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“Uncertainty-noise” Le Mans
37
Acoustique
&
Techniques n° 40
uncorrelated sources, while the automatically subdivided
subparts of an extended source may not be uncorrelated if
this source is a road or an area where a noisy device like a fork
lift is operating. If the line or area source consists in reality of
moving point sources, any assumption about the emission of
these point sources is valid for all subparts – the covariance
included in equation (4) cannot be neglected. Noise mapping
software implying uncertainty determinations as shown in fig.
4 – 6 should take this into account.
Uncertainty – What has to be included ?
It depends strongly on the deliverables of a calculation what
influences have to be taken into account when uncertainties
shall be estimated. The two terms in the sum equation (6) are
sums of the squared standard deviations of various influences
and in many cases it is better to split them up to be able to
quantify them. In the case of strategic noise mapping based
on the END the noise levels are not the end of the game – they
are calculated at the most exposed facades of the buildings
and according to Annex VI of END the people affected shall
be evaluated. Even the distribution of people versus level
intervals may only be an interim result – using dose-response
relationships the total annoyance of all people in a city [3] may
be the metric that shall be used to rank a situation.
If we calculate the strategic noise map, the distribution of
people affected and a total annoyance score of all people
as a single number we may ask about the uncertainty of this
final result. Millions of complex calculations are included to
come from the digital model of a city to this final result, and
it is only possible in realistic times because we accept a lot
of approximations and even assumptions in modelling and
calculation. In such cases where the whole process may be
improved with more detailed modelling and calculation, but
where time or financial budgets define the insurmountable
limits, a very thorough balancing of the accuracy of each step
is necessary to minimize the uncertainty of the end result. If
we invest calculation time and other restricted resources in
steps that contribute only little to the result the uncertainty of
this result will be increased (always taking into account that
restricted budgets define limits).
Source modeling
In simple cases sources can be modelled as omni directional
radiating point sources with A-weighted sound power level. In
many cases of industrial noise where hundreds of such sources
contribute, this is the best solution. The fewer dominating
sources define the noise at the receiver position, the more
it is necessary to take into account frequency distribution
and directivity of the radiation. Larger sources like machines,
trucks and railways may even be modelled as structural
extended objects with many sources distributed on their
surface. But as mentioned above – detailed modelling needs
more data and reduces transparency and understandability. If
the directivity of sources is negligible, we reduce the accuracy
of the result if we force people to enter hundreds of additional
unnecessary numbers.
For sources with sound power levels that have been
determined on the basis of the ISO 3740 series the source
related uncertainty can be oriented at the values given in
table 1.
Propagation calculation
With road, railway and aircraft noise the source description
as well as propagation calculation is generally part of national
or international standards. In many countries it is mandatory
what standard has to be used when calculating noise levels
to prove the compatibility with legal requirements. This is a
typical case where the result of a correct calculation using the
standardized routines is the “true value”, and each deviating
value – even if it fits better with measurements – has to be
treated as an error.
If the same situation is to be modelled and the levels at the
same positions shall be calculated by different people where
only the standard is the given frame we will get results that are
dispersed. We can distinguish three types of deviations.
- Type A: real errors in the software realization of equations
described in the standard. These are bugs and the best way
to find and minimize them is to publish with each of these
standards a set of test problems with step to step results.
These can also be used to certify the correctness of software
when the standardized methodology is applied.
- Type B: deviations that are caused by not precise or
ambiguously formulated procedures. Many of these cases
occur because most standards deal only with simple
situations, and it is obvious that we get different results if
different developers try to comply with such a problem. These
differences are part of the “natural” uncertainty of results
using this standard.
- Type C: deviations that are caused because situations that
occur in reality and in the model are not covered by the
standardized methodology.
Some authors try to show that software packages are
erroneous by using different programs for the same problem
and yamming about dispersing results. It is recommended to
classify the problem what type it is related to the classification
above – if it is type 2 or 3, it can only be treated as a motivation
to improve the standard.
Many experts claim since years that existing “traditional”
models are inaccurate and that meteorological effect should
be included more detailed. Much money has been invested in
Europe to improve this situation and to develop better models
for the near future.
Fig. 7 : Steps where uncertainties have to be taken into account in EU-Noise-Mapping
Uncertainties in the prediction of environmental noise and in noise mapping