Genetik algoritmaların meteorolojik uygulamaları /
Yazar: MEHMET ÖZTOPAL
Danışman: PROF. DR. ZEKAİ ŞEN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Meteoroloji Mühendisliği Ana Bilim Dalı
Derece: Yüksek Lisans, 1998
Konu: Meteoroloji = Meteorology
Dizin: Genetik algoritmalar = Genetic algorithms ; Meteoroloji = Meteorology

Özet:
ÖZET Bu çalışmanın esas amacı, uzman sistemlerden biri olan Genetik Algoritmalar'ın endüstrinin yanında atmosfer bilimlerinde de kullanılabileceğini göstermektir. Bununla bağlantılı olarak meteorolojik problemlerde çokça karşılaşılan objektif analiz, Angström denklemi, sınıflandırma ve sıcaklık modellemesi gibi dört farklı konu seçilmiştir. Bunlardan Objektif analiz çalışmasında, literatürde bulunan Cressman ve Barnes ifadelerinin, bölgesel bağımlılığı da yansıtan ağırlık fonksiyonlarını temsil eder hale getirilmesi amaçlanmıştır. Bunun için de en uygun tesir mesafesi (R) ve yumuşatma katsayısı (a) parametreleri Genetik Algoritmalarla bulunmuştur. Ayrıca bu çalışma ile R ve a parametrelerinin objektif olarak bulunabileceği de gösterilmiştir. Eldeki sayısal ve sözel verilerden yararlanarak iki farklı yapıyı (sınıfı) birbirinden ayırmak için literatürde çoklu regresyon yöntemi kullanılabilir. Bunun yanında böyle bir sınıflandırma probleminde Genetik Algoritmaları da kullanabilmek mümkündür. Bunun için Albany, Newyork'ta ölçülen düşey hız ve çiğ noktası depresyonu verileri kullanılmıştır. Toplam 91 günlük veriden 29 gününde yağış gözlenmiştir. Bu veriler için Panofeky ve Brier'm çoklu regresyon yöntemiyle buldukları doğru denklemi 15 hataya sahipken, Genetik Algoritmalarda hata sayısı 12 olarak bulunmuştur. Diğer bir uygulamada, meteorolojik bileşenlerin en önemlilerinden birisi olan sıcaklık parametresinin buhar basıncı ve bağıl nem parametrelerinden faydalanılarak öngörülmesine çalışılmıştır. Burada yöntem olarak Yapay Sinir Ağlarının bilgilerin sinirler arası iletilmesi prensibi ile beraber Genetik Algoritmalar kullanılmıştır. Veriler istanbul Göztepe istasyonuna ait sıcaklık, buhar basıncı ve bağıl nem verileri olup 1 Mart-20 Nisan 1996 tarihleri arasındaki günlük ortalama değerlerdir. Bilindiği gibi aylık ortalama güneş ışınımı hesaplamalarında Angstrom doğrusal ışınım denklemi kullanılmaktadır ve dolayısıyla bu klasik bir regresyon analizidir. Eldeki verilerden sadece bir tane a ve b katsayısı hesaplanır. Yapılan bu çalışmanın klasik regresyon analizinden farkı, Angstrom denklemindeki a ve b »katsayılarının hesabında tüm veriyi gözönünde bulundurmamasıdır. Birbirlerini takip eden her iki ay arasından bir a ve b katsayısı hesaplanabiliyor. Böylelikle tüm verilerden bir tane durağan a ve b katsayısı elde etmek yerine dinamiği olan bir a ve b zaman serisi elde etmek mümkündür. Ayrıca bu elde edilen zaman serisinden hava ve iklim parametrelerindeki değişim dolaylı da olsa görülebilir. Klasik regresyon analizinin bize vermediği a ve b katsayılarının istatistiksel analizi bu yöntemle yapılabilmektedir. Sonuç olarak Genetik Algoritmaların meteorolojideki en iyileme problemlerinin hepsinde rahatlıkla kullanılabileceği görülmüştür. XII

Abstract:
SUMMARY In the last decades the human being have started to imitate the behavior of living organisms in order to model them in the artificial media through logical approaches and by this manner they are able to solve actual problems through models. For instance, the existence of neurons in the living organism's body is a means of transferring knowledge and examination of this system lead human kind to artificial neural networks. On the other hand, considering the adaptability of living organisms to their environments lead to the emergence of genetic algorithm approaches in the modeling of natural phenomena. In the discipline of meteorology the modeling affairs are very significant. The prediction of future occurrence becomes rather simple and straight forward with the data available data recorded at meteorological stations. In addition to artificial neural network and fuzzy logic algorithms the Genetic algorithm may also be used successfully in these affairs. Especially, in the case of optimization problems Genetic Algorithm (GA) can be used most successfully. HOLLAND (1975) who studies machine-learning has tried to develop genetic operations in the artificial media and later explained the overwhelming success of these approaches by HOLLAND (1992). It was thought in the beginning that GA did not have any beneficial possibilities but when Holland's student GOLDBERG (1989) completed his Ph. D. thesis on the abilities and application of the Gas he was granted with National Science Foundation award and then the significance of GA started to slip into the current literature more effectively. After four years from his doctorate studies he published few papers and then onwards the GA started to appear in different domains of science and engineering. Gas use natural selection and genetic rules for survival. These rules can be understood as the continuance of the adaptable living organism to his/her environment to continue the survival whereas the others do not have a chance for survival. Gas employ these two rules for reaching the best of the solutions in an optimum manner. In short it is a method of searching and then finding the optimal solution. These algorithms require simple calculations and due to these simplicities their effectiveness does not lost any value. They do not require continuity and derivative prerequisites like other optimization techniques. Their applications do not base on heavy mathematical expressions or algorithms. It is possible to state the major differences between Gas and other classical search techniques as follows: 1) In Gas the parameters are used by a systematic coding procedure. In general the coding system is binary. 