# Calibration and Validation of a Measurements-Independent Model for Road Traffic Noise Assessment
## 3 Results and Discussions
### Validation of Field Measurements  
Once the model was calibrated, its validity was tested by simulating the \(L_{eq,h}\) of road traffic flows observed in a real case study. The used dataset is the aforementioned dataset built by the Universite Gustave Eiffel of Nantes in the city of Saint-Berthevin  
Figure 3: (**a**) Distribution of the simulated (blue) and the measured (orange) \(L_{eq,h}\) values; (**b**) scatterplot of the computed vs. measured \(L_{eq,h}\) values. Figure 2: (**a**) Linear regression for \(L_{eq,h}\) computed values and the \(X\) variable; (**b**) distribution of residuals. 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 (\(L_{eq,15 min}\)), number of light and heavy vehicles passing by, and average speeds for these vehicle categories. First of all, the \(L_{eq}\) 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 \(L_{eq}\) values, the following formula was applied:  
\[L_{eq,h}=10\log\biggl{[}\frac{1}{4}\biggl{(}10^{\frac{L_{1}}{10}}+10^{\frac{L_ {2}}{10}}+10^{\frac{L_{3}}{10}}+10^{\frac{L_{4}}{10}}\biggr{)}\biggr{]} \tag{7}\]  
where \(L_{1}\), \(L_{2}\)..., etc., are the \(L_{eq}\) 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 \(L_{eq}\), as in Equation (7). This operation reduced the number of usable occurrences, since, in the original LTMS database, some of the 15 min \(L_{eq}\) 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 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 \(L_{eq,h}\) 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 \(L_{eq,h}\) minus the simulated \(L_{eq,h}\). Figure 4: (**a**) Errors in the model vs. measured noise levels when working on the 1-hour timespan data; (**b**) distribution of error values. 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 \(L_{eq,h}\).