Stabilization Time of Running Equivalent Level L_Aeq for Urban Road Traffic Noise

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The efficiency of temporal sampling of road traffic noise could be improved considering the stabilization time ST of the running equivalent level L_Aeq,ST, rather than referring to a fixed measurement time t, often used in common practice and chosen regardless of the amount of road traffic flow.

Abstract

In urban areas, noise levels can largely vary in space and time due to the great complexity of these environments. The time required for the fluctuations of the running equivalent level L_Aeq to be limited within a preset variability range is a key issue for determining a statistically representative sample of the urban acoustic environment. The goal of the present study is to evaluate the potential of the stabilization time, defined as the minimum time ST 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 referred a longer time T, including ST, is never greater than a preset uncertainty interval ε. For this purpose, a dataset of road traffic noise continuously monitored in 97 sites in the city of Milan, Italy, is considered, providing 268 time series of 1 s short L_Aeq,1s, each lasting 24 h. The stabilization time ST referred the hourly L_Aeq,1h was determined for three preset uncertainty intervals ε, namely ±0.5, ±1.0 and ±1.5 dB(A). The results are promising and provide useful hints to obtain short-time noise monitoring as a statistically representative sample of the urban acoustic environment and, therefore, can be a tool to increase the low spatial resolution usually achievable by unattended permanent monitoring units.

1. Introduction

In 1982, Utley published a critical review of the existing practice of temporal sampling techniques for the measurement of environmental noise [1]. He concluded that whilst sampling techniques provide savings in human resources and equipment, the techniques were inadequate to determine accuracy except in a number of specific situations. He also pointed out that continuous monitoring was impractical due to the resource requirement.

Meanwhile, the increases in urbanization and mobility have led road traffic to become a major noise source in urban areas, with a large impact on the health of the exposed population (e.g., annoyance [2], psychological distress [3] and psychotropic medication use [4]). This noise shows large and random sound pressure level (SPL) fluctuations over time and, therefore, it is a challenge to track its time variability by sampling it. This subject has attracted the attention of many researchers, and several studies and surveys are reported in the literature (e.g., [5,6,7,8,9,10,11,12,13,14,15,16]).

Until relatively recently, local authorities and researchers have largely used short-duration localized noise measurements and computer-generated noise maps to comply with the Directive 2002/49/EC requirements [17]. The predictions of noise by numerical models of outdoor sound propagation and “on the spot” short-duration measurements are useful tools, even though a network of permanent noise monitoring stations measuring continuously may be a preferable solution. The high cost of installing and maintaining such networks is often the main reason for not implementing them on a large scale and with adequate spatial resolution. These limitations are even more evident in urban areas, where the complexity of outdoor noise propagation, due to the spatial configuration of the built environment and the noise source distribution, leads to high variability of sound pressure levels in space and time [18,19] and, therefore, requires spatially “dense” noise monitoring units. Despite the facts that the technology has improved significantly and the costs have been reduced, short-time noise monitoring is still an appealing measurement technique, also because it is usually performed by an operator, unlike the unattended permanent noise monitoring units. Among the advantages of attended noise measurement, nonrelevant sounds can be excluded or tagged in order to not be considered in post-processing and adverse weather conditions unsuitable for measurements can be avoided. Furthermore, the operator can stop the measurement when the running equivalent level L_Aeq shows time fluctuations within a preset range. This allows for saving time and moving to another location and, therefore, increases the spatial resolution of noise monitoring and saves resources. On the contrary, unattended continuous noise monitoring requires validation of the collected data that could be difficult, cumbersome and time consuming in the necessary post-processing phase.

In any noise time sampling, the value of the continuous equivalent sound pressure level L_Aeq,T referred to medium- and long-time T is estimated by the L_Aeq,t level measured for a shorter time t, usually much shorter than T (t << T). For instance, the Italian legislation on road traffic noise requires that T = 1 h, and it is common practice that the hourly L_Aeq,1h value is estimated to be equal to the measured value L_Aeq,t over time interval t within the selected hour. The duration of t and, therefore, the time sampling ratio m = t/T, which is always m ≤ 1 being t << T, is variable and in common practice is very often fixed at 10–15 min in urban areas and road traffic noise, regardless of the amount of road traffic flow. This procedure leads to an uncertainty ±ε in the L_Aeq,T estimate, which should be combined with other sources of uncertainty, such as that of instrumentation:

$$L_{Aeq,T}=L_{Aeq,t}\pm \epsilon \left[\mathrm{dB}\left(\mathrm{A}\right)\right],$$

(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 ε [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 ε. 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 ε = 0 dB(A).