2) Instead of a single point, in the Gas many points are used initially for optimization. Consequently, like in other classical techniques in such a search technique the system is not clogged at local best solutions. 3) In Gas only objective functions are used. There is no need for extra knowledge such as derivatives or integrations. These properties render the Gas to be away from the influence of many assumptions and conditions. xiii4) Gas use not the deterministic rules but the probability rules. 1110 0 1110 0 0 10 10 > Mutattion * 0 1 1 0 0 Crossover A 1 0 1 0 \) 1 1 0 0 Initial Population F(00111)=0.1 F(11100)=0.9 F(01010)=0.5 Updated Population Figure 1. Genetic Algorithm Operations (FORREST, 1993). The gene pools a reservoir where the chromosomes suitability is searched and the ones that are suitable are kept in the pool. For instance, in the Figure 1 F(00111) = 0.1, F(IHOO) = 0.9, F(01010) = 0.5 all show the suitability values. From these suitability values the ones with greater suitability are selected and then they are reproduced over the others with small suitability values. In later stages the individuals are passed through the cross-over and mutation operations. Over-crossing operation corresponds to procedure whereby the genes in two different chromosomes are overchanged with each other. First of all the pairs of chromosomes that will be operated through the cross-over are selected randomly from the pool. Later, again through another random operation the location within the chromosome is determined for cross-over and subsequently all the genes after this location are interchanged between two chromosomes. The purpose of such an operation is to be able to obtain different chromosome characteristics. As stated earlier both the selection of two chromosomes and the location of over-crossing are achieved through random processes. In the following the pairs of chromosomes, the location for cross-over operation and the numbers they represent are shown on the right hand side of the arrows. 1 0 0 /l 0 1 1 1 1 I/O 1 0 0 -»75 -H16 The chromosome pair above is cut at the third location and then the bold genes are interchanged between these chromosomes and the result is the following two new chromosomes. Under the light of the aforementioned explanation each chromosome represents a single decimal number and even a single change in the gene leads to different numbers. Mutation is an operation whereby each one of the genes in a single chromosome is changed randomly by its opposite gene which is not similar to interchange as in the cross-over. Hence, in the mutation operation ifa gene has 0 as XIVits value it will be rendered to 1 or if the value is 1 it will be replaced by 0. The benefit from such an operation is to be able to find the best of the bests in the search method. The mutation number i.e., the number of genes for mutation will be held rather small otherwise randomness become dominant in the overall search methodology. 1 0 0 1 0 1 1 -> 75 For instance, with the application of mutation operation at gene within the third location the chromosome will take the following sequence of binary numbers, 1 0 1 1 0 1 1 -» 91 Inversion of the chromosome is equivalent to read the chromosome from left to right from right to left. In the new chromosome the gene locations are similar to the gene locations from the end of the previous chromosome. Hence, the newly born chromosome in this manner exposes completely different numerical value. For instance, the reversal of chromosome 1 1 0 0 0 1 0 -» 98 leads to a new chromosome as 0 1 0 0 0 1 1 -» 35 APPLICATION 1 THIEBAUX and PEDDER (1987) have suggested the weighting functions for regional estimation of meteorological variables without taking into consideration the effects of the meteorological phenomena at all. They have considered the station configuration only and suggested that the weightings are as follows w(n^)= f"2 2 V R -r- for rl5in £ R (1) 0 for n>m£R Herein, R is the radius of influence and a the smoothing coefficient (power parameter). This equation becomes equivalent to the CRESSMAN (1955) approach when the smoothing coefficient is equal to one. It is possible to determine the radius of influence and the smoothing coefficient a according to the personal experience and ability subjectively. In fact, in the practical studies there appear some difficulties in the determination of especially a parameter. SASAKI (1960) and BARNES (1964) have suggested a different type of geometric function for weighting finding as follows XVW(ri>m)=exp -4 ri,m R J (2) In fact, the procedures for the weighting function determinations should take into consideration not only the station configuration but also the behavior of the meteorological phenomena regionally. Recently, ŞEN (1997) has proposed the cumulative semivariogram technique in the determination of the weighting functions as an alternative to Cressman and Barnes approaches. It has been observed that none of the classical techniques can be obtained by this procedure. It is necessary to determine the radius of influence and a rather objectively. Such a determination procedure is developed through the GA in this thesis. APPLICATION 2 It is possible to obtain the relationships between the precipitation event and related factors on a basic X-Y coordinate system. For instance, let us assume that X variable is verbal whereas Y and Z are the numerical data related to this verbal variable. Verbal data may have the forms of