
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12515-7
10.1016/j.heliyon.2024.e36484
e36484
Research Article
Road traffic noise prediction model based on artificial neural networks
Acosta Óscar oeacostaa@udistrital.edu.co
ab⁎
Montenegro Carlos cemontenegrom@udistrital.edu.co
a
Crespo Rubén González ruben.gonzalez@unir.net
b
a Universidad Distrital Francisco José de Caldas, Carrera 7 40b 53, Bogotá, 111711, Cundinamarca, Colombia
b Universidad Internacional de La Rioja, Av. de la Paz 137, Logroño, 26006, La Rioja, Spain
⁎ Corresponding author at: Universidad Distrital Francisco Jose de Caldas, Carrera 7 40b 53, Bogota, 111711, Cundinamarca, Colombia. oeacostaa@udistrital.edu.co
22 8 2024
15 9 2024
22 8 2024
10 17 e3648413 8 2024
16 8 2024
© 2024 The Author(s)
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
This paper proposes a model based on machine learning for the prediction of road traffic noise for the city of Bogota-Colombia. The input variables of the model were: vehicle capacity, speed, type of flow and number of lanes. The input data were obtained through measurement campaigns in which audio and video recordings were made. The audio recordings, made with a measuring microphone calibrated at a height of 4 meters, made it possible to calculate the noise levels through software processing. On the other hand, by processing the video data, the capacity, and speed of the vehicle were obtained. This process was carried out by means of a classifier trained with images of vehicles taken in the field and free databases. In order to determine the machine learning algorithm to be used, five models were compared, which were configured with their respective hyperparameters obtained through mesh search. The results showed that the Multilayer Perceptron (MLP) regression had the best fit with an MAE of 0.86 dBA for the test data. Finally, the proposed MLP regressor was compared with some classical statistical models used for road traffic noise prediction. The main conclusion is that the MLP regressor obtained the best error and fit indicators with respect to traditional statistical models.

Keywords

Noise
Road traffic
Machine learning
Regression
Artificial neural networks
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pmc1 Introduction

The effects of environmental noise on human health have been the subject of numerous studies and reports [1], [2], [3], [4]. Consequently, a variety of instruments and methodologies have been employed over time for the measurement and characterization of environmental noise. Furthermore, organizations such as the WHO have presented recommendations for the protection of people from exposure to environmental noise [5]. Among the sources of environmental noise, road traffic has particular significance due to the expansion of urban areas and the creation of new roads, which have resulted in an increased number of people being exposed to it. Indeed, this noise source is considered the most significant in Europe [6]. The costs associated with field measurements, which are necessary to ascertain compliance with government-mandated noise levels, are considerable. In the case of large cities, these costs are often prohibitive due to the distances and time requirements involved. Consequently, prediction models have been developed based on equations derived through statistical analysis of the relevant data.

These models are primarily developed in Europe with the objective of estimating road traffic noise levels, taking into account a range of input variables, including traffic volumes, speed, and road conditions. However, due to the fact that these data were collected in the context of each country, when they are applied to cities such as Bogota, their performance is diminished by the influence of different conditions that are not present in the original data set. In light of the aforementioned considerations, this research presents a methodology for characterizing vehicular noise and designing a model for predicting road traffic noise in Bogota. The model incorporates the distinctive characteristics of traffic in Bogota and is based on a regressor utilizing machine learning techniques.

Recently, machine learning algorithms have been used to model and predict various types of variables and have shown good performance compared to analytical methods [46], [47]. In the case of road traffic noise, one of the earliest applications of artificial neural networks (ANNs) was reported by Cammarata et al. [7]. The training data set consisted of 250 observations. The ANN had five input variables (number of cars, motorcycles, trucks, average building height, and road width). The hidden layer consisted of 20 neurons. At the output, one neuron was used to provide the Leq. Although no error indicator is provided, the comparison plots demonstrate that ANNs yielded superior results compared to the statistical methods based on logarithmic regression equations proposed by other authors. The proposal by Genaro et al. [8], published years later, utilized 200 training and 89 test data. Two distinct architectures were considered: one with 25 input variables and another with 11. Both were employed in a network with 26 neurons in the hidden layer and one output neuron estimating the Leq. The NMPB and RLS-90 statistical models exhibited overestimation of results, whereas the neural network recorded mean errors with the first configuration of 0.72 dB.

A further study on the prediction of noise levels utilizing artificial neural networks (ANNs) was conducted for the city of Tehran [9]. A total of 50 data sets were collected at a distance of less than 4 m from the edge of the nearby roadway for 5 roads at a height of 1.4 m above the ground. This data set was divided into 30, 10 and 10 for the purposes of training, validation, and testing. Additionally, five input variables were considered for training a four-neuron network in the hidden layer and an output neuron for LeqA. CoRTN, which was calibrated in another study for Tehran, was employed as a statistical model for comparison. The results of the comparisons between the calibrated CoRTN model and the neural network demonstrated no statistically significant differences. Torija et al. [10] presented a short-term (5-minute) ambient noise prediction model for the city of Granada, Spain. The model was based on a neural network and included gauging and speed data, as well as other variables such as period of the day, presence of vegetation, road geometry, and others. A total of 821 samples were available at 144 measurement points performed at 4 meters height. In addition to calculating the LeqA, the model provides output indicators of temporal variance and sound impulsivity, as well as noise levels for three frequency groups.

