applied
sciences
Article
Calibration and Validation of a Measurements-Independent
Model for Road Traffic Noise Assessment
Domenico Rossi *, Aurora Mascolo
and Claudio Guarnaccia *
Department of Civil Engineering, University of Salerno, Via Giovanni Paolo II 132, I-84084 Fisciano, Italy;
amascolo@unisa.it
* Correspondence: drossi@unisa.it (D.R.); cguarnaccia@unisa.it (C.G.)
Abstract: The assessment of road traffic noise is very important for the health of people living
in urban areas. Noise is usually assessed by field measurements, and predictive models play an
important role when experimental data are not available. Nevertheless, when they are based on
regression techniques, predictive models suffer from the drawback of strong dependence on the
calibration data. In this paper, the authors present a regressive model calibrated on computed noise
levels without the need for field measurements. The independence from field measurements makes
the model flexible and adjustable for any road traffic condition possible. A multilinear regression
technique is applied to establish the correlation between the computed equivalent noise levels and
several independent variables, including, among others, traffic flow and distance. The model is then
validated on a large field measurement database to check its efficiency in terms of prediction accuracy.
The validation is performed both via error distribution analysis and using different error metrics. The
results are encouraging, showing that the model provides good results in terms of the average error
(less than 2 dBA) and is not susceptible to the presence of outliers in the input data that correspond
to unconventional conditions of the traffic flow.
Keywords: road traffic noise; modeling and simulation; multilinear regression; error analysis
Citation: Rossi, D.; Mascolo, A.;
1. Introduction
Guarnaccia, C. Calibration and
Noise, especially when coming from road traffic, is one of the most pervasive pollutants. Especially in urban areas, a large percentage of the population is estimated to be
exposed to noise levels largely exceeding the limits fixed by laws [1]. Since urbanization has
expanded, people are constantly in contact with a large number of vehicles, and continuous
exposure to the generated noise levels leads to physical and psychological detriments, such
as high blood pressure and sleep deprivation, together with mental disorders [2–4]. Much
evidence for this correlation can be found in the literature; for example, some works show
that intrusive sounds can severely affect sleep [5] and mental health [6]. Traffic noise in
urban areas is not only related to the direct exposure of pedestrians but also accounts for
people in their houses since many buildings can be reached by high noise levels [4]. For this
reason, the estimation of the amount of noise in urban areas is very important for human
health assessments [7].
Aside from the measurement of such noise levels to ease inhabitants’ conditions, many
different models for the estimation of noise in a certain area can be found, all with the
common goal of best describing the noise level, starting with different parameters such as
the number and type of passing vehicles, the distance of the receiver from the noise source
(the vehicle itself), the presence of roundabouts and/or intersections [8], and speed, as well
as also climate conditions [9], the location or absence of acoustic barriers, and so on [10,11].
Such a comprehensive traffic noise model could provide a proper prediction of noise levels
to assist authorities and planners in setting up and applying noise mitigation measures, for
example, for the design of new roads or for the renewal of existing ones [7]. Models can
Validation of a MeasurementsIndependent Model for Road Traffic
Noise Assessment. Appl. Sci. 2023, 13,
6168. https://doi.org/10.3390/
app13106168
Academic Editor: Yat Sze Choy
Received: 17 April 2023
Revised: 12 May 2023
Accepted: 16 May 2023
Published: 18 May 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Appl. Sci. 2023, 13, 6168. https://doi.org/10.3390/app13106168
https://www.mdpi.com/journal/applsci
Appl. Sci. 2023, 13, 6168
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be generated at many different levels of complexity and efficiency, and a proper balance
between these two aspects is necessary to implement a practical and effective one. For
instance, computational fluid-dynamic approaches are often used in the automotive and
airplane industries to design noise reduction systems [12].
Generally speaking, the main types of models are statistic, analytic, microscopic,
macroscopic, semi-dynamic, and dynamic [13]. Focusing on time dependence, the models
are usually built to predict noise indices over a certain period of time dependent on selected
independent variables [14]. Variables chosen can vary in type and number, but the most
used are certainly traffic volume, the percentage of heavy vehicles, and the distance between
the source and receiver. Additional parameters considered can be the road slope, the texture
of the asphalt, the average speed of the flow, and the weather conditions. These kinds
of models are flexible and easy to use, including for non-expert users. They are basically
functions in which selected “independent” parameters are related to the noise level through
proper coefficients. Their efficiency strongly depends on the calibration step, that is, the
process that establishes and details the correlation between each parameter and the noise
level. When this process is run through regression using in-field-measured data, the model
belongs to the statistical category.
The importance of this process is evident when trying to apply such a model to a road
traffic framework very different from the one used for calibration. In such cases, in fact, the
efficiency of the model output can easily be lowered. For this reason, many national laws
establish which model can be used in the country. Some of the models adopted in national
regulations are listed in Ref. [15]: the CoRTN model in the United Kingdom [16], the RLS90
model in Germany [17], the NMPB model in France [18], the ASJ model in Japan [19],
and the SONROAD model in Switzerland [20]. In such a complex scenario, the European
Union issued the European Noise Directive related to the assessment and management
of environmental noise, in which the main definitions and rules are provided to member
states [21]. In particular, the noise indicators are defined as the equivalent continuous
sound levels calculated for the day (Ld ), evening (Le ), or night (Ln ) timespans, as well as for
the entire day (Lden ). The latter indicator includes a penalty for evening and night hours.
The effort to harmonize noise assessment for many sources, including road traffic, has
led to the development of the CNOSSOS model, which is nowadays the reference model
in Europe [22]. Regardless of the considered model, all of them assess the noise levels
using various indicators, usually estimated at a fixed distance over a given time range. The
most important is the equivalent continuous sound level, Leq , which is the constant sound
level in dBA, with the same total sound energy as the fluctuating level measured in the
considered timespan (such as 15 min, 1 h, a day, an evening, a night).
