Performance Analysis of ANFIS in short term Wind Speed Prediction
IJCSI International Journal of Computer Science Issues, Vol. 9, Issue 5, No 3, September 2012 ISSN (Online): 1694-0814 www.IJCSI.org
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Performance Analysis of ANFIS in short term Wind Speed Prediction Ernesto Cortés Pérez1, Ignacio Algredo-Badillo2, Víctor Hugo García Rodríguez3 1, 2
Department of Computer Engineering, UNISTMO University, Tehuantepec, Oaxaca, México, C. P. 70760 3
Department of Design Engineering, UNISTMO University, Tehuantepec, Oaxaca, México, C. P. 70760
Abstract Results are presented on the performance of Adaptive NeuroFuzzy Inference system (ANFIS) for wind velocity forecasts in the Isthmus of Tehuantepec region in the state of Oaxaca, Mexico. The data bank was provided by the meteorological station located at the University of Isthmus, Tehuantepec campus, and this data bank covers the period from 2008 to 2011. Three data models were constructed to carry out 16, 24 and 48 hours forecasts using the following variables: wind velocity, temperature, barometric pressure, and date. The performance measure for the three models is the mean standard error (MSE). In this work, performance analysis in short-term prediction is presented, because it is essential in order to define an adequate wind speed model for eolian parks, where a right planning provide economic benefits. Keywords: Wind, fuzzy, neural, ANFIS, prediction.
1. INTRODUCTION The success of eolian resource forecasting depends on precision. Indeed minimizing error implies to consider factors such as: the selected forecasting model, the model parameters, the available data history, etc. Fuzzy logic and neural networks are frequently employed for estimating and forecasting [1] when available data is not sufficiently reliable because it allows tolerance levels due to the imprecision associated with linguistic terminology, which, by their very nature, are less precise than numbers. Fuzzy logic is a useful technique because it makes use of uncertainty and calibrates vagueness to find robust solutions at low computational cost [2]. Furthermore, because they are inspired by and adapted from biological systems, artificial neuronal network models simulate the cognitive processes in so much as they possess the capacity to interpret the world in the same way human beings do. Each of these techniques has its advantages and disadvantages. A number of studies have reported successful results from the application of neural networks to wind velocity forecasts. For example, in 2009 [3] Monfared et al.
applied a strategy based on fuzzy logic and neuronal networks to forecast wind velocity. They employed statistical properties such as standard deviation, mean, and variable calculation relation gradient as neuro-fuzzy predictor model input. They did so by using real time data obtained in northern Iran from 2002 to 2005. Readings were taken at average intervals of 30 minutes. In 2009 in average Cadenas et al. used one hour intervals to forecast wind velocity by using data collected by the Federal Commission of Electricity (Comision Federal de Electricidad, CFE) during a period of seven years in the La Venta, Oaxaca, Mexico [4]. This was done using a backpropagation and Madaline neuronal network with a mean square error measured at 0.0039 during the training process. In another study, Adbel Aal, et al. [5] performed wind velocity forecasts by using tardy neuronal networks (TTND), particularly for the maintenance of wind farms where researchers used a wind velocity data base with one-hour intervals compiled in the Dhahran region of Saudi Arabia from 1994 to 2005. The proposed model was evaluated with data from May of 2006, and the forecasting time was from 16 to 24 hours. Therefore, the network precision measurement parameter had a mean absolute error (MAE) of 0.85 m/s, and the correlation coefficient was equal to 0.83 between the actual value and the forecast. In 2009 [6] Sancho Salcedo, et al. employed a multilayered network with the Levenberg-Marquadt training method in which the input variables were wind velocity chosen at two points of interest with wind direction at one point, temperature at one point, and solar radiation at two points. Hence, there are six values in the input layer, a hidden layer with six neurons with a sigmoidal logarithmic activation function, and an output layer with one neuron. The forecasting time was 48 hours. The data had been collected since 2006 in Albacete province in southern Spain. The goal of this study is to perform a comparative on the performance of an Adaptive Neuro-Fuzzy Inference System (ANFIS) in forecasting time intervals of 16, 24, and 48 hours. The meteorological
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sstation at the University of the Isthmuss, Tehuantepecc C Campus, Oaxaca, Mexico prrovided a data bank obtained d ffrom June 2008 to April 201 11. Wind veloccity readings at a thhe meteorolo ogical station are taken every minutee. H However, in th his research thee data bank was modified by y ccalculating averages at ten miinute intervals.. The following g vvariables are co onsidered:
Wind velocity (m/s) Tempeerature (◦C) Barom metric pressure (mb) Date (hh/dd/mm) (
22. ARTIFICIA AL NEURAL NETWORKS S (ANN) M McCulloch and d Pitts were th he first personss to introduce a m model of an eleementary comp puting neuron. Six years laterr, H Hebb proposed d learning rulees. ANN’s greew rapidly, and d thhey have been n applied wid dely in many fields, such as a ppattern classsification, approximation n, function liinear/nonlinearr identification n, multivariab ble systems. A ssimple ANN was w composed of o neuronal lin nks that connecct thhe neurons and assign weigh hts and a bias to them. ANN N ccomprises math hematical equ uations that miimic the brain n. S Since ANN iss made of seeveral neuronss and differen nt laayers, it is capable of performing p maassive paralleel ccomputations.
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Networrk (LRN). Alll of these strructures have specific advantaages and disaddvantages. Bacckpropagation based on error b ackward and iits correction is the most coommonly Actually, this algorithm is based on the gradient used. A descentt method whicch according to error surfacee tries to find thhe best weightt and bias coomposition in order to minimiize the netwoork error. Theere are two iimportant processses in a BP aalgorithm: first, the error coonsiderer calculatted accordingg to the inpuut passed throough the hidden layers of neurrons; second, according to tthis same error, there will bee backward ppropagation tto adjust weightss. However, thhis method haas some disaddvantages like sloow converges, a lack of robusstness, and ineffficiency. One off the most succcessful methodds which couldd be used to impprove the traaining processs is the LeevenbergMarquaardt (LM) metthod which is based on bothh GaussNewtonn nonlinear reggression and grradient steepesst descent methodd.