Yes/No, black/white, fogy/nonfogy, precipitation/non-precipitation. In the evaluation of these variables the following procedure is followed 12 8^ >- 6 0- i j i i i i r I I I I t I I I I I I I L 1 I I I I I I I I I I I I I I | I 1 I I I I I I I I I I I I A 8 12 16 20 z (a) A Figure 2. Scatter diagram; (a) classical regression; (b) discriminant regression (a) Plot the scatter diagram of Y and Z as shown in Figure 2a. The relationship between these two different variables can be expressed by the least squares technique. However, such an approach is very classical and it will not be used in this thesis. Herein, the purpose is not the determination of the equation form but the estimation of parameters. (b) If the regression technique is not suitable for the solution then the verbal data might be employed. Use of X verbal data discriminates the whole space of the Cartesian coordinate system into two distinctive areas as shown in Figure 2b. Herein the circles show precipitation and full triangles the non-precipitation events. The first question in this solution is whether the separation line is linear or nonlinear? Hence, the problem is completely different than the classical solutions. One should try and find the discriminant line or curve between these two areas for separation. XVIThe main problem here is not to find the best linear line fitting to the data with minimum squares of errors but to find a line that separates the verbal data into two distinctive parts with minimum error of miscounts. The purpose is to minimize the number of false points in these two areas. According to PANOFSKY and BRIER (1968) similar problems are solved classically in the literature according to the multiple regression approach. For this purpose Albany, New York data are adopted as the vertical axis representing vertical velocity X2 and dew point temperature Xi on the horizontal axis. These data are taken from PANOFSKY and BRIER (1968). All together there are 91 daily data out of which there are 29 precipitation days. X2 = 27.83 + 1.12 Xi (3) This line separates the verbal data with 12 miscounts hence the number of error is 12 out of 91 On the other hand, as presented by Panofsky and Brier (1968) the discriminant line through the regression procedure led to 15 miscounts. X2 = 37.53 + 0.75Xi (4) APPLICATION 3 In this application, one of the most significant meteorological variables as temperature is estimated from the water vapor pressure and relative humidity data. Herein, the artificial neural network procedure is coupled with the GA approach. In the application the data are adopted from Göztepe, Istanbul Meteorological Station. Among these data are temperature, vapor pressure and relative humidity which are recorded from 1 March - 20 April, 1996 daily. Detailed knowledge in Turkish concerning artificial neural network is available from SÖNMEZ and ŞEN (1997) and according to their methodology the GA is coupled and the applications are executed. For this reason detailed artificial neural network information is not furnished in this thesis. Temperature Î Vapour Pressure Relative Humidity Figure 3. Artificial neural network connections xvuAs can be seen from Figure 3 the input layer includes water vapour pressure and relative humidity through two cells and output layer includes the temperature variable in the form of a single cell. In the output in order to represent the associated nonlinearities a sigmoid function is also employed. The weightings a' s in the artificial neural network system are used for the backpropagation of the error through the whole system and their appearance in the backpropagation equation is given by MAMEZZ (1994) as w...yeni =w.eski- "<%L (5) JV J t 'wji As a result of this procedure the actual and predicted temperature values follow each other very closely. APPLICATION 4 As is well known from the literature ANGSTROM (1924) linear equation is invariably employed in the solar irradiation estimations through the following expression H S = a + b.* H0 S 0 <6> In this equation sunshine duration S and So and solar irradiation H and Ho are dominant. This equation has been solved through the data by ŞAHÎN and ŞEN (1997) through the assumption that the changes between two successive months is linear and then the substitution of the data values concerning two months lead to a solution of parameters a and b. They have used rather regression technique simply but the view taken in this thesis is the same except that the solutions of the parameters is achieved by the GA approach. Hence, a sequence of a and b parameter estimations is obtained instead of constant and single a and b values as resulting from the classical techniques. Availability of sequences of the parameters give ability to obtain their statistical evaluations at any level. In this thesis, four solar irradiation station data are used, namely, Istanbul, Izmir, Ankara and Diyarbakır from 1992 to 1993 inclusive. The results are as follows. 1) a and b parameters are mostly positive but occasional negative values are also possible. 2) Negative values are comparatively very little. In few stations big negative b values are possible. B parameter is related to the cloud coverage. 3) Summation of a and b in any time period is less than 1. 4) There is an inverse relationship between these two parameters. Hence, high a values are followed by low b values and vice versa. 5) It is possible to construct the histograms of parameters a and b. Although the concentration of a and b parameters is confined between 0 and 1 there are values outside of this range. These may be due to sudden air and weather changes or as a result of errors. XVlll