Study of temporal correlations in dynamic noise mapping

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Study of temporal correlations in dynamic noise

mapping

Roberto Benocci, Chiara Confalonieri, Hector Roman, Giovanni Zambon

To cite this version:

Roberto Benocci, Chiara Confalonieri, Hector Roman, Giovanni Zambon. Study of temporal

cor-relations in dynamic noise mapping.

Forum Acusticum, Dec 2020, Lyon, France.

pp.707-713,

�10.48465/fa.2020.0112�. �hal-03233640�

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STUDY OF TEMPORAL CORRELATIONS IN DYNAMIC NOISE

MAPPING

Roberto Benocci

1

_{H. Eduardo Roman}

2

_{Chiara Confalonieri}

1

Giovanni Zambon

1

_{Department of Environmantal Sciences, University of Milano Bicocca, Milano, Italy}

2

_{Department of Physics, University of Milano Bicocca, Milano, Italy}

Correspondence: [email protected]

ABSTRACT

An European Life project, DYNAMAP, has been devoted to provide a real image of the noise generated by vehic-ular traffic in urban and suburban areas developing a dy-namic acoustic map based on a limited number of low-cost permanent noise monitoring stations. In the urban area of Milan, the system has been implemented over the pi-lot area named Area 9. Traffic noise data within the pipi-lot area, collected by the monitoring stations, each one repre-sentative of a number of roads having in common similar characteristics (e.g. daily traffic flow) and otherwise called “groups”, are used to build-up a “real time” noise map. An important aspect of this project regards the “contem-poraneity” of noise fluctuations predicted by DYNAMAP with those effectively measured at an arbitrary location. In-tegration times heavily affect the result, with correlation coefficients up to 0.8-0.9 for updating times of 1h. As DY-NAMAP has a statistically-based approach, higher corre-lations are observed when averaging over groups of roads with similar traffic flow characteristics.

1. INTRODUCTION

Noise mapping are becoming more and more a neces-sary tool for evaluating the noise exposure of citizens in large cities, as it has been recognized by the strict dose-harmful effect relationships reported both in the Directive 2002/49/EC [1] and the 2018 WHO Environmental noise guidelines [2]. Strategic Noise Maps have been imple-mented to enable effective diagnostics on the acoustic envi-ronment and provide useful information for local interven-tion measures and policy-making [3, 4]. They have been introduced to evaluate the overall exposure to noise in a given area due to different sources, and together with Ac-tion Plans provide a framework to manage environmental noise and its effects. Thus, they represent the usual ap-proach for noise prevention and control [5, 6]. Noise maps are recently evolving towards a multi-source approach [7, 8] such as source-oriented sound maps enabling the inves-tigation of competition between sound sources [9]. How-ever, the introduction of dynamic noise maps constituted a further evolution in the direction of better representing the “real” noise exposure. In this regards, the European project

DYNAMAP [10] has been devoted to develop a dynamical acoustic map in two pilot areas: a large portion of the urban area of the city of Milan (Area 9) [11] and the motorway surrounding Rome [12]. In both cases, a method for pre-dicting the traffic noise in an extended area using a limited number of monitoring sensors and the knowledge of traffic flows has been developed. Traffic noise data, collected by the monitoring stations, each one representative of a num-ber of roads within the zone sharing similar characteristics (e.g. daily traffic flow) and otherwise called “group”, are used to build-up a “real time” noise map [13-15]. An im-portant aspect of this project regards the “contemporane-ity” of noise fluctuations predicted by DYNAMAP with those effectively measured at an arbitrary location. In or-der to study how traffic noise in different parts of the city is correlated, we first focused on the correlations among the 24 monitoring units belonging to DYNAMAP’s sensor network.

