Annoyance accumulation modeling in a community noise annoyance expert system


Annoyance accumulation modeling in a community noise annoyance expert system

Dick Botteldooren

Acoustics group, Department of Information Technology, Universi~ of Gent, Belgium

Abstract: When the state of the sound environment in a region is monitored by tracing the percentage of people that is
annoyed by noise, simulation models for community noise annoyance are needed. Building such simulation tools is not an
easy task because information is scarce and relations between quantities involved is uncertain. Tberefor an expert system
that makes optimal use of the scare information is constructed. Modifier fuzzyness is fully taken into account. Combination
of annoyance caused by different sources is an important part of the system. The probability approximation is used in this
paper to incorporate perceptual annoyance models for combined community noises. The uncertainty that still exists in this
field does not pose any problems to the system.

FUZZY AND ANNOYAN~

Annoyance is a vague concept. Often vague or fuzzy concepts are context dependent. In annoyance models this is
sometimes referred to as the principle of compromise (1). Modifiers (e.g. highly, moderately) show a similar fuzzy ness.
In annoyance surveys one often gets around the fuzzyness in modifiers by using a discrete numerical scale. In the

expert system proposed here, both numerical and verbal scales can be used, as long as consistency is maintained in all
calculations. It is advantageous to cover the whole range of modifiers in the calculations including for example zero
on a numerical scale or “not annoyed” on a verbal scale.

THE EXPERT SYSTEM

The expert system designed for community noise annoyance simulation, consists of an environment that allows to
take into account uncertainty and vagueness in all calculations, Uncertainty on quntities is represented by a probability
distribution. Interfaces to Gaussian and level set descriptions are provided. The latter approach is preferred for input in
many cases. It consists in fixing a number of uncertainty intervals for each input (e.g. 6870, 95?0 and l~~o certainty
intervals). Standard operations such as adding, multiplying, matrix multiplication or interpolation are defined for
uncertain variables. The key feature of the system is “consensus”. It allows to combine in a formal way, different
calculations or different expert opinions to obtain a possibly better approximation from the scarce pieces of uncertain
information. Details on the expert system were reported in (2).

ANNOYANE ACCUSATION

In community noise annoyance simulation, accumulation of annoyance caused by different sound sources is an
important step in the process. Several perceptual models backed up by laboratory experiments exist, but no detailed
data based on annoyance reports is available (1). In particular the principle of compromise poses major problems.

In this work a general approach based on probability theory is introduced. Assume two sources of annoyance A
and B. Let the subscript denote the quantifier of annoyance. The probability that a single individual in a population is
annoyed at level i is assumed to be equal to the percentage of individuals in that population that is annoyed at level i.
If the total annoyance is called H, than the probability that an individual is annoyed to level i is given by

P(Hk) = ~ P(Hk[Ai, ~j)~(At, ~j), (1)

a,j

where I indicates conditional probability. The only requirement for this equation to be valid is that all levels of annoyance
are covered by the subscripts. The advantage of using equation 1 lies in the fact that the conditional probability will
probably be less dependent on exposure levels. This is a basic assumption of most perceptual models. P(Ai, Bj ) gives
the probability of simultaneous theoretical annoyance in the absence of the other source. It therefor does not take into
account masking or inhibition. In some cases P(Ai, Bj ) can be obtained directly from an exposure model in other
cases it is useful to further expand it as P(Ai/Bj)P(Bj). In the absence of geographical clustering of noise sources
independence can be assumed, which leads to P(Aa, Bj) = PA. me probability tensor P(Hk lAi, Bj)

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TABLE 1. Comparison of annoyance accumulation and sound level summation for total annoyance calculation
model moderately annoyed higtiy annoyed

68% low mostprobable 68% high 68%1ow mostprobable 68% high

level summation 27 34 48 13 18 25
annoyance accumulation 41 53 66 19 26 34

includes the influence of the presence of the other source, the summation principle and the compromise principle. At
this moment there is not enough knowledge available about the probabilities ~(~k 1A,, Bj ). Therefor each element of
the tensor is implemented as an uncertain value. This allows to incorporate knowledge as vague as:

“if a person is hi~hlv annoyed by sound of source A and highlv annoved by sound of source B, then he
will QUITE LIKELY be highlv snnoved by the combination of both sources’!or
“if a person is not annoved by sound of source A end hi~hlv ennoved by sound of source B, then he will

PROBABLYbe less highly annoved by the combination of both sources”
where the fuzzy quantifiers are underlined and the uncertain element of~(HklAi, Bj) is written in capital letters.

In community noise annoyance calculations, introducing a secondary condition can often be very helpfulto accu-
ratelyquantify F(HklAi, Bj)andto verify the independence ofexposure, Agoodexample are well localized sources

(e.g. airports) where aregion can beidentified to which the impact ofone sourceis limited. As an example assume
that P(T) istheprobability that aperson lives within anareawhere both sources Aand Bcanbeimpoflant. In~
source A is not present. Total annoyance can than be split as P(~&) = P(Hk IT)P(T) + P(Hk l~)P(~) , or after
similar processing as Eqs 1

p(~~) = ~ P(H~lAi, BjlT)p(Ai, BjlT)p(T) + ~p(HklAo, BjlT)p(BjlT)P(T) (2)
~,~ j

The first part of the equation describes real accumulation, while the second part only includes the compromise principle.

EXAMPLE

Within the limited space of this written paper, only one extreme example is given to illustrate the technique. Traffic
noise annoyance is assessed in two different ways. First total noise exposure is determined (in a sample taken at
random) and multiplied by average dose-response relations to yield a distribution of the population over different
annoyance levels. Secondly the exposure to local traffic noise is obtained as well as exposure to highway traffic noise.
Both exposure lead to a distribution of the population over annoyance levels. Finally annoyance of both sources is
accumulated using the extreme assumptions of exposure independence, a strongest component perceptual model and
no context dependence. In this case the tensor p(~k /Ai, Bj ) is reduced to

Hnot Hmode.ateiu Hhighlv
An Am Ah An Am Ah An Am Ah

Bnl OOBn OIO Bnool (3)

BmOOOBml10 Bmool

BhOOOBh OOO Bhlll

without any uncertainty. Certainty intervals (68%) and most probable value for percentage of people highly and
moderately annoyed are given in table 1 for both approaches.

REFERENCES

1. B. Berghrnd and M.E. Nilsson, “Empirical issues concerning annoyance models for combined community noises;’ Proceedings
of Infemoise 97, Budapest, Hungary, 1053-1058, 1997
2. J. De Poorter and D. Botteldooren, “Vagueness and Uncertainty in Community Noise Annoyance Modeling;’ Proceedings Of
Internoise 97, Budapest, Hungary, 1207-1210, 1997

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