In their 2014 study, Nedic and colleagues [11] trained a neural network for road traffic noise prediction and compared their results with some classical statistical methods. The measurements were performed at a height of 1.2 m and 7.5 m from a two-lane road for both directions, resulting in a total of 120 samples. The input variables were vehicle capacity, categorized into four groups, and average speed. These were connected to two hidden layers, one with eight neurons and one with three neurons. At the output, one neuron delivered the Leq. In the analyzed conditions, all statistical models underestimated the noise levels. For example, for the case of RLS-90, the MAE was 11 dB. In the city of Tehran in 2018, 51 samples were taken to develop a neural network to predict vehicular noise [12]. The sound level meter was placed at a height of 1.2 m above the ground and 2 m from the road edge to take 5-min samples. Predictor variables included total traffic, percentage of heavy vehicles, gradient, speed, and information on density and reflection of buildings. A comparison with other statistical models revealed that these models overestimated the LeqA with respect to the measurements.

Finally, it is worth noting the development of a model for traffic noise prediction in the United Arab Emirates, where high temperatures represent a differential factor [13]. A total of 420 samples were collected over a 15-minute period on three roads and adjusted to one hour. The input variables included vehicle capacity by category, average speed, and road temperature. The results obtained with the neural network were compared with two statistical methods. The findings indicated that including the road temperature variable improved the accuracy of the predictions. Additionally, the researchers employed techniques to “illuminate the black box,” as neural network-based models are commonly known.

This article is made up of three main parts. The first part describes the methodology used to capture the data from which the artificial neural network was developed. Then, the descriptive statistical analysis to find the relationships between input and output variables is presented. Finally, the MLP architecture finally used and the comparison with other statistical road traffic noise

2 Methodology

Before starting the development of the predictive noise model, it is important to define the methodology to be used for the measurements. This is in order to obtain the data that will allow the definition of the input variables for the proposed model. These variables must be adapted to the conditions of the main urban roads in the city.

2.1 Bogota vehicular traffic

The main input variable for predicting traffic noise is the number of vehicles. Therefore, it is necessary to characterize the traffic in Bogota. In 2022, according to figures from the Secretariat of Mobility [14], private vehicles represented 75.5% of the vehicle fleet, while motorcycles, public service vehicles, and taxis represented 18.3%, 4.2%, and 2.0%, respectively. Based on these figures, the total number of vehicles in Bogota will double between 2008 and 2022, from 1.2 million to 2.5 million. During the same period, while the number of cars increased 2.1 times, the number of motorcycles increased 3.2 times, establishing themselves as an important means of transportation in the city with 467,422 vehicles. Public transport and taxis did not show much variation compared to motorcycles and private transport. This growing behavior of the vehicle fleet is one of the reasons for the congestion in the capital of the country. In addition, it is significant to include motorcycles as a study variable in the analysis of environmental noise in Bogota.

Regarding the age of the vehicles circulating in Bogota, it can be mentioned that in 2018, private cars were 14.1 years old on average and motorcycles were 8.4 years old. Meanwhile, public service buses and trucks for freight transport are on average 15.0 and 27.9 years old, respectively [15]. These figures are comparable to some Eastern European countries, while in Germany and France the average age of light and heavy vehicles is around 10 years [16]. Therefore, in a noise prediction model for Bogota, it is necessary to make field measurements to characterize the emissions of the vehicle fleet, given its high age and categorization (vehicle types).

2.2 Average speed

The increase in the number of vehicles in Bogota has led to a decrease in the speed of traffic on the city's roads. Data from the Secretariat of Mobility show that it went from an average of 30.73 km/h in 2005 to 24.86 km/h in 2015 [17]. Similarly, in Bogota, the average speed is maintained below 30 km/h during peak hours (6:00-20:00). Outside this period, the average maximum speed is close to the current 50 km/h limit in the city. Under these conditions, the predominant primary source of road traffic noise is the powertrain.

2.3 Measurement points

Using the urban area of Bogota as a reference, 30 geographical points were selected, located on the arterial and secondary road network of the city, as shown in Fig. 1. These points were chosen because they are located in areas of high vehicular traffic, where road traffic noise is the most relevant source of noise pollution.Figure 1 Measurement points (EPSG:WGS84).

Figure 1

Moreover, the points were distributed throughout the city because the research sought to cover as many variations in traffic noise behavior as possible (congestion conditions, speed, vehicle capacity, etc.). However, due to resource limitations, the location of each measurement point was optimized to take into account the typical characteristics of the avenue sections (type of pavement, cross-section, number of lanes, etc.).

2.4 Data collection

It was determined to measure at 4.0 meters above ground level. Although the main related international standards [18], [19] follow measuring at 1.2 meters from the ground, in everyday urban environments where spaces are not controlled, reflections from the ground and the influence of other noise sources different from road traffic such as pedestrians, and commercial activities, has a direct impact on the measured noise level. In addition, current local regulations require measurements at 4 meters for environmental noise assessment.