2. NETWORK OF SENSORS AND DYNAMIC NOISE MAPPING

From an initial analysis of the noise trend profiles of a sam-ple of roads, distributed all over the municipality of Milan, we demonstrated that it is possible to divide the entire road network into two main groups, called clusters, according to a known information about each single road, which we called non-acoustic parameter [16-18]. Thus, we described the noise profile of a generic road as a combination of the two aforementioned mean noise cluster profiles [19-21]. For the effective implementation of DYNAMAP, we had only 24 noise monitoring stations at our disposal which we diployed in the pilot area after dividing the distribution of x in Area 9 into six intervals, called groups, denoted as g1;g2; . . . ; g6 [22-23]. Each group of roads has been

represented by a single noise map; noise map which is the result of two contribution:

a) a reference static contribution derived by the calcula-tion of CadnaA at the time interval Tref = (08:00-09:00)

b) a dynamic contribution from each group gi taken

from 24 monitoring stations [24-25].

Thus, the level Leqa(t) at location a at time t can then be obtained by energetically adding the local contribution of each base map with its variation δ(gi) ,

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Leqa(t) = 10 · Log

6

X

i=1

10(Leqref (g,a)+δ(gi))/10_, ₍₁₎

where δ(gi) is obtained by averaging the sensors’

δ(gi,j) in each group [11]. Here, δ(gi,j) for the generic

monitoring sensor j, is obtained as:

δ(gi,j)(t) = Leq(gi,j)(t) − Leqref (gi,j)(Tref) (2)

3. MEASUREMENT CAMPAIGN

Prior to be used in DYNAMAP calculation process, the recorded noise time series from the 24 monitoring stations were cleaned by the presence of eventful anomalous noise events through a specifically developed detection algo-rithm [26] in order to account just for traffic noise sources. Testing the results of DYNAMAP predictions required a dedicated measurement campaign which was completed in 2019. The test measurements were performed in 21 loca-tions within Area 9, displayed with purple stars in Fig. 1, equally distributed in the six groups of roads. Sites were selected in order to test the system in complex scenarios where the noise from roads belonging to different groups may contribute. Figure 1 also contains the position of the 24 monitoring stations together with the indication of the six groups of roads represented by different colours.

Figure 1. Area 9 of the city of Milan. Colours correspond to the different groups of streets: g1;g2; . . . ; g6. Black

tri-angles and purple stars represent the sites where the mon-itoring stations are installed and the position of test mea-surements, respectively.

4. CORRELATIONS

In this section, we study the “contemporaneity” of noise fluctuations as recorded by the monitoring stations. In or-der to describe the temporal correlation between two roads (x, y) belonging to the same network, we will use the Pear-son’s correlation coefficient, ρ, defined as the covariance, cov(x, y), of the two variables divided by the product of their standard deviations, σ:

ρ(x,y)=

cov(x, y) σxσy

(3) being the covariance a measure of the joint variability of the two variables x and y and defined as the mean value of the product of the deviations from their mean values [28]. 4.1 Correlations among the network of monitoring stations

In order to study how DYNAMAP’s predictions are corre-lated with field measurements in different parts of the city, we first focused on the correlations among all the 24 mon-itoring units making up DYNAMAP’s network. As input data, we used the equivalent levels recorded over a period of five days. All anomalous noises not belonging to traffic noise have been removed by using the procedure described in [27]. In order to compare the data from each monitoring station, we operated a normalization on the time series. In particular, we used two normalization processes:

1) From each time series, we removed the hourly me-dian value. In this way, we obtain what we called a de-trended time series.

2) From each time series, we removed the mean Leq level calculated between (06 : 00) − (22 : 00).

Afterwards, we calculated the correlation coefficient, ρ, by applying Eqn. (2), and took the median value.

Fig. 2 reports the median of the correlation coeffi-cient among all the de-trended monitoring station nor-malized according to procedure 1). The reported band corresponds to the median absolute deviation, M AD defined as M AD =| xi− ˜X | where ˜X =

median(X). The correlation coefficient is rather low, around 0.1, for all the integratioin times considered (1s, 1min, 5min, 10min, 15min, 30min, 60min). The results within each group g are reported in Fig. 3.

Figure 2. Median of the correlation coefficient among all the de-trended monitoring stations normalized according to procedure 1). The reported band corresponds to the me-dian absolute deviation, MAD.

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Figure 3. Median of the correlation coefficient among the de-trended monitoring stations within each group g and normalized according to procedure 1).