In the present paper, developing an idea proposed by Afandizadeh et al. in Ref. [23],
the authors used a multilinear regressive model for the evaluation of noise from traffic in
which the estimation of the noise level is implemented from computed data and not from
real ones. The proposed model, in fact, aims to predict noise equivalent levels produced by
road traffic, calibrating on a dataset of computed noise levels. The independent variables
used for the calibration are the total traffic volume, the percentage of medium and heavy
vehicles, the mean speed of each type of vehicle, and the distance between the center of
the highway and the receiver. The computed level database is obtained with a random
sampling of the independent variables listed above that feed the formula proposed by
Quartieri et al. [14]. Once the computed level database is obtained, a multiple linear
regression technique—implemented with a self-written Python routine—is used to establish
the correlation between the independent variables and the Leq,t on a fixed time range, t.
This approach overcomes some shortcomings of the classic and statistical models. Firstly,
the model can be calibrated without any field measurements by using a computed set of
data. It is known, in fact, that model efficiency usually decreases when applying models
to a site different from the ones where they were calibrated [16]. Secondly, the model can
be recalibrated quickly when needed to include different traffic road conditions. Another
advantage of this approach is that its independence from measured data makes it suitable
Appl. Sci. 2023, 13, 6168
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to be applied to estimate the impact of traffic noise even for roads that do not yet exist,
providing useful information when designing new roads in urban or non-urban areas.
The outputs of the model are then validated with measured data coming from a LongTerm Monitoring Station (LTMS) system installed in the city of Saint-Berthevin (France)
by the Université Gustave Eiffel and Unité Mixte de Recherche en Acoustique Environnementale (UMRAE), Nantes. This study aims to deepen the understanding of physical
phenomena in the field of environmental acoustics, correlating noise measurements at
different acoustic masts with meteorological parameters collected over a period of ten years.
The model was applied to part of the dataset and a prevision of the hourly equivalent
level—Leq,h —was performed. The simulated data were compared with the measured ones
to evaluate the goodness of the model. The same process was repeated in a 15 min timespan
to check the robustness of the model in a different time range and on a larger set of data.
The results show, in both cases, how the model is able to provide a good approximation of
noise level distributions. The performance of the model has been quantitatively estimated
via error distribution analysis and error metrics.
2. Materials and Methods
An algorithm for the generation of a 2000-occurrences data frame was implemented.
Each row of the data frame represents a fictive traffic flow situation in which different
vehicles are moving at a given average speed, and the impact of the noise can be evaluated
in variable timespans—hours, fractions of an hour, or multiples of an hour—at variable
distances. Vehicles flowing can belong to “light”, “medium”, or “heavy” vehicle categories.
According to French regulations [24], for instance, “light” vehicles are common passenger
cars with a gross weight of less than 4500 kg, “medium” vehicles have a gross weight below
3500 kg but a length equal to or larger than 3 m, and “heavy” vehicles exceed 3500 kg of
gross weight.
The first step was the generation of a computed dataset, and it consists of the random
generation of 2000 fictitious traffic conditions identified by 6 independent variables and the
subsequent calculation of noise equivalent levels. The chosen six independent variables
are as follows: volume of traffic (Q), expressed as the number of moving vehicles per hour;
average velocity of each vehicle type (light vehicles, medium vehicles, and heavy vehicles,
respectively, VL , VM , and VH ); percentage, P, of heavy vehicles over the total flow; and the
distance between the center of the highway and the base of the acoustic masts (receiver), d.
The choice of working with average speeds and with a single value for the traffic flow
for both directions was necessary to reduce the complexity of the model and optimize the
computational effort. However, this choice may represent a limitation to the model, since
some hours of the day, in particular circumstances, are characterized by a large variation in
single vehicle speed and by a strong asymmetry in the flow’s directions.
The range of the values of the independent variables are as follows: P values range
from a minimum of 0 to a maximum of 20%, with steps of 0.1%; VL values range from
30 to a maximum of 130 km/h, with steps of 5 km/h; VM values span from 30 to a
maximum of 100 km/h, with steps of 5 km/h; and VH values span from 30 to a maximum
of 80 km/h, with steps of 5 km/h. Variable d values range from 10 to 100 m, with steps of
1 m. The independent variables were chosen with two different criteria: a ladder function
and a random function. The execution of the functions is sequential, as indicated by the
pseudocode available in the Supplementary Materials, where the ranges of each variable
value are also reported in detail.
The first independent parameter chosen is Q, and it is built with the ladder approach,
which is a simple function generating integer values from a minimum of 10 to a maximum
of 2000 veh/h, with intervals of 10 veh/h. For each of these flow generation step, the other
variables are added, finalizing the construction of the dataset. Specifically, for every Q value
sampling step, the algorithm implements 20× loops to associate all the other independent
variables, which were chosen using the second criterion, i.e., randomly. For each Q, then,
20 casual combinations of the other independent values (P, VL , VM , VH , d) are generated,
Appl. Sci. 2023, 13, 6168
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completing each final occurrence, now described by the whole set of independent variables
and useful for the Leq,h calculation. The random choice of the values of the independent
variables is performed in a specific order: after Q, P values are generated by randomly
picking a value from the described interval. Once a P value is obtained, the number of
medium and heavy vehicles is calculated from P by rounding the results to obtain an integer
number and dividing it by two (so that the number of heavy and medium vehicles is the
same for each occurrence). Finally, the number of light vehicles is obtained by subtracting
medium and heavy vehicles by the whole of Q. After that, values of distance, d, are casually
chosen from the indicated range, and then, the same approach is used for velocities, which
are randomly chosen in this order: VL , VM , and VH . In this last case, the generation of
velocities is completely random, but some constrictions are fixed. Specifically, the velocities
of the medium and heavy vehicles are forced to be lower than the velocity of light vehicles.
