Zadanie 5

GÓRNO‘LSKA WY›SZA
SZKOŠA HANDLOWA
Imi¦ i nazwisko
NR ALBUMU 000000
PRACA IN›YNIERSKA
PIERWSZA LINIA TEMATU PRACY
DRUGA LINIA TEMATU PRACY
PROMOTOR
TYTUŠ IMI† NAZWISKO PROMOTORA
K A T O W I C E ROK STWORZENIA PRACY
Wst¦p
In the paper we discuss the analysis of meteorological data. We consider the relationship between them using a special fuzzy number form. We also use a set of
historical data.
For the weather forecast chosen we nd similar weather forecasts. Next, we nd
real meteorological situations from the historical data which correspond to them and
we create fuzzy numbers, that is, the fuzzy weather forecasts. Then we estimate the
validity of the weather forecast on the basis of the historical data and its checkability.
We investigate it with the help of an indicators set, which corresponds to the parameters of the weather forecast, using the similarities rule of the weather forecast to
the meteorological situation, a proper distance and data analysis.
This comprehensive analysis allows us to investigate the eectiveness of forecasting
fuzzy numbers, putting the dependence between particular attributes describing the
weather forecast in order and proving the legitimacy of the applicable fuzzy numbers
in air pollution forecasting.
Rozdziaª 1
A fuzzy weather forecast is determined for each attribute individually and it is
evenly distributed on T hours. It is valued on basis of data similarity and proper
weights of classications. We researched the behavior of fuzzy weather forecast using
dierent sets of forecast data. This is necessary because we have weather forecasts
from a short period of time (only six years). Therefore, continuous work in a model
COSMO LM weather forecast is not heterogenous to nding the period of a weather
forecast which is the best estimate real meteorlogocal situations. In Fig fuzzy weather
forecasts are shown along with real meteorological situations. The fuzziness is a good
measure to mark the quality of a weather forecast both its elements and the whole
weather forecast because fuzziness characterises the scattering of real data around the
prognosis in 1.
Meteorological situations
Aerosanitary situations
Weather forecasts
1. Meteorological situations
2. Aerosanitary situations
3. Weather forecasts
Rozdziaª 2
Hurtownia danych
Wybranym narz¦dziem do przechowywania danych meteorlogicznych jest hurtownia danych. Jest to specyczny rodzaj bazy danych, który charakteryzuje si¦ czterema
cechami:
1. nieulotno±¢ - dane raz umieszczone w hurtowni pozostaj¡ w niej niezmienione,
czyli u»ytkownicy maj¡ pewno±¢, »e takie samo zapytanie zawsze zwróci ten sam
wynik,
2. zorientowanie na temat - dane znajduj¡ce si¦ w hurtowni dotycz¡ pewnego tematu
np. prognozy pogody, a nie dziaªa«,
3. zintegrowanie - dane s¡ jednolite np. daty przechowywane s¡ w tym samym formacie,
4. zmienno±¢ w czasie - gromadzone dane zmieniaj¡ si¦ w czasie, gdy» w tym przypadku tj. dla danych meteorologicznych zapytania kierowane do hurtowni danych
wymagaj¡ prze±ledzenia pewnego odcinka danych.
Dzi¦ki temu, »e dane przechowywane s¡ w hurtowni danych to mog¡ one by¢ w sposób
ªatwy dzielone wedªug odpowiednich wycinków terminów: czas, b¡d¹ rodzaj przechowywanych danych. Dost¦p do danych jest ªatwy i szybko otrzymywane s¡ w postaci
przebiegów czasowych. Na rysunku 2.1 widoczny jest zaproponowany sposób gromadzenia danych meteorologicznych.
