Article

A Novel Fault Diagnosis System on Polymer

Insulation of Power Transformers Based on 3-stage
GA–SA–SVM OFC Selection and ABC–SVM
Classifier
Xiaoge Huang 1,2,†, Yiyi Zhang 1,2,†, Jiefeng Liu 1,2,*, Hanbo Zheng 1,2,* and Ke Wang 3
1 Guangxi Key Laboratory of Power System Optimization and Energy Technology, Guangxi University,
Nanning 530004, Guangxi, China; nnhuangxg@163.com (X.H.); yiyizhang@gxu.edu.cn (Y.Z.)
2 National Demonstration Center for Experimental Electrical Engineering Education, Guangxi University,

Nanning 530004, Guangxi, China

3 China Electric Power Research Institute, Haidian District, Beijing 100192, China;

wangke1@epri.sgcc.com.cn
* Correspondence: liujiefeng9999@163.com (J.L.); hanbozheng@163.com (H.Z.);
Tel.: +86-199-6812-0257 (J.L.); +86-199-6801-1211 (H.Z.)
† These authors contributed equally to this work.

Received: 24 September 2018; Accepted: 1 October 2018; Published: 3 October 2018

Abstract: Dissolved gas analysis (DGA) has been widely used in various scenarios of power
transformers’ online monitoring and diagnoses. However, the diagnostic accuracy of traditional
DGA methods still leaves much room for improvement. In this context, numerous new DGA
diagnostic models that combine artificial intelligence with traditional methods have emerged. In
this paper, a new DGA artificial intelligent diagnostic system is proposed. There are two modules
that make up the diagnosis system. The two modules are the optimal feature combination (OFC)
selection module based on 3-stage GA–SA–SVM and the ABC–SVM fault diagnosis module. The
diagnosis system has been completely realized and embodied in its outstanding performances in
diagnostic accuracy, reliability, and efficiency. Comparing the result with other artificial intelligence
diagnostic methods, the new diagnostic system proposed in this paper performed superiorly.

Keywords: artificial bee colony (ABC); dissolved gas analysis (DGA); fault diagnosis; genetic
algorithm (GA); power transformers; simulated annealing (SA) algorithm; support vector machine
(SVM)

1. Introduction

1.1. Motivation
Transformers are distributed in almost all domains of the entire electrical network, changing the
values of AC voltage (current) at given points to another or several values without altering the
frequency. They not only guarantee the normal operation of the power grid, but also affect people’s
living environment [1]. However, the operating conditions of the transformer (including temperature
and electromagnetic conditions) are harsh and not conducive to its long-term health [2–4]. In the
meantime, the failure of power transformers is often attended by disastrous consequences, which
include equipment burning and large-scale blackouts. Undoubtedly, the operational safety of power
transformers deserves serious concern.
Fault diagnosis is regarded as one of the most important considerations in maintaining the safe
operation of the power transformer. Diagnostic and fault prognosis techniques have been widely and

Polymers 2018, 10, 1096; doi:10.3390/polym10101096 www.mdpi.com/journal/polymers

Polymers 2018, 10, 1096 2 of 20

successfully applied in numerous engineering dynamic systems [5], and are also of extreme
importance to researchers of electrical energy systems [6]. At present, fault diagnosis systems play a
critical role in maintaining the operational safety of power transformers, and their principles and
designs are constantly updated and strengthened [7,8].
We argue that a sound transformer diagnostic method should be strengthened in the following
aspects: (1) Economic efficiency and (2) solving the allowable-time problem. Economic efficiency is
related to diagnostic costs. The average annual failure rate of transformers is not very high; it usually
does not exceed 5% [9]. In other words, the expense of the transformer fault diagnosis is of minor
significance in most cases. When the transformer is operating properly, the diagnosis provides less
valuable guidance to maintenance staff. However, the traditional diagnosis costs for the transformer
are relatively prominent, due to the lack of online diagnostic methods. Transformers need to be shut
down periodically for maintenance and, during such shutdowns, the outage cost of the transformer
is huge. Therefore, it is necessary to control the diagnostic costs and improve the economic efficiency
of the transformer’s diagnostic method. On the other hand, the allowable-time problem is a noticeable
challenge to traditional transformer diagnosis. The fault of the transformer has no obvious
abnormality at the beginning, making the allowable-time for maintenance actions relatively short.
Under these circumstances, this paper aims to propose an online-diagnosis method that is economical
and capable of overcoming the allowable-time problem.