The actual range of the medium and heavy vehicles, then, has a fixed lower limit but a
moving upper limit so that a case where heavy vehicles move faster than light ones never
happens. Please note that, for each row of the dataset, the velocity value is applied to
all the vehicles involved. The first phase of the creation of the dataset, then, ends with a
set of randomly set conditions of road traffic flow. Please note each casual combination
is generated with a given seed to assure reproducibility (see “Pseudocode” image in the
Supplementary Materials, line 2).
Once the whole dataset is generated, the independent variables are used to compute
the corresponding values of Leq,h , completing the dataset. Leq,h computing starts from the
computing of the power levels, LW,L , LW,M , and LW,H , which are obtained by using a Noise
Emission Model (NEM) [25]. These NEMs usually provide the source power level as a
function of either the speed of a single vehicle or the average velocity of the flow. In this
paper, the REMEL model was used, as reported in the work of Wayson et al. [26]:
LW,L = 31.13 log10 (VL ) + 12.77 + 20 log10 (d0 ) + 11
L
= 18.765 log10 (VM ) + 43.697 + 20 log10 (d0 ) + 11
W,M
LW,H = 12.831 log10 (VH ) + 58.27 + 20 log10 (d0 ) + 11
(1)
The choice of the Noise Emission Model (NEM) is arbitrary, and the proposed formulation permits the potential application of different NEMs by only modifying the structure of
Equation (1). In particular, this modular approach can fit any existing framework, including
CNOSSOS-EU, which is suggested as a reference model by the EU. The choice of specific
NEMs, which include the noise emission of hybrid/electric cars [27,28], could also address
the necessity of properly simulating changes in the circulating fleets. The influence of
different NEMs and various propulsion systems on the validation results could be further
studied in a future paper.
Once the power level is obtained, the sound exposure levels (SEL) for each type of
vehicle involved are obtained following the set of Equation (2), as reported in the work of
Quartieri et al. [14].
SEL L = 10 log10 ( Q L ) + Lw,L − 20log10 (d) − 11
(2)
SEL M = 10 log10 ( Q M ) + Lw,M − 20log10 (d) − 11
SEL H = 10 log10 ( Q H ) + Lw,H − 20log10 (d) − 11
In these equations, the sound exposure levels (SEL) are computed as a function of the
number of vehicles moving (QL , QM , and QH , respectively, the number of light, medium,
and heavy vehicles); the power levels, LW ; and the distance from the receiver. The constant
value, 11, is related to the assumption of the spherical propagation of the noise with an
absorbing surface. Equations (1) and (2) are used to finally compute the Leq,h values with
Equation (3):
SEL M
SEL H
SEL L
1
Leq,h = 10 log
+ 10 log 10 10 + 10 10 + 10 10
(3)
3600
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In this formulation, the sound level is a function of the sound level emitted by each
type of vehicle passing, and it is computed over the whole span of 3600 s, i.e., an hour.
The idea is that the overall sound level is obtained by the (logarithmic) sum of the sound
exposure levels produced by the three considered vehicle types, divided by one hour
(3600 s). This constant can be adjusted for different timespans by simply modifying the
denominator value in the subject of the first logarithm. Here ends the second phase of the
first step of the generation of the algorithm.
The second step is the calibration of the model itself. The first phase of the calibration is
the implementation of a multiple regression technique, by which the dependencies existing
between the Leq,h levels and all six independent variables can be found. Equation (4) shows
the details of this multilinear regression.
Leq,h = c1 A1 + c2 A2 + c1 A3 + c1 A4 + c1 A5 + c1 A6 + m1
(4)
In Equation (4), A1 is log Q, A2 is log VL , A3 is log VM , A4 is log VH , A5 is log P, and
A6 is log d. In the same equation, c1 , c2 , etc., are the coefficients of the multilinear regression
and m1 , the intercept. The multiple linear regression accounts for the contemporary
contributions of all variables, establishing the best-fitting model for the data supplied. In
the second phase of the second step, the coefficients of the multiple linear regression are
used as in Equations (5) and (6) to retrieve, from a univariate linear regression, the final
calibration of the model. Specifically, in Equation (5), the linear dependence between the
Leq,h values and the same set of data, weighted by the coefficients retrieved in the previous
multilinear regression, is assumed.
Leq,h = cX + m2
(5)
Namely, c is the coefficient of the regression, m2 is the intercept, and X is the sum of
the coefficients of the multiple linear regression multiplied by the data of the calibration
model according to Equation (6):
X = (c1 log Q) + (c2 log VL ) + (c3 log VM ) + (c4 log VH ) + (c5 log P) + (c6 log d)
(6)
Multilinear regression, then, is a procedure used to compare the contemporary contributions of all the independent variables to the final Leq,h values, and it provides a coefficient
for each variable, together with an intercept. Please note that the coefficients do not simply
represent the single dependence of the Leq,h values from a variable; rather, they represent
the influence of every single variable when the overall convergence is achieved. An analysis
of the residuals is performed to assess the calibration process results.