3. FU UZZY LOGIC (FL) Fuzzy llogic was thouught of as a meethod of formallizing the kind oof imprecise reasoning thhat humans typically perform m. Everyday exxpressions like it’s too hot annd it’s not very higgh are impossiible to formulaate in classical llogic. Fuzzy llogic can proceess vague lingguistic variables such as too, veery, enough aas logical form mulations in ccomputer languagge. Fuzzy logic fits within the frameworrk of the multivaariate logic grooup (there are more truth vaalues than true andd false), and it is based on fuuzzy set theory.. A. Zadeh, a proofessor at the U University of C California Lofti A at Berkkeley founded tthis discipline in 1965. It cam me about throughh the applicatioon of multivarriate logic to seet theory. See figg. 2 for typical structure of a system based on fuzzy logic.
Fig. 1. Input and outpu ut of a neural netw work.
T The position an nd the differen nt neuron conn nections lead to o A ANN being classified c in different d group ps. First feed dfforward networrk which inclu udes single lay yer perceptron n, m multilayer percceptron, backp propagation (B BP) and radiaal bbasis functions. A second gro oup is the recu urrent networkss, ccompetitive nettworks, Kohon nen’s SOM, Ho opfield network k aand ART modeels. A third grroup consists of o the dynamicc nnetworks such as Focuses TimeT Delay Neural N Network k (FTDNN), Distributed Tim me- Delay Neeural Network k N auttoregressive network n with h (DTDNN), Nonlinear eexogenous inpu ut (NARX Neetwork) and Layer-Recurren L nt
Fig. 2. S System based on fuuzzy logic.
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44. ANFIS
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1. Evaaluating the rulle premises ressults in:
A Actually, ANF FIS (Adaptivee Neuro - Fu uzzy Inferencee SSystem) method d is similar to a fuzzy inferen nce system, bu ut itt uses a backkpropagation to t minimize the t error. This m method’s perfo ormance is eq quivalent to bo oth ANNs and d F FLs. In the case of both AN NN and FL, th he input passes thhrough the inp put layer (by input memberrship function n) aand the output could be seen in the output layer (by outpu ut m membership fun nctions). T The parameterss associated wiith the membeership functions aare modified th hrough learnin ng processes. The T adjustmen nt oof the parameteers is generated by the vecto or gradient. Thee aadjusted param meters are su ubsequently applied a to alll ooptimization routines r to reduce r measu urement errorr. U Usually, if yt iss the current value v of period d t and Ft is thee fforecast for the same period, then t the error is i defined as: et = yt – Ft
2. Evaluating tthe conseqquences gives:
implicattion
(3) and
tthe
rule
(4)
Or leavving the argumeents out:
(1)
A mean square error (MSE) iss defined as:
∑
wi = µA Ai(x) µBi(y), i= =1,2.
(5) This caan be separatedd into phases firrst by defining:
2) (2 (6)
W Where n is the number of time periods. A ANFIS uses a combination n of minimum m squares and d bbackpropagatio on for the estim mation of activ vation function n pparameters. In other words, ANFIS A utilizes the advantages oof FL and ANN N to adjust its parameters p and d find optimum m ssolutions.
Then f can be writtenn as: (7) mputations cann be seen in fig.. 3 and 4. All com
B Both FL and ANN A have theiir advantages. Therefore, it is ggood idea to co ombine their ability a and mak ke a strong too ol w which improves their weakneesses leads to minimum m errorr. JJang [7] comb bined both FL and ANN to produce a ppowerful proceessing tool calleed ANFIS. Thiis is a powerfu ul toool that has bo oth ANN and FL F advantages. A Assume that th he fuzzy infereence system haas two inputs x aand y and onee output f. Forr a first-order Sugeno fuzzy y m model, a comm mon rule set with w two fuzzy if-then rules is aas follows, Jang g [7]:
Fig. 3. First--order Takagi-Sugeno Fuzzy Model..
Rule 1: If x iss A1 and y is B1 , then f1 = p1 x + q1 y + r1 Rule 2: If x iss A2 and y is B2 , then f2 = p2 x + q2 y + r2 bership functio ons of fuzzy sets s Ai , Bi , i = Let the memb 1, 2, be µAi , µ Bi . In evaluatting the rules, choose c productt for T-norm (lo ogical and).
Fiig. 4. Equivalent A ANFIS architecturee with two inputs aand one output.
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55.
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DATA COL LLECTION
T The data for th his study was provided p by a meteorologicaal sstation located d at the Teehuantepec caampus of thee U University of th he Isthmus. Th his data base co overs the period d ffrom June 2008 8 to April 2011 1. It contains in nformation on a nnumber of variiables such ass wind velocity y, temperaturee, ssolar radiation n, barometric pressure, hu umidity, wind d vvelocity, direcction, etc. It is worth meentioning thatt, aalthough wind velocity is th he variable bein ng analyzed in n thhis research, more m informattion may be encountered e in n aanother time seeries. This dataa may be used for more exacct fforecasts by ussing what is caalled variable intervention or o inndicator interv vention, which represents add ditional data in n thhe time series or informatio on about the period p in which h thhe forecasting is realized. ful to review the t values of other variables It is very usefu w when creating g a forecastin ng model, forr example thee rrelationship bettween the variaable to be pred dicted and otheer vvariables. An information i ad dditional or otther variable is uusually selecteed to fall witthin the samee time intervaal rrelative to the variable v to be predicted. p S Some of the ad dditional variab bles (along with h wind velocity y inn m/s) to be co onsidered are:
Tempeerature (◦C) Barom metric pressure (mb) Date (hh/dd/mm) (
N Nevertheless, more m informattion does nott always mean n bbetter forecastts. Sometimess this can deegrade ANFIS S ccharacteristics; such as teach hing, learning, generalization n, aand forecasting g. It is always necessary n to geenerate relevan nt innformation forr the ANFIS, provided p that this t is possiblee. W Wind velocity in the Isthmuss of Tehuantep pec is shown in n ffigure 5.
Fig. 6 . Ten-minute interrval wind speed avverages from Januaary 2011 in thee Isthmus of Tehuaantepec.
