Because road traffic noise is a random phenomenon, the relevant legislation and standards often require the determination of the acoustic descriptors either on a medium or long term. For instance, the day-evening-night level L_den introduced by the European Directive 2002/49/EC (2002) [1], even if referred to 24 h, should be representative of the annual period, and, in Italy, the current legislation requires that the road traffic noise monitoring lasts at least one week [2].

The current instrumentation enables measurements over a long time, as it can store and transmit a large amount of data. However, such duration is not feasible for monitoring attended by an operator and, therefore, requires the time-consuming post processing validation of the acquired data to eliminate all of the sound events that are not associated with road traffic noise. In addition, the need of saving resources and improving the spatial sampling resolution where required often lead to use temporal sampling procedures [3].

These procedures offer the advantage of making the attended monitoring feasible and, therefore, enable to eliminate the data validation. However, the values of the noise descriptors for a medium or long term estimated by those measured at the sampling time are affected by uncertainty, the amount of which depends on the ratio between the measurement time and the medium or long term, as well as on the variability of the noise immission at the measurement point. Several studies on this aspect are available in the literature. For instance, Bordone-Sacerdote et al. [4] described a simple approximate criterion to calculate the uncertainty in evaluating the noise level due to N vehicles per hour, all of the same type, moving with constant speed on one line and direction. Alberola et al. [5] investigated the statistical variability of 2 week’s noise recordings at 50 locations in residential areas affected mainly by road traffic noise. The observed relationships between variability and either logarithmic or arithmetic mean L_Aeqover the time periods investigated may be of assistance when estimating the noise level variability and the uncertainty associated with a noise measurement affected by road traffic or other environmental noise sources. Theoretical approaches by Makarewicz et al. [6] proposed that the long-term average sound level L_AeqT can be approximated by a few, m, short-term, τ, average sound levels, L_Aeqτ, so that mτ << T, and the uncertainty of such approximation should be calculated by nonlinear uncertainty of Λ_Αεθτ for m<10. The analysis of 5 years of continuous noise measurements carried out at one site in Valencia yielded Gaja et al. [7] to conclude that a random day strategy gives a more accurate estimate of the annual equivalent level from the 24-h noise level than a consecutive day’s strategy. Other things being equal, further studies, such as Brambilla et al. [8], confirmed that random sampling is more efficient than continuous one. Bellucci et al. [9] analyzed the noise data collected at 10 sites along non urban roads to evaluate the accuracy of 10 and 20 minute continuous sampling in the estimate of the hourly L_Aeqh and the day- time (06 ÷ 22 h) L_Aeqh and night-time (22 ÷ 06 h) L_Aeqn values. For vehicle passbys during the measurement time greater than 100, the accuracy in the estimate of L_Aeqh from the measured L_Aeq was observed to be within ± 1 dB for both the sampling time. Brocolini et al. [10] analyzed acoustic measurements carried out continuously during three months in Paris at six locations, considering samples of 5-min, 10-min, 15-min, 20-min, 30-min and 1-h duration. The results showed that at least 10-min sampling duration is necessary to discriminate among homogeneous time periods.

Predicting the accuracy of the estimated values of L_Aeq is important because this accuracy can have a large influence on the compliance with the limits required by legislation and standards and the corresponding costs of mitigation actions.

Dealing with the above issue, this paper presents a practical approach for determining and predicting the above accuracy, and the results obtained from the statistical analysis performed on a large set of acoustic data collected from continuous monitoring during weekdays in 80 sites alongside the non-urban road network in the Lombardia region (Italy) are described. The roads have different layouts: from the widest two carriage ways with three lanes for each direction to the narrowest one carriageway with one lane for each direction.

The aim of the analysis has been twofold, that is to determine the accuracy of:

• the estimate of daytime (06 to 22 h) A-weighted equivalent level L_Aeqd and nighttime (22 to 06 h) A-weighted equivalent level L_Aeqn from the 24-hr hourly pattern of A-weighted equivalent level L_Aeqh;

• the estimate of hourly L_Aeqh from L_Aeqt measured continuously for different shorter durations, namely t=5, 10, 15, 20 and 30 minutes.

The analysis was performed considering the hourly traffic flow too.

The acoustic monitoring carried out on weekdays in the 80 sites alongside the network of non-urban roads in the Lombardia region in the years 2000-2006 has provided a large database containing not only the A-weighted equivalent level L_Aeq measured at a sampling rate of 1 minute (L_Aeq1m) but also, at 15 sites, the hourly traffic flow for 24 hours. At another 35 sites the traffic flow was available for 1 hour during the daytime. The traffic was always free flowing during the monitoring and the microphone was located at 3 up to 60 m from kerbside, as already described in Zambon et al. [11].

