Research on Model of Circuit Fault Classification

8/9/2019 Research on Model of Circuit Fault Classification

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D. Jin and S. Lin (Eds.): Advances in CSIE, Vol. 1, AISC 168, pp. 433–439.

springerlink.com © Springer-Verlag Berlin Heidelberg 2012

Research on Model of Circuit Fault Classification

Based on Rough Sets and SVM

Fu Yu, Zheng Zhi-song, and Wu Xiao-ping

College of Electronic Engineering, Naval Univ. of Engineering, Wuhan 430033 China

Abstract. Aiming at the characteristic of lacking swatches and paroxysmal

faults, A fault classification model based on rough sets and SVM is put forward.

The pretreatment of diagnosis data is constructed by attribute reduction in rough

sets. Redundancy attribute is deleted from the diagnosis decision-making table

without losing useful information, and the reduced diagnosis decision-making

table is used as original training sets of classification sub-system. The dimension

of fault symptom and the capability of classification is balanced. Finally an

example shows the model is effective and reasonable.

Keywords: rough sets, support vector machine, fault classification.

1 Introduction

In recent years, support vector machine (SVM) has been successfully applied to data

mining, machine learning and pattern recognition by virtue of solid theoretical base,

good generalization performance and broad application prospects of widespread

concern. SVM could solve the problem of small samples of machine learning, which

based multi-classifier has high classification accuracy and good generalization ability,

So SVM has been as a new method of intelligent diagnosis classification used in circuit

fault with high research value [1-3].

Circuit fault diagnosis in most cases is a small sample of machine learning problem.

There are two reasons: on the one hand, the circuit fault occurs with a certain surprise

which is not repeated and simulation. On the other hand, compared with the speech

recognition and image recognition and other issues, which have thousands of samples

and hundreds of feature dimension, the circuit failure mode is not only a relatively

small number of samples, but also the nodes which could obtain diagnostic information

are limited. Therefore the dimensions of fault samples are relatively small, so SVM

could fast fault classification[4-5]. In addition, the size of fault samples and normal

samples is imbalance, which causes "a bias" using the common effect of classifier.

While SVM can take effective measures to reconcile such “a bias” to ensure the

accuracy of diagnosis with the minority class samples based on the minimizationstructure risk[6]. Therefore, the article chose SVM to create a circuit fault classification

model, which is a good solution to the problem of circuit fault classification. In the

model, the different points of failure could produce the same fault characterization,

which could bring the uncertainty. To solve this problem, the method of rough set

theory and machine learning technology is introduced.


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434 Y. Fu, Z. Zheng, and X. Wu

2 A Fault Classification Model Based on SVM

Support vector machines applied to the circuit fault classification, which is established

in the diagnostic process model of support vector machine classification process. The

modeling process is: support vector machine classifier corresponds to the faultclassifier; training sample can be corresponded to fault circuit, and the voltage or

current value of the node consists of test vectors (usually obtained through fault

simulation); test samples and the corresponding circuit to be diagnosed node consist of

voltage and current values of test vectors. Classifier training process fault diagnosis

device corresponds to the establishment and initialization process, the sample testing

process to be diagnostic fault classifier corresponds to the fault diagnosis process [7].

The model is shown in Fig. 1.

Fig. 1. The frame of circuit fault diagnosis based on SVM

Model of treatment process: firstly to capture the signal flow of circuit system by the

data acquisition module, so the characteristic parameters could be extracted by the

parameters of the signal; secondly the characteristic parameters will be pretreated as the

input vector of the SVM. If it is in state of training, characteristic parameters will be

trained through the support vector machine modules, and the training results, ie a set of

support vector, will be storaged into the database; If it is in the state of predicting, the

input vector will be predicted through module of SVM to get the output value. When

the circuit is abnormal the failure event has occurred.

3 Major Steps in Fault Classification

The main steps of system fault classification are showed in figure 2 based on SVM and

rough set.

Fig. 2. The realization of fault classification based on SVM and rough set


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Research on Model of Circuit Fault Classification Based on Rough Sets and SVM 435

Step 1 Data discrimination

The system parameters of circuit fault diagnosis of state are usually numerical bariables

collected by the data acquisition module, which is not easy to be dealed with by the

rough sets. This paper uses fuzzy C means (FCM) clustering algorithm as a

pretreatment algorithm before reduction of rough set. FCM algorithm was first

proposed by the Bezkek, which is obtained by the iterative algorithm to approximate

the optimal value of the objective function. Consider a sample set X = {x1, x2, ..., xn},

where xi = (xi1, xi2, ..., xik ) is a k-dimensional vector, which will be divided into c fuzzy

subsets based on certain criteria where c is the number of clusters given by the user, and

the result of clustering center with a cluster membership matrix vector and expressed

as:

1 2

1, , ; 1, , ;

( , , , )

[ ]

c

ij i c j n

V v v v

u u= =

=

=

(1)

Where, uij is the membership which means the degree that x ij belong to the category i, uij

meet:

1

1

1 1, ,

0 1, ,

c

ij

i

n

ij j

u j n

u n i c

=

=

⎧= =⎪

⎪⎨⎪ < < =⎪⎩

∑

∑

(2)

Objective function of FCM algorithm is:

2

1 1

( , )c n

m

ij k ij j i

i j

J u v u x v= =

= −∑∑ (3)

Equation (3), m is index weight for the matrix of fuzzy degree

( ) ( )

1

1/ 1 1/ 12 2

1

1/ ( ) , 1, ,

1 / / 1/

nm

i ij j

j

cm m

ij j i j k

k

v u x i c

u x v x v

=

− −

=

⎛ ⎞= =⎜ ⎟

⎝ ⎠

= − −

∑

∑

(4)

Some membership values data can be gotten after the FCM clustering and the greatest

value of the corresponding membership category is selected as the sample

corresponding to discrete categories, which is easy to handle for rough set decision

table.Step 2 Rough Set Theory

To make each input as the condition attributes and each output as the decision attributes

for the decision table. The discernibility matrix based on logical operation on rough set

attribute reduction algorithm is as follows.