TIME SERIES: MO ODELED FOR NEURO-ADA APTIVE FUZZY Y INFERENC CE SYSTEM (A ANFIS) me series forrecast using aan ANFIS consists of The tim teachinng the network the history of a variable in a selected time innterval, therebyy indicating infformation to be learned in the ffuture. Past datta is entered ass input into thee network and daata represent ffuture ANFIS output. An A ANFIS is capablee of predicting different kindds of data; neveertheless, the focuus of this invesstigation is to fforecast a timee series of wind veelocity in the IIsthmus of Tehhuantepec. ment of a Wind vvelocity seriess demonstrate the developm value oover time. Otheer factors such as barometric pressure, humiditty, temperaturre, and solar radiation, can iinfluence this vaalue. With thee time series it is necessarry to be familiarr with the vaalues at pointt t in order to make forecassts at point (t + P). Hence, it is also necessary to create a map with D sample of daata points everyy Δ time unit. Thhus, the follow wing notation iss used: (8) with four Samplee for estimatinng 100 forwaard periods w sample values: D = 4,, Δ = 1, P= 1000. (9)
Fig. 5. Wind speeed from January 20 010 to April 2011 in the Isthmus of Tehuan ntepec.
This meethod is iteratiive. The constrruction of a maatrix with W sampples is desired and the numbeer of exampless depends on the dduration of thee time series. The wiind speed readdings were takken every minuute at the meteoroological stationn from June 20008 to April 20011.
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NFIS structure is as follows: The AN
66. TRAINING G OF ADAPTIIVE NEURO-F - UZZY INFERENC CE SYSTEM (ANFIS). (
T There are sev veral training steps involveed in ANFIS S. D During the firrst step, the form f of initiall fuzzy sets is ddetermined. Th he number of fuzzy f sets and the universe of o ddiscourse depen nd directly on the number an nd range of thee vvariables. Thatt is to say, a large variable set requires a laarge number of o fuzzy sets ass input. In geneeral, there is no o m method for deetermining thee ANFIS parameter valuess. H However, in acccordance with h a number of tests t performed d aand the author’’s recommendaation [3, 4, 5, 6, 7, 8, 9, 10]], thhe form of thee fuzzy sets is as shown in figure 8, and thee nnumber of inpu ut sets was estaablished as follo ows:
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Number off input valuues: 4 (tem mperature, barometric ppressure, date, w wind velocity) Number of ooutput values: 1 (wind velocitty)
It is neccessary to menntion that the nuumber of inputt sets and the num mber of ruless to be consttructed increasse if the numberr of variablees used to perform the forecast increas es. The forregoing structuure can be obseerved in figure 7.
Tempeerature: 81 Gau ussian sets Barom metric pressure: 81 Gaussian sets s Date: 81 Gaussian seets G sets Wind velocity: 81 Gaussian
T The Gaussian and Bell sets were created in accordancee w with the follow wing functions:
(10 0) F Fig. 7. ANFIS struucture.
(11)
F Forming a totall of 81 rules wiith the followin ng structure: 1. If d1 is D1 annd p1 is P1 andd t1 is T 1 and w1 is W1 , then y is Y1 22. If d2 is D2 an nd p2 is P2 and d t2 is T 2 and w2 is W2 , then y is Y2 33. If d3 is D3 an nd p3 is P3 and t3 is T 3 and w3 is W3 , then y is Y3 4 ... 881. If d81 is D81 and p81 is P81 and a t81 is T 81 an nd w81 is W81, then y is Y81
W Where: Di : date, Pi : barometric prressure, T i : teemperature, Wi : wind velocity,, y Yi : forecast (wind velocity y)
models were connstructed To carrry out trainingg, three data m to be inncorporated innto the ANFIS.. Minimizationn of error was atteempted by means of the learnning process. T The three data moodels were connstructed to maake forecasts w within 16 hours, 224 hours, and 448 hour time foorward periodss. mportant to m monitor and vverify input ass it goes It is im throughh the networrk learning pprocess while keeping processs parameters in mind annd making nnecessary adjustm ments to minim mize error. Som metimes a smalll error is enoughh to cause the nnetwork to perrform poorly w which can result inn overtrainingg. Another wayy to arrive at a solution is to esstablish stoppagge criteria in thhe training phaase when mum acceptabble error is typically establishhed. This a maxim is donee to maximize tthe network’s ggeneralization. models to Six epoochs were tessted with the three data m obtain a decrease in tthe mean standdard error (MSE E) and to achievee stability duriing training wiith a tolerancee level of 0.0000 1. The Takagii-Sugeno fuzzyy inference sysstem was trained to estimate the results pproduced by tthe three modelss.
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Figure 10 shows thhe ANFIS forrecast for a 224 hours This value is less than forwardd forecast withh r=80.8011. T the onee produced foor the 16 houurs period, in which a partial inference cann be made sugggesting, that the error increas es as the forecast intervals arre longer. NFIS forecast for a 48 hourss forward forecast with The AN r=77.09955 can be obsserved in figurre 11. This valuue is less than thee ones from thhe 16 hours andd 24 hours foreecasts, in which it is shown tthat the error increases witth longer forecassts periods. Tabble 1 shows thee results of the tests. Tablle 1: Performance of ANFIS for 16, 24 and 48 hours pperiods.
Time 16 h 24 h 48 h
r% 81.118 80.8001 77.0995
Epoch 6 6 6
Trraining 223 min. 2..7 min. 6.001 min.
MSE 1.6333 1.5699 1.5688
Fig. F 8. Input variab bles and their shap pes.
T The results obttained for the 16 1 hours forwaard forecast aree sshown in figurre 9. A lineal regression, with w a result of o rr=81.1185, wass applied in orrder to discoveer how close to o thhe original daata the data obtained o durin ng the forecasst w were.
Fig. 9. 16 hours forwaard forecast and coorrelation of originnal data withh forecast data, resspectively.
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Fig. 10. 24 hou urs forward forecasst and correlation of o original data with forecast data, d respectively.
Fig. 111. 48 hours forwaard forecast and coorrelation of originnal data withh forecast data, resspectively.
T The computational times forr training and for prediction n sshould be redu uced, which en nables examinin ng more layerrs oor neurons. Futture work is th he design and implementation i n oof specialized hardware arcchitectures on reconfigurablee ccomputing. Nowadays, N seeveral works in artificiaal inntelligent tech hniques are embedded e into o FPGAs, fo or eexample, a prredictor for global solar irrradiation [17]]. M Moreover, diffferent networrk schemes and a levels of o pprecision can be explored by using u hardwaree architectures.