The L_Aeq1m data have been pooled to obtain the corresponding values L_Aeqt at the times t of 5, 10, 15, 20, 30 and 60 minutes, as well as the daytime L_Aeqd and nighttime L_Aeqn levels.

The ranges of the daytime L_Aeqd and nighttime L_Aeqn in the 80 sites were very wide, as reported in Table 1, and the distributions of the hourly L_Aeqh levels, with a bin width of 1.5 dB, are shown in Figure 1. The difference between the mean values of day and night L_Aeqh distributions was 7.0 dB. (Table 1) (Figure 1).

Figure 1: Distributions of the hourly L_Aeqh levels, with a bin width of 1.5 dB, for the day and night periods in the 80 sites.

Table 1: Ranges of daytime L_Aeqd and nighttime L_Aeqn in the 80 sites.

At the 21 sites where the monitoring was performed for longer than 24 hr the median of the corresponding L_Aeqh values for each ith hour was considered. This led to 59 (80-21) profiles of hourly L_Aeqh available for the statistical analysis. The median was preferred to the mean value because the former is less influenced by outliers. This data pooling avoided that 24-h L_Aeqh profiles measured at the same road but on different days could be allocated to different groups by the subsequent cluster analysis.

Because the measurements were performed in various environmental setups, a direct comparison among the 24-h profiles of the hourly L_Aeqh was not meaningful. For this reason, and to perform further statistical analysis of the data, each i^th value of hourly L_Aeqh in the j^th temporal series was referred to the corresponding daytime level, L_Aeqdj, and the difference δ_ij was considered:

δ_ij=L_Aeqhij-L_Aeqdj[dB](i=1, ……., 24; j=1, ……., 59) (1)

as shown in the example in Figure 2.

Figure 2: Example of calculation of the hourly d_ij values.

The reference to the daytime L_Aeqd was chosen because this descriptor is more often available than the night time L_Aeqn. However, the methodology of the procedures described in the following for the estimate of daytime L_Aeqd can be also applied to develop similar procedures for estimating the nighttime L_Aeqn, providing that each i^th value of hourly L_Aeqh in the j^th temporal series is referred to the corresponding nighttime level, L_Aeqnj. Table 2 reports the distribution of the 24-h profiles of the hourly L_Aeqh available for the statistical analysis.

Table 2: Distribution among the weekdays of the 24-h profiles j^th of the hourly L_Aeqh.

The 24-h profiles were grouped according to the day of monitoring (Monday to Friday). In addition, the unsupervised technique of clustering was used to group together profiles which are “close” to one another in a multidimensional feature space, to uncover some inherent structure of the data. Various clustering algorithms were used, namely the hierarchicalagglomeration using the Ward method [12], the K-means using the Hartigan and Wong algorithm [13], the partitioning around medoids by Kaufman and Rousseeuw [14] and the model-based method. The results of these algorithms were compared and the most appropriate number of clusters for the data, a compromise between satisfactory discrimination and the need of limited number of clusters, was chosen. The range of solutions for clustering k was set from five groups (for a straightforward comparison with the categorization according to the day of monitoring) to two groups, which corresponds with the minimal discrimination. The Euclidean distance was chosen as the metric of the distance among observations.

The statistical software R (an open-source programming environment for data analysis, graphics and statistical computing) was applied for the above clustering and the package “clValid” by Brock et al. [15-17] was used to validate the results. For such validation, three features of the cluster partitions were considered, namely, compactness, connectedness, and separation. Connectedness relates to the extent to which observations are placed in the same cluster and is measured by the connectivity [18]. The connectivity has a value between zero and ∞ and should be minimized. Compactness assesses cluster homogeneity, usually by examining the intra-cluster variance, while separation quantifies the degree of separation between clusters (usually by measuring the distance between cluster centroids). Because compactness and separation demonstrate opposing trends (compactness increases with the number of clusters but separation decreases), popular methods combine the two measures into a single score, such as the Dunn index [19] and silhouette width [20]. The Dunn index has a value between zero and ∞ and should be maximized. The silhouette width lies in the interval (-1, 1) and should be maximized.