Figure 4. Power spectrum of a five-days time series recorded at the monitoring station hb129.

The normalization procedure described at bullet point 1), actually removes all long period fluctuations letting emerge just the high frequency fluctuation. To analyse this feature, we calculated the power spectrum of a five-day time series recorded at the monitoring station hb129. In this case, the normalizazion refers to a standard normal-ization, i.e. according to buttet point 2). The resulting periodgram is shown in Fig. 4. We can clearly identify two regions: a high period fluctuation (low frequency) and a low period fluctuation. The first one is associated with daily, morning and night large scale fluctuations (the max-imum period is at 86400 s corresponding to 1 day) and the second ones, with a much lower importance, at time periods of the order 1 min (see zoom of Fig. 4 in Fig. 5). Thus, the low correlation coefficient at ”high frequency” are much likely due to the low strength of the spectral den-sity observed for the de-trended time series. Calculating the correlation coefficient for the ”standard ” normalized

Figure 5. Power spectrum of a five-days time series recorded at the monitoring station hb129. Zoom at low time periods.

Figure 6. Median of the correlation coefficient among all the monitoring stations normalized according to procedure 2). The reported band corresponds to the median absolute deviation, MAD.

time series, its values increases considerably even at very low integration times. At 1s integration time the correla-tion coefficient is as high as 0.4 going up to about 0.8 at 1 h as displayed in Fig. 6 for all the monitoring stations. We repeated the calculation within each group and the re-sults are reported in Fig. 7. Both in Fig. 3 and Fig. 7, group g1presents the lower correlation. This is due to the group

classification process based on the road membership ac-cording to its non-acoustic parameter x. In fact, group g1

contains roads with x values within the interval (0 − 3), corresponding to a total daily flow of (1 − 1000) vehicles and therefore with a large dynamic variability. This vari-ability impacts considerebly on the intra-group correlation.

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Figure 7. Median of the correlation coefficient among all the monitoring stations normalized according to procedure 2).

5. DISCUSSION

Designing a dynamic noise mapping is a complex task ow-ing to the large number of parameters that need to be con-sidered in order to describe with suffiecient accuracy the traffic noise in urban areas [11]. Here, we are highlighting a further factor which could help reduce the redundancies of information carried by each monitoring station. When we want to describe a road network by using a statisti-cal approach such as the one in DYNAMAP project, we have to be sure that we are not taking in correlated infor-mation. As the traffic flow is highly fluctuating in time on short time scales, we espect the correlation among the monitoring sensors to be very low, and actually this is the outcome illustrated in Fig. 2 and Fig. 3 with the exception of g5. Within g5, we observe an increase of the

correla-tion coefficient for integracorrela-tion times of 30-60 min and this could be the sign of redundant information brought in the group. The other groups, instead, present low correlation and this information is useful to statistically describe the traffic source variability.

Fig. 8 illustrates the correlation matrix among the time series recorded by the monitoring network with integration time of 60 min and normalized according to procedure 1). Blackish boxes indicate higher correlation which are found within g5(hb106, hb136, hb151, hb123). A black box

ap-pears also in correspondance with sensors (hb108, hb121). These sensors are both installed in via Pirelli though be-longing to different groups (see map in Fig. 1). Also in this case, we are using redundant information. This character-istic emerges also analyzing the correlation matrix among the time series recorded by the monitoring network with integration time of 5 min as reported in Fig. 9. in order to better characterize these two locations, we considered the cross-correlation bewteen hb108 and hb121. It results that the maximum correlation is achieved with a lag of 163 s. As the distance between the two sensors is of 470 m, it means that the average traffic flow speed along via Pirelli is

Figure 8. Correlation matrix among the time series recorded by the monitoring network normalized according to procedure 1). Integration time 60 min. Blackish boxes indicate higher correlation.

like 10km/h which is quite reasonable if we consider the presence of a traffic light in-between the two monitoring stations.

Figure 9. Correlation matrix among the time series recorded by the monitoring network normalized according to procedure 1). Integration time 5 min. Blackish boxes indicate higher correlation.

