CC BY
9FORECASTING BY USING DIFFERENTIAL EVOLUTION
BASED CLUSTERING
Latafat A. Gardashova, Hashim A. Alimammadzade
Azerbaijan State Oil and Industry University
Abstract. In this paper it is analyzed a new approach to forecasting based on fuzzy neural network and differential evolution based clustering. The proposed method is applied to forecasting of kerosene production in the oil refinery enterprise. Experimental results have demonstrated efficiency of the proposed method and its advantages as compared to the existing classical methods.
Keywords: Fuzzy Inference Neural Network, diferential evolution, fuzzy clustering
I.INTRODUCTION
In the area of oil refinery plant control and management a number of problems should be settled by using a data obtained from the solution of the forecasting tasks. The uncertainty and incompleteness of the initial data as well as complexity and weakness of the conventional methods of forecasting complicate proper solving of the forecasting problems.The forecasting problems for the oil refinery plant are characterized by informal background description, subjectivity of the states estimations.
Some of forecasting tasks are complicated by the nonstationarity and nongraduality of the time-dependent fluctuations.It is necessary to choose adequate means for solving considered problems which would be able to carry out predictably hour-to-hour,day-to-day, week-to-week, month-to-month or year-to- year fluctuations of the technological and economic indexes in such complex environment.
In 1965 after Lotfi Zadeh's[1] fuzzy theory fuzzy logic new era began in the development of sciences including forecasting science. Since the middle of 70s by using this notion new forecasting methods were created and applied in practice. Several works have been written about the theoretical and practical problems of forecasting in Azerbaijan as well[2-7].
There is no universal forecasting method for economical indicators. There are many forecasting methods because of the diversity of forecasting conditions. We can classify the economical forecasting into two groups: qualitative and quantitative.
Quantitative methods are consist of traditional statistical methods, artificial neural network and other modern methods.
Sometimes we may have to use new type of time series like fuzzy time series, cost of this kind of time series is linguistic. Thus it is required to use soft computing methods based on application of fuzzy time series and fuzzy logic. Fuzzy Neural Network is effective for these purposes and fuzzy numbers, identity function and fuzzy operations are used. The basic idea of FNN is that results are acquired according to the fuzzy logic apparatus. Fuzzy Neural Network is used to find the parameters of identity functions. This system may use the information that was known beforehand, learn them , may even get new numbers, forecasting time series, etc. FNN is used to forecast different social economical problems, as well. FNN has been applied to forecast the regional electrical charges and consuming of electric power in Turkey[8]. The solution of forecasting with the help of FNN has resulted better than that of ANN. But FNN has also some shortcomings. Fuzzy Neural Network is not a dynamic network , it does not have a memory. But these shortcomings may be solved with help of Recurrent Fuzzy Neural Network. In Recurrent Fuzzy Neural Network neurons of certain layer may get signals from itself, both from the outside and from other neurons in the same layer with itself. Thus unlike non-recurrent network , recurrent networks have memories and it enables them to remember the information about the situation in the given period [9-10].
It must be noted that Recurrent Fuzzy Neural Networks are very effective. The methods that have been used are characterized with the small calculations complexity and feature of learning from the experiments. Fuzzy clustering is applied to improve the results of FRNN forecasting.
Qualitative methods of forecasting is used in case of impossibility of considering several factors because of insufficiencies and complexity of forecasting objects. In this case the application of expert assessment is applied in forecasting. In [7] is offered method for short-term forecasting which combines quantitative method( such as processing fuzzy time series using recurrent neural networks with DE -based learning) and qualitative method(such as the modified Fuzzy Delphi).
The present paper is devoted to the forecasting of kerosene production for the oil refinery enterprise based on fuzzy neural network and differential evolution based fuzzy clustering. The structure of this paper is organized as follows. Fuzzy Neural Network is presented in the section 2. Differential evolution optimization method is given section 3. The experiments results of computer simulations are described in the section 4. The conclusion is presented in the fifth section.
2. Fuzzy Inference Neural Network
The structure of the proposed Fuzzy Neural Network consist of 5 layer(Fig. 1). Let us elaborate on the functionality of the layers in more detail. Layer 1 consists of fuzzifiers that map inputs to fuzzy terms used in the rules. Layer 2 comprises nodes representing these rules. Each rule node performs the Min operation on the outputs of the incoming links from the previous layer. Layer 3 consists of output terms membership functions. Layer 4 computes the fuzzy output signal for the output variables. Layer 5 realizes the defuzzification using the Center-of-Gravity (COG) defuzzification.
