In this study we discuss the possibility to apply symbolic data mining methods to the problem of prediction. We employ our original algorithm KEX that is used for extraction of classification or prediction rules from data. When new data is coming, the active rules (rules with a fulfilled left-hand side) from the rule base are applied to the data and their weights are composed by the inference mechanism to the resulting weight of a given prediction. The presented approach is applied to the problem of short-term electric load forecasting

Berka, Petr

English

European Scientific Journal (European Scientific Institute)

European Scientific Journal  September 2014  /SPECIAL/ edition Vol.3   ISSN: 1857 – 7881 (Print)  e - ISSN 1857- 7431 325 RULE-BASED PREDICTION OF SHORT TERM ELECTRIC LOAD    Petr Berka, Prof, PhD University of Economics Prague & University of Finance and Administration Prague,  Czech Republic   Abstract  In this study we discuss the possibility to apply symbolic data mining methods to the problem of prediction. We employ our original  algorithm KEX that is used for extraction of classification or prediction rules from data. When new data is coming, the active rules (rules with a fulfilled left-hand side) from the rule base are applied to the data and their weights are composed by the inference mechanism to the resulting weight  of a given  prediction. The presented approach is applied to the problem of short-term electric load forecasting.   Keywords: Data mining, rule learning, electric load prediction  Introduction  One central insight of artificial intelligence (AI) is that expert performance requires domain-specific knowledge. Machine learning is the subfield of AI that studies the automated acquisition of such knowledge. The aim is to create intelligent systems that learn-that is, that improve their performance as the result of experience.   The mainstream of machine learning techniques is inductive learning (also called similarity-based learning). Let us assume, that there is a set of examples which should be classified into some (small amount of) classes. In case of supervised learning, the examples are pre-classified by the expert (or the class membership can be directly observed from the data). In case of unsupervised learning, the machine learning algorithm does the grouping into classes itself. Based on this limited number of examples we then try to  induce some kind of general description of each class. The underlying idea of this methodology is that there are some characteristics (usually values of attributes) of these examples such, that examples belonging to the same class have similar values of these attributes. Thus examples belonging to the same class create clusters in the attribute space.  The various inductive machine learning algorithms differ in the way how the induced knowledge is represented (decision trees, decision rules, neural networks, Bayesian networks, support vectors, prototypical instances) and how it is used for decision support. Among the tasks solved by machine learning methods, classification and prediction play a key role. While classification can be understood as the task of assigning new (unseen) examples into one of the predefined class, prediction can be understood as the task of ―computing‖ a next value of a variable that evolves in time. So for classification, methods that produce symbolic output are used while for prediction, methods that produce subsymbolic (numeric) output are preferred.  An interesting alternative to subsymbolic approach to  prediction (and forecasting) represent methods  based on application of the (symbolic) prediction rules. The rules can be  specified by experts or can be extracted automatically from data. Following the steps in the data mining process, the original data (e.g. time series) are selected, preprocessed and  transformed.  The main aim is to build a specific set of categorial indicators which can influence the attribute to be predicted. This is the most crucial and difficult step, especially European Scientific Journal  September 2014  /SPECIAL/ edition Vol.3   ISSN: 1857 – 7881 (Print)  e - ISSN 1857- 7431 326 when there is no apriori knowledge. The left-hand side (antecedent)  of a prediction rule is the conjunction of the indicators and the right-hand side (succedent) is the categorial prediction goal, which can be easily specified in many practical situations.  In the paper we present our algorithm KEX, that learns weighted decision rules from data. This algorithm is used for the short-term electric load forecasting problem by using the daily data of average load and average temperature.   Short Term Electric Load Prediction The Problem  Knowledge about the future behavior of the electric load is very important for  power generation, control, transmission, etc. The prediction horizon varies from several minutes up to months and years. In our study we try to predict the daily averaged value of the electric load for the next day. The crucial question here is, whether the electric load of the next day will exceed the given limit and whether additional  power units (generators)  should  be started.  