Health,Status,Assessment,for,New,Urban,Rail,Vehicle,Traction,Systems,Based,on,Cross,Entropy,and,SVM*

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(School of Power Technology,Liuzhou Railway Vocational Technical College,Liuzhou 545616,China)

Abstract: A health status assessment method based on cross entropy and support vector machine (SVM) is proposed for the new urban rail vehicle traction systems.First,an index system for health assessment of the traction system is established,and combined weights of the index layer are obtained via cross entropy.Then,an SVM assessment model considering actual operating data and each status level of the traction system is established.Finally,the model is simulated in Matlab to obtain assessment results.The results indicate that the proposed method can provide the health status information of the traction system intuitively and complete the health status assessment of the traction system of the new urban rail vehicle effectively,by exploiting the traction system’s layered analysis model.The health status can be assessed accurately and reliably by adopting the cross entropy theory and SVM theory.

Keywords: New urban rail vehicle,traction system,cross entropy,SVM,health status assessment

In the field of urban rail transit,the traditional mechanism to supply power is the overhead catenary system (OCS),but the OCS has a significant impact on the urban landscape,particularly in sensitive areas.To facilitate the integration with the urban landscape,the power supply mode has gradually developed into one without an OCS[1].Supercapacitors are widely used in new urban rail vehicles without an OCS to supply power,because they have faster charging and discharging speeds,have more charging and discharging cycles,and are more friendly to the environment than other types of batteries[2-3].Health status assessment for the traction system,which is the power source of the vehicle,is important for achieving condition-based maintenance (CBM)[4-7].

It was proposed that the multivariate normal distribution and the Gaussian mixture model are suitable as importance sampling densities within the cross-entropy method.The proposed method in the reference was found to be more efficient,more convenient,and more applicable than the previous methods[8].A support vector machine (SVM) was used to achieve ultimate load prediction by choosing the appropriate parameters,such as the network structures,penalty parameter,and kernel function width.The results indicated that the SVM had a higher prediction accuracy than the previous methods[9].An efficient hybrid image noise elimination method based on SVM classification was designed and developed,and it was found that the SVM had significant advantages in solving classification problems[10].On the basis of information fusion,a novel gate resource allocation method using an improved particle swarm optimization-based quantum evolutionary algorithm was proposed[11].An improved quantum-inspired differential evolution algorithm was used to achieve classification via data fusion in a deep belief network[12].To accelerate the data fusion,a differential evolution algorithm was used to solve the airport gate assignment problem by optimizing control parameters and employing a mutation strategy[13].An improved synthetic minority oversampling technique was proposed,along with a repeated sampling technique to train different but related classifiers,boosting the classification performance across the classes of the data[14].A new performance degradation prediction method based on high-order differential mathematical morphology gradient spectrum entropy,phase space reconstruction,and an extreme learning machine was proposed to predict the performance degradation trend of rolling bearings,and the effectiveness of the information fusion method based on entropy theory was proven[15].A transformer health status assessment model based on multiple-feature factors was proposed,whereby accurate results were obtained.However,the selected indexes were highly redundant,because the correlation among indexes was ignored[16].The status of the voltage source inverter was assessed,by using actual operating data.With regard to harmonics and efficiency,the indexes were not comprehensive enough and not convincing enough[17].The cloud theory was used to assess and complete the mutual conversion from qualitative concepts to quantitative data.However,the determination method of indexes’weights was not accurate[18].The triangular fuzzy numbers were used in the analytic hierarchy process(AHP).The accuracy of the weight determination process was improved,but the assessment method was too simple to obtain ideal results[19].

In the present study,to resolve the aforementioned shortcomings,the new urban rail vehicle traction system is taken as an analysis example.The health status assessment method based on cross entropy and the SVM is adopted,together with the AHP,entropy weight method,and grey correlation degree method with the cross-entropy theory.The subjective method,objective method,and data method are combined to obtain the combined weights with a high accuracy.A classification model of the health status levels is constructed using the SVM,which makes the final assessment result more scientific and reasonable.

In short,using the cross entropy and SVM theory,research on health status assessment for the new urban rail vehicle traction system is conducted in this paper.

2.1 Weight determination method

In this study,three methods the AHP,entropy weight method,and grey correlation degree method are used to determine the weight of each index.The method is indicated by the variablel,which can have a value of 1,2,or 3. represents the weight of thejthindex of theithcomponent calculated using thelthmethod.

2.1.1 Subjective method:AHP

The AHP is a subjective method widely used in weight determination[19-20].The calculation process is as follows.

(1) Establish a hierarchical analysis model of the researched system.

