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Influence of short-term sampling parameters on the uncertainty of the L
den
environmental
noise indicator
View the table of contents for this issue, or go to the journal homepage for more
2015 J. Phys.: Conf. Ser. 588 012026
(http://iopscience.iop.org/1742-6596/588/1/012026)
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Influence of short-term sampling parameters on the
uncertainty of the L
den
environmental noise indicator
M Mateus
1
, J Dias Carrilho and M Gameiro da Silva
ADAI/LAETA – Department of Mechanical Engineering, Faculty of Science and
Technology University of Coimbra – Pólo II, 3030-201 Coimbra, PORTUGAL
E-mail: mario.mateus@adai.pt
Abstract. The present study deals with the influence of the sampling parameters on the
uncertainty of noise equivalent level in environmental noise measurements. The study has been
carried out through the test of different sampling strategies doing resampling trials over
continuous monitoring noise files obtained previously in an urban location in the city of
Coimbra, in Portugal. On short term measurements, not only the duration of the sampling
episodes but also its number have influence on the uncertainty of the result. This influence is
higher for the time periods where sound levels suffer a greater variation, such as during the
night period. In this period, in case both parameters (duration and number of sampling
episodes) are not carefully selected, the uncertainty level can reach too high values contributing
to a loss of precision of the measurements. With the obtained data it was investigated the
sampling parameters influence on the long term noise indicator uncertainty, calculated
according the Draft 1st CD ISO 1996-2:2012 proposed method. It has been verified that this
method allows the possibility of defining a general methodology which enables the setting of
the parameters once the precision level is fixed. For the three reference periods defined for
environmental noise (day, evening and night), it was possible to derive a two variable power
law representing the uncertainty of the determined
values as a function of the two sampling
parameters: duration of sampling episode and number of episodes.
1. Introduction
The current draft document of the ISO 1996-2 standard [1] proposes two distinct sampling methods
for estimating environmental noise indicators: one making use of long-term measurements and the
other using short-term measurements. In both sampling methods, a measurement campaign may
consist of several measurement episodes distributed throughout the assessment period. The details on
how to design an appropriate sampling strategy, i.e., how to choose the number and duration of the
measurement episodes, are, however, left unspecified in the standard. In addition, there is no guidance
as to how the choice of the sampling strategy might influence the overall uncertainty in the
determination of environmental noise indicators.
There is, in the literature, some indication as to what extent a required accuracy might be achieved
with a particular sampling strategy [2–5]. Given the variability in propagation conditions and source
emission characteristics from site to site, however, the sampling strategy that produces the best results
in one particular site might not be adequate for a another site. With this problem in mind, the authors
have recently proposed a systematic analysis method for assessing the adequacy of a sampling strategy
for any given site [6]. The method is based on the bootstrap method, and it produces an estimate of the
uncertainty associated with determining environmental noise levels from short-term sampling
measurements, as a function of the duration and the number of measurement episodes. In the present
1
Corresponding author: Tel.:+351 239 708 580; fax: +351 239 708 589
E-mail address: mario.mateus@adai.pt
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Journal of Physics: Conference Series 588 (2015) 012026 doi:10.1088/1742-6596/588/1/012026
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
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paper, the authors demonstrate the application of this method in quantifying the influence of the
sampling strategy on the uncertainty of the long term environmental noise indicator
.
2. Mathematical formulation
In Ref [7] the expression for calculating the long term environmental noise exposure indicator appears:
(1)
The indicators
e
are the long term noise levels for the reference periods: day; evening;
and night. These, in turn, can be obtained by sampling during the long term period of assessment,
taking into consideration that weather conditions can have a significant influence in the way sound
energy propagates from source to receiver. ISO1996-2 deals with this by defining four meteorological
classes with respect to the propagation of sound energy: M1 – unfavorable; M2 – neutral; M3 –
favorable; and M4 – very favorable. If the a number of sample measurements
are performed for a
particular weather condition
, for which the probability of occurrence
is known or can be
estimated, the indicators for each reference period can be estimated from
(2)
By the law of propagation of uncertainties, the combined uncertainty of the indicators
is
(3)
Considering the results presented in (3), it is possible to write the expression for the combined
uncertainty of the indicator
, as follows: Assuming independence between the different variables
involved, as in Ref [1], the application of the methodology expressed in the GUM [8], considering also
due to sampling component, hereafter denoted by
, the following expression is obtained for the
uncertainty of sound level
:
(4)
were:
,
and
are the sensitivity coefficients, i.e. they express the change of
due
to changes in
,
and
, respectively;
,
and
are the standard uncertainty associated with the measurement
performed to characterize the noise in each reference period;
is the standard uncertainty associated with the location of the measurement point;
is the standard uncertainty associated with the measurement chain;
is the standard uncertainty associated with the process of sampling in the period under
review.