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① calculated the discernibility matrix M of decision table system S = :

{ | ( ) ( )}, ( ) ( )( , )

0 ( ) ( )

, 1, 2, ,

k k k i k j i j

i j

a a C a x a x d x d x M i j

d x d x

i j n

∈ ∧ ≠ ≠⎧⎪= ⎨

=⎪⎩

=

(5)

② establish the appropriate expression of disjunctive logic

, , 0,i ij

ij ij i ij ija M

L L a M M Φ ∈

= ∨ ≠ ≠ (6)

③ calculation of CNF L

0,ij ij M M

ij L LΦ ≠ ≠

= ∧ (7)

④ make L convert to CNF then

ii

L L= ∨ ;

Every item on the results of CNF is corresponding to the attribute reduction,

which contains the least number of attributes are asking for the minimum set of

attributes C [8].

Step 3 Least squares Support Vector Machine (LS-SVM)

The quadratic programming has been required for training solutions SVM. Although

the solution obtained is the only optimal solution, the complexity of the algorithm

depends on the number of sample data. An effective solution is to use least squares

support vector machine (LS-SVM) which can improve the convergence speed by

solving a set of linear equations [9].

Let the training data set1{ , } ,

N

t t t t m x y x R

= ∈

is the t sample of the input mode,

t y R∈ is the expected output corresponds to the t sample, while N is the number of

training samples. LS-SVM to take the following form:

( ) ( )T y x w x bφ = + (8)

To map input data into a high dimensional feature space in the equation (8). The

dimension of w is not pre-specified ( which can be infinite dimensional.)

In the LS-SVM, the objective function is described as:

2

1

min ( , ) (1/ 2) (1/ 2) N T

t

t

J w e w w eγ =

= = ∑ (9)

constraints are: ( ) ( ) , 1, ,T t t

y x w x b e t N φ = + + = (10)


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4 Example Calculation

The specific process of the method can be illustrated by the differential circuit.

Fig. 3. Differential circuitry

In the fig. 3 the resistance and the tolerance of capacitance components is 5%, when

there is a single soft fault, we can set the nominal value of resistance fluctuations in Rb

fluctuate to 25%, Rc1 fluctuate to -30%, Rc2 fluctuate to 30% . When a component

fluctuates beyond its tolerance, not only it will cause changes in the voltage across thedevice, but also it will lead the other node voltage change, what is more the voltage

values are different in different failure mode. The seven test points are selected as

samples which is Vo1 Vo2 Vo3 Vo4 Vo5 Vo6 and Vo7 shown in Table1.

Table 1. Sample data

Vo1 Vo2 Vo3 Vo4 Vo5 Vo6 Vo7 S

0.082 0.014 0.088 0.112 0.021 6.215 0.015 normal0.195 0.035 0.062 0.137 0.026 5.242 0.168 normal

0.104 0.101 0.006 0.072 0.051 6.101 0.385 failure

0.015 0.026 0.033 0.092 0.018 5.001 0.069 failure

0.206 0.014 0.128 0.032 0.188 6.284 0.110 failure

0.184 0.087 0.071 0.074 0.029 5.301 0.106 failure

0.274 0.012 0.011 0.165 0.006 3.329 0.076 normal

0.279 0.038 0.010 0.187 0.007 6.469 0.094 normal

0.206 0.022 0.128 0.197 0.171 2.968 0.170 failure

0.082 0.014 0.088 0.112 0.021 6.215 0.015 normal

0.206 0.022 0.128 0.197 0.171 2.968 0.170 failure


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The data obtained by FCM is shown in Table 2, then rough set attribute reduction

algorithm can be used for attribute reduction the result after which is that the inputs are

leaving only the {Vo1, Vo2, Vo3, Vo4}. In other words, through the reduction of rough

set input have not been greatly reduced. Simulation results show that the algorithms of

the model can be reduced greatly.

Table 2. The collection sample data

Vo1 Vo2 Vo3 Vo4 Vo5 Vo6 Vo7 S

1 2 1 2 2 1 1 1

2 1 1 2 2 1 2 1

1 1 2 2 2 1 2 2

1 2 2 2 2 1 1 2

2 1 2 1 2 1 2 2

2 2 1 2 2 1 2 2

2 1 2 2 2 2 1 1

2 1 2 2 2 1 1 1

2 1 1 2 1 2 1 2

5 Conclusion

The fault classification model is established based on rough set theory and SVM in this

paper. In addition, this paper uses the rough set theory get the pre-processor without

loss of valid information, which can remove the diagnostic decision-making table to

solve the problem of dimension and the classification.

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Research on Model of Circuit Fault Classification