(2) Construct the judgment matrixR.Use the T.L.Saaty 1-9 scale method (Tab.1) to compare the importance of the indexes to complete the structure ofR.

Tab.1 Values and meanings of the T.L.Saaty 1-9 proportional scaling method

(3)Rconsistency check.Calculate the random consistency ratioCR=CI/RIofR,whereCI= (λmax-n)/ (n-1) represents the standard value of the consistency ofR,λmaxrepresents the largest characteristic root ofR,nrepresents the number of indexes,andRIrepresents the average random consistency standard value ofR,taking the values presented in Tab.2.The conformance standard is as follows:whenn3≥,the value ofCRis 0 ＜CR＜0.1.IfCRdoes not satisfy the standard,Ris readjusted according to Tab.2 until it reaches the standard[19-20].

Tab.2 Values of 1-10 order pair comparison matrix RI

(4) Solve the characteristic vectorw(1).After the consistency ofRreaches the standard,useas the eigenvector belonging to the eigenvalueλmax.

2.1.2 Objective method:Entropy weight method

The entropy weight method is an objective method for determining the index weight[21].The detailed steps are as follows.

(1) Raw data processing.Assuming that the data matrix isP,there are a total ofmsets of data andnindexes.For the convenience of calculation,the normalized data matrixQis obtained using Eq.(1).

(2) Determination of information entropy.The information entropy of thejthindex in the system is defined as follows

whereα=1/lnm.

(3) Calculation of the weight.The weightof thejthindex based on the entropy method is defined as

The weight vector obtained via the entropy method is

2.1.3 Data method:Grey correlation degree method

The grey correlation degree method is a data-based method for determining the index weight[22].The detailed steps are as follows.

(1) Calculation of the absolute difference.For the normalized matrixQ,there are a total ofmsets of data andnindexes.

wheng=i,let the result be 0.

(2) Calculation of the degree of relevance.The correlation coefficient ofQijtoQig(g≠j)is

where the resolution coefficientρis set as 0.5[17].

The correlation degree of indexjto indexg(g≠j) is

wheng=i,let the result be 1.

(3) Calculate the weight.From step (2),the incidence matrixZis as follows

The weight vector obtained via the grey relational method is

2.1.4 Combination method:Cross-entropy theory

To accurately obtain the combined weights of subjective meaning,objective meaning,and data fusion,the three methods (AHP,entropy weight method,and grey correlation degree method) are combined using the cross-entropy theory.

When the probability space has consistency,the cross entropy is defined for two different measurespandq.The details are as follows.

Discrete situation

Continuous situation

Cross-entropy theory has advantages for solving global optimization problems.In the process of generating sample solutions,the probability density function is mainly investigated,and the probability distribution forms and function parameters determine the pros and cons of the solution[8].In the calculation of combined weights,the crossentropy theory is used to obtain the weight value of a single method,and then more accurate and reasonable combined weights are obtained via data fusion.The steps for calculating the weights of each method are as follows.

(1) Letf(x) be the combined weight vector after fusion of the three methods,andfn(x) be the weight vector of thenthmethod,which satisfies

(2) Determine the support vector and define the cross-entropy calculation formula.Establish support vectorS

Snis used to reflect the support degree between combined valuef(x) and single valuefn(x),andSnis smaller when the support degree is higher (i.e.,the intersection degree betweenf(x) andfn(x) is greater).

Sreflects the support degree betweenf(x) andfn(x).To makeAnreflect the support degree among the distributions,let

(3) Construct the objective function of Eq.(17) and solve the minimum cross entropy

(4) Solve the optimization problem ofF.According to Eqs.(14)-(17),the independent variable corresponding toFiskn,and the minimum value ofFcan be determined by solving a nonlinear programming problem.The problem above can be solved using the davidon fletcher powell (DFP)algorithm.

The steps of the DFP algorithm are given by Eqs.(18)-(25).Accordingly,Eqs.(20)-(25) are iterated,and the minimum cross entropy is solved.

1) Apply the second-order approximate Taylor expansion toF

whereωis the matrix of weight coefficients,ω0represents the initial value of the matrix,andAis the Hessian matrix.

2) Differentiate Eq.(18) and obtain the result for the gradient vector atω.

3) Establish the relationship between each iterationDiand the correspondingG.

Hihas symmetry and positive definiteness.DefineH0as the identity matrix.Hican be determined using Eqs.(21)-(25).

(5) Calculate the weights of each single method.Then,obtain the combined weights.A flowchart of the weight calculation for each method is shown in Fig.1.