It is assumed that the components of uncertainty associated with the measuring equipment and the
placement of the microphone are constant, i.e., always the same measuring equipment is used and the
IMEKO IOP Publishing
Journal of Physics: Conference Series 588 (2015) 012026 doi:10.1088/1742-6596/588/1/012026
2
sampling is performed on the same site. Regarding the uncertainty due to sampling, it is assumed that
it should correspond separately to those resulting from the sampling strategy followed in each period.
Generically, the sensitivity coefficients assume the following expression, were is 0 dB, 5 dB or
10 dB, for the day, evening and the night periods, respectively:
(5)
In Ref. [6], when implementing a fitting process of the observed experimental data with an
analytical function of two variables, it was found that a generic power function expression may be
used for the three reference periods, varying only the numeric coefficients. The expression is:
(6)
where α
1
, α
2
and α
3
are numerical coefficients found from least squares fitting to locally obtained data.
3. Materials and methods
The site where the study took place is relatively plane with no major obstacles between the source and
the adjacent buildings. The dominant noise source is a double lane collecting road following the most
recent bridge built over the Mondego river: the Rainha Santa bridge, in Coimbra, a city in the center of
Portugal.
Figure 1 shows an aerial photograph of the site, obtained from the web application Google Earth.
Superimposed on the photograph is a wind rose centered on the measurement location, showing that
the dominant wind direction is from northwest. The most probable velocity is in the range [1.0 m/s;
2.0 m/s].
The annual average daily traffic is about 37,000 vehicles per day, with approximately 10% of
heavy vehicles. The traffic is mostly fluid and decelerating, in the west-east direction, from 70 km/h,
over the bridge, to 50 km/h, after the bridge. In the east-west direction, the traffic is also fluid and
accelerates from 50 km/h to 70 km/h.
The measurement system was built around a National Instruments (NI) data acquisition system and
LabVIEW application development platform. The signal from a Brüel&Kjær ½” diameter microphone
model 4189, with pre-amplifier model 2671, is converted to digital format by a NI USB-9233 data
acquisition board. The microphone was mounted on the exterior of a window, at the third floor level of
the Laboratory of Industrial Aerodynamics, of the University of Coimbra. The distance to the road is
about 150 m.
Figure 1. Aerial photograph of the noise assessment site, with a wind rose
centered on the measurement location.
IMEKO IOP Publishing
Journal of Physics: Conference Series 588 (2015) 012026 doi:10.1088/1742-6596/588/1/012026
3
In order to determine the numerical coefficients in (6), a consecutive 17-day
time series
was selected from a continuous 4-year noise monitoring campaign. Figure 3 compares the 17-day
daily average levels with the 4-year daily average levels, showing that the 17-day sample is
representative of the expected daily noise level variation at the site. The two dotted lines represent an
uncertainty band for the 4-year measurements, considering that, in each period during the day, the
noise equivalent level has a Gaussian distribution. A coverage factor equal to 2 (95% probability) has
been used. Table 1 shows the numerical coefficients obtained from fitting (6) to the 17-day noise
sample.
Figure 3. Comparison between the 17-day daily average levels (solid line)
and the 4-year daily average levels (dashed line)
Table 1 – Numerical coefficients of equation (4.1) for each reference
period.
Coef.
Day
evening
Night
2.5224
2.2885
4.6034
-0.086
-0.181
-0.068
0.408
0.3695
0.4686
0.010
0.034
0.002
4. Results and discussion
In Ref [1] the values of uncertainty accounted as fixed components to the sound level meter and
microphone placement measurement, should be respectively, 0.5 dB and 0.4 dB. For the latter
component its value must be recorded in the case of noise from road noise sources, and whose impact
on the mounting location of the microphone is not grazing incidence.