1.2. Related Work

Mainstream transformers’ fault diagnostic methods include chemical quantity based methods
and electrical quantity based methods [10]. Chemical based methods typically include dissolved gas
analysis (DGA) [11], degree of polymerization (DP) measurements [12], moisture analysis (MA) [13],
and Furan analysis by high performance liquid chromatography (HPLC) [14], among others. The
electrical based methods involve the time domain method [15] and frequency domain polarization
measurement [16]. Among these, DGA is the most widely exploited [17]. Since DGA was proposed
in 1973, this online method has been widely accepted and exploited all around the world, owing to
its outstanding economic efficiency and capability to detect failure in advance, which effectively
alleviates the pressure brought on by the allowable-time problem [18]. The DGA works via detecting
hydrogen (H2), methane (CH4), acetylene (C2H2), ethylene (C2H4), ethane (C2H6), carbon monoxide
(CO), and carbon dioxide (CO2) gases dissolved in the transformer oil, which is produced by pyrolysis
of insulation paper (board) cellulose. In this proposal, we divided DGA methods into traditional
methods and intelligence methods. Traditional methods include: The Doernerburg Ratio Method
[19], Rogers Ratio [20], IEC 60,599 Method [21,22], Duval Triangles Method [23], and Pentagon
Method [24]. Despite having a long history, most of these methods are unstable in a complex
operating environment. On the other hand, while research of intelligent DGA diagnostic methods
has appeared, these are implemented less frequently compared with the traditional methods [25].
Therefore, this paper hopes to improve this situation as much as possible.
The development of an intelligent diagnosis of the power transformer is promising. In general,
intelligent diagnosis designs are built on the ideas of traditional methods. They combine most of the
advantages of both traditional ideas and intelligent algorithms. Recently, intelligent methods, such
as fuzzy logic inference systems [26], artificial neural networks [27], support vector machines (SVM)
[28,29], and some other machine learning algorithms have been applied to transformer fault diagnosis
and have had impressive performances [10,30,31]. However, limitations also exist with intelligent
diagnostic methods. For example, fuzzy inference depends excessively on the experience of
researchers [32]. In addition, “local minima” and “overfit” are two of the marked weaknesses of
Artificial Neural Network (ANN) [33]. Compared to these methods, the application of SVM in
abnormal detection and fault diagnosis has marked advantages [34]. It overcomes the local minimum,
dimension, and over-fitting problems, and requires less in the scale of the training sample.
Polymers 2018, 10, 1096 3 of 20

1.3. Contribution and Paper Orgnization

In this paper, we combined SVM with traditional DGA and proposed a two-stage SVM
diagnostic system, and the main structure of the system was depicted in Figure 1. The system contains
a feature selection module, which would extract the optimal feature combination (OFC) from DGA
information, and a multiclassifier, judging the type of fault in power transformers based on the OFC.
Accounting for the relatively low request of the speed and the highlighted accuracy and reliability, a
3-stage GA–SA–SVM selection model which combined a genetic algorithm (GA) [35] and simulated
annealing (SA) algorithm [36] with SVM was utilized to complete the selection of OFC. In addition
to these, the artificial bee colony (ABC) algorithm [37], which has the fastest iteration speed and the
highest search efficiency, was exploited in the diagnostic stage. The entire system has been fully
realized, with the accuracy of its result reaching 92%.
The remaining sections of this paper are structured as follows: In Section 2, a 3-stage GA–SA–
SVM method, which was used to determine the optimal feature combination of DGA feature sets, is
proposed. The ABC–SVM based diagnostic model is constructed in Section 3. A case study of the
entire system is illustrated in Section 4. Finally, we conclude the research and identify the direction
of future research in Section 5.