Fig.1 Flowchart of the weight calculation for each method

2.2 SVM assessment method

The SVM has significant advantages for solving nonlinear problems with nonlinear and small sample sizes.It can be used to solve regression problems but is mainly used for classification problems.For a two-classification problem,the optimal classification hyperplane is obtained by learning sample data.In Fig.2,the two types of data samples are represented by squares and triangles,respectively.Lis a classification line,additionally,L1andL2are parallel toLand pass through the sample data that are closest toLin the respective categories.Moreover,drepresents the classification interval,and the data thatL1andL2pass through constitute the support vector.According to the foregoing information,we can conclude thatLis the optimal classification hyperplane.When the problem turns into multiple classification,the solution to the two-classification problem can be expanded for finding multiple optimal classification hyperplanes[9-10].

Fig.2 Schematic diagram of the optimal classification surface

The “libsvm toolkit” is used to achieve multiple classification.It mainly includes two functions:a training function (calling form is svmtrain) and a prediction function (calling form is svmpredict).The model training process is as follows:model=svmtrain(training data category,training data,“relevant parameters”).The relevant parameters include the SVM type,kernel function type,and kernel function parameter.It must be emphasized that the relevant parameters in this study are “-c2 -g1”.For other parameters,default values are adopted.

The steps of libsvm classification are as follows.

(1) Data normalization.The most significant advantage of data normalization is the prevention of the features of large value intervals from overwhelming the features of small value intervals.Other major advantages are the reduction in computational complexity and improvement in computational accuracy.

(2) Application of the radial basis kernel function.

(3) Selection of the best parameterscandg.The parameter c is the penalty factor,indicating the degree of importance to the outlier data in the class.A smallercvalue corresponds to a smaller degree of importance.The outlier data can be discarded and the settings can be completed before training the model.The parametergis the gamma function’s parameter in the kernel function.

(4) Train the classification model with the optimalcandg.The svmtrain function is used to train the multiple classification model,and the return volume is a structure,indicating that the classification hyperplane is determined.

(5) Test.The svmpredict function is used to test the classification accuracy;thus,the trained model is used to predict the testing set samples for evaluating the accuracy of the model[9-10].

The traction system is the core part of the new urban rail vehicle,whose health status is affected by many factors;and it is difficult to consider all of them.Therefore,according to the correlation and influence degree of each factor,the representative assessment status parameters are selected from the system layer,component layer,and index layer.According to the specification[23-27],a layered analysis model is established as shown in Fig.3.

Fig.3 Schematic of the layered analysis model for the new urban rail vehicle traction system

3.1 Classification of health status levels of traction system

The health status of the traction system is divided into five levels:“better,” “good,” “ordinary,” “bad,” and“worse.” CBM can be achieved by adopting different maintenance strategies based on different health status levels.

Better:The values of each index are close to the optimal value,and the system is safe and reliable.No maintenance is required,and the maintenance plan can be extended.

Good:Individual indexes’ values are slightly reduced,but the system as a whole is not degraded and can operate normally.Maintain as planned.

Ordinary:Some indexes have decreased,but the system is working.Arrange priority maintenance.

Bad:Some indexes have decreased significantly,and the system status is poor;that is,the degradation is obvious.Maintain as soon as possible.

Worse:Some indexes’ values deviate significantly from the optimal values,and the system is no longer operating properly;that is,the degradation is obvious.Maintain or replace immediately.

3.2 Index parameters of traction system

Fig.4 shows the composition of the new urban rail vehicle traction system.

Fig.4 Composition of the new urban rail vehicle traction system

The total power of the new urban rail vehicle is 500 kW.The mode is one traction inverter with one motor(that is,1C1M;C:converter,M:motor).There are four groups of 1C1M,as shown in Fig.5.The DC-side voltage is 750 V,and the calculated current is 670 A.As the AC-side line voltage is 380 V,the mean value of the line current is calculated to be 180 A.The relevant data are used for setting the index threshold later.

Fig.5 Wiring diagram of 1C1M

According to the specification[23-27],together with the threshold determination method and onsite assessment experience[28-30],the threshold values of the traction system’s health status assessment[31-33]indexes are determined,as shown in Tab.3.

Tab.3 Threshold values of the traction system’s health status assessment indexes

The data of the new urban rail vehicle traction system are detected in three time periods,as shown in Tab.4.

Tab.4 Index detection data for the new urban rail vehicle traction system

4.1 Raw data processing

Because the scale types and dimensions of the indexes differ,it is necessary to use the normalization formula to compress the data between 0 and 1 to achieve dimensionless quantities.For an assessment problem withmcomponents andnindexes,xijrepresents the value of thejthindex of theithcomponent;then,the initial assessment matrix is

The following methods can be used for normalization as needed,where the data are processed with regard to three aspects:obverse index,reverse index,and optimal index.rijrepresents the processed data.