Rozdziaª 2. Hurtownia danych
Rysunek 2.1. Hurtownia dla danych meteorlogicznych
5
Rozdziaª 3
The rst trials of forecasting everyday phenomena, particularly meteorological,
began around 650 B.C. [1] by the Babylonians. They tried to predict short-term
weather changes based on the appearance of clouds. Methods of weather forecasting
were increasingly perfected in subsequent centuries. In the XX century, as a result of
the development of mathematics and physics, models which used partial dierential
equations were formulated. These equations which describe the state of the atmosphere, could be solved numerically. However, in 1961 E.Lorenz showed the limitation of
possibilities of these models rst of all their chaotic character. These models are
only eective for few a days maximum a week. However, for a 3-day term their
eectiveness is high.
In recent years many prediction approaches, such as statistical [2], fuzzy [3, 4], neural networks [5, 6], neuro-fuzzy predictor [7] have emerged. Using numerical short-term
weather prediction, research into the forecasting of air pollution concentrations began
[8, 9]. This task is very dicult because apart from the information about meteorological conditions, the emission of air pollution depends rst of all on the immission.
At this moment, emission is quite accurately measured from a single, high pointer
emitter (e.g. carbon power stations). Measurement of low emission, communal and
municipal, is almost impossible. Moreover, 3D models of immission calculating (e.g.
Gaussian pu modelling system) require a eld of wind and a eld of temperature
measure from several hundred metres above ground level. Such measurements are only
conducted in a very few places in the world with the help of a sodar.
Thus, input data for an Air Pollution Forecasting Model (APFM) must be estimated, therefore, they are both incomplete and imprecise. In this situation Fuzzy
sets theory is helpful [10, 11, 12]. Use of this method is known in many mathematical
forecasting models. It is usually used when the information transferred to the model is imprecise or incomplete [13, 14]. Many everyday phenomena of an ambiguous,
continuous and imprecise nature may be eectively described using this theory.
In [15] B. Hansen presented a very interesting way of using fuzzy sets and case-based
7
reasoning in weather forecasting. On the other hand fuzzy logic allows the inuence
of meteorological conditions on changes of air pollution levels and their quantication
to be researched. Being inspired by the paper [15], we propose a model to serve as a
forecaster of air pollution concentrations. We assume:
1. Aerosanitary situations air pollution concentration over several hours, the result
of the emission of this pollution and the meteorological situations (previous and
present). The progressive methodology for all pollutions will be homogeneous.
2. Future based on similar situations from the past similar meteorological situations bring about similar aerosanitary situations in a similar area. The basic idea
for forecasting is searching through history for meteorological situations which are
close to the expected meteorological situation.
Rozdziaª 3.
Zako«czenie
Ze wzgl¦du na to, »e interesuj¡ nas ró»ne warto±ci aerosanitarne np. o warto±ciach
skrajnych to ko«cowy przebieg rozmyty mo»e by¢ defuzykowany na ró»ne sposoby.
Bior¡c pod uwag¦ to, »e interesuje nas jedynie defuzykacja liczby rozmytej w postaci
dyskretnej to zajmiemy si¦ poni»ej tylko takimi metodami.
1. metoda ±rodka ci¦»ko±ci,
2. metoda maksimum funkcji przynale»no±ci.
Odwzorowujemy wtedy dany zbiór rozmyty w jedn¡ warto±¢ y ∈ Y nazywa¢ to
b¦dziemy wyostrzeniem.
Poni»ej zostan¡ przedstawione znane metody wyostrzenia.
1. Metoda ±rodka ci¦»ko±ci,
2. Metoda maksimum funkcji przynale»no±ci.
Zgodnie z metod¡ 1 otrzymujemy lepsze wyniki, w przeciwie«stwie do metody 2.
Napiszemy jeszce teraz nast¦puj¡ce symbole: ∞
∗
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Bibliograa
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Bibliograa
10
[14] B.K.Hansen, D.Riordan, Weather Prediction Using Case-Based Reasoning and Fuzzy
Set Theory, in: Proc. Workshop on Soft Computing in Case-Based Reasoning, International Conf. on Case-Based Reasoning, Canada, 2001, pp.175-178.
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MSc Thesis, Technical University of Nova Scotia, Halifax, Nova Scotia, Canada, 2000.