Figure 1 shows the concept of stabilization time ST for two values of the uncertainty interval ε set for the L_Aeq,T estimate. The green band corresponds to ε = ±0.5 dB(A) and the orange one to ε = ±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 ε = ±0.5 and ±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,1h level with a preset uncertainty ±ε from short-time L_Aeq,t 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,1h level, the intermittency ratio IR can be used and computed as follows [23]:

$$IR=\frac{{10}^{0.1L_{Aeq,Tevents}}}{{10}^{0.1L_{Aeq,T}}} ·100\left[\%\right],$$

(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]:

$$K=L_{Aeq,T}+C \left[\mathrm{dB}\right],$$

(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,1h level within a preset uncertainty ε, 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. A step ahead of this crude approach has been introduced by the standard ISO 1996-2:2017 [27], which relates the standard uncertainty ε with the total number n of vehicle pass-by in mixed road traffic:

$$\epsilon \cong \frac{10}{\sqrt{n}} \left[\mathrm{dB}\right],$$

(4)

For instance, to obtain a ε = 0.5 dB it is necessary that at least n = 400 vehicle pass-by in mixed road traffic are counted to end the measurement time t.

2. Materials and Methods

2.1. Experimental Data Set

Noise monitoring data collected in 97 sites in the city of Milan, Italy, were considered for the present study [28]. They consisted of 268 time series of 1 s short L_Aeq,1s level, each lasting continuously for 24 h. Road traffic noise was the predominant source in each site and, therefore, the reference time T for computing the stabilization time ST was set to T = 1 h, according to the current Italian legislation.

The selected sites were representative of the urban road network in Milan, which includes different types of roads according to the Italian road functional classification, namely motorways (class “A”), thoroughfare roads (class “D”), urban district roads (class “E”) and urban local roads (class “F”). The distribution of the sites across the road types is given in

Table 1. Distribution of the 97 sites considered in the study according to the Italian road functional classification.

Road Type	N. of Sites	N. of 24 h Time Series	N. of Sites with More than 1 Day Monitoring
A (motorways)	2	15	2
D (thoroughfare roads)	6	16	3
E (urban district roads)	30	91	22
F (urban local roads)	59	146	35
Total	97	268	62

, together with the number of 24 h time series of 1 s A-weighted short L_Aeq,1s level, monitored continuously by a class 1 sound level meter, set to time weighting Fast with the microphone placed at 4 m above the road. The unattended monitoring was carried out on weekdays only (Monday to Friday), and data collected with rain and wind speed >5 m/s were excluded from the study. In 62 sites, the monitoring lasted continuously for a few days. More details on the noise survey (e.g., locations of monitoring sites in the urban area) are available in [28].

In addition, for each site the hourly traffic flow Q_h was provided by the Municipal Agency of Mobility, Environment, and Land of Milan (AMAT). The road traffic flows were calculated by a model based on origin–destination matrices applied on the entire city road network, reported in Figure 2. It has to be addressed that the Italian functional classification of roads is mainly based on the geometry of the roads, and therefore does not always correspond to the roads’ actual use by urban traffic. In other words, roads of the same geometry and functional class could show quite different amounts of road traffic flow, depending on their actual function in the mobility road network. Such discrepancy has been already observed in previous investigations carried out on Milan road network [24,25,26].

2.2. Data Processing and Analysis

A script running in “R” software [29] was developed to import each of the 24 h time series of the 1 s A-weighted L_Aeq,1s as text files. Data were processed in order to compute for each T = 1 h the hourly L_Aeq,1h level, the running L_Aeq,t (red line in Figure 1), the difference L_Aeq,t—L_Aeq,1h for every second, the intermittency ratio IR, the stabilization time ST for three preset uncertainty intervals ε, namely ±0.5, ±1.0 and ±1.5 dB(A) and the standard deviation of the L_Aeq,1s level within each hour σ_h. Moreover, statistical analyses were carried out on the data.