A larger obverse index corresponds to better performance,and the obverse index should be normalized by Eq.(26).

A smaller reverse index corresponds to better performance,and the reverse index should be normalized by Eq.(27).

For the optimal index,the ideal value is a specific value,such as the pH of water.Assume that the optimal value of indexjisthe lower limit isand the upper limit isThe optimal index should be normalized by Eq.(28).

when 1≤i≤m,1≤j≤n.

Among them,obverse indexes areC13andC25,which should be normalized by Eq.(26).The reverse indexes areC23,C24,C31,C32,C41,andC42,which should be normalized by Eq.(27).The optimal indexes areC11,C12,C14,C21,C22,C26,C33,andC43,which should be normalized by Eq.(28).The results are presented in Tab.5.

Tab.5 Index normalization data for the new urban rail vehicle traction system

4.2 Weight determination

4.2.1 Index weight determination based on AHP

According to Refs.[19-20],the component(supercapacitor,traction inverter,circuit breaker,and traction motor) layer’s judgment matrix is constructed as follows

The component layer’s weight vector based on the AHP is obtained asw=[0.363 6 0.181 8 0.363 6 0.091 0].

Similarly,the supercapacitor index layer’s judgment matrix is constructed as follows

The supercapacitor index layer’s weight vector based on the AHP is obtained asw1(1)=[0.181 8 0.363 6 0.363 6 0.091 0].

The traction inverter index layer’s judgment matrix is constructed as follows

The traction inverter index layer’s weight vector based on the AHP is obtained asw2(1)=[0.058 9 0.117 6 0.235 3 0.235 3 0.235 3 0.117 6].

The circuit breaker index layer’s judgment matrix is constructed as follows

The circuit breaker index layer’s weight vector based on the AHP is obtained asw3(1)=[0.333 4 0.333 3 0.333 3].

The traction motor index layer’s judgment matrix is constructed as follows

The traction motor index layer’s weight vector based on the AHP is obtained asw4(1)=[0.428 6 0.428 6 0.142 8].

4.2.2 Index weight determination based on entropy weight method

According to Ref.[21],the supercapacitor index layer’s weight vector based on the entropy weight method is obtained asw1(2)=[0.157 2 0.327 9 0.357 7 0.157 2].The traction inverter index layer’s weight vector based on the entropy weight method isw2(2)=[0.186 6 0.290 2 0.081 4 0.177 3 0.077 9 0.186 6].The circuit breaker index layer’s weight vector based on the entropy weight method isw3(2)=[0.313 6 0.341 9 0.344 5].The traction motor index layer’s weight vector based on the entropy weight method isw4(2)=[0.333 4 0.333 3 0.333 3].

4.2.3 Index weight determination based on grey correlation degree method

According to Ref.[22],the supercapacitor index layer’s weight vector based on the grey correlation degree method is obtained asw1(3)=[0.245 4 0.242 8 0.257 3 0.254 5].The traction inverter index layer’s weight vector based on the grey correlation degree method isw2(3)=[0.154 5 0.168 9 0.167 4 0.166 9 0.176 6 0.165 7].The circuit breaker index layer’s weight vector based on the grey correlation degree method isw3(3)=[0.304 5 0.338 5 0.357 0].The traction motor index layer’s weight vector based on the grey correlation degree method isw4(3)=[0.361 6 0.319 8 0.318 6].

4.2.4 Index combination weight determination based on cross-entropy theory

According to the foregoing analysis,the resultsare calculated using Matlab as follows.

For the supercapacitor

Fig.6 presents the index weights obtained using the three single methods and cross-entropy theory.As shown,the index weights obtained using the cross-entropy theory are among the index weights obtained via the three single methods,which avoids the problem that a single method can lead to a poor weight accuracy.