On the other hand, each point was located 7.5 meters from the center of the nearest road or lane following the recommendations of the ISO 362 [19] and 11819-1 [18] series of standards. In cases where it was not possible to comply with these distances, the correction -10log(distance/7.5 m) was made: Likewise, a distance from the microphone to the facade or reflective surface (other than the ground) greater than 25 meters was sought. This is based on ISO 11819-1, a standard that is better suited to the measurement of varied traffic on different surfaces. Otherwise, as intermediate roads, corrections were applied based on ISO 1996-2 (microphone between 0.5 m and 2.0 m 3 dB correction). The lane section considered was 40 m (based on ISO 362).

Video and audio data were recorded at each geographic point. At least 2 samples were taken to have fluid and congested traffic, and the minimum sample time was 20 minutes. Any unwanted sound events, such as the honking of horns, the passage of aircraft, and the sound of ambulances, were removed from the audio recordings prior to the calculation of road traffic noise. The measurement campaigns were carried out between 2021 and 2022, after the pandemic-related mobility restrictions had been lifted.

The acoustic indicators were obtained by processing the audio recorded by a USB measurement microphone (Umik-1) with the dBFA Suite software. It is worth mentioning that the microphone was calibrated with a pistophone at 114 dB before and after each sample. In addition, a study was performed to validate the accuracy of this measurement approach before the audio data were collected in the measurement campaigns. This study found that the differences between the USB microphone (after frequency response curve adjustment) and a Type 1 sound level meter were 0.1 dBA and 0.2 dBZ in RMSE. A detailed description of this process can be found in [20].

Meanwhile, through video, the vehicle capacity and speed were automatically obtained. Related to the first, in the same study mentioned above ([20]), it can be said that the approximation error calculated was 3.3%, -2.2%, -15.5% and -10.7% for motorcycles, light, medium and heavy, respectively, when comparing manual and automatic counting. On the other hand, the difference between the average speed obtained manually and by software is about 2 km/h. This corresponds to a relative error of 5.6%. This error would have little impact on the estimation made with the prediction model proposed at the end of this paper, considering that the relationship between vehicle speed and noise emission is logarithmic ([42]).

Among the main challenges of information preprocessing, we can highlight the identification and elimination of audio events not associated with rolling noise. The time needed to process the raw video/audio data to select the samples can also be mentioned. Also, from the raw video data processed with Python, it took some time to obtain the capacity and speed data. All this in order to get an optimal database for training regressors based on machine learning.

Finally, it is noteworthy that the data recording was performed at the points indicated in Fig. 1 when the acceleration had already ceased.

2.5 Dataset

The initial step for the creation of the dataset, which would subsequently be employed for the training of the algorithm, was the selection of the time interval at each point. In order to achieve this, one of the samples was divided into sections according to the total measurement time. Initially, an interval of two minutes was selected, resulting in the collection of ten samples. The initial interval was selected based on the traffic light cycle time (2 min.). This time was measured at the majority of the points analyzed that had this traffic regulation system. Subsequently, pairs of contiguous samples were aggregated, resulting in five samples of four minutes. This was done to complete the total sample time, which was 20 minutes in total. This process was repeated until two samples of ten minutes were obtained. In each division of the dataset, the input variables and noise levels were obtained with the statistical descriptors mean (x‾), standard deviation (σ), and coefficient of variation (C.V.).

The difference between the LeqA obtained during 20 continuous minutes, two intervals followed by 10 minutes, and three intervals followed by 6 minutes was a maximum of 0.1 dBA. Similarly, when compared to five 4-minute back-to-back intervals, the difference widened to a maximum of 0.3 dBA. Finally, the differences in LeqA when measuring 20 minutes and 2-minute intervals was a maximum of 0.7 dBA. This value is within the stabilization interval of ±1 dB proposed by other studies in environmental noise studies [21]. Likewise, it can be observed that the coefficients of variation for all acoustic indicators, from the 2-minute samples, were below 3%, indicating homogeneity in the data. Based on the aforementioned considerations, it was determined that the 2-minute interval would be most appropriate for the creation of the data set. This approach allowed for the modeling of a greater number of scenarios where the cause-effect relationship between input and output data was evident, without necessitating an increase in the resources of the research.

To provide additional context, Fig. 2 illustrates the LeqA variations across four time intervals for the same sample, up to minute 10. It can be observed that the discrepancy between the LeqA values for the two time intervals, namely the two-minute and ten-minute windows, is 0.3 dBA. Therefore, despite the greater number of vehicles in the 10-minute interval relative to the 2-minute interval, the equivalent level remains comparable due to the averaging of energy over time with similar amplitude values. It is important to note that the model obtained in the present investigation is based on short-time measurements, where there are no significant variations in the characteristics of the source during the observation window.Figure 2 LeqA values for a given sample in a series of time intervals.

Figure 2

3 Exploratory data analysis

Once all the information had been processed, a total of 431 samples were obtained at the 30 selected points. To ensure comparability with other existing models, the gauging data were linearly extrapolated to one hour.