The third and last step is the validation of the model with field measurements, which
was performed using the long-term monitoring station (LTMS) database provided free for
scientific purposes by the Université Gustave Eiffel, Nantes, France [29]. In this long-term
database, data coming from several monitoring stations—acoustic, meteorological, road
traffic, and ground impedance—located in the city of Saint-Berthevin (France) have been
collected for 10 years and made available in a whole and unique database, at a base time of
15 min, referring to the period from 2002 to 2007 [29]. For the presented application, the
authors considered the acoustic and traffic data and, specifically, the measurements of a
reference sound level meter, which was positioned at 5 m height and at a fixed distance of
12.5 m from the center of the carriageway. The database was used to validate the goodness
of the model by evaluating the error calculated as the difference between the measured
equivalent levels and model simulations. Apart from the error distribution analysis, MAE
(mean absolute error), MPE (mean percentage error), and MAPE (mean absolute percentage
error) metrics were used for a quantitative evaluation of the model’s performance when
applied to the dataset.
The three steps of the complete process described above are graphically summarized
in the following flowchart (Figure 1).
ff
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Figure 1. Flowchart of the generation of the model in three steps: simulation, calibration, and
validation.
3. Results and Discussions
In this section, the results of the procedure described above are presented and discussed thoroughly.
3.1. Simulation and Calibration Results
Data obtained from simulations offfithe traffic flow performed in the first step of
the procedure described in Section 2 were collected in a unique dataset with a length
of 2000 rows, representing light and heavyffvehicles at different speeds at the center of
the carriageway. This dataset simulates the collection of the independent values used
for the computing of Leq,h according to Quartieri et al. [14]. In each step ffof Q values,
10 different combinations of velocities, the percentage of heavy vehicles, and the distance
are set, maximizing the combination of possible flow conditions simulated. Table 1 shows
a selection of lines from the used dataset. It is worth noting that the hourly Leq,h value
corresponding to very low values of vehicle flows are the levels produced just by the source
vehicle, neglecting any other source that can be active in the area under study. This confirms
that the model is computing the noise coming from
ffi road traffic only, and, thus, it could lead
to underestimation when comparing it with field-measured data since it does not account
for background noise. The introduction of a correction for background noise is under study
and will be included in future papers to extend the range of the applicability of the model.
The creation of the dataset was guided by the idea of reflecting as wide a range of traffic
as possible in order to create a final model able to efficiently perform at many different
sites. For example, the volume
of traffic, going from a minimum of 10 to a maximum
ffi
of 2000 vehicles per hour, easily reflects traffic in both night and daily hours and even
discriminates traffic in rush times (e.g., cars going to or coming back from work). As for
velocities, a minimum speed of 30 km/h makes the model suitable to cover urban area
conditions, while the peak speed reflects the cars moving at maximum velocity established
by law for highways. The interconnection between the two variables, on the other hand,
makes the model capable of distinguishing between standard situations (completely free
flow, no obstacles, no congestion) and particular ones (intersections, presence of obstacles
inducing sudden slowing down, congestion). It is also interesting to note the possibility
offered by the model of evaluating the interconnection between the velocities of the different
vehicle types since the inserted constraint makes the model more adherent to the real
condition in which speed limits decrease with an increase in vehicle weight.
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Table 1. Preview of the free flow traffic dataset showing some of the occurrences.
Q (veh/h)
VL (km/h)
VM (km/h)
VH (km/h)
P (%)
d (m)
Computed
Leq,h (dBA)
10
10
10
10
10
...
100
100
100
100
100
...
1000
1000
1000
1000
1000
...
2000
2000
2000
2000
2000
80
70
55
65
100
...
50
100
50
60
55
...
50
95
75
90
110
...
80
45
70
90
60
70
30
30
30
50
...
30
85
30
40
55
...
50
45
75
80
35
...
75
45
70
55
40
75
55
35
45
65
...
30
45
40
60
35
...
30
50
75
55
40
...
60
35
50
60
55
13.1
14.7
15.7
3.3
5.4
...
5.4
7.6
11.4
6.4
13.3
...
14.6
7.3
13.8
10.2
4.4
...
14.4
18.4
5.8
17.3
13.7
66
84
34
89
10
...
62
54
12
43
69
...
21
18
47
66
73
...
16
32
89
75
89
37.2
32.8
38.0
28.2
53.0
...
39.5
49.0
55.7
45.6
41.9
...
61.4
67.6
59.0
56.5
57.0
...
71.4
61.2
53.7
58.8
53.8
A closer look at the dataset makes evident that the strictest dependence is the one
between Leq,h and d since the highest values of emitted noise (Leq,h in the fourth quartile of
the distribution) are always related to the lowest values of d (first quartile of the distribution).
This connection will be confirmed by the results of the multiple linear regression (see below).
The interdependence between the variables for the generation of the noise levels is
clear when performing the multilinear regression technique, which was performed by
using statsmodel, a Python library for statistical analysis. The library permits us to tune the
regression calculation by adjusting several parameters in order to best fit the data and minimize errors. Three different models of linear regression have been tested: the Generalized
Linear (GLS), the Ordinary Least Squares (OLS), and the Weighted Least Squares (WLS)
models. The results were identical between the models in terms of coefficients, R2 , BIC, and
AIC; then, the authors decided to apply the OLS model. Table 2 shows the results of the
linear regression between Leq,h and the independent variables. Values of all the intercepts
and regression coefficients are listed, together with R2 , AIC, and BIC.
Table 2. Multilinear regression for the calibration of the model.
Model:
Df Model:
R-squared:
Log-Likelihood:
AIC:
BIC:
Intercept
Coeff. log(Q)
Coeff. log(VL)
Coeff. log(VM)
Coeff. log(VH)
Coeff. log(P)
Coeff. log(d)
OLS
6
0.986
−2664.5
5343
5382
27.362713
10.022377
19.902456
1.382846
1.921894
2.825697
−25.699334
ff
ff
ff
ff
ff
ff
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The results of the multilinear regression indicate how distance, d, is the independent
ff the L values, contributing at the highest level to the variance in
variable that most affects
eq,h
the model, followed by the velocities of light vehicles, VL and Q. The distance dependence
ffi as expected (the
from Leq,h is also the only one that is inverse with a negative coefficient,
higher the distance, the lower the Leq,h value).
