A Hierarchical Artificial Neural Network for Gasoline Demand Forecast of Iran

Transcription

1 Int. J. Humanities (202) Vo. 9 (): (-3) A Hierarchica Artificia Neura Network for Gasoine Demand Forecast of Iran A. Kazemi, M.R. Mehregan 2, H. Shakouri. G 3, M.B. Mehnaj 4, E. Asgharizadeh 5, M.R. Taghizadeh 6 Received: 2009/5/2 Accepted: 20/4/7 Abstract This paper presents a neuro-based approach for annua gasoine demand forecast in Iran by taking into account severa socio-economic indicators. To anayze the infuence of economic and socia indicators on the gasoine demand, gross domestic product (GDP), popuation and the tota number of vehices are seected. This approach is structured as a hierarchica artificia neura network (ANN) based on supervised muti-ayer perceptron (MLP), trained with back-propagation (BP) agorithm. This hierarchica ANN is designed propery. The input variabes are GDP, popuation, tota number of vehices and the gasoine demand in the ast one year. The output variabe is the gasoine demand. The paper proposes a hierarchica network by which the inputs to the ending eve are obtained as outputs of the starting eves. Actua Iranian data between 967 and 2008 were used to test the hierarchica ANN hence; it iustrated the capabiity of the approach. Comparison of the mode predictions with vaidation data shows vaidity of the mode. Furthermore, the demand for the period between 20 and 2030 is estimated. It is noticeabe that if there wi not be any price shock or efficiency improvement in the transportation sector, the gasoine consumption may achieve a threatening eve of about 54 biion iters by 2030 in Iran. Keywords: ANN; MLP; BP Agorithm; Forecasting; Gasoine Demand.. PhD Student, Operation Research Management, University of Tehran, Iran. aiyehkazemi@ut.ac.ir 2. Associate Professor, Department of Industria Management, University of Tehran, Iran 3. Associate Professor, Department of Industria Engineering, University of Tehran, Iran 4. Professor, Department of Eectrica Engineering, Amirkabir University of Technoogy, Iran 5. Associate Professor, Department of Industria Management, University of Tehran, Iran 6. PhD Student, Operation and Production Management, University of Tehran, Iran

2 A Hierarchica Artificia Neura Int. J. Humanities (202) Vo. 9 () Introduction The transportation sector in many deveoping countries reies heaviy on gasoine for its daiy mobiity. This reiance is even more acute in the under deveoping countries due to the ack of efficient pubic transportation. Gasoine demand forecast becomes an essentia function in panning for the future demand to design more efficient transportation systems as we as to contro the demand by a proper price mechanism. During past decades, a variety of technica and statistica methods for energy forecasting have been proposed with varying resuts. However, no technique or combination of techniques has been consistenty successfu enough to forecast the energy demand. ANNs one such method being used extensivey in forecasting different types of energy demands. Athough there are simper, faster, and easier aternatives, ANNs have been appied to the energy forecasting probem with considerabe success. Evidenty, an ANN yied more usefu insights than a regression based mode and that ANNs architecture used to forecast energy demands presents higher accuracy than a traditiona poynomia fit method (Nasr et a, 2003: ). Appications of artificia neura networks for energy forecasting probems have resuted in severa research papers (Nasr et a., 2003; Azadeh, 200: ). Kermanshahi and Iwamiya deveoped an artificia neura network mode to predict the peak eectric oad in Japan up to 2020 (Kermanshahi & Iwamiya 2002: ). Hsu and Chen coected an empirica data to formuate an artificia neura network mode to predict the regiona peak oad of Taiwan in 2003 (Hsu CC, Chen, 2003:94 9). Nasr et a formuated a neura network approach for the gasoine consumption prediction in Lebanon (Nasr et a, 2003). Murat and Ceyan deveoped yet another mode based on artificia neura network to predict transportation of energy demand in Turkey (Murat & Ceyan, 2006: ). Azadeh, Ghaderi and Sohrabkhani formuated a neura network mode to predict the annua eectricity consumption in high energy consuming industria sectors in Iran (Azadeh et a., 2008: ). Geem and Roper used neura networks to estimate energy demand in South Korea (Geem & Roper, 2009: ). Ekonomou deveoped a neura network mode to predict Greek ong-term energy consumption (Ekonomou, 200:52-7). The same year, Azadeh, Arab and Behfard came up with a mode to forecast ong-term gasoine demand in the US, Canada, Japan, Kuwait and Iran using artificia neura networks (Azadeh et a., 200: ). In this paper, the gasoine demand of Iran is forecasted using MLP trained by BP agorithm considering economic and socia indicators for 2

