approximatereductionmodelofelectrictractionsupplysystem.doc

Approximate Reduction Model of Electric Traction Supply SystemYing Li, Donghui Li, Yaping YuApproximate Reduction Model of Electric Traction Supply System1Ying Li, 2Donghui Li, 3Yaping Yu1, Hebei United University, Tangshan, Hebei, China, *2, Tianjin supply section of Beijing Railway Bureau, Tangshan, Hebei, China,83213633, Tangshan College, Tangshan, Hebei, China, AbstractBuild the relational data table for the complex information in the fault diagnosis on the electric traction supply system, and build the fault diagnosis model base on the approximate reduction method, in order to quickly predict potential failures, judge and deal with it, and effectively ensure the railway transport safety and improve transport efficiency. Collect 34 kinds of signals from the contract system and the electric transformer and distribution devices in the traction substation as the input of the data mining first; Secondly, build the fault diagnosis model on the electric traction supply system using the approximate reduction algorithm, and detailed introduce it on the data decentralization, approximate reduction and fault prediction; Finally, explain the effectiveness of the method by the example, and it also plays an active role in guiding on predicting device performance and fault condition.Keywords: Data Mining, Approximate Reduction, Electric Traction Supply System, Fault Diagnosis1. IntroductionThe running quality of the electric railways traction supply system directly related to the railway transport safety and benefit 1, 2, 3, 4. All kinds of advanced equipments and instruments are widely used with the construction of railway modernization 5, 6, 7. So it is very important to monitor their operating status in real time and ensure the operating safety 8, 9, 10. These intelligent devices will produce large amounts of data in real time running; we need to effectively organize and process of these massive data real-time, and understand the device performance and operating status, then we can arrange the train dispatching reasonably and improve the operation efficiency 11, 12, 13. Obviously, the traditional data processing methods cannot meet the requirements. So it is necessary to introduce the advanced data analysis and processing tools-data warehouse mining technology 20, 21, it will mine and analyze the massive data in real-time, and extract useful information 14, 15, 16. Then we can predict, judge and deal with the potential failures 17, 18, 19.Thus we can effectively ensure the railway transport safety and improve transport efficiency. The approximate reduction can yet be regarded as a good way for extracting useful information. The approximate reduction is a mathematical method proposed in 2007 by Chinese Scholar YangMing. It has become a relatively new academic focus in the field of artificial intelligence after years of continuous research and summary. And it has got more and more scholars concern. It has been successfully applied in the field of decision-making, forecasting, data fusion, and uncertainty reasoning.2. Proposed modelRough Set theory 1, 2, 3 has been developed by Z. Pawlak and his co-workers since the early1970s.It has recently received wider attention as a tool to conceptualize, organize and analyze various types data, in particular, to deal with inexact, uncertain or vague knowledge in applications related to Artificial Intelligence. Attribute reduction is not only one of important parts researched in rough set theory, but also widely applied to many fields such as machine learning, data mining and so on.A. Rough description of information theoryIn this section, we will review several basic concepts in rough set theory. Throughout this paper, we suppose that the universe U is a finite nonempty set.International Journal of Advancements in Computing Technology(IJACT) Volume5, Number7,April 2013doi:10.4156/ijact.vol5.issue7.81660667Decision table (DT) is an information systemDT = (U , C U d), whered , d Cis adistinguished attribute called decision, and the elements of C are called conditions, such thatf : U Vc for any c C , where Vc is called the value set of c .Each subset of attributes P C determines a binary indiscernibility relation ind (P) , as follows:ind (P) = ( x, y) U U c P, f ( x, c) = f ( y, c)The relation ind(P) , P C , constitutes a partition of U , which we will denote by U / ind (P) .(1)One can easily label partition classes with their cardinalities, measured relatively with respect to the universe. It enables to define the prior probability distribution over P-information vectors.Let P C be a partition of U with classes X i , i n , each having cardinalityX i .In compliancewith the statistical assumption o the rough set model we assume that the elements of U are randomlydistributed within the classes of P , so that the probability of an element x being in classX i is justXi .We define prior probability byUp ( X i ) =X i , i = 1, 2,L, nU(2)Conditional probabilities are usually derived in purpose of expressing a chance of occurrence of a given pattern under information about occurrence of another one. In the basic form, it leads to the analysis of association rules, where both the left and right sides consist of condition involving disjointsubsets for attributes P, Q Cand their values.The entropy reducts have first been introduced in 1993/1994 by Skowron in his lectures at Warsaw University 4, 5. Based on the idea, Slezak introduced Shannons information entropy to search reducts in the classical rough