The calibration step goes on with a second linear regression, univariate, which was
implemented by correlating Leq,h as a function of all the independent values together,
according to the X variable defined in Equation (6). The results of the regression are
reported in Figure 2a. Figure 2b shows a distribution of the residuals that presents a mean
× (5.4− × 10−15 dBA) and a standard deviation of 0.92 dBA. The
value that is basically null
kurtosis index is 1.07, making the distribution slightly “leptokurtic”, and the skewness
is 0.69, meaning that its right tail is slightly more pronounced than the left one. Figure 3
shows the distributions of Leq,h values simulated by the presented model and the Leq,h
measured and reported in the original database, as well asttthe scatterplot between the two
sets of noise levels.
(a)
(b)
Figure 2. (a) Linear regression for Leq,h computed values and the X variable; (b) distribution of
residuals.
(a)
(b)
tt
Figure 3. (a) Distribution of the simulated (blue) and the measured (orange) Leq,h values; (b) scatterplot of the computed vs. measured Leq,h values.
3.2. Validation of Field Measurements
Once the model was calibrated, its validity was tested by simulating the Leq,h of
road
ffi traffic flows observed in a real case study. The used dataset is the aforementioned
dataset built by the Université Gustave
Eiffel of Nantes in the city of Saint-Berthevin.
ff
ff
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The experimental setup was made of five acoustic masts positioned at different distances
from the road and at two heights from the ground. Since the aim of this work was not
focused on propagation issues, only measurements coming from the closest receiver to the
carriageway were taken into account in order to simplify the output investigation. The
chosen receiver was the “reference” one, sited at 5 m height and at 12.5 m—axial distance—
from the border of the carriageway. This long-term monitoring station (LTMS) dataset
contains 30,347 measurements based on 15 min intervals, in which the following variables
are present: sound equivalent levels (Leq, 15min ), number of light and heavy vehicles passing
by, and average speeds for these vehicle categories.
First of all, the Leq values of the LTMS database were converted into a 1 h time range.
To perform a comparison with the model, which was calibrated on 60 min Leq values, the
following formula was applied:
L4
L1
L3
L2
1
(7)
Leq,h = 10 log
10 10 + 10 10 + 10 10 + 10 10
4
where L1, L2 . . . , etc., are the Leq values recorded in the first and second quarters, and so
on. Only hours in which all four quarters are present have been selected to reconstruct the
hourly Leq , as in Equation (7). This operation reduced the number of usable occurrences,
since, in the original LTMS database, some of the 15 min Leq values were removed in a
cleaning process, as they were affected by sources other than the highway under study [27].
In addition, in order to adapt the dataset to the inputs of the model, the authors had
to perform a data transformation on the number of heavy vehicles passing by and on their
velocities. The original dataset only contains information on vehicles exceeding the normal
“passenger” category, which are considered “heavy vehicles” in the database. The number
of the vehicles tagged as “heavy” in the database was divided by two, assuming that 50%
of them were medium vehicles and the other half heavy ones. As for the speed of medium
and heavy vehicles, the authors assumed that it was the same. The source distance receiver
was not variable in the case study, since the receiver was at a fixed position; thus, the
authors calculated the distance (as reported in the detailed description of the experimental
setup [29]) and set it as the value of d.
A statistical analysis of the distribution indicates a certain similarity between the
distributions, highlighting a slight overestimation of the model. The mean values of
ff
ff
the distributions
differ for an absolute value of 0.82 dBA and their skewness
differs for
an absolute value of 0.48. The kurtosis indexes are 4.87 and 2.06 for the measured and
computed Leq,h values, respectively. Error analysis was also performed on the specific
application of the model, resulting in Figure 4a, where errors are calculated as the measured
Leq,h minus the simulated Leq,h .
(a)
(b)
Figure 4. (a) Errors in the model vs. measured noise levels when working on the 1-hour timespan
data; (b) distribution of error values.
−
−
Appl. Sci. 2023, 13, 6168
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The cloud of data in the graph in Figure 4a shows that the majority of the errors
−
lie between −5 and +5 dBA, except for some outlier values, especially at high levels of
−
measured Leq,h . The mean value of the errors is −0.82 dBA, and the standard deviation is
2.25 dBA, while the skewness and kurtosis of the distributions are, respectively, 0.68 and
1.64. The overall error analysis, then, indicates a good-performing model for the case study
of the LTMS database.
Nevertheless, the authors wanted to deepen the investigation of the performing
metrics of the model itself. To do so, the relationship between the error outliers and some
specific independent variables was investigated. The investigation was at first carried out
using a boxplot analysis (Figure 5a), where the data falling into the interquartile range
were represented in the box, and the black diamonds refer to the data falling outside the
boundaries of the box ± 1.5 times the interquartile range. The total number of outliers so
calculated was 3.93% of the total. These data are also represented by red dots in Figure 5b,c,
where error values are represented as a function of Q and P. The outlier data are listed in
Appendix A.
(a)
(b)
(c)
Figure 5. (a) Boxplot of the errors of the model when applied to the LTMS database with indications
tt
of whiskers and outliers (black diamonds); (b) and (c) are scatterplots of the errors as functions of Q
and P, respectively, where red dots are the occurrences corresponding to error outliers as indicated
in (a).
As for the graph in Figure 5b, it is clear that the outlier positive values of errors
mostly correspond to a low Q value, meaning that the most significant underestimations of
the model have to be investigated in periods in which uncommonly high Leq,h values are
associated with a limited amount of traffic. These Leq,h values are generally related to low P
values and high speeds. Such conditions suggest an expectation of values of noise levels
lower than those measured (see Table A1 in Appendix A). This discrepancy can be related
to several reasons; one of them could be the presence of other noise sources occurring
during the measurement. Similarly, outliers corresponding to large overestimations are
associated with low measured Leq,h values for the observed flows and speeds. This suggests
that some specific situations, not considered in the presented model, could happen during
measurements.