The Data  The data that were available for the analysis consists of the values of the 963 daily average loads and daily average temperatures. Beside this, we also knew the weekday and whether this day was holiday or not. We turned this original data (as shown in Table 1) into following attributes: LT ―long trend‖, coded to up/down by the   comparing the load  values from the two following weeks ST ―short trend‖, coded to up/down by comparing  the load values from   the two following days TT ―temperature trend‖, coded up/down by comparing the temperatures  from   the two following days T1 ―previous temperature trend‖, it is the shifted ―temperature trend‖ TYPEDAY type of the day to be predicted,  (Mo: Monday, Tu: Tuesday,...,Su: Sunday) HOLIDAY holiday (yes/no)   The prediction goal was set to  ―next load up‖ to predict the increase or decrease of the today‘s load.         We used the data recorded for two consecutive years (first 730 days) for training and the data for next January till September (next 233 days) for testing. day weekday holiday avg load avg temp. 1 6 0 5789 2 2 7 0 6193 0,5 3 1 0 7607 2,7 4 2 0 7856 4,6 5 3 0 7805 4,3 6 4 0 7784 4,4 7 5 0 7681 6,6 8 6 0 6609 4,3 9 7 0 6368 3,5 10 1 0 7695 3,6 . . .     Tab. 1:  Example of original data   European Scientific Journal  September 2014  /SPECIAL/ edition Vol.3   ISSN: 1857 – 7881 (Print)  e - ISSN 1857- 7431 327  Fig. 1:  Daily average load data  The Method  To find reasonable rules that will allow to predict the daily load for the next day, we used the KEX (Knowledge EXplorer) algorithm (Berka, Ivánek, 1994; Berka, 2012). KEX performs symbolic empirical multiple concept learning from examples, where the induced concept description is represented as weighted decision rules in the form  Ant ==> C(w)  where: Ant is a combination (conjunction) of selectors,         C is a single category (class), and         weight w from the interval [0,1] expresses the uncertainty of the rule.  During knowledge acquisition, KEX works in an iterative way, in each iteration testing and expanding an implication Ant ==> C. This process starts with an „empty rule― weighted with the relative frequency of the class C and stops after testing all implications created according to the user defined criteria. During testing, the validity (conditional probability P(C|Ant)) of an implication is computed. If this validity significantly differs from the composed weight (value  obtained when composing weights of all subrules of the implication Ant ==> C, then this implication is added to the knowledge base. To test the difference between validity and composed weight, we use the chi-square goodness-of-fit test. The weight of this new rule is computed from the validity and from the composed weight using inverse composing function (Hájek, 1985). For composing weights we use a pseudobayesian (Prospector-like) combination function (Duda and Gashing, 1979): x yxyxy x y   ( )( )1 1.                                                      (1) The Results  Table 3 presents the found prediction rules. Each row in the table shows the number of the rule, the number of examples covered by the left-hand side of the rule (frequency left), the number of examples covered by the right-hand side of the rule (frequency right), the number of examples covered by both left-hand and right-hand side of the rule (frequency both), the weight used when combining rules (weight) and the rule itself. Notice, that weights smaller than 0.5 denote rules that will predict the decrease of the load.  When using this set of rules for prediction, all applicable rules are found and their weights are combined using the formula (1). Thus the result of prediction is the weight assigned to the class ―load up‖. We can use these weights in following decision strategy:                if the  weight of the prediction  >  α, then the next load will be UP,                if the  weight of the prediction   <  (1 - α ),  then the next load will be DOWN,   0200040006000800010000120001285582109136163190217244271298325352379406433460487514541568595622649676703730757784811838865892919946Daily average loadTraining period Testing period European Scientific Journal  September 2014  /SPECIAL/ edition Vol.3   ISSN: 1857 – 7881 (Print)  e - ISSN 1857- 7431 328                if the weight is in the interval [1 - α, α], then  we do not predict.    Here α is a threshold that can be set by the user. Table 2 shows the impact of this parameter on the accuracy of our prediction model (in terms of percentage of correctly predicted testing days) and on the number of days for which no prediction is done. It can be seen, that when increasing the value of α, the percentage of correct prediction increases but the number of days, for which the model makes a decision decreases.        Tab. 2:  Prediction performance of KEX on testing data for various values of α                                 Tab. 3: A rule base generated by KEX using  730 daily averaged  electric load and temperature data.  