3. Results and Discussion

Figure 3a reports the histogram of the 6426 hourly L_Aeq,1h considered, together with some descriptive statistics. The range is rather wide (≅47 dB(A)), and the dataset is likely representative of the road traffic noise in the urban area. This is also reasonable for the standard deviation σ_1h of the L_Aeq,1s level within each hour, the distribution of which is given in Figure 3b, where the histogram varies from σ_1h = 1 to 12 dB(A).

Figure 4 shows the median of ST values for each hour and the three preset uncertainty intervals ε of the L_Aeq,1h estimate plotted versus the median hourly road traffic flow Q_h, as well as the regression lines according to the equation

$$ST=a·{\left(Q_h\right)}^b \left[\min \right],$$

(5)

where a and b are constants, the values of which are obtained by least squares data fitting. The ST values decrease with increases in the uncertainty ε and with increases in the road traffic flow Q_h. The trend is rather similar to that reported in [21]. The green dashed line corresponds to the measurement time t = 15 min, often used in common practice for road traffic noise measurement. It is clear that this approach, which uses a measurement time selected regardless of the road traffic flow, can lead to low accuracy in the L_Aeq,1h estimate, as reported in the first row in

Table 2. Percentage of ST values ≤ 15 min for each road type and uncertainty ε.

Road Type	Uncertainty ε of the LAeq,1h Estimate [dB(A)]
	±0.5	±1.0	±1.5
All	17	46	64
A (motorways)	46	77	93
D (thoroughfare roads)	26	60	74
E (urban district roads)	21	52	67
F (urban local roads)	10	38	58

.

The stratification of the dataset by road type leads to more meaningful outcomes of the statistical analysis, as pointed out in some studies [26,30]. Table 2 reports the percentage of the observed ST values ≤ 15 min for each road type and uncertainty interval ε. As expected, these percentages decrease from road types A to F and increase with increasing of the uncertainty ε. This outcome points out that the stabilization time ST could be an efficient tool to guide in selecting the measurement time t adequate to the SPL time variability and, therefore, for increasing the accuracy of the L_Aeq,1h estimate.

The Kruskal–Wallis test applied to the ST values obtained for each uncertainty ε showed significant differences at 95% confidence levels for the road types and the Dunn test detected these significant differences for all six pairwise comparisons. This outcome confirms the importance of the dataset stratification by road type.

Moreover, the Kolmogorov–Smirnov test showed a non-normal distribution of the ST values for all the combinations road type, hours and uncertainty ε. This result is in agreement with that observed in [22], suggesting the use of the percentiles instead of the mean to summarize the ST values in each group. In the present study, adopting a precautionary approach, the third quartile of the ST values in each group was considered, corresponding to the 75th percentile; that is, 75% of the ST values were shorter than the third quartile. These values for each of the uncertainty intervals ε are plotted in Figure 5 for each road type versus the median value of the hourly road traffic flow Q_h together with regression lines according to Equation (5).

The ST values decrease with road traffic flow increasing and from F road type to A, as well as with increasing of the uncertainty ε. The horizontal dotted green line corresponds to the time t = 15 min, often used in common practice for road traffic noise measurement. It is evident that this duration of the measurement time is acceptable only for road type A and low accuracy of the L_Aeq,1h estimate (Figure 5a), barely acceptable for road types D and E for road traffic flow Q_h > 700–1200 vehicles/h (Figure 5b,c), and never acceptable for road type F (Figure 5d), unfortunately the more diffuse in an urban area.

Table 3. Values obtained for the constants a and b in the regression Equation (5).

Road Type	Uncertainty ε of the Hourly LAeq,1h Estimate [dB(A)]
	±0.5		±1.0		±1.5
	a	b	a	b	a	b
All	89.32	−0.15	115.52	−0.32	102.47	−0.40
A (motorways)	324.46	−0.30	443.14	−0.45	360.25	−0.53
D (thoroughfare roads)	97.59	−0.13	195.21	−0.32	277.03	−0.45
E (urban district roads)	77.45	−0.08	102.32	−0.18	171.34	−0.34
F (urban local roads)	58.14	−0.04	54.87	−0.10	51.58	−0.17

reports the values obtained for the constants a and b in the regression Equation (5), showing for A and D road types a stronger dependence of stabilization time on the traffic flow. This is essentially due to the more regular traffic dynamics observed for these types of roads.