The scatterplot of errors vs. P (Figure 5c) represents a similar pattern, and yet, it is
more spread over the whole P range. Once they identified the outliers, the authors removed
such data and performed a new step of simulation with the “cleaned” dataset to validate
the model excluding nonstandard conditions. For the new dataset, the same approach
described before was applied by investigating the distributions and the scatterplot of the
measured vs. simulated Leq,h levels reported in Figure 6. A visual comparison between the
two histograms is good, and the statistical analyses are comparable: the mean values of the
measured and simulated Leq,h differ in an absolute value of 1.02 dBA; the skewness index
of the measured and simulated Leq,h differs by 0.55, where the kurtosis indexes are now
5.09 and 2.24 for the measured and simulated Leq,h . The mean and the standard deviations
of the error distribution after the removal of the outliers are, respectively, −1.02 dBA and
1.91 dBA, showing a slight worsening of the mean error and a small improvement in the
tt
ff
ff
Appl. Sci. 2023, 13, 6168
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−
standard deviation with respect to the analysis including the outliers (mean error and
standard deviation, respectively: −0.82 dBA and 2.25
− dBA). This result confirms that the
model can also provide a good average performance when nonstandard conditions of
traffic and/or background
levels occur.
ffi
(a)
(b)
Figure 6. (a) Distribution of the simulated (green) and the measured (orange) Leq,h values; (b) scatterplot of the computed vs. measured Leq,h values for the dataset without outliers.
3.3. Analysis on a 15 Min Timespan
Additional validation of the model’s functioning was performed on the field measurements extracted from the raw LTMS database to evaluate the performance of the model
when applied to a set of data provided over 15 min. The choice of applying the model to
the same data but with a different
timespan thus allowed us to verify the model’s reliability
ff
and its usage in situations where an hourly time range is not suitable (for instance, strong
variations in the sources) and check the performance of the model using a larger and more
detailed set of data.
As mentioned in the previous sections, the computed Leq,h values used for the calibration of the model were obtained with a logarithmic sum where a time-dependent factor was
ff step
present (1/3600; see Equation (3)). In order to change the timespan to 900 s, a different
tt
of calibration for the model was performed, setting the time factor of Equation (3) to 1/900.
The results of the multilinear regression confirm that the Leq slope lies on the coefficientffi
of
the regression, while the intercept accounts for the vertical shift in the simulations (Figure 7).
ff
The difference between
the intercepts of the two regression lines is 6.02 dBA, which is
10 log(3600/900)
exactly a result of 10 log(3600/900
), i.e., the conversion from 1 h to 15 min.
Figure 7. Regression lines of computed Leq,t when the computation is performed with a 3600 s
database (Leq,h , red dots) or a 900 s database (Leq, 15min , blue dots).
Appl. Sci. 2023, 13, 6168
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Such an interesting result strongly confirms the possibility of rescaling the computation
to any desired time interval, thus adapting to whatever situation needs to be simulated.
As for the comparison between the measured and simulated Leq, 15min values, the authors
performed the very same approach described above by analyzing the calibration residuals
and the validation errors and performing a study on the model performance with and
without outlier values. In Figure 8a, the linear regression of the Leq, 15min values vs. the X
variable is presented, while in Figure 8b, the distribution of the residuals of the calibration
is shown.
(a)
(b)
Figure 8. (a) Linear regression for computed Leq, 15min values and the X variable; (b) distribution of
residuals.
Just like the previous application, the residual distribution has a mean value that is
basically null (4.3 × 10−−14 dBA) and a standard deviation of 0.92 dBA. The kurtosis index is
1.07, making the distribution slightly “leptokurtic”, and the skewness is 0.69, with the right
tail more pronounced than the left one. Statistical indexes of residuals, then, are basically
equal to the ones obtained when the model was run for Leq,h , suggesting the goodness of
the calibration is independent of the selected timespan.
The next step is the validation of the model by using the real traffic data provided by
the LTMS database for a 15 min time range and a comparison between the measured and
the simulated equivalent levels. In Figure 9, the results are summarized: in the same way as
hourly data, the superimposition of the Leq, 15min value distributions shows their similarity,
confirmed using statistical indexes. The absolute difference between the mean values is
0.72 dBA. The skewness of the measured Leq, 15min value distribution is −2.04, while the
one for the simulated Leq, 15min is −1.52 (absolute difference, 0.51). The kurtosis indexes are
6.11 and 4.24, respectively, for the measured and simulated Leq, 15min value distributions
(absolute difference, 1.87).
Figure 10a shows the scatterplot of the validation errors versus the measured Leq, 15min .
The error distribution reported in Figure 10b has a mean value of −0.72 dBA and exhibits a
quite symmetric shape. The statistical indexes to confirm this visualization are 0.84 for the
skewness and 5.11 for the kurtosis.
In performing the outlier analysis, the authors discovered a behavior similar to the
one found for the 1 h timespan application of the model. Specifically, outlier values
corresponding to the largest errors occurred at low values of Q, as shown in Figure 11b. The
error of 37.9 dBA, for instance, corresponds to the measurement performed on 22 September
2004, from 10:30 to 10:45 a.m. In this time slot, the measured Leq, 15min is 72.7 dBA with a
total flow of two vehicles over 15 min, one light and one heavy, with a speed of 45 km/h
for the light vehicle and 28 km/h for the heavy vehicle. Of course, something occurred
in the measurement that is either the presence of an event that altered the noise level
measurement or, most probably, a problem in the car counting system.
ff
ff
−
Appl. Sci. 2023, 13, 6168
−
ff
13 of 18
ff
tt
(a)
tt
(b)
−
tt
Figure 9. (a) Distribution of the simulated (blue) and measured (orange) Leq, 15min values; (b) scatterplot of the computed vs. measured Leq, 15min values.
tt
(a)
−
(b)
Figure 10. (a) Errors in the model vs. measured sound levels; (b) distribution of error values.
