1. MILAN DYNAMIC NOISE MAPPING FROM FEW MONITORING STATIONS:
STATISTICAL ANALYSIS ON ROAD NETWORK
Giovanni Zambon, Roberto Benocci, Alessandro Bisceglie, H. Eduardo Roman
Dipartimento di Scienze dell’Ambiente e del Territorio e di Scienze della Terra, University of Milano – Bicocca, Italy

2. DESCRIPTION OF THE URBAN NETWORK
DATA COLLECTION
Acoustic data
Processing of the acoustic measurements
Production of a Geodatabase

3. 2233 road stretches The Urban Network AREA TO BE MAPPED:
Milan Pilot Area
2233 road stretches
belonging to all different types of urban roads:
principal arterial roads
collector arterial roads
local roads

4. Campaign of acoustic monitoring of road traffic noise in city of Milan
Collection of temporal trends of noise levels in order to create a significant sample for a
statistical analysis
Steps:
collection and selection of previous noise data
selection of monitoring sites based on specific criteria
acquisition of the acoustic data
correlation of acoustic data with weather data
identification and deletion of abnormal events
acquisition of series of equivalent sound levels
storing data in a GEODATABASE

5. RESULTS OF NOISE MONITORING CAMPAIGNS
The patterns of traffic flows (and therefore of noise) are very regular and repetitive. The streets can be joined together in a limited number of groups (clusters).

6. 3. STATISTICAL ANALISYS OF THE MONITORED STRETCHES Acoustic Database
Cluster analysis
Comparative analysis among profiles of different temporal discretization
Error Analysis at Different Temporal Discretization
Error Analysis for different cluster composition

7. Parameter used for roads comparison
Each i-th value of the temporal series was referred to the corresponding daytime LAeqdj (06-22 h) taken as reference level, that is for each hour the following parameter ᵟij was computed:
[dB] (j= 1, ………., 93)
Example of the normalization of the 24 h profile of the hourly LAeqh

8. Cluster analysis of hourly noise profile MDS Cluster
The Multi-Dimensional Scaling (MDS) applied to the data provides a visual representation of the pattern of proximities among the data. The distinction among clusters, marked by different colors, is rather good.
By means of a cluster analysis we obtain two clusters clearly distinct

9. Distribution of the different road classes D,E,F in the two clusters
Hourly
cluster
Road category
Total D E F
Cluster 1 5 12 39 56
(9%)
(21%)
(70%)
Cluster 2 4 20 13 37
(24%)
(54%)
(35%) 9 32 52 93

10. Comparison among mean profiles with different temporal discretization
Good stability of noise profiles for all temporal resolution

11. Error Analysis at Different Temporal Discretization
Standard deviations as a function of daily time for the different integration intervals for all arches considered for cluster 1 and 2
High variability of standard deviations

12. Updating time as a function of daily period
5 min
15 min
60 min
Time Interval 07h - 21h
Mean standard deviations, σ, [dB] as a function of integration time (for the different time intervals)
Time Interval 21h - 01h
Time Interval 01h - 07h

13. 4. AGGREGATION OF THE ROAD STRETCHES
The non-acoustic parameter (x)
Determination of the optimal non-acoustic parameter
Receiver Operating Characteristic (ROC) analysis
Interpolation method between the two mean noise behaviors
Discretization of the parameter x
Identification of monitoring network sites inside Zone 9

14. AGGREGATION OF THE ROAD STRETCHES
Roads stretches of the whole pilot area have to be grouped together when they display a similar traffic noise behavior.
One group
One basic noise map
(Afterwards we’ll see that starting from cluster analysis results (2 cluters), we can interpolate the behavior of noise of every stretch between the two regimes)
Road traffic noise is not known, so we look at the corresponding values of hourly traffic flows, which are known for all stretches in the urban area:
We introduce a suitable ‘non-acoustic’ parameter which should accurately represent the traffic flow and be sufficiently correlated with the corresponding traffic noise level
Determination of an optimal non-acoustic parameter