3.1 Input variables

Table 1 presents a summary of the descriptive statistics. With regard to vehicle capacity, the majority of the data was composed of light vehicles (60.1%), followed by motorcycles (30.5%). The remaining data was divided between medium and heavy vehicles (8.1% and 1.3%, respectively). It should be noted that these overall percentages reflect the distribution of capacity across all samples, and that variations may be observed within each sample. Similarly, the total capacity (q) indicates that the data encompasses a range of values, from 330 vehicles per hour to 9120 vehicles per hour. With regard to the data on medium and heavy vehicles, the results of the coefficient of variation (C.V.) are noteworthy, particularly in light of the low or null presence of this category in some samples analyzed.Table 1 Statistical descriptors for input data (significance value α = 5% for K-S). Motorcycles, light, medium, and heavy correspond to the number of vehicles in these categories per hour. The variable q represents the total vehicle capacity per hour. The speed of the traffic is given in kilometers per hour. The number of lines in the analyzed segment is the variable lanes. The variable flow is a categorical dimensionless variable that is explained at the end of section 3.1.

Table 1Stat.	Motorcycles	Light	Medium	Heavy	q	Speed	Lanes	Flow	
x‾	1.16k	2.29k	0.31k	.05k	3.82k	40.8	4.3	1.2	
σ	0.92k	1.33k	0.31k	.09k	2.30k	11.7	1.2	0.7	
Min.	30.0	210.0	0.0	0.0	330.0	13.3	2.0	0.0	
Max.	4.92k	5.52k	1.65k	0.45k	9.12k	60.1	6.0	2.0	
Range	4.89k	5.31k	1.65k	0.45k	8.79k	46.8	4.0	2.0	
IQR	1.17k	2.1k	240.0	60.0	3.69k	14.6	2.0	1.0	
C.V. (%)	79.4	57.5	100.3	160.1	60.1	28.7	27.9	59.3	
Kurtosis	1.5	-0.7	4.9	4.8	-0.8	-0.3	-0.9	-0.9	
Asy. Coe.	1.2	0.5	2.2	2.2	0.5	-0.7	-0.3	-0.2	


	
Kol. Smi.	p<0.001	


	
Proportion	30.5%	60.1%	8.1%	1.3%					

With respect to speed, data were recorded from 13.3 km/h to 60.1 km/h, thereby enabling the acquisition of information pertaining to fluid and congested traffic. Although the mean value was 40.8 km/h, the coefficient of variation is close to 30%, indicating high variability and rendering the mean an inadequate representation of the data set. It is noteworthy that the aforementioned observations pertain to all input variables where the coefficient of variation was within the range of 30% or greater, thereby indicating a heterogeneous behavior of the data [22]. It should be noted, however, that the samples were collected in a field setting where complete environmental control is not feasible. Additionally, the diversity of traffic patterns in urban areas and the extensive range of conditions represented introduce further complexities. This enables the representation of diverse scenarios regarding the behavior of noise caused by vehicular traffic in urban areas. Furthermore, the statistical descriptors presented in Table 1 demonstrate that the gauges and speed do not exhibit a normal statistical distribution. For the training of the model based on automatic learning (Section 4), we employed algorithms that do not require this condition to be explicitly met.

In order to take into account the physical characteristics of the road, the number of lanes was included as a variable in the analysis. In order to obtain a representative sample, a variety of streets and avenues with different numbers of lanes were selected for measurement. These included streets and avenues with two, three, four, five, and six lanes. The majority of the data were collected on principal thoroughfares (Fig. 1) with high vehicular capacity, where noise pollution due to vehicular traffic is more prevalent. Finally, the condition of vehicular traffic was taken into account with the flow variable, which was deemed to be of importance due to the daily traffic jams that are a common occurrence in Bogota. This nominal categorical variable was transformed to a discrete numerical variable in the following way: 0 = traffic congestion, 1 = periodic (flow control by traffic lights), 2 = fluid.

3.2 Output variables

With regard to the output variables, the data exhibit less dispersion in comparison to the input variables. The coefficient of variation (C.V.) ranges from 4.8% to 7.2%. The normality and descriptor tests presented in Table 2 indicate that the distributions are not Gaussian. In general, the equivalent noise levels (LeqA) commence at 59.8 dBA and reach a maximum of 77.3 dBA. The frequency bands with the highest energy are 1000 Hz and 2000 Hz, followed by 500 Hz, 250 Hz, and 4000 Hz. This behavior is typical of road traffic noise when applying type A frequency weighting.Table 2 Statistical descriptors for noise indicators (significance value α = 5% for K-S). LeqA represent the equivalent noise level. The other columns contain the equivalent acoustic energy per band frequency.

Table 2Stat.	LeqA	63 Hz	125 Hz	250 Hz	500 Hz	1 kHz	2 kHz	4 kHz	8 kHz	
[dB]	
x‾	71.6	49.5	56.4	60.2	63.5	67.3	65.6	59.8	50.5	
σ	3.4	3.6	3.7	3.7	3.6	3.7	3.4	3.4	3.6	
Min.	59.8	36.3	41.6	46.7	51.9	55.6	53.1	47.0	38.3	
Max.	77.3	57.8	63.9	67.4	72.0	73.4	71.1	66.3	58.5	
Range	17.5	21.5	22.2	20.7	20.1	17.8	18.0	19.3	20.2	
IRQ	4.3	4.5	4.6	4.9	4.5	5.1	4.4	3.9	4.2	
C.V. %	4.8	7.2	6.6	6.2	5.7	5.4	5.2	5.6	7.0	
Asy. Coe.	-1.0	-1.0	-1.0	-0.7	-0.7	-0.9	-0.9	-1.0	-0.7	
Kurtosis	0.7	0.9	1.1	0.5	0.3	0.4	0.6	0.9	0.6	