3 Kazemi A. and others Int. J. Humanities (202) Vo. 9 () the time span 20 to For the estimation, time series data covering period between 967 and 2008 are used. The remaining parts of the paper are organized as foows. In Section 2, ANNs are introduced. Detais of the proposed forecast strategy and numerica resuts are described in Section 3.A brief review of the paper and future researches are given insection 4. Artificia Neura Networks ANNs are computationa modeing toos that have recenty emerged and found extensive acceptance in many discipines for modeing compex rea-word probems. In an ANN mode, a neuron is an eementa processing unit that forms part of a arger network. ANNs consist of an inter-connection of a number of neurons. There are varieties of connections under study; however, ony one type of network caed the muti-ayer perceptron (MLP) wi be discussed here. A MLP consists of (i) input variabes, (ii) an output ayer with nodes representing the dependent variabes (i.e. what is being modeed), and (iii) one or more hidden ayers containing nodes to hep capture the noninearity in the data. Using supervised earning, these networks can earn the mapping from one data space to other using exampes. In MLPs, the data are feed-forward into the network without feedback. These networks are so versatie and can be used for forecasting. Fig. shows a typica two ayer feed-forward mode. In this figure, R is the number of inputs, p is the vector of inputs, S is the number of hidden nodes, S 2 is the number of output, therefore the construction is defined as foow: R S S 2 () f and f 2 are transfer functions such as the sigmoid function: inear function: f ( x) = and the + exp( x) f ( x) = x, W is a matrix of weights from the inputs to the hidden nodes, W 2 is a matrix of weights from the hidden nodes to the output nodes. The vector b and b 2 are the weights of arcs eading from the bias terms, which have vaues aways equa to. n and n 2 are vectors of net input and a and a 2 are vectors of actua output. To buid a mode for forecasting, the network is processed through three stages: () The training stage where the network is trained to predict future data based on past and present data. (2) The test stage where the network is tested to stop training or to keep in training. (3) The evauation stage where the network ceases training and is used to forecast future data and to cacuate different measures of error (Kermanshahi & Iwamiya 2002: ). 3

4 A Hierarchica Artificia Neura Int. J. Humanities (202) Vo. 9 () Input FirstLayer SecondLayer R P W n R R * S * R + n S * R b S S * S *S f a S * W 2 S 2 * S b 2 * S 2 + n 2 f 2 a 2 S 2 S * S * 2 2 * a = f ( W p + ) a = f W a + ) b Fig A Two-ayer MLP Network [Menhaj, 2005] 2 2 ( 2 b2 The most popuar earning rue of MLPs is the error BP agorithm. BP earning is a kind of supervised earning introduced by Werbos and ater deveoped by Rumehart and McCeand [Azadeh et a., 2008]. At the beginning of the earning stage, a weights in the network are initiaized to sma random vaues. The agorithm uses a earning set, which consists of input, target pattern pairs. Each input output pair is obtained by offine processing of historica data. These pairs are used to adjust the weights in the network to minimize the sum squared error (SSE), which measures the difference between the rea and the target vaues over a output neurons and a earning patterns. After computing SSE, the backpropagation step computes the corrections to be appied to the weights. With input, target pairs: {, T ),( P, T ),...,( P Q, T )} ( 2 2 Q P, the BP agorithm can be written as (Menhaj, 2005):. Forward path: The first step is to propagate the input forward through the network: a a (0) + = P( k) ( k) = F a( k) = a L + ( k) ( W + ( k) a + b + ( k)) = 0,,..., L (2) where L is the number of ayers of a neura network. 2. Backward path: The next step is to propagate the sensitivities backward through the network: δ ( k) = 2F L δ ( k) = F.. L ( n) e( k) ( n )( W T + ) δ +, = L,..., (3) e( k) = T( k) a( k) 3. Weights adjustment: Finay, the weights and biases are updated using the approximate 4