Fig. 1. Fuzzy Inference Neural Network
3. DE Optimization Method
Recently many heuristic algorithms have been proposed for global optimization of nonlinear, non-convex, and non-differential functions [11-12]. These methods are more flexible than classical as they do not require differentiability, continuity, or other properties to hold for optimizing functions. Some of such methods are genetic algorithm, evolutionary strategy, particle swarm optimization, and differential evolution (DE) optimization.
Earlier we have applied genetic algorithm to training FRNN [7]. At all advantages the genetic algorithm has a series of lacks. First, the problem of convergence, and in general absence of a theoretical design is the main lack of genetic algorithm. Second, necessity of coding of area of the valid variables for area of bit numbers too to concern to weakness of genetic algorithms. And the third lack, but, low computing speed of genetic algorithms is very basic.
As a stochastic method, DE algorithm uses initial population randomly generated by uniform distribution, differential mutation, probability crossover, and selection operators. The population with ps individuals are maintained with each generation. A new vector is generated by mutation which in this case is randomly selecting from the population 3 individuals: vector indexes r ^ r2 ^ r3 and adding a weighted difference vector between two individuals to a third individual (population member).
The mutated vector is then undergone crossover operation with another vector generating new offspring vector.The selection process is done as follows. If the resulting vector yields a lower objective function value than a predetermined population member, the newly generated vector will replace the vector with which it was compared in the following generation.
Extracting distance and direction information from the population to generate random deviations results in an adaptive scheme with excellent convergence properties. DE has been successfully applied to solve a wide range of problems such as image classification, clustering, optimization etc.
In paper [3] shows the process of generation new trial solution Xnew vector from randomly selected population members Xrl, Xr2, Xr3 (Vector X is then the candidate for replacement by the
new vector, if the former is better or lower in terms of the DE cost function). Here we assume that the solution vectors are of dimension 12 (i.e. 12 optimization parameters).
3.Forecasting amount of kerosene production in the oil refinery enteprise by using fuzzy neural network and differential evolution based fuzzy clustering.
The goal is to determine kerosene production predicting value by using numerical data. Dataset contains 90 records with the data about 90 day. Input: X1-amount of the without petrol oil ;u1-Temperature of k2 block(top);u2- Temperature of k2 block (below);u3- difference of the temperature between k2-k6 blocks; u4- difference of the temperature between k2-k7 block;u5- difference of the temperature between k2-k9 block; z3-pressure of k2 block; z4-water steam; z5-temperature of acute irrigating gasoline; u6- temperature of first periodical irrigation; z1- temperature of second periodical irrigation; z2- temperature of third periodical irrigation. Output: amount of kerosene
For simulation DEO fuzzy clustering initial data are: Cluster numbers=12, Max iteration =100 000, exponent =2, pop_size=600
Fragment of input data is given in Table 1, fragment of clusters and their membership functions in Tables 2 and 3, membership function of the property prediction model by using DEO fuzzy clustering is given in fig. 2.
Table 1. Fragment of input data
670 125 356 177 239 305 87 128 114 0,65 3,7 58 80
670 127 354 182 243 298 95 135 121 0,5 3,5 61 81
670 125 351 176 234 297 90 135 116 0,4 3,5 54 84
670 125 358 183 245 308 90 135 115 0,5 3,5 60 82
670 125 357 183 242 307 86 123 110 0,55 3,5 55 83
670 124 360 180 240 305 85 120 110 0,5 3,7 55 85
670 125 360 180 240 305 85 120 110 0,5 3,7 54 85
From this fuzzy model, we can use the linguistic hedges approach [13] to derive the corresponding interpretable linguistic model as follows
Rules :
1) IfXi is about 668.9 AND U1 is about 125.9 AND u2 is about 358 AND u3 is about 181.2 AND u4 is about 241.3 AND u5 is about 306.8 AND z3 is about 87.2, and z4 is about 122.5 And z5 is about 109.6 AND u6 is almost 0.5 AND z1 is about 3.4.AND z2 is about 56.7 THEN y2 may be about 83.3.
2) IfX is about 664.4 AND U1 is about 126.7 AND u2 is about 356.8 AND u3 is about 176.3 AND u4 is about 238.3 AND u5 is about 309.9 AND z3 is about 96.2, and z4 is about 130.5 And z5 is about 111.9 AND u6 is almost 0.6 AND z1 is about 3.6.AND z2 is about 70.2 THEN y2 may be about 77.
3) IfX is about 659.8 AND U1 is about 125 AND u2 is about 356.3 AND u3 is about 178.7 AND u4 is about 237.2 AND u5 is about 304.2 AND z3 is about 101.3 and z4 is about 138 And z5 is about 109.5 AND u6 is almost 0.5 AND z1 is about 3.3.AND z2 is about 69.3 THEN y2 may be about 79.3.