Fig.6 Traction system’s index layer weight value

4.3 SVM health status assessment model

4.3.1 Model establishment

The SVM health status assessment model is constructed according to the 16 indexes,the weight of each index,and the five assessment levels of the new urban rail vehicle traction system.A sample matrixYis constructed,whose order number is 403×16 (403 groups of data and,16 indexes).Rows 1-80 ofYcorrespond to the “better” level (category 1),rows 81-160 correspond to the “good” level (category 2),rows 161-240 correspond to the “ordinary” level(category 3),rows 241-320 correspond to the “bad”level (category 4),rows 321-400 correspond to the“worse” level (category 5),and rows 401-403 present three groups of actual operating data (normalized values).According to Refs.[9-10],the five levels are quantified by normalized data as follows:random numbers between 0.875 and 1 correspond to the “better”level,random numbers between 0.625 and 0.875 correspond to the “good” level,random numbers between 0.375 and 0.625 correspond to the “ordinary”level,random numbers between 0.125 and 0.375 correspond to the “bad” level,and random numbers between 0 and 0.125 correspond to the “worse” level.The training sample corresponds to the first 40 groups,and the testing sample corresponds to the last 40 groups.Because the indexes differ in importance,the sample matrixYmust be optimized;that is,the weights should be introduced into the sample matrix as follows.

In the first step,the component layer weightwis introduced into the sample matrixY:the first element ofwis multiplied by the 1stto 4thcolumn elements ofY(the component layer weight of the supercapacitor optimizes its data),the second element ofwis multiplied by the 5thto 10thcolumn elements ofY(the component layer weight of the traction inverter optimizes its data),the third element ofwis multiplied by the 11thto 13thcolumn elements ofY(the component layer weight of the circuit breaker optimizes its data),and the fourth element ofwis multiplied by the 14thto 16thcolumn elements ofY(the component layer weight of the traction motor optimizes its data).The optimized matrix is denoted asY1.Clearly,the optimization process accurately reflects the component layer weights.

In the second step,the index layer weightsw1,w2,w3,andw4are introduced into the sample matrixY1:the first element ofw1is multiplied by the first column element ofY1(the first index layer weight of the supercapacitor optimizes its data),the second element ofw1is multiplied by the second column element ofY1(the second index layer weight of the supercapacitor optimizes its data),the third element ofw1is multiplied by the third column element ofY1(the third index layer weight of the supercapacitor optimizes its data),the fourth element ofw1is multiplied by the fourth column element ofY1(the fourth index layer weight of the supercapacitor optimizes its data),the first element ofw2is multiplied by the fifth column element ofY1(the first index layer weight of the traction inverter optimizes its data),and so on.The corresponding index layer weights are used to optimize the corresponding data in the proper order.The optimized matrix is denoted asY2.Clearly,the optimization process accurately reflects the index layer weights.

4.3.2 Results of model simulation in Matlab

The model was simulated in Matlab.Fig.7 shows the actual classification and prediction classification results for 200 groups of testing data.

As shown in Fig.7,the actual classification and prediction classification of the testing set are completely consistent,indicating that the established SVM health status assessment model is credible.Three groups of actual operating data were predicted using the model,and the results are shown in Fig.8.

Fig.7 Actual classification and prediction classification diagram for the testing set

As shown in Fig.8,the prediction classification results for the three groups of actual operating data are all in category 1;that is,the result of the health status assessment of the new urban rail vehicle traction system is “better,” which is consistent with the actual situation that the project is new.Each index’s detection value is near the optimal value,and the traction system has a safe operating status.According to the status assessment result,no maintenance is required,and the maintenance plan for the traction system can be extended.

Fig.8 Prediction classification results for three groups of actual operating data

By calculating the weight of each index through the cross-entropy theory,the theory of information entropy is introduced,which transforms the problem of index weight calculation into a problem of information fusion.This compensates for the shortcomings of the three single weight calculation methods,i.e.,the subjectivity of the AHP,ignorance of experts’ experience of the entropy weight method,and overdependence on data of the grey correlation degree method.The fusion of three single weight calculation methods is not only comprehensive but also reflects the differences between the methods,resulting in more accurate calculation results.

Through the SVM theory,the assessment problem is transformed into a classification problem,and the SVM can overcome the local minimum problem in the neural network when solving small-sample size,nonlinear,and high-dimensional problems,making the assessment result more accurate and reliable.

The new urban rail vehicle traction system was taken as a research object,and the effectiveness of an assessment method based on cross entropy and an SVM was verified.The constructed traction system’s index system comprehensively and accurately reflects its health status.In the assessment method,using cross-entropy theory to calculate the weights of the traction system’s index layer can compensate for the shortcomings of the three single methods.In the assessment method,using the component layer weights and index layer weights to optimize the sample data profoundly reflects the essence of the weights,which makes the assessment more credible.In the assessment method,setting the training samples and testing samples of the SVM with random numbers can make the ambiguity and randomness in the assessment process more thorough.The assessment method can achieve the transformation of qualitative analysis (health status levels) and quantitative analysis(operating data).In summary,the health status assessment method for the new urban rail vehicle traction system can obtain accurate results.

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