There aare two typess of membershhip function: Gaussian and Beell membershiip functions. The Bell mem mbership functionn has some addvantages suchh as being a litttle more flexiblee than the Gaussian m membership ffunctions. Therefoore the param meters of AN NFIS would bbe better adjustedd by using thhe Bell membbership functioon. Also, both m membership funnctions have addvantages suchh as being smoothh and non-zeroo at all pointss. In order too test the perform mance of ANFIIS after traininng, the tested ddata were presentted to the A ANFIS. Each predicted vaalue was comparred against the actual observeed value to meeasure the networkk performancee. The coefficiient of determ mination r gives innformation aboout the training of network, having a value of between [0, 100]. IIf the coefficient of determiination is closse to (100), it shows how suuccessful the learrning is. MSE E is used to determine how m much the networkk has reachedd the desired output valuess. In the particullar case of thee Isthmus of T Tehuantepec thhe results from thhree models w were presented.. In each of thhem, data sets weere constructedd to carry out w wind velocity foorecasts.
77. CONCLUSSIONS O One of the mo ost important steps in hybrrid neuro-fuzzy y m modeling is th he fuzzy memb bership values definition. As ppreviously men ntioned, the generalized g Beell membership p ffunctions speciified by four parameters p weere used in thee ppresent model.
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Each model made forecasts within periods of 16, 24 and 48 forward hours. This involved wind velocity, barometric pressure, temperature and date as variables. With regard to the forecast periods, one can conclude that error increase as the forecast period increases. Training with the first model, which had 17,320 data samples, for a 16 hours forward forecast produced D=1, Δ=1 y P=100 since 100*10=1000, and 1000/60=16 hours, producing r=81.1185. Subsequently, training with a second model with 17,273 data samples was performed for a 24 hours forward forecast period, producing D=1, Δ=1 and P=144, since 144*10=1440, and 1440/60=24 hours producing r=80.8011 with a difference of 0.3174. Later training was performed with a model containing 17,132 data samples for a 48 hours forward forecast that produced D=1, Δ=1 y P=288, since 288*10=2880, and 2880/60=48 hours producing r=77.0955 and an incremental difference of 4.023. It is worth mentioning that the three models were trained within six epochs. The training time was less for a hybrid like ANFIS than for a neuronal network. It is necessary to add that for future work, the utilization of other variables such as solar radiation, humidity, wind direction, etc., has not been discarded. The better performance of ANFIS with regard to the other intelligent methods is due to the combination of FL and ANN. Both mentioned membership functions (Bell and Gaussian) have been tested. It is important to mention that the rules used are generally based on the model and variables which depend on user’s experience and trial and error methods. Furthermore, the shape of membership functions depends on parameters, and changing these parameters will change the shape of the membership function. These problems are also seen in neural networks. Most of their parameters in a neural network are selected by trial and error method and most of them are dependent on the user’s experience.
ACKNOWLEDGMENT The authors would like to thank to the PROMEP project 103.5/11/5266, UNISTMO-PTC-056 for providing financial support.
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Application of Adaptive Neuro-Fuzzy Inference System for Grade Estimation; Case Study, Sarcheshmeh Porphyry Copper Deposit, Kerman, Iran. [2] Mohammed Monfared, Hasan Rastegar, Hossein Madadi, A new strategy for wind speed forecasting using artificial intelligent methods, Renewable Energy 34(2009):845-848. [3] Erasmo Cadenas, Wilfrido Rivera, Short term wind speed forecasting in La Venta, Oaxaca, Me´ xico, using artificial neural networks, Renewable Energy 34 (2009) 274-278. [4] R. E. Abdel-Aal, M. A. Elhadidy, S. M. Shaahhid, Modeling and forecasting the mean hourly wind speed time series using GMDH-based abductive networks, Renewable Energy, 34 (2009) 1686-1699. [5] Sancho Salcedo-Sanz, A´ ngel M. Pe´rez Bellido, Emilio G. Ortiz Garcia, ”Accurate short term Wind speed prediction by exploiting diversity in input data using Banks of artificial neural networks”, Neurocomputing 72 (2009) 1336-1341. [6] Jang, J.-S. R., ”Fuzzy Modeling Using Generalized Neural Networks and Kalman Filter Algorithm,” Proc. of the Ninth National Conf. on Artificial Intelligence (AAAI91), pp. 762-767, July 1991. [7] Jang, J.-S. R., ”ANFIS: Adaptive-Network-based Fuzzy Inference Systems,” IEEE Transactions on Systems, Man, and Cybernetics, Vol. 23, No. 3, pp. 665-685, May 1993. [8] Elliot D. Schwartz, Scott G. Haymes S, Heimiller D. Wind Energy resource Atlas of Oaxaca, NREL/TP-50034519, 2005. [9] Ichikawa, Y. and Sawa, T. (1992). Neural network application for direct feedback controllers, IEEE Transactions on Neural Networks, 3(2), 224-231. [10] Ishibuchi, H., Nozaki, K. and Tanaka, H. (1992). Distributed representation of fuzzy rules and its application to pattern classification, IEEE Transactions on Fuzzy Systems, 3(3), 260-270. [11] Ishibuchi, H., Nozaki, K., Yamamoto, N. and Tanaka, H. (1995). Selecting fuzzy If-Then rules for classification problems using genetic algorithms, Fuzzy Sets and Systems, 52, 21-32. [12] Russell, S.J. and Norvig, P. (2002). Artificial Intelligence: A Modern Approach, 2nd edn. Prentice Hall, Englewood Cliffs, NJ. [13] Schaffer, J.D., Whitley, D. and Eshelman, L.J. (1992). Com- binations of genetic algorithms and neural networks: a sur- vey of the state of the art, Proceedings of theInternational Workshop on Combinations of Genetic Algorithms and Neu- ral Networks,COGANN-92, D. Whitley and J.D. Schaffer, eds, IEEE Computer Society Press, Baltimore, MD, pp. 137. [14] Sestito, S. and Dillon T. (1991). Using single layered neural net- works for the extraction of conjunctive rules, Journal of Applied Intelligence, no. 1, 157-173. [15] Von Altrock, C. (1997). Fuzzy Logic and NeuroFuzzy Appli- cations in Business and Finance. Prentice Hall, Upper Saddle River, NJ. [17] Whitley, D. and Hanson, T. (1989). Optimizing neural networks using faster, more
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accurate genetic search, Proceedings of the Third International Conference on Genetic Algorithms, J.D. Schaffer, ed., Morgan Kaufmann, San Mateo, CA, pp. 391396. [16] Zadeh, L. (1996). Computing with words - A paradigm shift, Proceedings of the First International Conference on Fuzzy Logic and Management of Complexity, Sydney, Australia, 15- 18 January, vol. 1, pp. 3-10. [17] A. Mellit, H. Mekki, A. Messai, S. A. Kalogirou. (2011). FPGA-based implementation of intelligent predictor for global solar irradiation, Part I: Theory and simulation. Expert Systems with Applications, Vol. 38, Issue 3, March 2011, pp. 2668-2885. [18] Artificial Intelligence: A Guide to Intelligent Systems, Michael Negnevitsky, 2da edicion, ed. Addison Wesley.