Considering the estimate of the hourly L_Aeqh from the L_Aeqt level measured continuously for a shorter time t:

t=m·M [s]with 0 < m < 1 (2)

where M=3600 s, the L_Aeqt values referring to the measurement times t of 5, 10, 15, 20 and 30 minutes were compared with the corresponding hourly L_Aeqh to determine the difference:

ε_τ=L_Aeqt - L_Aeqh [dB] (3)

Thus, with the assumption that the estimated L_Aeqh is equal to the measured L_Aeqt, the above difference represents the error ε_t of such estimate. The errors ε_τ were analyzed as function of the standard deviation of the L_Aeqt belonging to the relevant hour and the hourly traffic flow, as well as in terms of the probability P_tE that the accuracy of the hourly L_Aeqh estimate from L_Aeqt is within a specific interval E, namely ± 0.5 and ± 1.0 dB with an interval width of 1 and 2 dB respectively. The value of probability P_tE was obtained by the number of measurements within the selected interval divided by the total number of measurements.

The available data sets for the above analyses are reported in Table 3.

Table 3: Data sets available to determine the difference ε_t = L_Aeqt - L_Aeqh.

The main results of the estimate of the daytime L_Aeqd from the hourly L_Aeqh and those of the estimate of the hourly L_Aeqh from the L_Aeqt values measured continuously for shorter time t are described separately.

Estimate of daytime L_Aeqd from the hourly L_Aeqh

Figure 3 shows the 24-h profiles of the average δ_ij for each weekday from Monday to Friday. By this data grouping overlaps of the profiles occur very often, especially during the day period from 06 to 22 h. For the night period (22 to 06 h) the highest and lowest average profiles correspond to Friday and Monday, respectively.

Figure 3: Average profiles of d_ij for each weekday.

A different classification was obtained by clustering. Table 4 summarizes the output of the validation of the results obtained by the various clustering methods in terms of the optimal scores observed for the connectivity, the Dunn index and the silhouette width.

Table 4: Optimal scores obtained by the “clValid” package for the cluster validation.

After the analysis of the detailed results for each clustering method, the two groups obtained by the K-means were considered to be a reasonable solution, also because the corresponding values of the Dunn index and the connectivity were not too much different from the optimal scores (0.13 and 18.55 respectively). Figure 4 shows the results of the multidimensional scaling (MDS) applied to the data to provide a visual representation of the pattern of proximities among the data.

Figure 4: Multidimensional scaling of the data for visualizing the results obtained by K-means clustering. The clusters’ centroids are reported by the star symbol.

The discrimination between the two clusters is rather good; the centroids C1 and C2 are reported by stars in the plot. Cluster 1 and 2 are formed by 33 and 26 profiles respectively and their correspondence (in percentage) with the categorization based on weekdays is reported in Table 5. For each day the 24-h profiles are not too much unevenly splitted into the two clusters. Cluster 2 groups the majority of profiles observed on Monday, whereas Cluster 1 is formed by the majority of profiles of the other weekdays.

Table 5: Distribution (%) of 24-h profiles of δ_ij in each cluster considering the day of monitoring.

The average profiles δ_ik for each cluster and the standard error of the mean at 95% confidence interval are shown in Figure 5. Because the distributions of data were not normal for some hours, the mean and its confidence intervals were calculated using the bootstrap method [21] considering 1000 samples with replication.

Figure 5: Average profiles of d_ik for each cluster and standard error of the mean at 95% confidence level. Median values and standard deviation, between (), of L_Aeqd – L_Aeqn are also reported.

The hourly intervals with significant differences between the two average profiles at the confidence level of 95% were identified by the Mann-Whitney test and are listed in Table 6 with the corresponding significance value. The best discrimination between the clusters occurs during the nighttime (22-06 h). In the 07-19 h period, the average profile of cluster 1 has very small fluctuations around the L_Aeqd, whereas that of cluster 2 shows larger fluctuations, but still within 1 dB. The median value of the difference L_Aeqd – L_Aeqn, together with the standard deviation value given within ( ), is also reported in Figure 5: cluster 1 show a value 1.7 dB lower than that observed for cluster 2. As the noise emission of the road under consideration is not known “a priori”, additional information linked to such emission, i.e. traffic flow is necessary for the selection of the average profile most appropriate for the road itself. For this purpose, the average daily traffic flows (ADT) and their 95% confidence intervals for all the roads belonging to each cluster were calculated by the bootstrap method. The results are reported in Table 7.

Table 6: Hourly intervals of the average profiles of the two clusters with significant differences at the confidence level of 95%.

Table 7: Average daily traffic flow of the roads according to their cluster membership.

The boxplot of the ADT values given in Figure 6 shows a clear overlap of the data associated to the two clusters which leads to uncertainty in the selection of the appropriate profile. Thus, this parameter is not suitable for the above purpose. To overcome this problem a deeper analysis of traffic flows was performed on hourly basis. The Mann-Whitney test, which was applied to the hourly traffic flows of the roads according to their cluster membership, showed that the differences among means were not different at the 95% confidence level for the period between 10 and 16 h, as shown in Figure 7, where the hourly average values of traffic flow and the corresponding 95% confidence interval are reported.

