Fuzzy neural network and deo based forecasting Текст научной статьи по специальности «Энергетика и рациональное природопользование»

Аннотации:

В статье проводится оценка влияния свойств среды на логические каналы DTCH и DCCH системы UMTS, использующая в качестве радиодоступа стандарт WCDMA, с помощью имитационной модели.

У стати проводиться оцшка впливу власти-востей середовища на лопчш канали DTCH i DCCH системи UMTS, що використовуе у якостi радюдоступу стандарт WCDMA, за допомогою ímí^^to! моделi.

In this article simulation model is used for estimating the environment's impact on properties of logical channels DTCH and DCCH for UMTS, which uses radio as a standard for WCDMA.

УДК 681.1-665.52

LATAFAT A. GARDASHOVA (Azerbaijan State Oil Academy). Fuzzy neural network and deo based forecasting

Introduction

In the area of oil refinery plant control and management a number of problems are usually solved by using data obtained from solutions of various 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.

Forecasting problems for oil refinery plants are characterized by an informal background description and subjectivity of the states estimations.

Some of forecasting tasks are complicated by nonstationarity and nongraduality of time-dependent fluctuations.

It is necessary to choose adequate tools for solving the 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 technological and economic indexes in the complex environment.

In 1965 after Lotfi Zadeh's [1] fuzzy theory, fuzzy logic new era began in the de-

velopment 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 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. Thus it is required to use soft computing methods based on application of fuzzy time series and fuzzy logic. Fuzzy Neural Networks are efficient for these purposes, they use fuzzy numbers, and fuzzy operations over them. The basic idea of FNN is that results are acquired according to the fuzzy logic apparatus. FNN can be used, for example, to forecast the regional electrical charges and

consuming of electric power in Turkey[8]. The solution of forecasting with the help of FNN is appeared to be better than that obtained using traditional ANN. However, FNN has also some shortcomings. Fuzzy Neural Network is not a dynamic network, it does not have a memory. Fortunately these shortcomings may be removed with the 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 nonrecurrent network, recurrent networks have memories and it enables them to remember the information about the situation in past periods [9-10].

Recurrent Fuzzy Neural Networks have the feature of learning from experiments, are very efficient due to smaller number of calculations as compared with traditional networks for the same number of inputs and outputs. Fuzzy clustering can be applied to improve the results of FRNN learning and forecasting.

Qualitative methods of forecasting are used in case of impossibility of considering several factors simultaneously because of insufficiencies and complexity of forecasting objects. In this case the application of expert assessment is applied in forecasting. In [7] authors offer a method for short-term forecasting which combines a quantitative meth-

od (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 considers the forecasting of kerosene production in an oil refinery enterprise based on fuzzy neural network and differential evolution based fuzzy clustering. The paper is organized as follows. Fuzzy Neural Network is presented in the section 2. Differential evolution optimization method is given in section 3. The experimental results of computer simulations are described in the section 4. The conclusion is presented in the fifth section.

Fuzzy Inference Neural Network

The structure of the proposed Fuzzy Neural Network is shown in Figure 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 de-fuzzification using the Center-of-Gravity (COG) defuzzification

Fig. 1. Fuzzy Inference Neural Network

DE Optimization Method

Recently many heuristic algorithms have been proposed for global optimization of nonlinear, non-convex, and nondifferential 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 train 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 Xr1, Xr2, Xr3 (Vector X4 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).

Forecasting amount of kerosene production in the oil refinery enterprise by using fuzzy neural network and differential evolution based fuzzy clustering

The objective is to determine kerosene production predicting value by using numerical data. Dataset contains 90 records with the data on 90 days. Input: X1-amount of the without petrol oil ;u1- Temperature of k2 block(top);u2- Temperature of k block (below);u3- difference of the temperature between k2-k6 blocks;u4- difference of the

2 7

temperature between k -k block;u5-

2 9

difference of the temperature between k -k 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 Ta-ble3.1, fragment of clusters and their membership functions in Tables 3.2 and 3.3, membership function of the property prediction model by using DEO fuzzy clustering s given in figure 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

