# Calibration and Validation of a Measurements-Independent Model for Road Traffic Noise Assessment
## 2 Materials and Methods
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: \(V_{L}\), \(V_{M}\), and \(V_{H}\). 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 \(L_{eq,h}\), completing the dataset. \(L_{eq,h}\) computing starts from the computing of the power levels, \(L_{W,L}\), \(L_{W,M}\), and \(L_{W,H}\), 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 [PERSON] et al. [26]:  
\[\left\{ \begin{array}{l}L_{W,L}=31.13\log_{10}\left(V_{L}\right)+12.77+20\log_ {10}(d_{0})+11\\ L_{W,M}=18.765\log_{10}\left(V_{M}\right)+43.697+20\log_{10}(d_{0})+11\\ L_{W,H}=12.831\log_{10}\left(V_{H}\right)+58.27+20\log_{10}(d_{0})+11\end{array} \right. \tag{1}\]  
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 [PERSON] et al. [14]. \[\left\{ \begin{array}{l}SEL_{L}=10\log_{10}\left(Q_{L}\right)+L_{w,L}-20 \text{log}_{10}(d)-11\\ SEL_{M}=10\log_{10}\left(Q_{M}\right)+L_{w,M}-20\text{log}_{10}(d)-11\\ SEL_{H}=10\log_{10}\left(Q_{H}\right)+L_{w,H}-20\text{log}_{10}(d)-11\end{array} \right. \tag{2}\]  
In these equations, the sound exposure levels (\(SEL\)) are computed as a function of the number of vehicles moving (\(Q_{L}\), \(Q_{M}\), and \(Q_{H}\), respectively, the number of light, medium, and heavy vehicles); the power levels, \(L_{W}\); 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 \(L_{eq,h}\) values with Equation (3):  
\[L_{eq,h}=10\log\biggl{(}\frac{1}{3600}\biggr{)}+10\log\biggl{(}10^{\frac{SEL_ {L}}{10}}+10^{\frac{SEL_{M}}{10}}+10^{\frac{SEL_{H}}{10}}\biggr{)} \tag{3}\]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).