Accounting for only these two components of uncertainty, in which we consider the remaining
components in (4) to be zero, leads to a fixed component of the expanded uncertainty
which
cannot be less than 1.3 dB.
IMEKO IOP Publishing
Journal of Physics: Conference Series 588 (2015) 012026 doi:10.1088/1742-6596/588/1/012026
4
Following the measurement model assumed in this paper, the accounting of the
component
will always be affected by the sensitivity coefficients associated with each period. These coefficients
have a strong dependence of the noise levels of each period, as shown in Table 2.
Table 2. Sound levels for three different situations, and their respective
sensitivity coefficients, used to analyze the influence of sampling in the
expanded uncertainty
.
Case
(dB(A))
(dB(A))
(dB(A))
A
61
60
50
0.423
0.354
0.224
Ref
61
60
54
0.316
0.264
0.420
B
61
60
58
0.193
0.162
0.645
The accounting of the
component, for the three cases considered, the results are presented in
Figure 10, providing evidence of the influence of sampling component in the expanded uncertainty
, also highlighting its dependence on the number of episodes and duration, as well as
differences in the level of indicators
,
e
.
(a)
(b)
Figure 10. Variation range of
:
a) case A; b) case Ref; c) case B.
(c)
The influence that the sound level of nighttime have on the results presented for
, is greater
the smaller the difference to the levels of other periods. This feature results from the weight that is
given by the respective sensitivity coefficient and also due to the uncertainty of the noise level in this
period.
IMEKO IOP Publishing
Journal of Physics: Conference Series 588 (2015) 012026 doi:10.1088/1742-6596/588/1/012026
5
The results presented in these figures refer only to fixed components, not yet part of the uncertainty
inherent to the repeatability of the measurements, which will naturally increase further the limits
presented.
5. Conclusion
A systematic analysis method, based on the bootstrap method, is proposed by the authors for assessing
the quality of sampling strategies for estimating long-term environmental noise indicators at any given
site.
The methodology developed allows to determine the best sampling strategy that meets a given
requirement regarding measurement uncertainty. Implicitly it follows also that distinct effort should be
placed in measurement strategies depending on the contribution that each component has on the final
result as well as the precision value associated with it.
Acknowlegment
This work has been partially supported by Fundação para a Ciência e a Tecnologia (FCT) under
project Pest-OE/EME/LA-0022/20011. First author acknowledges FCT PhD grant Ref
SFRH/BD/37828/2007.
References
[1] Draft 1st CD ISO 1996-2:2012, Acoustics – description, measurement and assessment of
environmental noise - Parte 2: determination of environmental noise levels; 2012.
[2] Gaja E., Gimenez A., Sancho S., Reih A. Sampling Techniques for the estimation of the annual
equivalent noise level under urban traffic conditions, Appl Acoust 2003; 64(1); 45-53.
[3] Kuehne D. Long-term Leq Errors Expected and how long to Measure (Uncertainty and Noise
Monitoring), ForumAcusticum 2005, Budapest (Hungary), Aug 29 - Sep 2; 2005.
[4] Brambilla G., Lo Castro F., Andrea C., Verardi P. Accuracy of temporal samplings of
environmental noise to estimate the long-term Lden value, Internoise 2007, Istanbul
(Turkey), August 28-31; 2007.
[5] Jagniatinskis A., Fiks B. Assessment of environmental noise from long-term window
microphone measurements, Appl Acoust 2014; 76; 2014.
[6] Mateus M, Dias Carrilho J and Gameiro da Silva M. Assessing the influence of the sampling
strategy on the uncertainty of environmental noise measurements through Bootstrap method.
Manuscript submitted for publication (copy on file with corresponding author).
[7] Directive 2002/49/EC, of the European Parliament and of the Council of 25 June 2002 relating
to the assessment and management of environmental noise; 2002.
[8] JCGM 100, Evaluation of measurement data – Guide to the expression of uncertainty in
measurement, Paris: Joint Committee for Guides in Metrology (JCGM/WG 1), 2008.
IMEKO IOP Publishing
Journal of Physics: Conference Series 588 (2015) 012026 doi:10.1088/1742-6596/588/1/012026
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