74,2

27

14:00:00

15:00:00

2784

224

74,3

28

15:00:00

16:00:00

3319

338

74,6

29

16:00:00

17:00:00

2506

229

74,1

30

17:00:00

18:00:00

1924

199

73,7

31

13:00:00

14:00:00

2110

229

74,2

32

14:00:00

15:00:00

2028

223

74,0

33

15:00:00

16:00:00

2462

273

74,4

34

16:00:00

17:00:00

1446

142

72,5

35

17:00:00

18:00:00

1381

155

72,6

36

13:00:00

14:00:00

2658

231

74,2

37

14:00:00

15:00:00

2158

255

74,1

38

15:00:00

16:00:00

2094

209

73,8

39

16:00:00

17:00:00

2141

193

73,8

40

17:00:00

18:00:00

1621

161

72,9

41

13:00:00

14:00:00

2198

246

74,2

42

14:00:00

15:00:00

2050

229

74,1

43

15:00:00

16:00:00

2038

206

73,8

44

16:00:00

17:00:00

2053

204

73,8

45

17:00:00

18:00:00

1499

166

72,9

46

13:00:00

14:00:00

2132

211

74,0

47

14:00:00

15:00:00

1845

200

73,4

48

15:00:00

16:00:00

2159

279

74,3

49

16:00:00

17:00:00

2001

221

73,7

50

17:00:00

18:00:00

1768

188

73,2

Table
1: Relation between
vehicle volume and Leq

Souce: Survey data (2018)

Considering that, in this study, the noise
level is represented by the random variable Y and the number of vehicles that
traveled through Colombo Avenue as the predictor variable X, the data pairs (X,
Y) were plotted in the scatter diagram shown in Figure 1.

Figure 1: Graphic relation between vehicle volume and sound level

Source: The authors (2018)

From Figure 1, we verify that the relation
between the variables X and Y does not resemble a line, suggesting that the
mathematical function of X that explains Y must actually be nonlinear. In order
to confirm this fact, a linear model was fitted to the data (AIC = 2.98), but
the residuals showed non-random behavior, indicating the presence of patterns
in the data not modeled by the adjusted linear curve.

The nonlinear function suitable to describe the
relation between the variables X: "number of vehicles" and Y:
"noise level" was the Logistics curve, which has three parameters A, μ and λ, being defined by equation 3.

(3)

Where: μ is the maximum
slope and A is the horizontal asymptote representing the maximum noise. In many
nonlinear models, the parameters are characteristic points of the function and,
not rarely, some parameters in the model do not have direct interpretation, such
as the λ in the logistic curve, are necessary to
guarantee flexibility to the model.

The estimates of the parameters A, μ and λ of the Logistics curve and their
respective standard errors for the sample of vehicles collected in this study
are represented in Table 2.

Parameter

Estimate

Standard error

0.025

0.003

= -2464.138

474.207

A

74.705

0.109

Table 2: Estimates and standard error of the logistic curve parameters

Souce: The authors (2018)

Also, the AIC was -45.18 while in the linear
model it was 2.98.  Besides that, the Confidence
Intervals (CI) for the parameter estimates, with 95% reliability, were
calculated to indicate the significance of the parameters. The results obtained
were expressed in Table 3.

Estimator

IC
(95%)

Inferior
limit

Superior
limit

0.019

0.0314

-3393.583

-1534.693

74.491

74.920

Table
3: 95% Confidence Intervals for
Estimates

Souce:
The authors (2018)

Therefore, the nonlinear regression model
adjusted to the data and describing the relationship between the variables X:
"number of vehicles", light or heavy, and Y: "noise level"
is the logistic model given by equation 4.

(4)

From equation 3, and from the data collected in
Table 1, the graph that shows the relation between the variables X and Y
described by the adjusted logistic model, in accordance with Figure 2, was
drawn in red.

Figure 2: Graphic of the adjusted logistic regression model (in red) describing
the relation between the variables X and Y

Source: The authors (2018)

It is noted in Figure 2 that the model seems to
fit the data well. However, when adopting a regression model, some assumptions
are assumed. By performing a residual analysis of the adjusted logistic model,
we observed that the assumed assumptions regarding the random error were
verified, as shown in the graphs of Figure 3.

Figure 3: Residual analysis

Source: The authors (2018)

By the histogram and qq-plot presented in
Figure 3, it is verified that the errors present normal distribution. Although
not presented, correlograms and hypothesis tests that corroborated with the
normality (Shapiro-Wilk) and the errors independency, that is absence of
autocorrelation, were also verified.

Thus, from the tests of equation three, it was
possible to conclude that the logistic model is valid to describe the variables
under study.

From the nonlinear regression equation, the Leq
was calculated, using equation 3, according to Table 4, in order to demonstrate
the dispersion between the measured and calculated data.