	
Kol. Smi.	p<0.001		

3.3 Relationship between variables

The initial correlation matrix (Fig. 3) indicated that all input variables, except speed and flow, displayed correlation coefficients between 0.40 and 0.66 with regard to the output data. This suggests that there is a moderate to strong direct relationship between the gauging and noise level data, as proposed by Cohen [23], [24] and Weinberg & Abramowitz [25]. Similarly, it can be observed that the correlation coefficients for LeqA are higher for each vehicle category in the following order: light, motorcycles, medium, and heavy. This can be attributed to the proportion in which each category participates in the total gauging. However, it is noteworthy that, despite representing 8% and 1% of the total proportion of medium and heavy vehicles, these types of vehicles exhibit correlation values above 0.41 in all scenarios. In contrast, the lanes variable exhibited the second-highest correlation with respect to LeqA, reaching a coefficient of 0.6.Figure 3 Correlation matrix input and output data.

Figure 3

With regard to motorcycles, the lowest correlation value is evident in the 1000 Hz band, wherein rolling noise is typically observed. This finding may be attributable to a comparatively diminished presence of these vehicles, potentially due to the limited interaction surface between the tire and pavement. In contrast, light vehicles and speed demonstrate higher correlation values in this same band, which would be in alignment with the aforementioned observations regarding rolling. Similarly, motorcycles exhibited the highest correlation for low (63 Hz, 125 Hz) and high (4 kHz, 8 kHz) frequencies, which can be substantiated by their emission spectrum and percentage of participation in the total capacity.

The correlation coefficient between speed and the total noise level LeqA is relatively low (r = 0.29). In this variable, only the 1 kHz and 2 kHz frequency bands exhibited moderate correlations, while the other bands displayed relatively weak relationships [23], [24], [25]. This finding aligns with those of other studies that have observed the emission spectrum of light and medium vehicles to concentrate its energy in these medium frequencies [26]. Therefore, it can be inferred that the inclusion of this independent variable will facilitate the modeling of this characteristic of road traffic noise observed in the study areas. Finally, vehicular flow demonstrated a behavior analogous to speed, exhibiting higher correlation values in the central bands of 500 Hz, 1000 Hz, and 2000 Hz.

Similarly, the interrelationships between the independent and dependent variables were subjected to analysis. The data are presented in Fig. 4. The positive logarithmic correlation between all variables except speed and flow is noteworthy. Motorcycle, medium, and heavy vehicles exhibited some discrepancies and groupings with respect to total equivalent noise levels (LeqA) and by frequency bands. This was observed during the fieldwork, where in all the samples taken, there was always a presence of light vehicles, but vehicles of the other categories could be absent. For example, on secondary roads, the presence of light vehicles is rare, and heavy vehicles are absent.Figure 4 Relationship between input variables and noise levels.

Figure 4

4 Regression algorithms

Once the data had been subjected to characterization and the relationships between the different study variables had been analyzed, the machine learning model was selected. The programming language utilized was Python, with the Scikit-learn library. The selection was based on the extensive development that has taken place in the implementation of machine learning algorithms in that platform, as well as its popularity and comprehensive documentation available [27]. In this study, we chose to work with regression models supported in supervised input because we had labeled samples of the input and output variables [27]. The flowchart shown in Fig. 5 presents the procedure performed for training and validation.Figure 5 Flowchart used to build machine learning models.

Figure 5

The data were processed and visualized using a variety of libraries, including Pandas, Numpy, SciPy, Plotly, and Scikit-learn. The data were loaded from a text file containing the results of all measurements with the variables described in Section 3 of this document. Subsequently, the dataset was separated into two parts, training and test, in a ratio of 75% to 25%, respectively.

In order to identify the optimal hyperparameters for each regression model and assess their performance concurrently, the grid search technique was employed using Scikit-Learn's GridSearchCV. This function enables the user to define ranges and intervals for the hyperparameters of the models. Subsequently, the combination of these parameters allows for the identification of those that demonstrate the best performance according to an error or fit indicator. The incorporation of cross-validation within GridSearchCV obviates the necessity for the creation of an additional independent set for validation. Similarly, this process reduces the impact of randomness in the assessment of the model's performance, while facilitating more effective data management.

Once the optimal hyperparameters had been identified, we proceeded with the training of each regression model. Their performance was evaluated using the test data set, with particular attention paid to the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and coefficient of determination (R2). It is also noteworthy that standardization was applied to the predictor variables at the time of training and testing the regression models that benefit from this process.

4.1 Results obtained with the regressors

Following the acquisition of the hyperparameters for the regressors outlined in the preceding sections, we proceeded with the training and testing of each one. It should be noted that the test data set utilized was independent and separated from the outset, as previously stated in this chapter. The outcomes of this process are presented in Fig. 6. A lower density of points is evident below 69 dBA. This is due to the fact that the majority of samples were collected on major roadways, where noise levels exceeded this value. However, these low values were excluded because they align with the logarithmic behavior of road traffic noise with respect to vehicular flow.Figure 6 Measured vs estimated data with regression algorithms.