Ernesto Cortés Pérez received his M.S. degree in Computer Science, from ITA-LITI (Laboratory research on intelligent technologies) in Apizaco, Tlaxcala, Mexico. Since 2007 he has been Professor- Research at the University Isthmus, Oaxaca, Mexico. His current research interests include Intelligent Systems, Fuzzy Logic, Patterns Classification, Artificial Neuro-Fuzzy Networks, Bio-Inspired Algorithms and Artificial Vision. Ignacio Algredo-Badillo received the B.Eng in Electronic Engineering from Technologic Institute of Puebla (ITP) in 2002 and the M.Sc and Ph.D degrees in Computer Science from National Institute for Astrophysics, Optics and Electronics (INAOE) in 2004 and 2008, respectively. Since 2009, he has been professor of Computer Engineering at University of Istmo. He has involved in the design and development of digital systems, reconfigurable architectures, software radio platforms, cryptographic systems, FPGAs implementations, microcontrollers-based systems and hardware acceleration for specific applications. Victor Hugo Garcia Rodriguez received the M. Sc. degree in Electronic Engineering from Universidad de las Americas Puebla (UDLAP) in Cholula, Puebla, Mexico. Since 2002 he has been research professor at the University of Isthmus, Oaxaca, Mexico. His current research interests include power electronics, instrumentation and control.
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Performance Analysis of ANFIS in short term Wind Speed Prediction Ernesto Cortés Pérez1, Ignacio Algredo-Badillo2, Víctor Hugo García Rodríguez3 1, 2
Department of Computer Engineering, UNISTMO University, Tehuantepec, Oaxaca, México, C. P. 70760 3
Department of Design Engineering, UNISTMO University, Tehuantepec, Oaxaca, México, C. P. 70760
Abstract Results are presented on the performance of Adaptive NeuroFuzzy Inference system (ANFIS) for wind velocity forecasts in the Isthmus of Tehuantepec region in the state of Oaxaca, Mexico. The data bank was provided by the meteorological station located at the University of Isthmus, Tehuantepec campus, and this data bank covers the period from 2008 to 2011. Three data models were constructed to carry out 16, 24 and 48 hours forecasts using the following variables: wind velocity, temperature, barometric pressure, and date. The performance measure for the three models is the mean standard error (MSE). In this work, performance analysis in short-term prediction is presented, because it is essential in order to define an adequate wind speed model for eolian parks, where a right planning provide economic benefits. Keywords: Wind, fuzzy, neural, ANFIS, prediction.
1. INTRODUCTION The success of eolian resource forecasting depends on precision. Indeed minimizing error implies to consider factors such as: the selected forecasting model, the model parameters, the available data history, etc. Fuzzy logic and neural networks are frequently employed for estimating and forecasting [1] when available data is not sufficiently reliable because it allows tolerance levels due to the imprecision associated with linguistic terminology, which, by their very nature, are less precise than numbers. Fuzzy logic is a useful technique because it makes use of uncertainty and calibrates vagueness to find robust solutions at low computational cost [2]. Furthermore, because they are inspired by and adapted from biological systems, artificial neuronal network models simulate the cognitive processes in so much as they possess the capacity to interpret the world in the same way human beings do. Each of these techniques has its advantages and disadvantages. A number of studies have reported successful results from the application of neural networks to wind velocity forecasts. For example, in 2009 [3] Monfared et al.
applied a strategy based on fuzzy logic and neuronal networks to forecast wind velocity. They employed statistical properties such as standard deviation, mean, and variable calculation relation gradient as neuro-fuzzy predictor model input. They did so by using real time data obtained in northern Iran from 2002 to 2005. Readings were taken at average intervals of 30 minutes. In 2009 in average Cadenas et al. used one hour intervals to forecast wind velocity by using data collected by the Federal Commission of Electricity (Comision Federal de Electricidad, CFE) during a period of seven years in the La Venta, Oaxaca, Mexico [4]. This was done using a backpropagation and Madaline neuronal network with a mean square error measured at 0.0039 during the training process. In another study, Adbel Aal, et al. [5] performed wind velocity forecasts by using tardy neuronal networks (TTND), particularly for the maintenance of wind farms where researchers used a wind velocity data base with one-hour intervals compiled in the Dhahran region of Saudi Arabia from 1994 to 2005. The proposed model was evaluated with data from May of 2006, and the forecasting time was from 16 to 24 hours. Therefore, the network precision measurement parameter had a mean absolute error (MAE) of 0.85 m/s, and the correlation coefficient was equal to 0.83 between the actual value and the forecast. In 2009 [6] Sancho Salcedo, et al. employed a multilayered network with the Levenberg-Marquadt training method in which the input variables were wind velocity chosen at two points of interest with wind direction at one point, temperature at one point, and solar radiation at two points. Hence, there are six values in the input layer, a hidden layer with six neurons with a sigmoidal logarithmic activation function, and an output layer with one neuron. The forecasting time was 48 hours. The data had been collected since 2006 in Albacete province in southern Spain. The goal of this study is to perform a comparative on the performance of an Adaptive Neuro-Fuzzy Inference System (ANFIS) in forecasting time intervals of 16, 24, and 48 hours. The meteorological
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sstation at the University of the Isthmuss, Tehuantepecc C Campus, Oaxaca, Mexico prrovided a data bank obtained d ffrom June 2008 to April 201 11. Wind veloccity readings at a thhe meteorolo ogical station are taken every minutee. H However, in th his research thee data bank was modified by y ccalculating averages at ten miinute intervals.. The following g vvariables are co onsidered:
Wind velocity (m/s) Tempeerature (◦C) Barom metric pressure (mb) Date (hh/dd/mm) (
22. ARTIFICIA AL NEURAL NETWORKS S (ANN) M McCulloch and d Pitts were th he first personss to introduce a m model of an eleementary comp puting neuron. Six years laterr, H Hebb proposed d learning rulees. ANN’s greew rapidly, and d thhey have been n applied wid dely in many fields, such as a ppattern classsification, approximation n, function liinear/nonlinearr identification n, multivariab ble systems. A ssimple ANN was w composed of o neuronal lin nks that connecct thhe neurons and assign weigh hts and a bias to them. ANN N ccomprises math hematical equ uations that miimic the brain n. S Since ANN iss made of seeveral neuronss and differen nt laayers, it is capable of performing p maassive paralleel ccomputations.