(a)
(b)
(c)
Figure 11. (a) Boxplot of the errors in the model when applied to the LTMS database with indications
tt
of whiskers and outliers (black diamonds); (b) and (c) are scatterplots of the errors as functions of Q
and P, respectively, where red dots are the occurrences corresponding to error outliers as indicated
in (a).
In general, given the structure of the model, which mimics only the contributions to
ffi is very small, the background
the noise level from vehicles passing by, when the traffic flow
sound level is not negligible.
Following the same approach already described, the authors removed the outliers and
performed a new validation process, obtaining the results presented in Figure 12.
ffi
Appl. Sci. 2023, 13, 6168
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(a)
(b)
Figure 12. (a) distribution of the computed (green) and measured (orange) Leq, 15min values; (b) scatterplot of the measured vs. computed Leq, 15min values for the dataset after removing the outliers.
ff
The absolute difference
in the mean values of the Leq, 15min distributions is now 0.88 dBA;
ff in the skewness of the distributions is now 0.50; and the absolute
the absolute difference
differenceff in the kurtosis indexes is 1.88.
Tables 3 and 4 summarize, respectively, the statistical values of the measured and
simulated equivalent level distributions and error metrics, with and without outliers. It
is possible to see how the statistics of the distributions for the simulation levels are very
close to those from the measured distributions, even including outlier data. Similarly,
the error metrics are comparable, showing a slight improvement just when the absolute
error is considered for the MAE and the MAPE. The removal of outliers, in fact, was not
“symmetric” since they were more gathered in the underestimation region; thus, the error
metrics that consider the sign of the error tend to move away from zero (see the mean
error and MPE in Table 4). On the contrary, the mean absolute error and mean absolute
percentage error adopt the absolute value and, thus, decrease thanks to the removal of both
high underestimations and overestimations.
Table 3. Statistical values of the distribution of the Leq,h and Leq, 15min values, with and without
outliers.
Distribution
Statistics
Measured
Simulated
Measured without
Outliers
Simulated without
Outliers
Leq,h
Mean (dBA)
Std dev (dBA)
Skewness
Kurtosis
72.1
2.0
−1.68
4.87
72.9
2.5
−1.20
2.07
72.1
2.0
−1.72
5.09
73.1
2.6
−1.16
2.24
Leq, 15min
Mean (dBA)
Std dev (dBA)
Skewness
Kurtosis
71.6
2.9
−2.04
6.11
72.3
3.0
−1.52
4.24
71.6
2.8
−1.94
5.27
72.5
2.8
−1.44
3.39
Furthermore, the data show that the model output does not have a significant improvement after the removal of outliers, neither for the Leq,h nor Leq, 15min simulations, suggesting
that the model can work properly, on average, when nonstandard conditions occur.
In addition, since all the regulations usually fix limits on day, evening, or night
equivalent levels, as well as on entire day levels (Lden ), as defined in the European Noise
Directive [21], the on-average good performance of the model suggests that this tool can
be successfully used to predict these indicators both in proximity to existing road traffic
networks and when designing new infrastructures.
Appl. Sci. 2023, 13, 6168
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Table 4. Error metrics for 1 h and 15 min timespan datasets, with and without outliers.
Reference Timespan
Error Metrics
Full Dataset
Dataset without
Outliers
1h
Mean error (dBA)
Std dev of the error (dBA)
MAE (dBA)
MPE
MAPE
−0.82
2.25
1.90
−1.17%
2.65%
−1.02
1.92
1.76
−1.44%
2.46%
15 min
Mean error (dBA)
Std dev of the error (dBA)
MAE (dBA)
MPE
MAPE
−0.72
2.28
1.85
−0.36%
2.12%
−0.88
1.91
1.69
−0.76%
1.56%
4. Conclusions
In this paper, a new model for road traffic noise level assessment was presented. The
idea was to build a model with a multilinear regression technique calibrated with computed
data rather than measured ones. The implemented formula for computing the Leq values
for the model calibration is simple and versatile since it easily permits to choose a different
the Noise Emission Model for the computation of source power levels and provides the
opportunity to compute equivalent noise levels over different timespans. The modularity
of the choice of the NEM makes the model compatible with any national model and with
the EU’s harmonized CNOSSOS framework, also allowing for the inclusion of different
propulsion systems, such as electric and hybrid engines, which are more and more present
in national fleets. Such a paradigm permitted the creation of a calibration dataset that
is as general as possible to cover a multiplicity of traffic flow situations. The random
generation of the independent variable values used for the calibration of the model most
likely improved this characteristic of the model even more. It is worth noting that the
multilinear regression technique allows for the inclusion of different variables according to
the situation. All these features make the model usable in a very large number of situations.
A statistical analysis of the residuals of the model in the calibration phase and the errors
when validating it with a real dataset allowed us to investigate the model performance as a
function of the measured noise levels, total traffic flow, and percentage of heavy vehicles.
The validation was performed also removed unconventional conditions related to
traffic and/or the measured levels, thus removing the outliers identified during the analysis.
The error metrics confirmed a slight improvement in the absolute errors, although the
model also provided average errors lower than 2 dBA, including nonstandard situations.
This result is promising since the indicators usually adopted by national regulations are
defined by a large time range average, which can be day, evening, or night timespans,
as well as full days (Lden ). Thus, a model that provides good performance on average is
expected to furnish reliable predictions for these time ranges.