Figure 6

The MLP algorithm exhibited the most favorable performance, with an MAE of 0.86 dBA, an RMSE of 1.14 dBA, and a R2 value of 0.88. For this reason, the MLP was selected for comparison with statistical models that are typically employed in commercial software for road traffic noise prediction. Fig. 6e illustrates that the measured data and estimated data, generated by this algorithm, exhibit the smallest amplitudes in both the prediction and confidence intervals (of the mean), indicating a lower variance in the prediction.

The results obtained with decision trees exhibited the highest error and lowest fit compared to the other algorithms. As illustrated in Fig. 6c, several points are stacked vertically, indicating their location in plateaus defined by the shape of the tree. This results in many regression outputs having the same value at certain intervals. Nevertheless, the random forests corrected this problem by getting closer, but still ranked second to last. Notably, some points are far from the prediction interval.

Table 3 illustrates the error and fit indicators with the MLP algorithm as a reference point. It should be noted that the improvements in MAE range from 9.3% to 20.9%. With respect to the RMSE, the performance improves from 8.8% to 28.9%. Therefore, the MLP-based regression model, according to the RMSE, would have fewer large errors compared to the other models. This is illustrated in Fig. 6e, where the extreme points are situated closer to the prediction interval. Finally, for the R2 fit, the percentages are lower, but nevertheless fall within the range of 3.4% to 10.2%.Table 3 Error indicators and adjustment of regressors with all input variables.

Table 3Regression	Error and adjust	Relative Error	
MAE	RMSE	R2	MAE	RMSE	R2	
MLP	0.86	1.14	0.88	0.0%	0.0%	0.0%	
SVR	0.94	1.26	0.85	9.3%	10.5%	3.4%	
k-NN	0.96	1.24	0.85	11.6%	8.8%	3.4%	
Random forest	1.00	1.31	0.83	16.3%	14.9%	5.7%	
Decision tree	1.04	1.47	0.79	20.9%	28.9%	10.2%	

5 MLP regression model

The main hyperparameters considered to obtain the architecture of the MLP regressor were: number of hidden layers, activation function for the hidden layer, solver for weight optimization and alpha. More details can be found in Scikit-learn documentation [43].

The grid search approach produced a total of 18000 combinations. It was determined that the solver and activation function that gave the best results were sgd and tanh, respectively. Once these first two hyperparameters were defined, the MAE was calculated by varying the number of neurons in the hidden layer. The best MAE values (0.86 dBA) were found for architectures with a hidden layer of 26, 35, and 38 neurons and alpha = 0.001. However, in order to have a simplified architecture that consumes less computational resources, the lowest value of hidden layer neurons was used.

After establishing that the MLP-based regression model yielded the most optimal outcomes, we proceeded to employ diverse methodologies to elucidate the internal dynamics and interactions between the input and output variables. The principal findings are presented below.

5.1 ANN diagram

Over time, a number of approaches have been put forth with the aim of interpreting the connections and weights between neurons that comprise an Artificial Neural Network (ANN). One such approach, proposed by Özesmi et al. [28], involves the plotting of connections with positive and negative weights in black and gray colors, respectively. In addition, the thickness of the connection is directly proportional to its absolute value. This principle was employed to generate a graphical representation of the MLP regressor architecture presented at the conclusion of Section 4. A Python library was employed for this purpose, which enables the plotting of ANNs from their weights and connections [29], but with the limitation of not showing the bias. However, this library does not display the bias. This library was adjusted using orange color for positive connections and gray for negative ones. Likewise, after observing all the weights, a “pruning” of the ANN was made showing the most relevant connections, for the present study absolute value greater than 1, as shown in 7.Figure 7 ANN diagram.

Figure 7

The interpretation of the neuronal diagram is based on an approximation of the signs of the weights and the interaction between neurons [30]. Accordingly, the orange lines represent excitatory signals, whereas the gray lines indicate inhibitory ones. In consideration of the conventions observed for the input layer in Fig. 7, it can be stated that the variables with the most significant impact are lanes, flow, light, fast, and medium. These variables predominantly generate inhibitory signals towards the hidden layer, except lanes and light, which generate a notable excitation signal. The output signals from motorcycles and medium-sized vehicles were relatively weak. Conversely, it is notable that these connections, upon reaching the hidden layer, exhibited outputs with relatively minor excitatory signals, compared to the other neurons in the hidden layer that had weak inputs. However, it is challenging to identify a completely identical order of importance in the variables indicated by the correlation in Fig. 3. Therefore, alternative approaches to understanding the model and exploring the importance of the variables are being investigated further.

5.2 Residual analysis

As part of the study of the model behavior, a residual analysis was conducted. For this, the measured noise values were compared to those predicted by the MLP model using the test data set.

First, the distribution of the residuals was obtained. This showed concentrations around 0 dB (Fig. 8a). Subsequently, a K-S statistical test was conducted (with a significance value of α = 5%), yielding a p-value of 0.087. This indicated that the data may be drawn from a normal distribution. This conclusion was further supported by the Q-Q plot (Fig. 8b), which demonstrated that the majority of observations aligned with the straight line. Furthermore, it is evident that there is a greater concentration of data towards the center of the line, accompanied by a more pronounced dispersion at the ends, which is indicative of long tails. This observation aligns with the histogram.Figure 8 Ordinary residuals MLP regressor.