Figure 5 shows the large influence of road traffic flow on the length of stabilization time and, therefore, the knowledge of this data is essential for an estimate of ST values. Figure 6 shows the median hourly road traffic flow computed for the examined dataset and the four road types. The pattern is rather similar for all roads, with peaks at 8 and 18 h, more pronounced for local roads (F) than for the other types. The flows decrease from 18 to 4 h and increase again afterwards.

The flow data in Figure 6 can be input in the regression equations (Equation (5)) to obtain an estimate of the ST₇₅ value for each type of road and uncertainty ε. For instance, Figure 7 reports the estimated ST₇₅ values for each type of road at each hour for an uncertainty ε = ±1.0 dB(A). The values are rather stable in the daytime from 8 to 18 h; afterwards they increase until 2–4 h in the night, depending on the road type, and decrease again until 8 h. The horizontal green dotted line at ST₇₅ = 15 min clearly shows that this measurement time is not appropriate for all roads at any hour, with the exception of motorways (type A), excluding the night period 0–4 h. The above pattern is rather similar for the other two accuracy intervals, and

Table 4. Mean values in the day period 7–19 h of 75th percentile of ST values ¹ estimated by Equation (5) for each road type and uncertainty ε.

Road Type	Uncertainty ε of the LAeq,1h Estimate [dB(A)]
	±0.5	±1.0	±1.5
A (motorways)	20	7	3
D (thoroughfare roads)	36	17	9
E (urban district roads)	41	25	12
F (urban local roads)	45	30	18

¹ ST₇₅ [min].

gives the mean values in the day period 7–19 h of ST₇₅ values estimated by Equation (5) for each road type and uncertainty ε. It is clear that the measurement time t = 15 min is appropriate only for a large uncertainty, ε ≥ ±1.5 dB(A), and acceptable for motorways (road type A) for uncertainty ε = ±1.0 dB(A).

From an applicative point of view, it is important to know the cumulative probability P_ST75,ε that a preset ST₇₅ value provides a L_Aeq,1h estimate within a fixed uncertainty ε [14]. This probability was computed for all the road types and uncertainties ε of the L_Aeq,1h estimate and the results are shown in Figure 8 for some values of ST₇₅.

Table 5. Cumulative probability [%] of the L_Aeq,1h estimate computed by Equation (5) for each road type and uncertainty ε for some ST₇₅ values and daytime mean hourly road traffic flow Q_h.

Road Type	A		D		E		F
Mean hourly road traffic flow Qh in the daytime (6–22 h) [vehicles/h]	10,100		2140		2120		420
Stabilization time ST75 [min]	Uncertainty ε of the LAeq,1h Estimate [dB(A)]
	±0.5	±1.0	±0.5	±1.0	±0.5	±1.0	±0.5	±1.0
10	51	79	28	62	16	56	8	38
20	60	92	45	79	37	70	21	58
30	81	92	62	88	54	77	38	74
40	92	95	76	88	71	91	58	88

shows that for a measurement time t = 10 min, the cumulative probability of ST₅ to obtain a L_Aeq,1h estimate within ε = ±0.5 dB(A) is above 50% only for motorways (type A) and remains below 50%, even doubling the uncertainty up to ε = ±1.0 dB(A), for local roads (type F). Doubling the time t up to 20 min increases the cumulative probability but does not change the pattern observed for the accuracy interval of ±0.5 dB(A) and road type, unless t was at least tripled or even longer.

Regarding the presence of sound events and their contribution to the hourly L_Aeq,1h level, Figure 9 shows the median values of the hourly IR for each hour and type of road. The IR time pattern is similar for the road types, with hourly values increasing from roads A to F. During the day, from 9 to 18 h, the IR time patterns show limited fluctuations (around 10%) and increase afterwards to reach the maximum value at 2–3 h in the night. Comparing these patterns with those reported in Figure 6, it is evident that IR is negatively correlated with the hourly values of road traffic flow Q_h, as shown in

Table 6. Pearson’s correlation coefficients for each road type for IR and L_Aeq,1h versus Q_h.