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Networrk (LRN). Alll of these strructures have specific advantaages and disaddvantages. Bacckpropagation based on error b ackward and iits correction is the most coommonly Actually, this algorithm is based on the gradient used. A descentt method whicch according to error surfacee tries to find thhe best weightt and bias coomposition in order to minimiize the netwoork error. Theere are two iimportant processses in a BP aalgorithm: first, the error coonsiderer calculatted accordingg to the inpuut passed throough the hidden layers of neurrons; second, according to tthis same error, there will bee backward ppropagation tto adjust weightss. However, thhis method haas some disaddvantages like sloow converges, a lack of robusstness, and ineffficiency. One off the most succcessful methodds which couldd be used to impprove the traaining processs is the LeevenbergMarquaardt (LM) metthod which is based on bothh GaussNewtonn nonlinear reggression and grradient steepesst descent methodd.
3. FU UZZY LOGIC (FL) Fuzzy llogic was thouught of as a meethod of formallizing the kind oof imprecise reasoning thhat humans typically perform m. Everyday exxpressions like it’s too hot annd it’s not very higgh are impossiible to formulaate in classical llogic. Fuzzy llogic can proceess vague lingguistic variables such as too, veery, enough aas logical form mulations in ccomputer languagge. Fuzzy logic fits within the frameworrk of the multivaariate logic grooup (there are more truth vaalues than true andd false), and it is based on fuuzzy set theory.. A. Zadeh, a proofessor at the U University of C California Lofti A at Berkkeley founded tthis discipline in 1965. It cam me about throughh the applicatioon of multivarriate logic to seet theory. See figg. 2 for typical structure of a system based on fuzzy logic.
Fig. 1. Input and outpu ut of a neural netw work.
T The position an nd the differen nt neuron conn nections lead to o A ANN being classified c in different d group ps. First feed dfforward networrk which inclu udes single lay yer perceptron n, m multilayer percceptron, backp propagation (B BP) and radiaal bbasis functions. A second gro oup is the recu urrent networkss, ccompetitive nettworks, Kohon nen’s SOM, Ho opfield network k aand ART modeels. A third grroup consists of o the dynamicc nnetworks such as Focuses TimeT Delay Neural N Network k (FTDNN), Distributed Tim me- Delay Neeural Network k N auttoregressive network n with h (DTDNN), Nonlinear eexogenous inpu ut (NARX Neetwork) and Layer-Recurren L nt
Fig. 2. S System based on fuuzzy logic.
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44. ANFIS
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1. Evaaluating the rulle premises ressults in:
A Actually, ANF FIS (Adaptivee Neuro - Fu uzzy Inferencee SSystem) method d is similar to a fuzzy inferen nce system, bu ut itt uses a backkpropagation to t minimize the t error. This m method’s perfo ormance is eq quivalent to bo oth ANNs and d F FLs. In the case of both AN NN and FL, th he input passes thhrough the inp put layer (by input memberrship function n) aand the output could be seen in the output layer (by outpu ut m membership fun nctions). T The parameterss associated wiith the membeership functions aare modified th hrough learnin ng processes. The T adjustmen nt oof the parameteers is generated by the vecto or gradient. Thee aadjusted param meters are su ubsequently applied a to alll ooptimization routines r to reduce r measu urement errorr. U Usually, if yt iss the current value v of period d t and Ft is thee fforecast for the same period, then t the error is i defined as: et = yt – Ft
2. Evaluating tthe conseqquences gives:
implicattion
(3) and
tthe
rule
(4)
Or leavving the argumeents out:
(1)
A mean square error (MSE) iss defined as:
∑
wi = µA Ai(x) µBi(y), i= =1,2.
(5) This caan be separatedd into phases firrst by defining:
2) (2 (6)
W Where n is the number of time periods. A ANFIS uses a combination n of minimum m squares and d bbackpropagatio on for the estim mation of activ vation function n pparameters. In other words, ANFIS A utilizes the advantages oof FL and ANN N to adjust its parameters p and d find optimum m ssolutions.
Then f can be writtenn as: (7) mputations cann be seen in fig.. 3 and 4. All com
B Both FL and ANN A have theiir advantages. Therefore, it is ggood idea to co ombine their ability a and mak ke a strong too ol w which improves their weakneesses leads to minimum m errorr. JJang [7] comb bined both FL and ANN to produce a ppowerful proceessing tool calleed ANFIS. Thiis is a powerfu ul toool that has bo oth ANN and FL F advantages. A Assume that th he fuzzy infereence system haas two inputs x aand y and onee output f. Forr a first-order Sugeno fuzzy y m model, a comm mon rule set with w two fuzzy if-then rules is aas follows, Jang g [7]:
Fig. 3. First--order Takagi-Sugeno Fuzzy Model..
Rule 1: If x iss A1 and y is B1 , then f1 = p1 x + q1 y + r1 Rule 2: If x iss A2 and y is B2 , then f2 = p2 x + q2 y + r2 bership functio ons of fuzzy sets s Ai , Bi , i = Let the memb 1, 2, be µAi , µ Bi . In evaluatting the rules, choose c productt for T-norm (lo ogical and).
Fiig. 4. Equivalent A ANFIS architecturee with two inputs aand one output.
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55.