Table 2.Fragment of clusters
Found prototypes: cluster 1 cluster 2 cluster 3 cluster 4
cluster 1 cluster 2 cluster 12
128.495594083883 129.117783608458 659.83739234422
355.020689509184 357.02006180546 125.044183322668
180.073442694066 178.821224977363 356.351255676488
240.210243546848 241.86762492768 178.67624152879
303.919039544974 307.953261706567 237.226540879474
3.45997480406256 3.57984493378822 0.510425618771378
64.6592296528415 68.0942650315422 3.34727342624666
64.4988106575175 61.4179733896838 69.316493645817
76.5102793124439 77.1599300888537 79.3843807815471
Table 3.Fragment of cluster membership functions
cluster 1 cluster 2 cluster 12
0.154989220046483 0.0468183262275264 0.0260572285687654
0.039498627747395 0.0418811131348201 0.0411250912385224
0.0805146169952612 0.0552568150699175 0.0554382075190092
0.0822846149706745 0.0569516936816942 0.0403717996851094
0.758102946449517 0.0169861156497116 0.0109007957201321
0.593694789786065 0.0313785818983953 0.0205250415801762
У2
О 20 40 SO 80 100
Fig 2. Fragment graphical representation of the extracted fuzzy rules (third rule)
The mean square errors (MSE) produced by different methods were: 6.89% by the ANFIS and subclustering method, 5.11% by the method of fuzzy neural network and DEO based clustering, 8.39% by the method of regression. The results show that application of forecasting methods based fuzzy neural network and DEO based clustering are superior to other methods.
5. Conclusion Fuzzy rule extraction from numerical data are presented in this paper. For training of fuzzy neural network differential optimization method is used. In the experimental part of paper, the process of forecasting of the amount for kerosene by the fuzzy neural network and DEO clustering method is demonstrated. The results were compared with the results produced by other methods including ANFIS and subclustering method, fuzzy neural network and DEO based clustering, regression. All calculation were made in Matlab, environment, using C++ and MS Excel.
REFERENCES
I. Zadeh Lotfi. Fuzzy Sets. // Information and Control, 1965, v. 8(3), pp. 338-353.
2 Aliev R.A., Fazlollahi B., Aliev R.R., Soft Computing and Its Applications in Business and Economics. Springer Verlag, 2004, 450 p.
3 Aliev R.A., Pedrycz W., Guirimov B., Aliyev R.R., Ilhan U., Babagil M., Mammadli S., Type-2 Fuzzy Neural Networks with Fuzzy Clustering and Differential Evolution Optimization, Information Sciences, 2011.
4 Тагиев Н.Ф. возможности устойчивого прогнозирования ситуаций на фондовом рынке Азербайджана нейросетевыми методами. // Онлайн журнал, № 3,2005.
5 Джабраилова З.Г., Мамедова М.Г. Нечёткий логический подход к задаче оценки кадрового потенциала. // Менеджмент в России и за рубежом,2004,№5 http://www.dis.ru/manag/arhiv/2004/5/rdiscomarket.
6 Мамедова М. Г., Джабраилова 3. Г. Применение нечеткой логики в демографическом прогнозе. // Информационные технологии, 2004, №3, http://www.informika.ru /text/magaz/it/2004/03/.
7 K.W.Bonfig,, Sh.F.Mehdi, L.A.Gardashova .Neural Network Based Forecasting of time series and its application in the forecasting of oil prices in the world Market. ICAFS-2008, 8-th ICAFS and Soft Computing, Helsinki, Finland,p.275-281, 2008
8 Hamzacebi C., Kutay F. Electric Consumption Forecasting of Turkey Using Artificial Neural Networks Up to Year 2000. // J. Fac. Eng. Arch. Gazi Univ.2004., v. 19, No 3, pp. 227 - 233
9 Алиев Р.А., Алиев Р.Р., Теория интеллектуальных систем и ее применение. Баку: Чашыоглы, 2001, 720 с.
10 Aliev R.A. SOFT COMPUTING: Fuzzy Logic, Neural Networks and Distributed Artificial Intelligence. / Eds. F. Aminzadeh, M. Jamshidi. Prentice Hall PTR, 1994., 301 p.
II. W.Pedrycz, K.Hirota, "Fuzzy vector quantization with particle swarm optimization: A study in fuzzy granulation-degranulation information processing", Signal Process, 2007, doi:10.1016/j.sigpro.2007.
12. Y.-J.Wang, J.-S.Zhang, G.-Y. Zhang, "A dynamic clustering based differential evolution algorithm for global optimization", European Journal of Operational Research 183, 2007, pp. 56-73.
13 Min -You Chen, D.A.Linkens. Rule-base self -generation and simplification for data-driven fuzzy models.J. Fuzzy sets and Systems,2004,pp.243-265.