Data

X (number of vehicles)

Leq measure period (dBA)

Leq calculated period (dBA)

Differences dB(A)

1

2858

74,1

74,3

-0,2

2

2949

74,3

74,4

-0,1

3

3280

74,5

74,5

0

4

2508

74

74,1

-0,1

5

2360

73,9

74

-0,1

6

2593

74,3

74,2

0,1

7

2698

74,3

74,2

0,1

8

2546

74,1

74,1

0

9

2469

74,1

74,1

0

10

2630

74,2

74,2

0

11

3217

74,5

74,5

0

12

2786

74,1

74,3

-0,2

13

2400

74

74

0

14

2312

73,6

73,9

-0,3

15

2078

73,3

73,6

-0,3

16

3560

74,6

74,6

0

17

2661

74,1

74,2

-0,1

18

2161

73,8

73,7

0,1

19

2777

74,2

74,3

-0,1

20

2131

73,5

73,7

-0,2

21

2326

74,1

73,9

0,2

22

2454

74,2

74

0,2

23

2897

74,3

74,3

0

24

3064

74,4

74,4

0

25

2617

74,3

74,2

0,1

26

2398

74,2

74

0,2

27

3008

74,3

74,4

-0,1

28

3657

74,6

74,6

0

29

2735

74,1

74,3

-0,2

30

2123

73,7

73,7

0

31

2339

74,2

73,9

0,3

32

2251

74

73,8

0,2

33

2735

74,4

74,3

0,1

34

1588

72,5

72,6

-0,1

35

1536

72,6

72,4

0,2

36

2889

74,2

74,3

-0,1

37

2413

74,1

74

0,1

38

2303

73,8

73,9

-0,1

39

2334

73,8

73,9

-0,1

40

1782

72,9

73,1

-0,2

41

2444

74,2

74

0,2

42

2279

74,1

73,9

0,2

43

2244

73,8

73,8

0

44

2257

73,8

73,8

0

45

1665

72,9

72,8

0,1

46

2343

74

73,9

0,1

47

2045

73,4

73,6

-0,2

48

2438

74,3

74

0,3

49

2222

73,7

73,8

-0,1

50

1956

73,2

73,4

-0,2

Table 4: Measured Leq and calculated Leq

Souce: The authors (2018)

It can be seen that the differences between
measured and predicted traffic noise levels ranged from -0,3 dB (A) to +0,3 dB
(A) and the mean difference was -0,006 dB (A).

Considering the regulatory norm that guides the
evaluation of noise in inhabited areas, with the purpose of promoting comfort
to the community, we established the limits of noise level, considering the
type of environment in which the measurements were accomplished, represented by
the value of the evaluation criterion level (NCA).

Considering the environment to which the
measurements were made as a mixed area, predominantly residential, and, that
the measurements were carried out during the daytime period, it is assumed that
the limits pre-established is 55 dBA. Thus, from the measured and calculated
Leq values, and the limit established by norm for a given region, it was
possible to carry out the data scatter, comparing it with the Leq limit,
according to Figure 4.

Figure 4: Scatter between measured and calculated Leq

Source: The authors (2018)

Therefore, from the graphic of scatter of SPL,
measured and calculated, it was possible to analyze that the limit imposed by
NBR 10151: 2000 is not being fulfilled, directly affecting the quality of life
of the population in the area. Besides that, it was possible to conclude that
the equation 3, Logistic Model, allows to perform the calculations of the noise
level of the place under study, in a reliable and representative form. The
suggested model allows to perform the noise level calculations in cities
similar to the study, having the same contour conditions of the analyzed
pathway.

It should be noted that the volume of traffic
flow plays a significant role in the emission of traffic noise, which reflects
the environmental impact on public health. The present study showed that the
use of the environmental noise prediction model could be used in urban planning
in order to reduce traffic noise levels and minimize public health problems
around busy highways.

4 FINAL CONSIDERATIONS

Globalization and
urbanization in centers cause great flows of movement of cargoes and people.
Urban logistics has been applied in order to bring greater harmony in the
transport sector and urban planning, contributing to the fulfillment of the
economic objectives and environmental laws, enabling an improvement in the life
quality of the population. The evidence available on the impacts of vehicular
pollution on human health is overwhelming and sufficient for many years to
demonstrate the importance of controlling emissions from mobile sources.

Thus, we studied the
relation between vehicle volume and sound level at Colombo Avenue, which
crosses the city of Maringá, in order to find a function capable of
representing the relation between these variables at the location described.
Hence, with the regression model found, we measure the noise level from a
vehicle count in the area, facilitating the monitoring and supporting the
decision-making and better control of the variables. Since, as said, they
influence the quality of life of the surrounding population and are responsible
for a portion of environmental pollution and degradation of public roads.

The results showed
that the sound levels in the place exceeded the reference value, established by
the Brazilian standard NBR 10151: 2000, thus requiring actions that reduce the
vehicle volume and noise level. In addition, the results showed that the
nonlinear regression model, Logistic Model, allows to perform the calculations
of the noise level of the place under study, in a reliable and representative
form, and can be used in other areas similar to the study, having the same
contour conditions of the analyzed road.

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