Figure 6: Box plot of the ADT values of the roads according to their cluster membership.

Figure 7: Average hourly traffic flow of roads according to their cluster membership.

Thus, the hourly traffic flow is suitable for the appropriate selection of the cluster average profile, providing that it is not measured in the 10-16 h period. After all, traffic flow data are usually available for rush hours, which usually are outside the overlapping period, as shown in Figure 7. Cluster 1 includes the busiest roads. On the other hand, looking at the hourly cluster profiles and their corresponding 95% confidence intervals plotted in Figure 5, and zoomed in for the day period 7-19 h in Figure 8, the hourly intervals most suitable for the best accuracy in the L_Aeqd estimate are observed in the period from 12 to 16 h for both clusters.

Figure 8: Mean cluster profiles and corresponding 95% confidence intervals for the day period 7-19 h.

Estimate of hourly L_Aeqh from L_Aeqt measured for shorter time interval t

The hourly L_Aeqh is not often measured continuously, whereas it is frequently estimated by the L_Aeqt values measured for a shorter time t according to the following relationship:

(4)

To evaluate the accuracy ετ of such an estimate, the differences εt in equation (3), calculated for the measurement times t of 5, 10, 15, 20 and 30 minutes, were determined for all the monitoring data considering their cluster memberships. Figure 9 shows the box plots of the obtained values of ε_t for each measurement time t and cluster.

Figure 9: Box plots of the error e_t of the L_Aeqh estimate for each measurement time t and cluster.

As expected, the amplitude of the error ε_t decreases with the increase of the measurement time t and the means and median tend to the null value. For each measurement time t, the mean closest to zero and smallest standard deviation are observed for cluster 1 which includes roads with the highest traffic flows. The Kolmogorov-Smirnov test showed that all the distributions were not normal at 95% significance level, with means and standard deviations reported in Table 8.

Cluster		Measurement time t [minute]
		5	10	15	20	30
1		-0.29	-0.16	-0.11	-0.08	-0.05
	s	1.79	1.32	1.11	0.99	0.82
2		-1.08	-0.68	-0.50	-0.38	-0.23
	s	3.61	2.80	2.38	2.10	1.67

Table 8: Means and standard deviations s of the error ε_t [dB] for each measurement time t and cluster.

In order to predict the error ε_t for each measurement time, the median absolute value of the error of the L_Aeqh estimate obtained from L_Aeqt was related to the hourly traffic flow. The traffic flow data were grouped in bins with a width of 100 vehicles/hour, and the median absolute value of the error in each bin was considered. The plots in Figure 10 report the traffic flow on the x axis on a log scale and show the regression lines for the five t measurement times and the two clusters. For a fixed hourly traffic flow, the errors observed for cluster 2 are greater than those for cluster 1 and, as expected, for both clusters the errors decrease with increasing of traffic flow and measurement time t. In addition, for a fixed measurement time t the regression line for cluster 2 is steeper than that for cluster 1.

Figure 10: Median absolute value of the error of the L_Aeqh estimate versus hourly traffic flow and cluster for the measurement times t.

Table 9 reports the values of parameters A and B in the relationship used for the data interpolation, together with the adjusted Pearson’s correlation coefficient R². The last column gives the parameters obtained by interpolation of all the data, regardless their cluster membership.

Figure 9: Values of A and B parameters in the relationship used for the data interpolation of median and hourly traffic flow (x).

The differences in the accuracy of the L_Aeqh estimate obtained by the sampling times decrease with the increasing of the hourly traffic flow, as clearly shown in Figure 11 for all the data pooled together. The 30 minute sampling was taken as reference as it was the most accurate in the L_Aeqh estimate and the y axis reports the corresponding differences of the median absolute value of the error for the sampling times t=5, 10, 15 and 20 minutes; greater this difference lower the accuracy. It can be seen that above 4000 vehicles/hour the 10 minute sampling performs slightly better than the 15 minute one, but the former is more dependent on the traffic flow rather than the latter (slope of the regression line steeper).

Figure 11: Differences of the median absolute value of the error for the sampling times t= 5, 10, 15 and 20 minutes referred to the 30 minute sampling regardless the cluster membership.

The results for the measurement time t=10 minutes were compared with those obtained in a previous similar study carried out along nonurban roads in the Lazio region in Italy [9]. As can be seen in Figure 12, the regression relationship of the data collected in the Lazio region is steeper than that obtained for the present study, but the differences are rather small and increase with increasing of hourly traffic flow.