The limitations of the model can be highlighted firstly in the use of average speed
for the light, medium, and heavy vehicle categories. To achieve a fully dynamic and
microscopic model, in fact, the speed of each vehicle is needed. In addition, the presented
model assumes that the traffic flows are equally distributed in both direction lanes, resulting
in possible underestimation and overestimation during special hours of the day, in which
there is a privileged direction of vehicles (for instance, ingoing or outgoing from downtown,
respectively, at the beginning and end of working days). To address such limitations, the
future steps of this research will be in the direction of the generation of a fully microscopic
model, which will take into account the single velocity of each vehicle and its position
with respect to the receiver. Finally, as discussed in the outlier analyses, there are possible
phenomena that can lead to overestimation or underestimation in the low- and high-value
regions of the considered variables. A detailed study of unconventional situations is beyond
Appl. Sci. 2023, 13, 6168
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the scope of this paper and could be a subject of further research, in which the ranges of
applicability for the model can be quantitatively estimated.
Supplementary Materials: The following supporting information can be downloaded at: https://
www.mdpi.com/article/10.3390/app13106168/s1. In particular, the calibration data and a graphical
representation of the programming lines used for the generation and calibration of the dataset are
included in the supplementary materials.
Author Contributions: Conceptualization, D.R. and C.G.; methodology, D.R. and C.G.; software,
D.R.; validation, D.R., A.M. and C.G.; investigation, D.R., A.M. and C.G.; resources, C.G.; data
curation, D.R., A.M. and C.G.; writing—original draft preparation, D.R.; writing—review and editing,
D.R., A.M. and C.G.; visualization, D.R., A.M. and C.G.; supervision, C.G.; funding acquisition, C.G.
All authors have read and agreed to the published version of the manuscript.
Funding: This research was supported by the Sustainable Mobility Center (MOST)—Spoke 7: Connected Networks and Smart Infrastructure (PNRR—Missione 4 Componente 2 Investimento 1.4—
project No. CN 00000023).
Data Availability Statement: The data used for the calibration, i.e., the database of Q, P, VL , VM ,
VH , and d used for the computation of the Leq,h according to Equations (1)–(3), are reported in the
Supplementary Materials. The data used for the validation are available upon request at http://ltms200
2-2007.ifsttar.fr/ [29] (accessed on 15 April 2023).
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
The outliers removed during the validation step are reported in Tables A1 and A2 for
the sake of clarity.
Table A1. List of overestimation outlier data.
ID
Leq,h (dBA)
VL (km/h)
VM (km/h)
VH (km/h)
P (%)
Q (veh/h)
Error (dBA)
12
221
222
1165
1166
1167
1168
1169
1170
1171
1180
1188
1190
1191
1198
1199
1201
1202
1245
1246
1247
1248
1249
1250
73.47
73.58
74.62
72.17
71.80
72.09
70.87
68.28
73.88
71.44
70.43
72.29
72.81
72.75
73.64
74.20
72.98
73.83
74.65
74.36
73.78
73.02
72.82
70.16
122.38
101.41
103.98
120.70
105.31
106.02
102.65
102.23
103.55
104.99
120.51
119.09
115.43
115.30
119.97
117.93
121.09
119.65
117.91
119.95
119.13
119.93
118.60
120.35
85.11
81.26
76.97
6.00
90.75
97.50
93.00
92.00
94.50
90.50
83.13
82.11
84.67
90.00
79.06
79.01
79.30
80.05
83.83
83.83
88.99
80.10
84.88
81.63
85.11
81.26
76.97
6.00
90.75
97.50
93.00
92.00
94.50
90.50
83.13
82.11
84.67
90.00
79.06
79.01
79.30
80.05
83.83
83.83
88.99
80.10
84.88
81.63
6.89
19.33
11.10
0.91
0.65
0.30
1.14
0.42
0.43
1.60
2.15
23.16
1.71
0.90
35.92
25.67
38.44
22.93
0.61
1.01
2.79
2.17
3.29
7.39
508
600
901
220
619
656
439
236
462
563
325
285
350
558
348
522
320
458
1315
988
610
461
334
230
4.75
4.66
4.43
12.75
5.34
5.50
5.77
6.44
8.95
4.86
4.94
4.99
7.52
5.80
4.94
4.29
4.48
4.48
4.08
4.61
5.32
6.10
6.94
5.01
Appl. Sci. 2023, 13, 6168
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Table A2. List of underestimation outlier data.
ID
Leq,h (dBA)
VL (km/h)
VM (km/h)
VH (km/h)
P (%)
Q (veh/h)
Error (dBA)
328
357
448
450
451
452
453
667
668
669
670
671
672
895
66.34
66.93
70.86
69.71
69.10
68.19
66.65
70.29
69.36
68.61
67.90
66.72
64.60
67.23
130.71
132.19
124.99
129.62
127.94
128.47
126.53
131.70
131.44
131.94
131.85
130.98
128.07
138.22
84.53
85.23
86.31
87.09
86.95
84.85
83.85
86.27
86.80
87.60
88.18
87.43
85.47
88.49
84.53
85.23
86.31
87.09
86.95
84.85
83.85
86.27
86.80
87.60
88.18
87.43
85.47
88.49
7.05
7.09
7.06
4.27
5.37
6.25
7.29
4.31
4.55
3.85
3.29
3.61
5.13
8.22
1134
1326
3101
2457
2235
2033
1495
2764
2547
2259
1855
1276
779
1095
−6.46
−6.68
−5.97
−5.91
−6.23
−6.89
−7.11
−5.97
−6.60
−6.71
−6.41
−5.99
−6.08
−6.14
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