DGA Samples

OFC Binary
Feature Selection
Sequence
System

OFC Sample Multiclassifier

State of
Transformer

Figure 1. The structure of the diagnostic system.

2. Optimal Feature Combination Selection

2.1. The Candidate DGA Feature Sets

In recent years, the DGA gas ratio is used as the characteristic parameter, such as in the
Doernerburg Ratio Method [19] and the Rogers Ratio Method [20]. Inspired by [38], eight categories
of gas: H2, CO, CO2, CH4, C2H2, C2H4, C2H6, and the total hydrocarbon (TH, TH = CH4 + C2H2 + C2H4
+ C2H6) were taken into account in this paper. Therefore, there were 28 DGA candidate ratios in total,
which are shown in Table 1 below.

Table 1. Dissolved gas analysis (DGA) Ratios.

Ratios Ratios Ratios Ratios Ratios

H2/CO H2/CO2 H2/CH4 H2/C2H2 H2/C2H4
H2/C2H6 H2/TH CO/CO2 CO/CH4 CO/C2H2
CO/C2H4 CO/C2H6 CO/TH CO2/CH4 CO2/C2H2
CO2/C2H4 CO2/C2H6 CO2/TH CH4/C2H2 CH4/C2H4
CH4/C2H6 CH4/TH C2H2/C2H4 C2H2/C2H6 C2H4/TH
C2H4/C2H6 C2H4/TH C2H6/TH H2/C2H2 H2/C2H4
Polymers 2018, 10, 1096 4 of 20

2.2. DGA Feature Selection Model

The DGA feature selection is necessary due to the ambiguous relationship between the DGA
features and the types of transformer fault. According to [39], parts of DGA gas ratios are unrelated
to the fault diagnosis, which means that blindly selecting DGA features or even focusing on all
features is unwise. To address this problem, it is necessary to select the key DGA features carefully,
which was mostly suitable in the following diagnosis. Accounting for the low request of the speed
and the highlighted accuracy and reliability, a 3-stage GA–SA–SVM selection model was constructed
to complete the selection. The flowchart of the selection process is illustrated in Figure 2, and a brief
description of the 3-stage GA–SA–SVM model constructing process is as follows:

Randomly Initialize
Generation = 1
The Population

Generation=Gener
Decoding
ation+1

Selected Sample Training Sample Output The OFC

SVM Fitness Evaluation

YES
Sort The Generation>= NO Inverse Simulated
Chromosome MaxIteration? Annealing Operation

Genetic
Operations
YES

Generate New NO Simulated

Decoding Generation>= 180?
The Generation Annealing Operation

Selected Sample Training Sample

YES
NO
SVM Fitness Evaluation Generation>= 40?

Figure 2. Flowchart of optimization selection based on 3-stage GA–SA–SVM.

2.2.1. Multiclass Nonlinear SVM Model

The principle of SVM is to find the optimal hyperplane which satisfies the classification
requirements and extends the distance of the two data sets on the hyperplane as much as possible.
The model of the SVM is depicted in Figure 3.
Assuming that xi  Rn and yi  Rn are the input and output of the training set, respectively,
the training set {(x1, y1), …, (xi, yi), …, (xl, yl)} was obtained. At the same time, a class table yi  {−1,
+1} was introduced, which was determined through the given xi. The constraints of the training set
data can be written as (1):

 T  ( xi ) + b  −1, if yi = −1
(1)
 T  ( xi ) + b  +1, if yi = +1
Polymers 2018, 10, 1096 5 of 20

where the φ(xi) is a nonlinear mapping. Both the φ(xi) and ω contain infinite dimensions. They form
the optimal hyperplane together.

Input Space Feature Space

Figure 3. The model of support vector machine (SVM).