set model 6-8.Wang et al. used conditional entropy of Shannons entropy to calculate the relative attribute reduction of a decision information system9. In fact, several authors also have used variants of shannons entropy or mutual information to measure uncertainty in rough set theory and construct heuristic algorithm of attribute reduction in rough set theory 10, 11.Definition1 The partition is induced by Q(U ind (Q) I P(U ind ( P)in X i I Y j : i n, j m, and its associated parameters are defined byp(Y j X i ) = Y j I X i / X iare the nonempty sets(3)Now, we definen mH (Q P) = - p( X i ) p(YjX i ) log p(YjX i )(4)i =1j =1Given a decision system DT = (U , C U d) , we can useH (d / B) to label eachB C with theamount of uncertainty concerning d under the information about B provided.Definition 2 Let aDT = (U , C U d) andB C be given. B is a decision reduct, iff we haveH (d C ) = H (d B) (B C ) and c B , H (d C ) H (d B c) .Definition 3 LetDT = (U , C U d) be a decision table,B Cand a B .The significancemeasure of a in B is defined assig inner (a, B, d ) = H (d | B - a) - H (d | B )(5)For a given decision table, the intersection of all attribute reducts is said to be indispensable and is called the core. Each attribute in the core must be in every attribute reduct of the decision table. The core may be an empty set. The relationship between the core and all attribute reducts can be displayed by Figure 1.Theorem 1 Let DT = (U , C U d) be a decision table and a C . If sig inner (a, C, d ) 0 , then a is a core attribute of DT .Figure 1. The Relationship between The Core and All Attribute ReductsFrom the definition of core, one can see that each attribute in the core must be in every attribute reduct of the decision table. It is well known that, if sig inner (a, C, d ) = 0 , then one still can find at least one attribute reduct when a is deleted. If sig inner (a, C, d ) 0 , then the attribute a is indispensable in allattribute reduct. Therefore, the attribute a must be a core attribute of DT .The literature 10 compares the knowledge reduction on the algebra view with the knowledge reduction on the information view, and proves that the attribute reduction definition of conditional information entropy in the case of consistent decision tables and attribute reduction definitions of algebraic view are equivalent; in inconsistent decision tables, the two definitions are not equivalent. Following theorem can be obtained from the literature 9.Theorem 2: If A is the knowledge reduction of the conditional entropy, then A is candidate knowledge reduction in the algebra view, but it may not be the knowledge reduction in the algebra view.Definition 4 Let e 0,1) ,DT = (U , C U d)andB C be given. We say that B is ane - approximate information reduct, iff it satisfiedH (d C )- H (d B) e(6)and none of its proper subsets does it.B. The main idea of simulated annealingSimulated annealing algorithm is originated from the simulation of Annealing process of solid in statistical physics. It uses Boltzmann guideline to accept the new solution, with a parameter called the cooling coefficient to control the process of the algorithm, so that it can give an approximate optimal solution in polynomial time. Parallel simulated annealing achieves parallelism in solving the optimization process. The basic elements of simulated annealing (SA) are the following:(i) A finite set S.(ii) A real-valued cost function J defined on S. Let S * Sfunction J, assumed to be a proper subsets of S.be the set of global minima of the(iii) For each i S , a set S (i) S - i , called the set of neighbors of i.(iv) For every i, a collection o positive coefficients qij ,j s(i) , such that jS (i )qij= 1 .It isassumed thatj S (i ) if and only if i S ( j ) .(v) A nonincreasing function T:N (0, ) , called the cooling schedule. Here N is the set ofpositive integers, and T (t) is called the temperature at time t. (vi) An initial “state” x(0) S .Given the above elements, the SA algorithm consists of a discrete-time inhomogeneous Markov chain x (t), whose evolution we now describe. If the current state x (t) is equal to i, choose a neighbor jof i at random; the probability that any particularthe next state x (t+1) is determined as follows: If J ( j ) J (i ) , then x(t + 1) = j .j S (i ) is selected is equal to qij .Once j is chosen,If J ( j ) J (i ) , then x(t + 1) = j with probability exp- J ( j) - J (i) / T (t ) x(t + 1) = iotherwise.Formally,P x(t + 1) = j | x(t ) = i = qijexp-1T (t )max0, J ( j) - J (i)if j i, j S (i)(7)If j i, j S (i) , then P x(t + 1) = j | x(t) = i = 0 .The rationale behind the SA algorithm is best understood by considering a homogeneous Markovchain xT (t) in which the temperature T (t) is held at a constant value T. Let us assume that the Markov chain xT (t ) is irreducible and aperiodic and that qij = q ji for all i, j . Then xT (t) is a reversible Markovchain, and its invariant probability distribution is given byp T (i) =1 exp - J (i) ,i S(8) ZT T where ZTis a normalizing constant. (This is easily shown by verifying that the detailed balanceequations hold.) It is then evident that as T 0 , the probability distribution p Tis concentrated on theset S * of global minima of J. This latter property remains valid if the condition qij = q ji is relaxed.The probability distribution (8), known as the Gibbs distribution, plays an important role in statistical mechanics. In fact, statistical physicists have been interested in generating a sample element of S, drawn according to the probability distribution pT . This is accomplished