Figure 8

A residual vs. predicted LeqA plot revealed that the data is distributed around zero in general (Fig. 8c). However, in some areas, concentrations may be observed that could arise due to samples sharing similar characteristics. Additionally, a higher density of data is observed between 68 dB and 76 dB, which is consistent with the majority of data captured in the field being within this interval, which encompasses the main roads. While the elevated noise levels resulting from road traffic are a significant concern, future models must incorporate a greater number of measurements in areas with minimal vehicular traffic. This enhances the quality of the data and addresses this issue more effectively. Fig. 8d presents the box plot, which once again reveals the long tails and concentration of data around zero. It is notable that four outliers are present, three of which show positive differences, indicating underestimation of the model. These outliers correspond to two points taken on two-lane roads with low capacity and traffic-light controlled flow, where the influence of other noise sources different from road traffic is evident. The other point corresponds to a five-lane main street with fewer motorcycles and medium-sized vehicles. In contrast, an atypical value of -3 dB (overestimation) was presented for a four-lane road with continuous flow. Despite having higher flows than its peers, the noise values measured were not higher than 1 dB.

5.3 Permutation feature importance

Models based on ANNs are frequently classified as “black boxes” due to the lack of knowledge regarding the relationships between the variables involved. In light of this, various authors have put forth methodologies aimed at “illuminating” these black boxes and gaining deeper insights into their internal workings ([30], [31], [32], [33]). New approaches to determine the importance of input variables have been proposed based on the proportion by which the total variance of the predicted variable changes when each input variable is permuted in turn ([34]). These approaches have demonstrated an accuracy above 95% in most tests performed, and they fit well for data sets with linear and nonlinear relationships. Additionally, this method, which was initially used with the R2 fit indicator, can be applied with RMSE or MAE in the case of regression problems.

In light of the aforementioned considerations, the present research employs an algorithmic approach based on the permutation of input variables to ascertain the relative importance of predictor variables. To this end, the permutation feature importance tool, accessible via the Scikit-Learn framework, was employed. This process was then applied to the test data set, with MAE employed as the metric. First, one of the input variables is permuted, and the resulting error is evaluated with the selected metric. Then, the difference between the metric before and after the permutations is calculated, allowing the importance of that predictor variable in the model to be determined. Due to this difference, the result is presented in terms of the loss of precision of the metric. This process is performed for all variables in the case of regression problems.

The results of the permutation are displayed in Figs. 9a and 9b. The box diagram presents the results in a tabular form, whereas the bar diagram depicts the mean amplitude of the variables in each bar, with a central line representing the standard deviation. This analysis revealed that, for the model obtained, all variables considered generate mean MAE variations with values ranging from 0.44 dB to 0.93 dB. This is significant, as despite observing similar behaviors for the flow-rapidity and lane-height variables in the descriptive statistical analysis of Section 3 (Fig. 3), it can be concluded that the predictor variables do not exhibit strong collinearity effects.Figure 9 Loss of accuracy using permutation of variables.

Figure 9

The four most important input variables were identified as light, number of lanes, vehicle flow type, and motorcycle traffic. This was followed by heavy vehicles, medium vehicles, and speed. This order of importance is consistent with the correlation values obtained in Fig. 3. It can be seen that this is how the model captures the relationships between variables found in the initial exploratory analysis. It is notable that the type of vehicle flow is the third most relevant variable, a situation that differs from the correlation study where it was placed second to last.

It should be noted that the results obtained represent the importance of the input variables for the model obtained by MLP under the conditions in which it was trained. Other architectures and configurations of the MLP regressor may generate different orders of importance.

5.4 Comparisons of measurements, simulation, and ANN

The regressor obtained by MLP was compared with five statistical models used for road traffic noise prediction. The first of these is CoRTN [35]. In this model, the L10A percentile was estimated for one hour and then the equation 0.94LA10,1h+0.77 was applied to obtain the equivalent level. Additionally, the calculations were adjusted to account for geometric divergence, heavy vehicle correction, and surface area. The second model was the RLS-90 [36]. As with the CoRTN model, the correction for own geometric divergence was considered.

Consequently, as a result of the elevated complexity of the models, software was employed. To this end, geographic information layers were created to represent roads and receptors, to which the input variables were subsequently added. The aforementioned layers were then imported into a simulation software program, which enabled the calculation of the LeqA at each point over the course of one hour. In regard to the USA TNM model, its values were obtained through the use of TNM software [37]. Conversely, for the CNOSSOS-EU [38] and NMPB Routes-96 [39] models, CadnaA was employed. It is noteworthy that vehicle capacity data by category was entered for both the CNOSSOS-EU and TNM models.

Once all the estimates were in hand, a classification was made of the differences between the measurements and the calculations for all the models (Δ). To facilitate the grouping of the data, three categories were established: differences greater than 2 dB (Δ>2dB), differences less than 2 dB (Δ<2dB), and the interval between the two previous categories (−2dB≤Δ≤2dB). This approach was taken in accordance with the recommendation of the European Commission for the evaluation of noise exposure, which suggests an absolute accuracy of 2 dB in noise maps [40]. As illustrated in Fig. 10, the proposed model with the MLP regressor exhibited the most favorable performance, with 90% of the samples exhibiting differences within the −2dB≤Δ≤2dB interval. The remaining 10% was distributed almost equally across the other two categories. This is further supported by the findings presented in Fig. 7e, which illustrate that the width of the 95% confidence interval was 4.5 dB, resulting in four samples (out of 108) being identified as outliers in Fig. 8d.Figure 10 Grouped differences between measurements and prediction models in percentage.