When the data are linearly inseparable, a non-negative slack variable ξi is introduced to
transform the SVM into (2):
l
1
min  ( ,  ) =  + C  i
2

2 i =1

 yi ( T xi + b )  1 − i (2)
s.t. 
i  0, i = 1, 2,..., l

where parameter C is the penalty factor. C was determined through optimization, which depends on
the GA and SA algorithms.
Build a Lagrangian function to solve the QP problem of (2):
L( , b,  ,  ,  ) = (,  )
l l
(3)
−  i { yi [ T  ( xi ) + b] − 1 + i } −  ii
i =1 i =1

Among them, αi > 0 and βi > 0 are Lagrange multipliers; then, the original problem has been
transformed into a quadratic programming problem:

1 l l
max ( ) = − 
2 i =1
i j yi y j K ( xi , x j ) + i
i =1
(4)

 y
i =1
i i = 0, i  [0, C ], i = 1,..., l (5)

where K(xi, xj) is called the kernel function that satisfies (6). σ was a given parameter, which was
determined through the GA and SA optimization.

 xi − x j 
K ( xi , x j ) = exp  −  (6)
 2 

Using the One-Against-One (OAO) method to extend the two-class SVM to a multiclass SVM,
the optimization problem translated into (7):
l
1 jk T jk
min  ( ,  ) = ( )  + C  i jk
2 i =1

( jk )T  ( xi ) + b jk  1 − i jk , yi = j (7)

s.t. ( jk )T  ( xi ) + b jk  i jk − 1, yi = k
 jk
i  0, i − 1, 2,..., l
Therefore, the expression of the decision function is written as (8):
Polymers 2018, 10, 1096 6 of 20

f jk ( x) = sign[( jk )T  ( x) + b jb ] (8)

2.2.2. Application of Genetic Algorithm

Genetic algorithms contributed to the OFC selection for determining C and σ. They contained
three main units: Coding, fitness calculation, and genetic operation.
• Chromosome coding
The chromosome in GA was abstracted as the solution of the objective function. The abstract
process is known as coding. As shown in Figure 4, three sets of parameters: C, σ, and DGA ratio sets
need to be optimized. They match three segments of binary codes which were represented by L1, L2,
and L3, respectively. In the first two codes, namely L1 and L2, the value of binary encoding in the
decimal form is equivalent to the value of its corresponding C and σ. The binary code on the L3
segment reflects the combination of selected DGA ratios. The “1” on each bit in L3 means the
corresponding DGA ratio is selected, and “0” reflects the opposite meaning.

c σ DGA

1 ... 0 1 ... 1 0 ... 0

L1 L2 L3

Figure 4. The binary encoding of chromosomes.

• Genetic fitness calculation

Genetic fitness is calculated as follows in (9), which is the standard to evaluate the performance
of a single chromosome:

1 k  lTi 
f ( L1 , L2 , L3 ) = −   i 100% 
k i =1  l
(9)

i
where, li is the number of samples in the ith verification set; lT is the correct classified number in the
verification set; and k is the number of cross validation. The concept of K-fold cross-classification will
be illustrated in the following description.
• Genetic operations
The old solution generates new solutions through genetic operations.
Genetic operation refers to the fact that in each generation, individual chromosomes are chosen
according to their selection probability. After that, chromosomes still need to experience crossover
and mutation in order to generate a new population. This process ensures that the new population is
more adaptable to the environment than the previous generation. The selection probability of each
individual is calculated as follows in (10):
fi
Pi = N
(10)
f
i =1
i

fi is the ith genetic fitness.

Crossover operations followed (11) with a given certain probability:
xi = axi + (1 − a ) xi +1
(11)
xi +1 = (1 − a ) xi + axi +1

where a is a random number in the interval [0, 1].

Polymers 2018, 10, 1096 7 of 20

The mutation operation (12) refers to randomly selecting a mutation bit j in the mutated
chromosome and setting it as a normalized random number U(ai, bi). ai, bi are the upper and lower
constraints of the corresponding mutation.

U (ai , bi ) if i = j
xj =  (12)
 xi otherwise

2.2.3. Combination of SA Algorithm and GA

The SA operation and the inverse SA operation were combined with the GA to acquire a more
impressive performance in optimization. The flowcharts of the SA operation and the inverse SA
operation are presented in Figure 5.

Exist A Old Solution i, Exist A Old Solution i,

Produces a New Produces a New
Solution j Solution j

YES NO YES NO
(Ei-Ej)<=0? (Ei-Ej)>=0?

