# Calibration and Validation of a Measurements-Independent Model for Road Traffic Noise Assessment
## 3 Results and Discussions
### Simulation and Calibration Results  
Data obtained from simulations of the 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 heavy vehicles at different speeds at the center of the carriageway. This dataset simulates the collection of the independent values used for the computing of \(L_{eq,h}\) according to [PERSON] et al. [14]. In each step of \(Q\) 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 \(L_{eq,h}\) 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 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 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. Figure 1: Flowchart of the generation of the model in three steps: simulation, calibration, and validation. A closer look at the dataset makes evident that the strictest dependence is the one between \(L_{\alpha\alpha,h}\) and \(d\) since the highest values of emitted noise (\(L_{\alpha\alpha,h}\) 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, R\({}^{2}\), BIC, and AIC; then, the authors decided to apply the OLS model. Table 2 shows the results of the linear regression between \(L_{\alpha\alpha,h}\) and the independent variables. Values of all the intercepts and regression coefficients are listed, together with R\({}^{2}\), AIC, and BIC.