X. FEI

562

region of interest; denotes the scaling parameter or

scale, and measures the degree of compression. In the

frequency domain, this function is expressed as

a

*

(,)( ),

2

aj

x

WT axae d

(2)

where ()x

is the Fourier transform of ()

t; ()

is the Fourier transform of ()t

.

Selecting an appropriate wavelet converts ()t

in the

time domain into a finite support and turns ()

in the

frequency domain into a relatively concentrated variable.

Implementing wavelet transform in the time and fre-

quency domains also characterizes local signal features.

The energy distribution of various power disturbance

signals differs at various frequency bands. Thus, we can

incorporate different energy distributions in different

frequency bands as bases for distinguishing power dis-

turbances.

On the basis of references [7, 8], we choose sym4 as

the mother wavelet, and decompose power disturbance

signals into 11 layers. A total of 23 characteristic values

constitute a feature vector. 111

represents the quad-

ratic sum of the eleventh to the first layers of coefficients.

are calculated as follows [9]:

~VV

12 23

~VV

10

12 13

11 10

8

14 15

11 8

76

16 17

76

4

18 19

54

,10,9 8,7

20 21

11,10,9 8,7

22

, ,

, ,

, ,

, ,

, ,

std D

std

VV

meamean D

std D

std

VV

meamean D

stdstd D

VV

meamean D

std std D

VV

meanmean D

stdstd D

VV

meamean D

std

V

11

11

5

11

D

n D

D

n D

D

n D

D

D

D

n D

6,

n D

5,4 3,2,1

23

6,5,4 3,2,1

, ,

DstdD

V

meamean D

where 11

td D is the standard deviation of the eleventh

layer of decomposition coefficients, 11,10,9

std D de-

notes the standard deviation of the ninth to eleventh lay-

ers of decomposition coefficients, and 11

mean D

represents the average of the absolute value of decompo-

sition coefficients.

3. Multi-class SVM Classification Model

The commonly used multi-class SVM classification al-

gorithm is 1-to-1 (1-vs-SVM). When a classification

problem is highly complicated, however, training time

and computational complexity significantly increase. To

illustrate, let us consider types of samples that need

to be classified. To solve this problem, we construct a

k

(1)/2kk

hyper-plane.

To reduce computational complexity, researchers cre-

ated another classification algorithm, 1-VS-allSVM, this

involves hyper-plane classification that distinguishes

between one class of samples and the rest of several class

samples. Only the hyper-plane can solve the

previous problem-- types of samples that need to be

classified. This method is an extension of two types of

SVM. The prediction accuracy of the classifier is imper-

fect because of the huge difference between the number

of a single class of samples and the number of the rest of

the class samples.

(2kk

k)

)

In this paper, we use the BT-SVM method to improve

the accuracy and efficiency of the classifier.

types of samples require classification. First, we con-

struct by assigning the 1st sample type as a posi-

tive sample and the 2nd, 3rd … k th types as negative sam-

ples. We then construct by denoting the 2nd

sample type as a positive sample and the 3rd, 4th … kth

types as negative samples. According to the previous

method, we construct subsequent classifiers

(2kk

3SVM

1SVM

(1)k

2SVM

SVM

. The number of negative samples gradually

decreases; training time also decreases. We choose

BT-SVM [10] to classify different scenarios of power

quality disturbance. The algorithm is implemented as

follows:

1) Divide training sample into sub-

sets T and F, and regard as positive and negative

samples, respectively. These samples consist of a classi-

fication fu nct ion

(1,2,...,)

i

Ci k

F

,...,2 )

,T

1,2( )(

i

2) Take fxi

).

(

i

x as the root node for constructing a bi-

nary tree.

3) Repeat steps (1) and (2), then use T as the training

data for the left subtree and F to generate a classification

function for the right subtree. T is also used to construct

the classification function.

4) Repeat step (3) until training sample (1,2,

i

Ci

is converted into a group of child nodes; ..., )k

5) Input testing sample ii

c to the corresponding

binary tree()

i

x.

6) If all testing samples ii

c belong to the ith

sample type, then the classification is completed. The

same applies when all testing samples ii

c are re-

quired to traverse from the root node to pass through all

the nodes until the category to which the samples belong

are identified.

We use different support vector machines to match

different scenarios of power quality disturbance. Thus,

every support v ector machine can solve a particular clas-

sification problem and improve accuracy by using train-

ing samples.

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