6. CORRELATION OF DYNAMAP PREDICTIONS As already described in Sect. 2, DYNAMAP predictions can be obtained by using Eqn. (1). They are the result of the superposition of the six noise maps the entire Area 9 has been devided into according to the non-acoustic pa-rameter x. Each map is the product of a static map, calcu-lated at the reference time T ref = (08 : 00–09 : 00), and the fluctuations recorded by the field monitoring stations Eqn. (2). The predefined updating time of DYNAMAP

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Figure 10. Correlation coefficient between DYNAMAP predictions and field measuremets within group 1. The group-average correlation is also shown.

within the day are:

τ = 5min for (07 : 00–21 : 00); τ = 15min for (21 : 00–01 : 00); τ = 60min for (01 : 00–07 : 00).

This choice has been motivated by the need to provide the shortest time interval for the update of the acoustic maps keeping the associated error approximately constant over the entire day [19]. In 2019 we completed a mea-surement campaign devoted at evaluating the accuaracy

of DYNAMAP predictions. The test measurements were performed in 21 locations within Area 9 (purple stars in Fig. 1) equally distributed in the six groups of roads ( 4 in g1, 3 in g2, 4 in g3, 3 in g4, 3 in g5, 2 in g6) . The

mea-surement sites were located at arbitrary points distributed within the pilot area of Milan and with different noise prop-agation conditions. In particular, sites were selected in order to test the system in complex scenarios where the noise from roads belonging to different groups may con-tribute. Special attention was given to avoid non-traffic

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noise sources such as technical systems (thermal power stations or ventilation systems), construction sites, railway, and tram lines, interfering with the measurements. Fig. 1 also contains the position of the 24 monitoring stations to-gether with the indication of the six groups of roads repre-sented by different colours.

Fig. 10 through Fig. 15 present two different correlation results:

1) The correlation of each single measurement (sk, k =

1, ..., 21) with the corresponding DYNAMAP prediction 2) The correlation between the mean correlation of mea-surements and the mean DYNAMAP predictions (gi, i =

1, ..., 4).

All the time series have been normalized according to procedure 2). Regarding bullet point 1), the correlation has been calculated in the time interval (07 : 00 − 21 : 00) for the integration (updating) time 5min and 10min, (07 : 00 − 01 : 00) for the integration time 15min and 30min and around the clock for the integration time of 1h. In all the reported figures, the correlation coefficient increases with the integration time and presents quite low values at integration times of 5 and 10 min. Actually, if we look at the typical noise profile recorded by a mon-itoring station (such as the one reported in Fig. 16 for hb136), we cannot see specific patterns in the time period (07 : 00 − 21 : 00). These patterns are more evident al larger time scales which include the evening and night pe-riod (see also Fig. 4). These latter are taken into account at higher integration times and, therefore, explain the in-crease of correlation.

Figure 16. Normalized Leq profile according to proce-dure 2) for the monitoring station hb136. Integration time: 5min

.

As for bullet point 2), the correlation has been calcu-lated with the same criteria of bullet point 1) but averaging over all the measurements and predictions in each integra-tion interval τ . The correlaintegra-tion results get better for all the integration times. This outcome may be explained if we consider that Dynamap has a statistically-based approach to noise description and, therefore, its performance is en-hanced by averaging over more observations.

7. CONCLUSIONS

In this paper, we studied the correlation among a network of monitoring sensors that make up the dynamic noise mapping of DYNAMAP. In general, in statistically-based noise mapping over large areas, each monitoring sensors must bring in as much as possible of information as it represents not just the noise locally collected but also the noise of a broader area (group). For this reason, as a gen-eral rule, each sensor should be uncorrelated with respect to the other sensors, both inside its own group and within the whole network. On the contrary, we want DYNAMAP prediction to be as much as possible correlated with lo-cal ”real” noise. Integration times have a great influence on it because they imply correlations over longer periods. Indeed, DYNAMAP for construction tend to favour large updating times (60min) with correlation coefficients up to 0.8-0.9. As DYNAMAP has a statistically-based approach, higher correlations are observed when averaging both mea-surements and predictions inside each group.

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