# Optimized Sensors Network and Dynamical Maps for Monitoring Traffic Noise in a Large Urban Zone
## 4 Results
### Correlations between Sensor Locations: How to Optimize the Network
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(g_{i}\) & \(\left\langle\boldsymbol{e_{\text{Leq}}}\right\rangle_{\text{N}}\) & \(\left\langle\boldsymbol{e_{\text{Leq}}}\right\rangle_{\text{C}}\) & \(\left\langle\boldsymbol{e_{\text{Leq}}}\right\rangle_{\text{M}}\) \\ \hline
1 & 5.3 & 5.1 & 5.2 \\
2 & 4.2 & 3.2 & 2.8 \\
3 & 2.5 & 2.5 & 2.8 \\
4 & 5.3 & 2.4 & 2.1 \\
5 & 2.6 & 2.4 & 2.2 \\
6 & 3.4 & 1.3 & 1.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Mean group deviations (in dB) of Dynamap predictions from measurements, for groups (\(g_{1}-g_{6}\)). Here, \(\left\langle\boldsymbol{e_{\text{Leq}}}\right\rangle_{\text{N}}\) are the deviations obtained without systematic error corrections, \(\left\langle\boldsymbol{e_{\text{Leq}}}\right\rangle_{\text{C}}\) those obtained with systematic error corrections, and \(\left\langle\boldsymbol{e_{\text{Leq}}}\right\rangle_{\text{M}}\) the median of the corrected group predictions [91]. over the day, while, for P2, it clearly retains the typical shape observed in the original noise profiles (see, e.g., Figure 7). The median correlation coefficients obtained for P1 and P2 are shown in Figure 11, as a function of time interval \(\tau\). The reported 'error' bands correspond to the median absolute deviation, MAD = \(\mid x_{i}-\widehat{X}\mid\), where \(\widehat{X}=\text{median}(X)\) and \(X\equiv(x_{1},\dots,x_{n})\) is a generic time series. As one can see from Figure 11 in the case of P1, the median correlation coefficients over all stations \(s_{j}\) are quite small (\(\sim\)0.1-0.2). This is because procedure P1 removes all long period fluctuations, thus only high frequency fluctuations remain (see [92; 93], where a power-spectrum analysis in the frequency domain has been performed). These results suggest that, on average, short time (high frequency) correlations among stations are low, as we expect from a 'well-designed' network. The situation changes a bit if one looks in more detail to intra-group correlations separately. They can be seen in the lower panel of Figure 11 (P1). Now, all groups behave similarly as the global mean, except for group \(g\)s.  
Figure 11: Median correlation coefficients among all stations (**upper panels**) and within groups (**lower panels**), for the two normalization procedures: P1 and P2. **Upper panels**: The reported bands correspond to the median absolute deviation (MAD). **Lower panel**: The dashed lines are the median correlations among all stations (taken from the corresponding **upper panels**) and are included for comparison [92; 93]. This is an indication that one or more stations inside \(g_{5}\) need to be moved to other more suitable locations. Such analysis remains to be performed. The situation for procedure P2 is quite different (see Figure 11 (P2)), providing useful information on Dynamap performance. Since P2 retains long-time fluctuations, we can actually observe that sensors remain quite correlated on long-times, a feature that is at the basis of the good performance of Dynamap. In particular, the upper panel shows that the median correlation coefficient grows to 0.8 for \(\tau=60\) min, suggesting that all noise sensors respond similarly to fluctuations around the mean hourly noise profiles. This result supports a posteriori our approach based on the two-cluster mean profiles discussed in previous sections. The lower panel of Figure 11 (P2) confirms that all groups behave the same at all time intervals \(\tau\).