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DATA COL LLECTION
T The data for th his study was provided p by a meteorologicaal sstation located d at the Teehuantepec caampus of thee U University of th he Isthmus. Th his data base co overs the period d ffrom June 2008 8 to April 2011 1. It contains in nformation on a nnumber of variiables such ass wind velocity y, temperaturee, ssolar radiation n, barometric pressure, hu umidity, wind d vvelocity, direcction, etc. It is worth meentioning thatt, aalthough wind velocity is th he variable bein ng analyzed in n thhis research, more m informattion may be encountered e in n aanother time seeries. This dataa may be used for more exacct fforecasts by ussing what is caalled variable intervention or o inndicator interv vention, which represents add ditional data in n thhe time series or informatio on about the period p in which h thhe forecasting is realized. ful to review the t values of other variables It is very usefu w when creating g a forecastin ng model, forr example thee rrelationship bettween the variaable to be pred dicted and otheer vvariables. An information i ad dditional or otther variable is uusually selecteed to fall witthin the samee time intervaal rrelative to the variable v to be predicted. p S Some of the ad dditional variab bles (along with h wind velocity y inn m/s) to be co onsidered are:
Tempeerature (◦C) Barom metric pressure (mb) Date (hh/dd/mm) (
N Nevertheless, more m informattion does nott always mean n bbetter forecastts. Sometimess this can deegrade ANFIS S ccharacteristics; such as teach hing, learning, generalization n, aand forecasting g. It is always necessary n to geenerate relevan nt innformation forr the ANFIS, provided p that this t is possiblee. W Wind velocity in the Isthmuss of Tehuantep pec is shown in n ffigure 5.
Fig. 6 . Ten-minute interrval wind speed avverages from Januaary 2011 in thee Isthmus of Tehuaantepec.
TIME SERIES: MO ODELED FOR NEURO-ADA APTIVE FUZZY Y INFERENC CE SYSTEM (A ANFIS) me series forrecast using aan ANFIS consists of The tim teachinng the network the history of a variable in a selected time innterval, therebyy indicating infformation to be learned in the ffuture. Past datta is entered ass input into thee network and daata represent ffuture ANFIS output. An A ANFIS is capablee of predicting different kindds of data; neveertheless, the focuus of this invesstigation is to fforecast a timee series of wind veelocity in the IIsthmus of Tehhuantepec. ment of a Wind vvelocity seriess demonstrate the developm value oover time. Otheer factors such as barometric pressure, humiditty, temperaturre, and solar radiation, can iinfluence this vaalue. With thee time series it is necessarry to be familiarr with the vaalues at pointt t in order to make forecassts at point (t + P). Hence, it is also necessary to create a map with D sample of daata points everyy Δ time unit. Thhus, the follow wing notation iss used: (8) with four Samplee for estimatinng 100 forwaard periods w sample values: D = 4,, Δ = 1, P= 1000. (9)
Fig. 5. Wind speeed from January 20 010 to April 2011 in the Isthmus of Tehuan ntepec.
This meethod is iteratiive. The constrruction of a maatrix with W sampples is desired and the numbeer of exampless depends on the dduration of thee time series. The wiind speed readdings were takken every minuute at the meteoroological stationn from June 20008 to April 20011.
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NFIS structure is as follows: The AN
66. TRAINING G OF ADAPTIIVE NEURO-F - UZZY INFERENC CE SYSTEM (ANFIS). (
T There are sev veral training steps involveed in ANFIS S. D During the firrst step, the form f of initiall fuzzy sets is ddetermined. Th he number of fuzzy f sets and the universe of o ddiscourse depen nd directly on the number an nd range of thee vvariables. Thatt is to say, a large variable set requires a laarge number of o fuzzy sets ass input. In geneeral, there is no o m method for deetermining thee ANFIS parameter valuess. H However, in acccordance with h a number of tests t performed d aand the author’’s recommendaation [3, 4, 5, 6, 7, 8, 9, 10]], thhe form of thee fuzzy sets is as shown in figure 8, and thee nnumber of inpu ut sets was estaablished as follo ows:
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Number off input valuues: 4 (tem mperature, barometric ppressure, date, w wind velocity) Number of ooutput values: 1 (wind velocitty)
It is neccessary to menntion that the nuumber of inputt sets and the num mber of ruless to be consttructed increasse if the numberr of variablees used to perform the forecast increas es. The forregoing structuure can be obseerved in figure 7.
Tempeerature: 81 Gau ussian sets Barom metric pressure: 81 Gaussian sets s Date: 81 Gaussian seets G sets Wind velocity: 81 Gaussian
T The Gaussian and Bell sets were created in accordancee w with the follow wing functions:
(10 0) F Fig. 7. ANFIS struucture.
(11)
F Forming a totall of 81 rules wiith the followin ng structure: 1. If d1 is D1 annd p1 is P1 andd t1 is T 1 and w1 is W1 , then y is Y1 22. If d2 is D2 an nd p2 is P2 and d t2 is T 2 and w2 is W2 , then y is Y2 33. If d3 is D3 an nd p3 is P3 and t3 is T 3 and w3 is W3 , then y is Y3 4 ... 881. If d81 is D81 and p81 is P81 and a t81 is T 81 an nd w81 is W81, then y is Y81
W Where: Di : date, Pi : barometric prressure, T i : teemperature, Wi : wind velocity,, y Yi : forecast (wind velocity y)
models were connstructed To carrry out trainingg, three data m to be inncorporated innto the ANFIS.. Minimizationn of error was atteempted by means of the learnning process. T The three data moodels were connstructed to maake forecasts w within 16 hours, 224 hours, and 448 hour time foorward periodss. mportant to m monitor and vverify input ass it goes It is im throughh the networrk learning pprocess while keeping processs parameters in mind annd making nnecessary adjustm ments to minim mize error. Som metimes a smalll error is enoughh to cause the nnetwork to perrform poorly w which can result inn overtrainingg. Another wayy to arrive at a solution is to esstablish stoppagge criteria in thhe training phaase when mum acceptabble error is typically establishhed. This a maxim is donee to maximize tthe network’s ggeneralization. models to Six epoochs were tessted with the three data m obtain a decrease in tthe mean standdard error (MSE E) and to achievee stability duriing training wiith a tolerancee level of 0.0000 1. The Takagii-Sugeno fuzzyy inference sysstem was trained to estimate the results pproduced by tthe three modelss.
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Figure 10 shows thhe ANFIS forrecast for a 224 hours This value is less than forwardd forecast withh r=80.8011. T the onee produced foor the 16 houurs period, in which a partial inference cann be made sugggesting, that the error increas es as the forecast intervals arre longer. NFIS forecast for a 48 hourss forward forecast with The AN r=77.09955 can be obsserved in figurre 11. This valuue is less than thee ones from thhe 16 hours andd 24 hours foreecasts, in which it is shown tthat the error increases witth longer forecassts periods. Tabble 1 shows thee results of the tests. Tablle 1: Performance of ANFIS for 16, 24 and 48 hours pperiods.