15. Determination of the optimal non-acoustic parameter
The optimal non-acoustic parameter is the one that best discriminates the two clusters objects.
The reliability of non-acoustic parameters was assessed by ROC (Receiver Operating Characteristic) curves, a graphical method to evaluate the performance of a binary classifier. The curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings. The index related to the Area Under the Curve (AUC) is equivalent to the probability that the result of the test on a group of roads with non-acoustic parameter over the threshold belongs to the proper cluster.
In table, the threshold values and the correspondent AUC are reported for each non-acoustic parameter considered.
Non-Acoustic Parameter
Threshold Value
Area Under the Curve (AUC)
(%)
log Tt
4.45
79.6
log Td
4.42
79.1
log Tn
3.21
81.3
( log F 8−9 ) 2 +( log F 21−22 ) 2
4.16
78.9
( log F 8−9 ) 2 +( log F 18−19 ) 2
4.69
77.5
( log F 8−9 ) 2 +( log F 3−4 ) 2
3.65
79.2
( log F 8−9 ) 2 +( log F 21−22 ) 2 +( log T t ) 2
6.20
( log F 8−9 ) 2 +( log T n ) 2
4.47
80.1
( log T d ) 2 +( log T n ) 2
5.30
80.8
( log T d ) 2 −( log T n ) 2
1.02
72.1
F 8−9
2007
76.2

16. Determination of the optimal non-acoustic parameter
The best result is obtained for LogTN and its combinations.
However, due to the uncertainty of the night flow rate calculated by the traffic model, we opted for LogTT.
ROC curve for the non-acoustic parameter LogTT. The AUC of 79.6% is reported together its 95% confidence level interval.

17. Results of the aggregation for the non-acoustic parameter X=LogTT
Frequency distribution of parameter x (histogram) and corresponding probability functions for the sample of monitored roads, inside Cluster 1 and 2
Due to the large superposition of the two cluster distributions P1(x) and P2(x), we consider a linear combination between the two time dependencies of the traffic noise from each cluster, for the given value of x. The weights (α1, α2) of the linear combination can be obtained for each value of x using the relations: α1=P1(x) and α2=P2(x). That is, for a given value of x we find the ‘components’ α1 and α2 from the analytical expressions of P(x). The values of α1,2 represent the ‘probability’ that a given road characterized by its own value of x belongs to the corresponding Cluster, 1 and 2. As one can see, we do not consider a sharp threshold for x, based for instance on the VFRH (vehicular flow rush hour), but the resulting hourly behavior h of the road noise is a linear combination of the mean noises measured for Cluster 1 and 2, denoted respectively as δC1(h) and δC2(h). The predicted traffic noise behavior, δpred(h), of a given value of x is then obtained by normalizing the values of α1,2 denoted as β:
Probability distribution functions P(x) for Cluster 1 and 2, for the parameter: X = Log TT
We observe a large superposition of the two cluster distributions P1(x) and P2(x)

18. Interpolation method between two mean noise behaviors
linear combination between the two trends of the traffic noise from each cluster, for the given value of x. The weights (α1, α2) of the linear combination can be obtained for each value of x using the relations: α1=P1(x) and α2=P2(x). That is, for a given value of x we find the ‘components’ α1 and α2 from the analytical expressions of P(x).
The values of α1,2 represent the ‘probability’ that a given road characterized by its own value of x belongs to the Cluster 1 and 2.
So the resulting hourly behavior of the road noise is a linear combination of the mean noises (noise ∆) measured for Cluster 1 and 2, denoted respectively as δC1(h) and δC2(h). The predicted traffic noise behavior, δpred(h), of a given value of x is then obtained by normalizing the values of α1,2 denoted as β:
Using the values of β we can predict the hourly variations δ(h) for a given value of x according to:
δpred(h) = β1* δC1(h) + β2* δC2(h)
The error made in using previous eq. can be estimated by calculating the standard deviation ε of the prediction δpred(h) from the measured values δmeas(h), that is:

19. Aggregation of the road stretches for the selected non-acoustic parameter
X=LogTT
Parameter X = LogTT has been calculated for all the road stretches within Milan pilot area (about 2200 roads).
Their distribution is compared with the probability distribution function P(x) obtained from the measurements at the 93 noise recording stations
Frequency distribution of parameter x (histogram) for the whole pilot area roads and probability functions (blue line) for the sample of monitored roads
Their distribution is reported in figure. As we can see, the distribution of X obtained from the measurements at the 93 noise recording stations is consistent with the whole distribution of X from the zone 9. This is a very important requirement for the chosen stations so that their X values cover essentially all the range of X values from the zone to be predicted the behavior of the traffic noise.

20. Mean values of β for the six groups of x = log TT.
Aggregation of the road stretches for the selected non-acoustic parameter
X=LogTT
From this distribution we have chosen 6 equally populated intervals of X (cake graphic).
To each group of X values a noise map will be associated and will be updated in real time by measuring the noise trend in few selected locations for the roads inside each group.
Mean values of β for the six groups of x = log TT.
Range of X
0,0 – 3,0
3,0 - 3,5
3,5 - 3,9
3,9 - 4,2
4,2 - 4,5
4,5- 5,2 β1
0,99
0,81
0,63
0,50
0,41
0,16 β2
0,01
0,19
0,37
0,59
0,84
Inside each group n, we determine the mean value Xn and obtain the corresponding values of β1(n) and β2(n).
These mean values of β can be used according to equation:
δpred(h) = β1* δC1(h) + β2* δC2(h)
in predicting the traffic noise associated to roads belonging to a given group.