by simulating theMarkov chainxT (t )until it reaches equilibrium, and this method is known as the Metropolisalgorithm. In the optimization context, we can generate an optimal element o S with high probability if we produce a random sample according to the distribution p T , with T very small. One difficulty with this approach is that when T is very small, the time it takes for the Markov chain xT (t ) to reach equilibrium can be excessive. The SA algorithm tries to remedy this drawback by using a slowing decreasing “cooling schedule” T (t).The SA algorithm can also be viewed as a local search algorithm in which (unlike the usualdeterministic local search algorithms) there are occasional “upward” moves that lead to a cost increase. One hopes that such upward moves will help escape from local minima.C. Reduction algorithmIn rough set theory, attribute reduction is about finding some attribute subsets that have the minimal attributes. In fact, there may be multiple reducts for a given decision table. It has been proven that finding the minimal reduct of a decision table is a NP hard problem 12. After summarizing the classic attribute reduction algorithms 13-17, a novel algorithm to search the optional solution is presented.To design a heuristic attribute reduction algorithm, three key problems consisting of significance measures of attributes, search strategy and stopping (termination) criterion should be considered. In this algorithm, for a decision table DT= (U, Cd), simulated annealing algorithm is used as a searchalgorithm,H (d subset ) - H (d C ) e is used as the end condition. That is to say, subset is said to bean attribute reduct. The main program of searching relatively minimal reduction is shown in N_Sfigure 2.Figure 2. The Programming of ReductionH (D/C) is conditional entropy of Decision table. Core is the core attribute. Subset is an attribute set. Subset has cardinality |subset|.Simulated Annealing Algorithm: An attribute reduction algorithm. Input: Decision table DT, core;Output: One reduct subset.Step1: for a given length L of Markov chain, if |subset|T0), k=1, go to step 3.1; otherwise go to step4.Step 3.1: if k L, go to step a; otherwise go to step3.2.Step a: Randomly generate a set n_redu of attributes, then Calculate entropy entr_nr of n_redu; Step b: if entr_nrentr_s, then subset=n_redu; k=k+1, go to step3.1.Step3.2: T= a T, a (0, 1), go to step3.Step4: Return subset and end.We summarize two advantages of this algorithm as follows: This search algorithm starts with the core and finds an attribute reduct by gradually adding selected attributes to the core attributes. This makes the range of choice of adding attributes reduced and improves the search efficiency. With the increasing number of attributes, Markov chain length changes. When the|subset|C|/2, the search times gradually increased. Otherwise, the search times are reduced. Based on the change in the number of combinatorial dimension of attributes, this effectively improves the search efficiency.3. Experimental resultsThe most data of the fault diagnosis in the electric railways traction supply system come from power SCADA (supervisory control and data acquisition) system, EMS (energy management system) and PMIS (power management intelligent system). The electric traction supply system is made up of the traction substation system, the contract system and the electric locomotive current collection system; the input signals required by the approximate reduction come from the first two parts. The current collection condition of the electric locomotive can be fed back to the signal and communication department by the railway locomotive signal, and it could be dealt with separately in the electric locomotive. We collect 34 kinds of signals for the contract system and the electric transformer and distribution devices in the traction substation as the input of the approximate reduction, some of the data are real-time acquisition signal, some of the data are static test value, analysis value, reasoning value, calculated value and the estimate (A part of the data is provided by the simulation experiment). The output which has three variables will be taken as the evaluation of system performance and status. The dispatchers in the dispatching station can monitor and analyze the power supply running state of all the sections by the data mining system. They can analyze and judge the running mode of the power supply system, and can adjust the optimal power supply mode of the system. So they can achieve the purpose of analyzing the failure in time, dealing with the fault, forecasting the fault and preventing the expansion of fault.Example 1: The objective of the following experiments is to show the time efficiencies of the algorithm for selecting a reduct. The data used in the experiments are Ionosphere Data Set and Iris Data Set, which were all downloaded from UCI Repository of machine learning databases. Ionosphere dataset has 351 samples, 34 condition attributes and 1 decision attribute. The iris data set has 150 samples, 4 condition attributes and 1 decision attribute. The programming being used is Visual C+. The results are shown in Table 1.Table 1. The Results of Reduction and Execution TimeDecision tableReductionApproximateReductionAccuracy Execution times/sIonosphereIrisC4, C16, C28C1, C3, C4 C16, C28 C3, C40.010.051.920.28It is well known that, the attribute reduce induced by Shannons information entropy keeps the probabilistic distribution of original data set, which is based on a more strict definition of attr