Time 16 h 24 h 48 h
r% 81.118 80.8001 77.0995
Epoch 6 6 6
Trraining 223 min. 2..7 min. 6.001 min.
MSE 1.6333 1.5699 1.5688
Fig. F 8. Input variab bles and their shap pes.
T The results obttained for the 16 1 hours forwaard forecast aree sshown in figurre 9. A lineal regression, with w a result of o rr=81.1185, wass applied in orrder to discoveer how close to o thhe original daata the data obtained o durin ng the forecasst w were.
Fig. 9. 16 hours forwaard forecast and coorrelation of originnal data withh forecast data, resspectively.
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Fig. 10. 24 hou urs forward forecasst and correlation of o original data with forecast data, d respectively.
Fig. 111. 48 hours forwaard forecast and coorrelation of originnal data withh forecast data, resspectively.
T The computational times forr training and for prediction n sshould be redu uced, which en nables examinin ng more layerrs oor neurons. Futture work is th he design and implementation i n oof specialized hardware arcchitectures on reconfigurablee ccomputing. Nowadays, N seeveral works in artificiaal inntelligent tech hniques are embedded e into o FPGAs, fo or eexample, a prredictor for global solar irrradiation [17]]. M Moreover, diffferent networrk schemes and a levels of o pprecision can be explored by using u hardwaree architectures.
There aare two typess of membershhip function: Gaussian and Beell membershiip functions. The Bell mem mbership functionn has some addvantages suchh as being a litttle more flexiblee than the Gaussian m membership ffunctions. Therefoore the param meters of AN NFIS would bbe better adjustedd by using thhe Bell membbership functioon. Also, both m membership funnctions have addvantages suchh as being smoothh and non-zeroo at all pointss. In order too test the perform mance of ANFIIS after traininng, the tested ddata were presentted to the A ANFIS. Each predicted vaalue was comparred against the actual observeed value to meeasure the networkk performancee. The coefficiient of determ mination r gives innformation aboout the training of network, having a value of between [0, 100]. IIf the coefficient of determiination is closse to (100), it shows how suuccessful the learrning is. MSE E is used to determine how m much the networkk has reachedd the desired output valuess. In the particullar case of thee Isthmus of T Tehuantepec thhe results from thhree models w were presented.. In each of thhem, data sets weere constructedd to carry out w wind velocity foorecasts.
77. CONCLUSSIONS O One of the mo ost important steps in hybrrid neuro-fuzzy y m modeling is th he fuzzy memb bership values definition. As ppreviously men ntioned, the generalized g Beell membership p ffunctions speciified by four parameters p weere used in thee ppresent model.
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Each model made forecasts within periods of 16, 24 and 48 forward hours. This involved wind velocity, barometric pressure, temperature and date as variables. With regard to the forecast periods, one can conclude that error increase as the forecast period increases. Training with the first model, which had 17,320 data samples, for a 16 hours forward forecast produced D=1, Δ=1 y P=100 since 100*10=1000, and 1000/60=16 hours, producing r=81.1185. Subsequently, training with a second model with 17,273 data samples was performed for a 24 hours forward forecast period, producing D=1, Δ=1 and P=144, since 144*10=1440, and 1440/60=24 hours producing r=80.8011 with a difference of 0.3174. Later training was performed with a model containing 17,132 data samples for a 48 hours forward forecast that produced D=1, Δ=1 y P=288, since 288*10=2880, and 2880/60=48 hours producing r=77.0955 and an incremental difference of 4.023. It is worth mentioning that the three models were trained within six epochs. The training time was less for a hybrid like ANFIS than for a neuronal network. It is necessary to add that for future work, the utilization of other variables such as solar radiation, humidity, wind direction, etc., has not been discarded. The better performance of ANFIS with regard to the other intelligent methods is due to the combination of FL and ANN. Both mentioned membership functions (Bell and Gaussian) have been tested. It is important to mention that the rules used are generally based on the model and variables which depend on user’s experience and trial and error methods. Furthermore, the shape of membership functions depends on parameters, and changing these parameters will change the shape of the membership function. These problems are also seen in neural networks. Most of their parameters in a neural network are selected by trial and error method and most of them are dependent on the user’s experience.
ACKNOWLEDGMENT The authors would like to thank to the PROMEP project 103.5/11/5266, UNISTMO-PTC-056 for providing financial support.
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accurate genetic search, Proceedings of the Third International Conference on Genetic Algorithms, J.D. Schaffer, ed., Morgan Kaufmann, San Mateo, CA, pp. 391396. [16] Zadeh, L. (1996). Computing with words - A paradigm shift, Proceedings of the First International Conference on Fuzzy Logic and Management of Complexity, Sydney, Australia, 15- 18 January, vol. 1, pp. 3-10. [17] A. Mellit, H. Mekki, A. Messai, S. A. Kalogirou. (2011). FPGA-based implementation of intelligent predictor for global solar irradiation, Part I: Theory and simulation. Expert Systems with Applications, Vol. 38, Issue 3, March 2011, pp. 2668-2885. [18] Artificial Intelligence: A Guide to Intelligent Systems, Michael Negnevitsky, 2da edicion, ed. Addison Wesley.
Ernesto Cortés Pérez received his M.S. degree in Computer Science, from ITA-LITI (Laboratory research on intelligent technologies) in Apizaco, Tlaxcala, Mexico. Since 2007 he has been Professor- Research at the University Isthmus, Oaxaca, Mexico. His current research interests include Intelligent Systems, Fuzzy Logic, Patterns Classification, Artificial Neuro-Fuzzy Networks, Bio-Inspired Algorithms and Artificial Vision. Ignacio Algredo-Badillo received the B.Eng in Electronic Engineering from Technologic Institute of Puebla (ITP) in 2002 and the M.Sc and Ph.D degrees in Computer Science from National Institute for Astrophysics, Optics and Electronics (INAOE) in 2004 and 2008, respectively. Since 2009, he has been professor of Computer Engineering at University of Istmo. He has involved in the design and development of digital systems, reconfigurable architectures, software radio platforms, cryptographic systems, FPGAs implementations, microcontrollers-based systems and hardware acceleration for specific applications. Victor Hugo Garcia Rodriguez received the M. Sc. degree in Electronic Engineering from Universidad de las Americas Puebla (UDLAP) in Cholula, Puebla, Mexico. Since 2002 he has been research professor at the University of Isthmus, Oaxaca, Mexico. His current research interests include power electronics, instrumentation and control.
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