Table 2

Fragment of clusters_

Found prototypes: cluster 1 cluster 2 cluster 3 cluster 4

668.910862945012 664.41806170565 663.751356592796 662.450231502893

125.925941906836 126.67444136993 127.514707112226 127.911234197383

358.020679044478 356.847878979197 354.652750035343 356.645161708219

181.201426581614 176.296512590142 178.845391458024 181.619694820938

241.29067307793 238.311816874499 241.982554649856 242.627117450253

306.825086526627 309.984257805003 306.910690824636 305.839466598401

87.2488493267326 96.1670763452697 94.8121431514706 90.7543048863168

122.531597010781 130.513787677436 130.49578192516 131.703860222323

109.565796306201 111.851688501859 115.449304059415 111.304226789787

0.47872830760691 0.620658680125957 0.479307077004581 0.442141229076906

cluster 5 cluster 6 cluster 7 cluster 8

665.871093731774 662.531288570488 669.88571261202 664.135386203208

128.495594083883 129.117783608458 124.281927839803 127.137306479223

355.020689509184 357.02006180546 357.977139300829 353.446300556819

180.073442694066 178.821224977363 179.639589499206 181.229634673555

240.210243546848 241.86762492768 241.524239727998 236.203007840626

303.919039544974 307.953261706567 302.09366933458 303.932059441958

97.7915937464932 99.100547189519 98.8661941929618 101.875484459766

133.598240216313 130.96149139918 128.681116355948 135.268642222427

117.201081472983 112.647379038544 117.251916882111 119.989193569607

0.649994069593133 0.48335731825459 0.499978518361563 0.563220258184942

cluster 9 cluster 10 cluster 11 cluster 12

663.611289789538 667.473465249153 667.455950778213 659.83739234422

128.115683210116 127.31658456489 128.324812722436 125.044183322668

355.922437485131 354.538901602733 356.79055462792 356.351255676488

179.669880642491 178.084126918537 180.128433820595 178.67624152879

240.375229124785 238.061674000313 237.498913394036 237.226540879474

304.577053795661 302.45978174607 306.620478803171 304.390440539517

92.7702566514386 89.9264791341205 92.5262750358956 101.337660937818

132.631738179572 127.93606799368 142.636021010734 137.910937889356

117.889213356086 113.132358579744 120.058921818765 109.471159289057

0.532495840387055 0.580933783071742 0.507539897071138 0.510425618771378

Table 3

Fragment of cluster membership functions

cluster 1 cluster 2 cluster 3 cluster 4

0.154989220046483 0.0468183262275264 0.0748790159407517 0.101999198411524

0.039498627747395 0.0418811131348201 0.0782806098809937 0.0736814412507036

0.0805146169952612 0.0552568150699175 0.0775657315134204 0.0933224116054812

0.0822846149706745 0.0569516936816942 0.0909520958317501 0.166538483096889

0.758102946449517 0.0169861156497116 0.0237483800354946 0.0421796553713255

0.593694789786065 0.0313785818983953 0.0380058692637003 0.059528773651366

cluster 5 cluster 6 cluster 7 cluster 8

0.0596882516254292 0.0385844089763519 0.0638382802130333 0.0333771964091293

0.177626411375194 0.0499605643488582 0.127069434472588 0.0906878017311136

0.105638356155811 0.0512223039976838 0.0833040163532679 0.0778349140927834

0.104958809514653 0.0574401879212651 0.0809866563939284 0.0486281312142304

0.0198231898714608 0.0157854296082028 0.0217560799704625 0.0122229178836611

0.0340682595008493 0.0276885443406942 0.0397775993349595 0.0218579155154396

cluster 9 cluster 10 cluster 11 cluster 12

0.0796615169744754 0.284776119281839 0.0353312373246911 0.0260572285687654

0.120485144037642 0.0847488906469375 0.0749548701352315 0.0411250912385224

0.0959793282126171 0.15090949229297 0.0730138061917778 0.0554382075190092

0.108421806049416 0.0901797016281396 0.0722860200122507 0.0403717996851094

0.0223116134299594 0.0444388292958961 0.0117440467141768 0.0109007957201321

0.0376323715844886 0.0749246014195133 0.0209176521243523 0.0205250415801762

From this fuzzy model, we can use the linguistic hedges approach [13] to derive the corresponding interpretable linguistic model as follows

Rules :

If Xi 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.

If X 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..

If X1 is about 663.7 AND U1 is about 127.5 AND u2 is about 354.6 AND u3 is

about 178.8 AND u4 is about 242 AND u5 is about 306.9 AND z3 is about 94.8, and z4 is about 130.5 And z5 is about 115.4 AND u6 is almost 0.5 AND z1 is about 3.6.AND z2 is about 63 THEN y2 may be about 73.8..