Figure 12: Median absolute value of the error of the L_Aeqh estimate versus hourly traffic flow for the data collected in the Lazio and Lombardia region. Dashed lines are the confidence band at 95% of the regression relationships.

Dealing with the probability PtE that ετ is within a specific accuracy range, Figure 13 reports the regression lines obtained by fitting the data of the hourly traffic flow with those corresponding to the five measurement times for the accuracy range of ± 0.5 dB and for both the clusters. The values of regression parameters obtained from fitting are given in Table 10, together with the adjusted Pearson’s correlation coefficient R2. The last column gives the parameters obtained by interpolation of all the data, regardless their cluster membership. The probabilities Pt0.5 obtained for cluster 2 are lower than those for cluster 1 and these differences decrease with increasing of hourly traffic flow.

Figure 13: Probability that e_t is within k= ± 0.5 dB for the L_Aeqh estimate from the five measurement times and for each cluster.

Table 10: Values of regression parameters obtained from the ε_t data fitting as a function of hourly traffic flow and for the accuracy range E = ± 0.5 dB (x is the hourly traffic flow).

The above mentioned probabilities P_t0.5 were compared with those computed according to the following relationship proposed by Bordone-Sacerdote et al. [4]:

(5)

where T=3600 s, t is the measurement time [s], N the hourly traffic flow, n the vehicles counted in the measurement time t calculated by:

(6)

n1 and n2 the uncertainty in vehicle counting corresponding to the uncertainty E=± 0.5 dB in the noise level, that is:

(7)

(8)

Equation 5 provides values P_t0.5 with the assumption of N vehicles per hour, all of the same type, moving with constant speed on one line and direction. Figure 14 shows that the experimental data and their fitting (solid lines) are rather lower than the corresponding values provided by equation (5), reported by dashed lines. This is most likely due to the difference between real traffic conditions and those assumed for equation (5).

Figure 14: Comparison between experimental data and values from equation (6) of probability that e_t is within k= ± 0.5 dB for the L_Aeqh estimate from the five measurement times regardless the cluster membership

Regarding the accuracy range of E= ± 1.0 dB, as expected higher probability P_t1.0, other factors being equal, were observed as shown in Figure 15, dealing with all the data, regardless their cluster membership. For instance, for t=15 minute at the hourly traffic flow of 1000 vehicles/ hour, widening the accuracy range from ± 0.5 to ± 1.0 dB increases the probability P_15mE by 26.1% (from 49.4 at ± 0.5 dB up to 75.5% at ± 1.0 dB).

Figure 15: Comparison of probability that e_t is within the E range for the L_Aeqh estimate for the five measurement times.

Example of application

To illustrate the features of the procedures above described and the associated uncertainties in the estimation, let assume that the road traffic monitoring carried out continuously for 15 minutes in the interval 8:15-8:30 h gives L_Aeq15=64.0 dB(A) and traffic flow=250 vehicles during the 15 min measurement time. Assuming that the traffic flow is evenly distributed throughout the hourly interval from 8 to 9 h, the corresponding hourly traffic flow is 250×4=1000 vehicles/hour. Thus, the road can be associated with cluster 2 (see Figure 7) and for the 15 min measurement time, the median value of is estimated to be as shown in Figure 10 and Table 9

(9)

which can be assumed as standard uncertainty of the estimate of the hourly L_Aeqh from the measured L_Aeq15m for 15 minutes. For the 8-9 hourly intervals and cluster 2, Figure 8 provides the corresponding δ_η value:

(10)

Thus, the estimated value of the day L_Aeqd is equal to:

(11)

(12)

With standard uncertainty of 0.65 dB. The combined uncertainty of the two procedures, under the simplifying hypothesis that they are uncorrelated, is calculated by:

(13)

Considering the coverage factor k=1.96 corresponding to the 95% confidence level, the estimated daytime L_Aeqd with the expanded uncertainty is as follows:

(14)

Considering the estimate of L_Aeqn, in addition to the similar procedures which can be developed as described for L_Aeqd estimate, a straightforward calculation can be based on the estimated value of L_Aeqd, considering the median value of the differences L_Aeqd – L_Aeqn and taking as standard uncertainty of such estimate the standard deviation of these differences. Thus, Figure 5 shows for cluster 2 the median value and standard deviation s as follows:

(15)

(16)

Then:

(17)

with a standard uncertainty of 1.4 dB.

However, the above uncertainty budgets are limited to the proposed procedures under the simplified hypothesis that these are uncorrelated; the standard uncertainties due to the other sources, at least that due to the instrumentation, should be considered, for instance as described by Craven et al. [22].