5 Kazemi A. and others Int. J. Humanities (202) Vo. 9 () steepest descent rue: W ( k ) = W ( k) αδ ( k)( a ( k)) b ( k + ) = b ( k) αδ ( k), =,2,..., L + T (4) 4. Stop: when the sum squared error dips beow a particuar error threshod or the chosen maximum number of epochs is reached then stops. It shoud be mentioned that some constraints woud appear when ANN modes are appied to socio-economic systems. In such cases, it woud be necessary to adjust the ANN mode by force in order to prepare the feasibe outputs forecasts. Hierarchica ANN Mode Deveopment and Appication In Iran, a sharp growth in the gasoine consumption started during 970s. This was due to the first oi price shock as we as the positive foreign exchange. The.2bn iters consumption in 970 jumped to 5.7bn by 979. Even the rationing of gasoine during the Iraq- Iran war between 980 and 988 coud not cause gasoine consumption to decrease. After the war, gasoine consumption increased and reached to a eve of 8.2bn iters in 990. Gasoine rationing vanished in 992. As a resut, gasoine consumption jumped sharpy. In 994, the gasoine price doubed athough, it was expected that the price hike woud ed to fa in the gasoine consumption. One reason was the increasing number of vehices. In fact, consumption increased to about.6 miiard iters in The average growth rate of gasoine consumption was 6.44% per year during 200 to Then gasoine consumption was 24.5% miiard iters in In this section gasoine demand in Iran from 20 to 2030 is forecasted regarding socioeconomic and transport reated indicators using a hierarchica ANN mode. The structure of the designed hierarchica ANN is given in Fig. 2. The main ANN (4) takes popuation, GDP, the tota number of vehices and the gasoine demand in the ast year as inputs and produces the gasoine demand. The inputs to the ending eve are obtained as outputs of the starting eves. Popuation, GDP and the tota number of vehices are forecasted using ANNs. Tabe summarizes the ANNs inputs and output. The genera strategy of the hierarchica ANN mode is given in Fig. 3. ANN GDP ANN 2 Popuation ANN3 Number of Vehices ANN4 Gasoine Demand Fig 2 Structure of Designed Hierarchica ANN 5

6 A Hierarchica Artificia Neura Int. J. Humanities (202) Vo. 9 () Designing an ANN for forecasting popuation () Designing an ANN for forecasting GDP (2) Designing an ANN for forecasting the number of vehices (3) Des gning an ANN for forecasting gasoine Data coection (growth rate of popuation from 968 to 2008) Data preprocessing ANN modeing Data coection (growth rate of GDP from 968 to 2008) Data preprocessing ANN modeing Data coection (popuation, GDP and the number of vehices from 968 to 2008) Data preprocessing Data coection (popuation, GDP, the number of vehices and gasoine demand from 968 to 2008) Data preprocessing ANN modeing ANN modeing Forecasting popuation from 20 to 2030 Forecasting GDP from 20 to 2030 Forecasting the number of vehices from 20 to 2030 Forecasting gasoine demand from 20 to 2030 Data preprocessing Divide data into train, evauation and test. Data normaization ANN modeing Training Test Evauation Seect the best ANN architecture Fig 3 Strategy of the Hierarchica ANN mode 6

7 Kazemi A.and others Int. J. Humanities (202) Vo. 9 () Tabe ANNs Inputs and Output ANN Inputs Output - Growth rate of popuation in the ast year 2- Growth rate of popuation in the ast two years Popuation 2 - Growth rate of GDP in the ast year 2- Growth rate of GDP in the ast two years GDP 3 - Popuation Tota number of 2- GDP vehices 3- Tota number of vehices in the ast year 4 - Popuation 2- GDP 3- Tota number of vehices Gasoine demand 4- Gasoine demand in the ast year Data reated with gasoine modeing are coected from different sources. GDP and popuation are coected from Iran Ministry of Energy. The tota number of vehices is coected from Ministry of Industries and Mines. The gasoine consumption is coected from Nationa Iranian Oi products Distribution Company. Data are given in Tabe 2. Tabe 2 Popuation, GDP, Tota Number of Vehices and the Gasoine Demand in Iran Years (t) Popuation (0 6 ) GDP (0 2 R) Number of Vehices (0 3 ) Gasoine Demand (0 9 iters) Years (t) Popuation (0 6 ) GDP (0 2 R) Number of Vehices (0 6 ) Gasoine Demand (0 9 iters) NA