If X1 is about 662.4 AND U1 is about 127.9 AND u2 is about 356.6 AND u3 is about 181.6 AND u4 is about 242.6 AND u5 is about 305.8 AND z3 is about 90.7, and z4 is about 131.7 And z5 is about 111.3 AND u6 is almost 0.4 AND z1 is about 3.5.AND z2 is about 60.7 THEN y2 may be about 79.5

If X1 is about 665.9 AND U1 is about 128.5 AND u2 is about 355 AND u3 is about 180 AND u4 is about 240.2 AND u5 is about 304 AND z3 is about 97.8 and z4 is about 133.6 And z5 is about 117.2 AND u6 is almost 0.6 AND z1 is about 3.5.AND z2 is about 64.7 THEN y2 may be about 80.

If X1 is about 662.5 AND U1 is about 129.1 AND u2 is about 357 AND u3 is

about 178.8 AND u4 is about 241.9 AND u5 is about 308 AND z3 is about 99.1 and z4 is about 131 And z5 is about 112.6 AND u6 is almost 0.5 AND z1 is about 3.6.AND z2 is about 68.1 THEN y2 may be about 74.8.

If X1 is about 669.9 AND U1 is about 124.3 AND u2 is about 358 AND u3 is about 179.6 AND u4 is about 241.5 AND u5 is about 302.1 AND z3 is about 98.9 and z4 is about 128.7 And z5 is about 117.2 AND u6 is almost 0.5 AND z1 is about 3.8.AND z2 is about 64.4 THEN y2 may be about 76.8

If X1 is about 664.1 AND U1 is about 127.1 AND u2 is about 353.4 AND u3 is about 181.26 AND u4 is about 236.2 AND u5 is about 304 AND z3 is about 101.9 and z4 is about 135.3 And z5 is about 120 AND u6 is almost 0.6 AND z1 is about 3.8.AND z2 is about 64.1 THEN y2 may be about 75.5.

If X1 is about 663.6 AND U1 is about 128.1 AND u2 is about 356 AND u3 is about 179.7 AND u4 is about 240.4 AND u5 is about 304.6 AND z3 is about 92.8 and z4 is about 132.6 And z5 is about 117.9 AND u6 is almost 0.5 AND z1 is about 3.6.AND

z2 is about 64.5 THEN y2 may be about 76.5

If X1 is about 667.5 AND U1 is about 127.3 AND u2 is about 354.5 AND u3 is about 178.1 AND u4 is about 238.1 AND u5 is about 302.5 AND z3 is about 90 and z4 is about 128 And z5 is about 113.1 AND u6 is almost 0.6 AND z1 is about 3.8.AND z2 is about 61.4 THEN y2 may be about 77.2.

If X1 is about 667.5 AND U1 is about 127.3 AND u2 is about 356.8 AND u3 is about 180.1 AND u4 is about 237.5 AND u5 is about 306.6 AND z3 is about 92.5 and z4 is about 142.6 And z5 is about 120.1 AND u6 is almost 0.5 AND z1 is about 3.7.AND z2 is about 67.7 THEN y2 may be about 77.3

If X1 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.

Graphical representation of the extracted fuzzy rules fragment for third rule is given in fig.2.

Fig. 2. Fragment graphical representation of the extracted fuzzy rules (third rule)

The values of obtained error measure are given below.

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 allow a significant performance gain as compared to other methods.

5. Conclusion Fuzzy rule extraction from numerical data are presented in this paper. For training of fuzzy neural network, differential evolution optimization method is used. In the experimental part of the 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 AN-FIS and subclustering method, fuzzy neural network and DEO based clustering, regression. All calculation were made in Matlab environment, using C++ and MS Excel.

References

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yev, U. Ilhan, M. Babagil, S. Mammadli. -Information Sciences - 2011.

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Anotations:

In this paper a new approach to forecasting is analyzed based on fuzzy neural network and differential evolution based clustering. The proposed method is applied to forecasting of kerosene production in an oil refinery enterprise. Experimental results have demonstrated efficiency of the proposed method and its advantages as compared to the existing classical methods.

Приводится новый метод прогнозирования на основе нечеткой нейронной сети и дифференциального использования кластеров. Предлагаемый метод применен к прогнозированию производства керосина на масляном предприятии нефтеперегонного завода. Экспериментальные результаты продемонстрировали эффективность предлагаемого метода и преимущества по сравнению с существующими классическими методами.

Приводиться новий метод прогнозування на основi нечггко! нейронно! мережi й диференщаль-ного використання кластерiв. Запропонований метод застосований до прогнозування виробництва керосину на масляному шдприемсга нафтопере-пнного заводу. Експериментальш результата про-демонстрували ефектившсть пропонованого методу й переваги в порiвняннi з юнуючими класични-ми методам