Figure 10

The second best-performing model was CoRTN, with 50% of the samples falling within the −2dB≤Δ≤2dB interval. Subsequently, the following models were identified in descending order of performance: TNM, CNOSSOS-EU, RLS-90, and NMPB Routes 96. It is notable that, in contrast to CoRTN, the majority of the other models exhibited a tendency to overestimate the LeqA values, with a particularly pronounced effect observed in NMPB-96 (87%) and RLS-90 (67%). This discrepancy can be attributed to two primary factors. Firstly, the emission database on which these models were based was created in the 1980s [41], [36], when the physical technical characteristics of vehicles differed from those of today. In this regard, it was initially anticipated that the results would be more closely aligned with those of the two models (RLS-90 and NMPN Routes-96) due to the age and characteristics of the city's vehicle fleet as described in Section 2. However, this did not occur. Secondly, the statistical models are primarily employed for continuous flow modeling on freeways, which differs from the conditions typically encountered in Bogota. The error and fit indicators serve to corroborate the order of performance of the aforementioned models (Table 4).Table 4 Error and fit indicators for prediction models.

Table 4Model	Error y fit	Absolute error	
MAE	RMSE	R2	MAE	RMSE	R2	
MLP	0.86	1.14	0.88	0.00	0.00	0.00	
CoRTN	2.18	2.73	0.57	1.32	1.59	0.31	
TNM	2.73	3.23	0.58	1.87	2.09	0.30	
CNOSSOS-EU	2.75	3.17	0.65	1.89	2.03	0.23	
RLS-90	3.34	3.78	0.61	2.48	2.64	0.27	
NMPB Routes-96	4.70	5.31	0.48	3.84	4.17	0.40	

Upon examination of the prediction outcomes for each point in the test set (Fig. 11), it was discerned that the majority of samples exhibiting overestimation were associated with roadways comprising four or more lanes. The most prevalent measurement points were identified as 2 and 3 (specifically the Avenida Ciudad de Cali and Avenida Calle 17). These points are notable for their high prevalence of heavy and varied traffic conditions, given the presence of vehicles transporting cargo to and from Bogota city. In contrast, the samples with underestimation are predominantly associated with points 21, 22, 23, and 12 (Autopista Norte and Av. Americas). In these locations, there was no presence of heavy vehicles during the measurements. From this perspective, when employing statistical techniques, a comprehensive examination of this variable is essential, and adjustments should be investigated to ensure its alignment with the traffic conditions in Bogota. Ultimately, the optimal fit of the proposed model in these scenarios is emphasized.Figure 11 Measurements and calculations results with ANN and statistical models.

Figure 11

6 Future work

The model estimates the LeqA emission at 7.5 meters from the center of the nearest lane and at a height of 4 meters. The following variables were considered: light vehicle, motorcycle, medium, heavy, speed, number of lanes and type of flow. However, it would be worthwhile to study other variables such as building density, slope (in areas where applicable) or the presence of atypical noise events, as studied by other authors [8], [10]. Similarly, the situation in sections with intersections, such as roundabouts, can be studied [44], [45]. In addition to the above, the output variables can be extended to include other acoustic descriptors (L10, L90, etc.) and levels by octave bands or groups of them.

On the other hand, larger databases and more robust models could be trained with noise monitoring systems that allow continuous audio and video recording and automatic processing. It would also be possible to work with longer time windows to assemble the data set. In addition, it would be possible to identify events and classify acoustic sources.

Finally, it is important to keep in mind that the proposed model has been trained with data that are in accordance with the traffic conditions of the city of Bogota. Therefore, its use in other locations will require the acquisition of new data that take into account the variables that have an impact on road traffic noise in that environment.

7 Conclusion

A model for predicting road traffic noise is proposed to provide information to support the management of noise pollution in Bogota, taking into account some characteristics of Bogota traffic. For this purpose, after obtaining data on noise, capacity, speed, type of road and traffic flow, a regression model based on Artificial Neural Networks (MLP) has been developed. With the above input variables, the proposed model estimates the LeqA emission at a distance of 7.5 m from the center of the nearest center at a height of 4 m. The results showed that the trained model had the best performance when compared to statistical methods typically used to estimate noise from this acoustic source. Of the 108 samples that made up the test data set, 90% were found to be within the ± 2 dB error interval suggested by the European Commission for noise exposure assessment. Meanwhile, the CoRTN, RLS-90, TNM, CNOSSOS-EU and NMPB Routes-96 models recorded percentages of 50, 27, 38, 36 and 11.2, respectively, for the same interval. In terms of MAE, the proposed MLP-based model showed a value of 0.86 dBA. While for the other models, the MAE ranges from 2.18 dBA to 4.70 dBA following the same order mentioned above. The MLP model also had better RMSE error and R2 goodness of fit indicators.

CRediT authorship contribution statement

Óscar Acosta: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Visualization, Writing – original draft. Carlos Montenegro: Conceptualization, Funding acquisition, Project administration, Resources, Writing – review & editing. Rubén González Crespo: Project administration, Supervision, Validation, Funding acquisition, Writing – review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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