# Stabilization Time of Running Equivalent Level \(\mathbf{L_{Aeq}}\) for Urban Road Traffic Noise
## 1 Introduction
This procedure leads to an uncertainty \(\pm\varepsilon\) in the \(L_{Aeq,T}\) estimate, which should be combined with other sources of uncertainty, such as that of instrumentation:  
\[L_{Aeq,T}=L_{Aeq,t}\pm\varepsilon\ \ \ \ \ [\mathrm{dB(A)}], \tag{1}\]  
A further important parameter in noise time sampling is the stabilization time \(ST\) of the running equivalent level, defined as the minimum time after which the difference between the corresponding continuous equivalent sound pressure level \(L_{Aeq,ST}\) and the continuous equivalent sound pressure level \(L_{Aeq,T}\) at the reference time \(T\), which includes \(ST\), is never greater than a preset uncertainty interval \(\varepsilon\)[20]. In other words, the stabilization time \(ST\) is obtained by comparing the \(L_{Aeq,T}\) level at the reference time \(T\), usually equal to 1 h, with the running \(L_{Aeq,t}\) computed from the beginning of \(t\) onward, until the time \(ST\), from the beginning of \(t\), after which Equation (1) is always fulfilled for the preset \(\varepsilon\). Naturally, when the time \(t\) continues to run after \(ST\) until reaching \(T\), then the running \(L_{Aeq,t}\) is equal to \(L_{Aeq,T}\) and \(\varepsilon=0\) dB(A). Figure 1 shows the concept of stabilization time \(ST\) for two values of the uncertainty interval \(\varepsilon\) set for the \(L_{Aeq,T}\) estimate. The green band corresponds to \(\varepsilon=\pm 0.5\) dB(A) and the orange one to \(\varepsilon=\pm 1.0\) dB(A). The blue and red lines represent the sequence of SPL values and the running \(L_{Aeq,t}\), respectively, whilst the horizontal dashed black line corresponds to the \(L_{Aeq,T}\) level. In the example shown in Figure 1, the stabilization time is reached at \(ST_{0.5}=370\) s and \(ST_{1.0}=90\) s for the accuracies \(\varepsilon=\pm 0.5\) and \(\pm 1.0\) dB(A), respectively. Some studies [20; 21; 22] showed that \(ST\) is useful for characterizing the temporal composition of urban soundscapes and for estimating the hourly \(L_{Aeq,Ih}\) level with a preset uncertainty \(\pm\varepsilon\) from short-time \(L_{Aeq,I}\) measurements. As observed in [21], the presence of sound events, such as those produced by vehicle pass-by, influences the duration of the stabilization time \(ST\) because it increases the SPL fluctuation over time. To evaluate the contribution of these events on the hourly \(L_{Aeq,Ih}\) level, the intermittency ratio \(IR\) can be used and computed as follows [23]:  
\[IR=\frac{10^{0.1L_{Aeq,Tevents}}}{10^{0.1L_{Aeq,T}}}\cdot 100\ [\%], \tag{2}\]  
where \(L_{Aeq,Tevents}\) accounts for all sound energy contributions that exceed a given threshold, \(K\), that is clearly standing out from background noise, and \(L_{Aeq,T}\) is the continuous equivalent level referred to the measurement time T. The threshold \(K\) for sound event detection is computed as [23]:  
\[K=L_{Aeq,T}+C\ [\mathrm{dB}], \tag{3}\]  
where \(C=3\), as stated in [23] as an outcome of the numerical simulations of different urban road traffic situations. The \(IR\) metric has been fruitfully used in a previous study to classify urban roads on the basis of their acoustic features, rather than their functional classification according to the Italian legislation [24; 25; 26]. The present paper describes the main results of an analysis on the stabilization time of running equivalent level \(L_{Aeq,t}\), based on a large dataset of urban road traffic noise collected in the city of Milan, Italy. The results showed that in selecting the measurement time \(t\) to obtain an estimate of the hourly \(L_{Aeq,Ih}\) level within a preset uncertainty \(\varepsilon\), referring to the stabilization time \(ST\) is much more suitable and efficient than using a fixed time sampling \(t\), usually lasting 10-15 min, frequently applied in common practice regardless of the amount of road traffic flow.