Conclusion  The problem of short-term electric load prediction (forecasting) can be treated by different machine learning approaches. Ceperic et al. (Ceperic et al., 2012) or  Matijac et al. α Correct predictions Wrong predictions no. of predictions prediction accuracy 0.5 206 27 233 88.0% 0.55 200 17 217 92.2% 0.6 197 15 212 92.9% 0.7 189 12 201 94.0% 0.8 159 8 167 95.2% 0.9 136 4 140 97.1% RULE BASE                   Frequency                  No. left  right  both  weight                                                           rule  -------------------------------------------------------------------------------------------------    1.   730   325 325  0.4452                                                           0  ==>  load up   2.   405   325 132  0.3760                                             ST=down  ==>  load up   3.   333   325 167  0.5563                                            TT=down   ==>  load up   4.   325   325 193  0.6456                                                  ST=up  ==>  load up   5.   324   325 162  0.5548                  TT1=down  &  holiday=no  ==>  load up   6.   241   325   89  0.4219                                TT1=up & TT=up  ==>  load up   7.   171   325   85  0.4033                                 ST=up & TT=up   ==>  load up   8.   105   325     1  0.0118                                         typeday=Sa   ==>  load up   9.   105   325     4  0.0470                                         typeday=Su   ==>  load up 10.   104   325   99  0.9610                                         typeday=Mo  ==>  load up 11.   104   325   94  0.9213                                         typeday=Tu   ==>  load up 12.   104   325   57  0.6018                                         typeday=We  ==>  load up 13.   104   325   18  0.2069                                          typeday=Fr   ==>  load up 14.     99   325   89  0.3420                          typeday=Tu & ST=up  ==>  load up 15.     98   325   98  0.9082                  typeday=Mo & holiday=no  ==>  load up 16.     95   325   47  0.4011               ST=up & LT=up &  TT1=up  ==>  load up 17.     94   325   55  0.3896                        typeday=We & ST=up   ==>  load up 18.     75   325   57  0.6334        ST=up & TT=down & LT=down  ==>  load up 19.     52   325   32  0.6660                   typeday=Th & TT1=down  ==>  load up 20.     49   325   49  0.8915    typeday=Mo & LT=up & ST=down  ==>  load up 21.     48   325   34  0.7071                     typeday=Th & TT=down  ==>  load up 22.     39   325   35  0.2606                   typeday=Mo &  TT=down  ==>  load up 23.     29   325     4  0.2146        typeday=Th & TT1=up & TT=up  ==>  load up 24.     18   325     1  0.1336         typeday=Fr & ST=up & TT1=up  ==>  load up 25.     17   325     2  0.1425                                          holiday=yes  ==>  load up 26.       6   325     1  0.0573                holiday=yes &  typeday=Mo  ==>  load up European Scientific Journal  September 2014  /SPECIAL/ edition Vol.3   ISSN: 1857 – 7881 (Print)  e - ISSN 1857- 7431 329 (Matijac et al., 2011) use support vector machines, Ling et. al. (Ling et al., 2003) use fuzzy-neural network, Gupta and Sarangi (Gupta and Saranagi, 2012) combine genetic algorithms and neural networks. In this paper we present an alternative method based on symbolic prediction rules. We see the advantage of our approach in the fact, that the learned rules can be better understood by the domain experts.  References: Berka, P.: Learning compositional decision rules using the KEX algorithm. Intelligent Data Analysis, Vol. 16, No. 4, 2012, 665-681.   Berka, P. and Ivánek, J.: Automated Knowledge Acquisition for PROSPECTOR-like Expert Systems. In. (Bergadano, deRaedt eds.) Proc. ECML'94, Springer 1994. Ceperic, E., Ceperic, V. and Baric, A.: A Strategy for Short-Term Load Forecasting by Support Vector Regression Machines. IEEE Transactions on Power Systems,  Vol. 28,  No. 4, 2013, 4356 - 4364 Duda, R.O., and  Gasching, J.E.: Model Design in the PROSPECTOR Consultant System for Mineral Exploration. In:Michie, D. (ed.), Expert Systems in the Micro Electronic Age, Edinburgh University Press, UK, 1979. Gupta, A. and . Sarangi, P.K.: Electrical Load Forecasting Using Genetic Algorithm based Back-propagation Method. ARPN Journal of Engineering and Applied Sciences, Vol. 7, No. 8, August 2012, 1017-1020 Hájek, P.: Combining Functions for Certainty Factors in Consulting Systems. Int.J. Man- Machine Studies 22, 1985, 59-76. Ling, S.H.,  Leung, F.H.F., Lam, H.K. and Tam, P.K.S.: Short-Term Electric Load Forecasting Based on a Neural Fuzzy Network. IEEE Transactions on Industrial Electronics, Vol. 50, No. 6, December 2003, 1305-1316 Matijac, M, Vukicevic, M. and Krajcar, V.: Supplier Short Term Load Forecasting Using Support Vector Regression And Exogenous Input. Journal of Electrical Engineering, Vol. 62, No. 5, 2011, 280–285                       

RULE-BASED PREDICTION OF SHORT TERM ELECTRIC LOAD

European Scientific Journal, ESJ

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RULE-BASED PREDICTION OF SHORT TERM ELECTRIC LOAD

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