Accept j, Accept j Based On Accept j, Accept j Based On

i = j, Ei = Ej Probability P i = j, Ei = Ej Probability P

Generation>= Generation>=
NO MaxIteration? MaxIteration?
NO
YES YES

(a) (b)
Figure 5. The flowcharts of the simulated annealing operation and the inverse annealing operation.
(a) The simulated annealing operation; (b) The inverse simulated annealing operation.

• Simulated annealing operation

The SA operation is the most noticeable difference between the SA algorithm and other greedy
algorithms. The SA operation refers to a reservation principle for the new solution set up in iterations.
In the SA operation, the solution of a new generation is retained based on a probability, which is
calculated following the Metropolis criterion.
• Metropolis criterion
The SA algorithm draws on the relationship between the temperature T and the internal energy
E in the solid annealing principle. The Metropolis criterion describes the relationship between the
probability of accepting a solution of the new generation and T and E. Assuming that, at temperature
T, the number of current iterations is i and the number of new iterations is j, if Ej < Ei, save j as the
current generation; otherwise, follow the probability P to determine whether j would be saved, where
P followed (13). In the SA algorithm, T is positively related to the number of iterations, and Ei is
numerically equal to the fitness of the ith generation.

 E j − Ei 
P = exp  −  (13)
 KT 

• Inverse simulated annealing operation

Inverse simulated annealing operation is the opposite of simulated annealing operation: If Ej >
Ei, accept j as the current generation; otherwise, follow the probability P to accept j as the current
generation.
Polymers 2018, 10, 1096 8 of 20

• Multi stage of GA–SA-combination

In order to obtain the result of selection with high accuracy, sound stability, and a relatively
short time-consumption, we utilize the GA algorithm, the GA hybrid SA (GA–SA) algorithm, and the
Inverse SA hybrid GA (Inverse SA–GA) algorithm in multiple stages of generation intervals. Only
one of these algorithms runs in each interval to optimize the SVM parameter and OFC.
Through combining GA and SA in multiple stages, we obtained a multistage-GA–SA–SVM
selection model.

2.2.4. K-Fold Cross-Validation

K-fold cross-validation (CV) was hired to verify the accuracy of selection. To imply K-fold CV,
the initial sample is divided into K subsamples, a separate subsample is retained as the data for the
validation model, and the other K − 1 samples are employed for training. The cross-validation will
repeat for K times. Each subsample will act as a verified sample once. The average result of
validations in K times is viewed as the estimation result [29]. Here we set K = 5.

3. Fault Diagnosis Model Based on ABC–SVM

ABC is a mature algorithm which has been widely applied in solving numerous optimization
problems due to its prominent convergence characteristics [37,40]. In order to obtain the highest
operating efficiency and the highest diagnostic accuracy, we utilized the ABC algorithm to optimize
the SVM parameters, and constructed the ABC–SVM based transformer fault diagnosis model.

3.1. The Mechanism of ABC

There are four key components in ABC: Honey sources which abstract into points in the solution
space, lead bees, follow bees, and reconnaissance bees. The bees represent the potential solution to
the problem. The tasks for each bee are different. As shown in Figure 6, they extend the known honey
source to search for the global optimal solution in predetermined manners. Search manners consist
of three steps: (1) Lead bees discover a source of the honey and share the source information; (2) each
follow bee selects the source to collect the honey according to the information and evaluates the
quality of the source; (3) the lead bee converts into a reconnaissance bee and continues to search for
new sources near the hive when a source is found repeatedly, but the quality is not improved. When
a high-quality source is found, he turns his role back into that of a lead bee. These three steps will be
replicated until the best honey source is found.

Bees: Possible
Solutions
All of The Possible Solution

Initial Solution

Task of the Bees: Expand

This Area And Obtain
Global Optimal Solution

Figure 6. Mechanism of artificial bee colony (ABC).