21. Aggregation of the road stretches for the selected non-acoustic parameter
X=LogTT
Procedure to select the locations of the noise recording stations inside each one of the six groups of x. The choice is based on the use of the hourly flows taken from the traffic simulation model. To do that, we calculate the hourly mean traffic flow inside each group
Inside each group, we calculate the mean standard deviation of each road flow with respect to its mean δ.
The following list of roads is sorted from the closest distance to the mean (top road) till the 20th distance
This graph shows the mean hourly variations of the flow for each of the 6 groups, normalized using the rush hour values (08-09)

22. Identification of monitoring network sites inside Zone 9 (Milan pilot area)
Group 1
Group 2
Group 3
Group 4
Group 5
Group 6
0,0-3,0 δ
3,0-3,5
3,5-3,9
3,9-4,2
4,2-4,5
4,5-5,2
10531:10532
0,24
2168:10517
0,23
9247:9342
0,17
3103:8808
0,09
12039:16188
0,06
Stelvio_H
12093:13727
0,25
2953:11972
11845:11847
0,19
11927:12023
0,10
3121:16188
11985:11986
11966:11967
0,30
2953:3124
12161:12193
8808:11926
0,11
6974:12039
Murat_A
11966:33166
2158:13703
12167:12193
Fermi_AD
3064:8774
2160:11984
12092:13727
0,32
3154:11639
12157:12194
3103:11927
8774:12026
11984:11985
0,07
3029:3042
0,33
3165:11995
0,26
12161:12194
3132:11965
0,12
6974:12008
Zara_K
20540:31375
23024:23028
0,27
3939:13730
0,20
11926:11965
12994:13767
Zara_L
3965:3968
23028:23033
2479:31157
Pirelli_C
3168:12008
Zara_M
2172:27405
0,34
23035:23036
2103:8286
Pirelli_D
3031:3907
Sauro_A
27405:31375
3668:23035
2116:9353
0,21
Emanueli_D
2108:27223
Zara_D
3397:12121
2769:12083
12035:16179
Emanueli_E
2141:27223
Zara_C
4196:12121
2527:23161
16178:16179
3931:10314
12026:16189
Zara_E
5049:5051
2527:2554
2156:8286
3094:12023
0,13
3121:16189
Zara_N
34391:34392
0,35
11968:11969
3921:4065
10313:10314
2093:31418
Zara_O
34392:34393
3934:13721
0,28
27227:31381
3095:3096
0,14
3064:12024
Zara_B
0,08
3032:3041
0,36
3935:13721
27227:31383
3095:3102
12145:12146
Istria_A
3032:6031
2538:23161
2083:2162
3172:3173
12146:12147
Gioia_M
3042:6032
5049:13710
12103:16003
3173:13822
Pasta_A
Fermi_AA
6031:6032
16019:23024
12104:16003
Cozzi_G
Girardengo_B
Fermi_AB
3382:12017
5047:16019
11887:31396
10322:16000
0,15
Girardengo_C
Fermi_Z
In the Table we report the first 20 roads for each group of x in which their logarithm of the flow has the lower distance from the mean group value calculated over the 24 hours

23. Milan Pilot Area 𝑥= log 𝑇 𝑇 Top 20 locations LEGEND 0,0 - 3,0
3,0 - 3,5
3,5 - 3,9
3,9 - 4,2
4,2 - 4,5
4,5- 5,2
DYNAMAP Noise Monitoring Points
Pilot area

24. δpred(τ) = β1* δC1’(τ) + β2* δC2’(τ)
Pilot Area (~2200 roads)
Acoustic dataset (~100 roads)
Two clusters
δC1(τ) , δC2(τ) over 24 hours
τ = 5, 15,…, 60 min
Cluster analysis
Distribution analysis
Non-acoustic parameter X
6 groups n
δpred(τ) = β1* δC1(τ) + β2* δC2(τ)
β1 ,β2 = parameters of probability
function
Mean Xn ,corresponding values of β1(n) and β2(n)
Low cost terminals measures
(assigned to two clusters (C1’, C2’) analysing starting data recordings)
6 basic noise maps
Noise calculation:
δpred(τ) = β1* δC1’(τ) + β2* δC2’(τ)
Noise updating for each point of map n
Sum of updated maps