# Calibration and Validation of a Measurements-Independent Model for Road Traffic Noise Assessment
## 2 Materials and Methods
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 \(L_{\alpha,h}\) levels and all six independent variables can be found. Equation (4) shows the details of this multilinear regression. \[L_{\alpha,h}=c_{1}A_{1}+c_{2}A_{2}+c_{1}A_{3}+c_{1}A_{4}+c_{1}A_{5}+c_{1}A_{6 }+m_{1} \tag{4}\]  
In Equation (4), \(A_{1}\) is \(\log\ Q\), \(A_{2}\) is \(\log\ V_{L}\), \(A_{3}\) is \(\log\ V_{M}\), \(A_{4}\) is \(\log\ V_{H}\), \(A_{5}\) is \(\log\ P\), and \(A_{6}\) is \(\log\ d\). In the same equation, \(c_{1}\), \(c_{2}\), etc., are the coefficients of the multilinear regression and m\({}_{1}\), 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 \(L_{\alpha,h}\) values and the same set of data, weighted by the coefficients retrieved in the previous multilinear regression, is assumed. \[L_{\alpha,h}=cX+m_{2} \tag{5}\]  
Namely, \(c\) is the coefficient of the regression, \(m_{2}\) 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):  
\[X=(c_{1}\log\ Q)+(c_{2}\log\ V_{L})+(c_{3}\log\ V_{M})+(c_{4}\log\ V_{H})+(c_{5 }\log\ P)+(c_{6}\log\ d) \tag{6}\]  
Multilinear regression, then, is a procedure used to compare the contemporary contributions of all the independent variables to the final \(L_{\alpha,h}\) 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 \(L_{\alpha,h}\) 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 Universite 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).