8 A Hierarchica Artificia Neura Int. J. Humanities (202) Vo. 9 () The study spans the time period from 968 to This period is used to train, evauate and test the ANN modes. The mode samping is based on a 33 year training set i.e. 968 to 2000, whie the test stage covers the period from 200 to Aso, the evauation stage covers the period between 2006 and A data are normaized before to be appied to each ANN. Normaization (scaing) of data within a uniform range (e.g., 0 ) is essentia (i) to prevent arger numbers from overriding smaer ones, and (ii) to prevent premature saturation of hidden nodes, which impedes the earning process. This is especiay true when actua input data take arge vaues. There is no one standard procedure for normaizing inputs and outputs. One way is to scae input and output variabes ( z i ) in interva λ, ] [ λ2 corresponding to the range of the transfer function (Basheer &Hajmeer, 2000:3-3): z xi = λ + ( λ2 λ )( z where max z i and i max i z min i min zi x i is the normaized vaue of minimum vaues of respectivey. ) (5) z i, and min z i are the maximum and z i in the database, popuation, GDP, the tota number of vehices and the gasoine demand. The impementation procedure for ANNs is as foows:.divide the avaiabe data into training, test and vaidation set 2. Seect architecture and training parameters 3. Train the mode using the training set 4. Test the mode using the test set 5.Repeat steps 2 through 4 using different architectures and training parameters 6.Seect the best network architecture from the training and test set 7.Assess this fina network architecture using the evauation set Severa MLP networks were generated and tested. The transfer function for the first ayer was sigmoid and for the second ayer was inear. The BP agorithm was used to adjust the earning procedure. For forecasting the gasoine demand the MLP network with 4 5 construction based on definition () had the best output with estimated 2.7% average absoute error percentage (AAEP) on the vaidation data. The AAEP is cacuated with the foowing equation: A computer program, written in MATLAB programming anguage, is used for estimating AAEP = n n a( t) T( t) T ( t) t= (6) 8

9 Kazemi A. and others Int. J. Humanities (202) Vo. 9 () where a (t) is the estimated gasoine demand and T (t) is the actua vaue of gasoine demand. 2 miion in For forecasting popuation and GDP the MLP network with 2 3 and 2-4- construction had the best output with estimated 0.02% and 2.34% AAEP on the vaidation data. As mentioned in Section 2, for the existing socio-economic mode of the tota number of vehices a constraint on the tota maximum is appied. Regarding restrictions on some parameters ike roads status, parking paces, Fig 4 Estimated Popuation number of vehices per househod, environmenta protections; an upper bound of 6% is considered on the maximum rate of the tota number of vehices. This constraint which forces on the output of ANN3 is derived from some experts opinion in this regard. a ( t + ) a( t).06 (7) MLP network with 3-4- construction had the Fig 5 Estimated GDP best output with estimated 3.33% AAEP on the test data. The estimation of popuation, GDP and the tota number of vehices are given in Fig. 4, 5 and 6. These graphs show the actua data versus the ANN resuts. Popuation wi reach to a eve of about 0 miion, GDP is about 300 triion Fig 6 Estimated the Tota Number of Vehices Rias and the tota number of vehices is about 9

10 A Hierarchica Artificia Neura Int. J. Humanities (202) Vo. 9 () After seecting the best architecture ANNs, the estimated popuation, GDP and the tota number of vehices from 20 to 2030 were passed to the network and the gasoine demand for these years was forecasted. The estimated gasoine demand from 20 to 2030 can be seen in Tabe 3. The gasoine demand wi reach to a eve of about 54 miiard iters in Years Tabe 3 Forecasted Gasoine Demand Gasoine Demand (0 9 L) Years Gasoine Demand (0 9 L) forecasted. This paper considered four standard variabes as inputs to the main ANN for forecasting of the gasoine demand. Other input variabes ike the average energy usage of the vehices, the price of energy, technoogica deveopments, etc., may be identified and inserted in to the mode. Aso, a future study may incorporate integration of a genetic agorithm (GA) and an ANN to foresee whether the estimated error is further decreased. References [] G.E. Nasr, E.A. Badr, C. Joun. (2003), Backpropagation neura networks for modeing gasoine consumption. Energy Conversion and Management, No. 44, Pp [2] M. Beccai, M. Ceura, V. Lo Brano, A Marvugia (2004), Forecasting daiy urban eectric oad profies using artificia neura networks, Energy Conversion and Concusion Management, No. 45, Pp This paper focused on forecasting the annua gasoine demand regarding socio-economic and transport reated indicators using a hierarchica artificia neura networks. An ANN was designed to take popuation, GDP, the tota number of vehices and the gasoine demand in the ast year as inputs and produce the gasoine demand. Popuation, GDP and the tota number of vehices were forecasted using ANNs. Actua data from 967 to 2008 were used and the [3] Benjamin F. Hobbs, Udi Heman, Suradet Jitprapaikusarn, Sreenivas Konda, Dominic Maratukuam (998), Artificia neura networks for short-term energy forecasting: Accuracy and economic vaue. Neurocomputing, No. 23, Pp [4] Bahman Kermanshahi, Hiroshi Iwamiya (2002), Up to year 2020 oad forecasting using neura nets. Eectrica Power and Energy Systems, No. 24, Pp gasoine demand of Iran from 20 to 2030 was 0

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