Road Type	Pearson’s Correlation Coefficient r
	IR vs. Qh	LAeq,1h vs. Qh
A (motorways)	−0.83	0.82
D (thoroughfare roads)	−0.50	0.27
E (urban district roads)	−0.70	0.56
F (urban local roads)	−0.28	0.50

reporting the Pearson’s correlation coefficients for each road type for IR and L_Aeq,1h versus Q_h.

The presence of sound events increases the SPL time variability and, therefore, rises the duration of the stabilization time ST. This influence is more evident at nighttime and low road traffic flows, when sound events clearly exceed the background noise. Figure 10 shows the 75th percentile of ST values for each hour and road type plotted versus the corresponding median values of the hourly IR. It is observed that the rise rate of ST₇₅ with IR does not significantly depend on the road type. The higher dispersion of data for roads of type A, especially at low values of IR, can be noted. Such dispersion can also be inferred by the time pattern of IR in Figure 9, where the day–night variation is much higher than for the other three types of roads. The regression equations used for data fitting are in the form of Equation (5) and

Table 7. Values obtained for the constants a and b in the regression Equation (5) between ST₇₅ and IR.

Road Type	$\mathit{S}{\mathit{T}}_{75} = \mathit{a}·\mathit{I}{\mathit{R}}^{\mathit{b}}$
	a	b
A (motorways)	9.67	0.39
D (thoroughfare roads)	8.12	0.42
E (urban district roads)	4.88	0.52
F (urban local roads)	6.81	0.45

reports the values obtained for the constants a and b in the regression equation between ST₇₅ and IR.

4. Conclusions

The present study concerns the stabilization time ST, 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 referred a longer time T > ST, including ST, is never greater than a preset accuracy interval ε. This parameter is very important for obtaining samples of urban road traffic noise representative of those over the longer time T taken as a reference, where T = 1 h normally. The observed non-normal distribution of the ST values for all the combinations of road type, hours and uncertainty ε suggests summarizing the ST values in each of these combinations by means of the 75th percentile instead of either the mean or the median. This is a precautionary approach, being 75% of the ST values in each combination shorter than the considered ST₇₅.

The results obtained by the analysis on the large dataset collected on the roads in Milan clearly show that a fixed measurement time t of 10–15 min, frequently used in common practice regardless of the amount of road traffic flow, is very often not suitable for obtaining an estimate of the hourly L_Aeq,1h level within a preset accuracy ε. On the contrary, the stabilization time ST, which is affected by the SPL time variability and the presence of sound events, is an efficient tool to choose the appropriate measurement time t. Furthermore, the intermittency ratio IR is an efficient metric to detect sound events, to determine their contribution to the continuous equivalent level L_Aeq and their influence on the stabilization time.

An important parameter is the value chosen for the uncertainty ε of the L_Aeq,1h estimate. As shown by the results, this value largely affects the duration of ST: the wider ε, the shorter ST. The SPL time variability of road traffic in urban environments is rather high, and setting an uncertainty ε = ±0.5 dB(A) leads to very long ST durations. At the same time, one must remember that the uncertainty ε in the L_Aeq,1h estimate must be combined with the other sources of uncertainty, such as that from instrumentation. As already reported in [21], setting ε = ±1.0 dB(A) seems to be a reasonable compromise, enabling good discrimination of different urban scenarios as well as SPL fluctuations throughout the measurement time t.

Moreover, the stratification of the dataset by road type was effective, as it showed that E and F roads, due to the low road traffic flow and the presence of noticeable sound events clearly exceeding the low background noise, are the most critical for noise measurement time t because the stabilization time ST has a long duration. In addition, these road types are the most numerous in urban areas and cannot be neglected, considering their potential noise impact on the health of the exposed population and the large number of people living close to these roads.

As a general conclusion, the stabilization time ST is much more suitable and efficient than using a preset fixed time sampling t, chosen regardless of the amount of road traffic flow. Thus, ST could be a very useful tool to guide in the selection of a more adequate time sampling t, also taking into account the cumulative probability to estimate the medium- and long-term L_Aeq,T levels within a preset accuracy interval ε. A measurement time t shorter than ST would likely not be adequate to obtain the L_Aeq,1h estimate within the preset accuracy ε.

Even though the results refer to data collected in Milan, the structure of this large city is similar to those of other cities, at least in Europe, and the analysis carried out could be interesting if its methodological approach was to be replicated in other urban contexts.