Polymers 2018, 10, 1096 9 of 20

3.2. ABC Optimization Model

In the ABC model, the quality of the honey source i (i = 1, 2, ..., NP) corresponds to the fitness
value fiti of the solution, and NP is the number of honey sources. The numbers of lead bees and follow
bees equal to half of the bee colony, respectively, which also equal the number of honey sources. A
honey source accommodates only one bee at any one time.
Let the dimension of the solution problem be D. The position of the honey source at the tth
generation is denoted as X i = [ xi1 , xi 2 ,..., xiD ] , where xid  ( Ld ,U d ) , Ld and Ud denote the lower and
t t t t

upper constraints of the search space, respectively, and d is a random integer in [1, D]. The initial
position of the honey source i is randomly generated in the search space according to (14).
xid = Ld + rand(0,1)  (U d − Ld ) (14)

To start the search, the lead bee searches around the honey source i according to (15) to generate
a new honey source:
vid = xid +  ( xid − x jd ) (15)

where j {1, 2,..., NP}, j  i , this indicates randomly selecting a honey source that is not equal to i
among the NP honey sources; φ is a random number of [−1, 1], which is uniformly distributed and
determines the magnitude of perturbation.
Then, the follow bee calculates the fitness of the new honey source Vi = [vi1vi 2 ...vid ] according to
(16) and decides whether or not to replace Xi or keep Xi by using the greedy choice method.

1/ (1 + fi ), f  0
fiti =  (16)
1 + abs( fi ), otherwise
fi represents the objective function whose functional value is numerically equal to the mean
square error (MSE) of the accuracy of the SVM prediction model.
After that, follow bees use the Roulette Wheel Selection to determine the lead bees they follow.
The probability in the Roulette Wheel Selection was calculated through (17):
fi
Pi = N
(17)
f
i =1
i

During the search process, if a source Xi reaches the limit through trial iterations without finding
a better source, the source Xi will be abandoned. The lead bee turns into the role of reconnaissance
bee and generates a new source of honey in the search space followed randomly (18). ABC algorithm
flowcharts were depicted in Figure 7.

 Ld + rand(0,1)  (U d − ld ), t  limit

X it +1 =  t (18)
 X i , t  limit


3.3. Leave-P-Out Cross Validation

In the diagnostic phase, the LpO CV was exploited for verification. The LpO CV refers to using
the p elements in the full set X as the testing set, and the remaining n-p elements as the training set.
As a result, p verification results will be obtained in the end. The final result is numerically equal to
the percentage of correct results in p results.
Polymers 2018, 10, 1096 10 of 20

N Generation Honey Source Initialization

Number of sources
n . found in one
generation N=1

The Lead Bee Found a New

Honey Source

n=1

N+1
YES
The Follow Bee Marks The
NO
New Source, Calculating n+1, n>100?
The Quality of Honey

Generate The Reconnaissance

Has the quality of honey NO
Bees and Finds The New Source
improved?
to Replace The Tagged Source

YES
Obtained The Contemporary
Tagged Source

NO YES
Condition Satisfied? Output

Figure 7. Flowchart of ABC.

3.4. Process of Classification Based on ABC–SVM

The established ABC model is applicable for selecting the optimal parameters of a nonlinear
multiclass SVM (C and σ). The flowchart of ABC–SVM is given in Figure 8, which contains four steps:
Step 1. Utilize LpO CV to generate a training set and a testing set. The training set was sent to the
ABC model.
Step 2. Use training set and nonlinear multiclassification support vector machine to construct
unknown parameters and to form the optimal objective function.
Step 3. Apply ABC to find the best solution to determine the best parameters of SVM. The best
parameters are obtained when the training accuracy meets the threshold of checking;
otherwise, step 3 is replayed.
Step 4. Input testing is set to SVM, then the output will be obtained.
Polymers 2018, 10, 1096 11 of 20

Input Data
Set

LpO CV

ABC
Testing Set Training Set

Parameter
Optimization

NO
Evalaute
YES

SVM

Output Classification Result

Figure 8. Flowchart of ABC–SVM classification.

4. Case Study and Analysis

4.1. Data Preprocessin

In this research, 118 sets of transformer fault data which originated from International
Electrotechnical Commission Technical Committees (IEC TC) 10 databases [20] were engaged to carry
out the test. We labeled the 118 datasets with five states of transformers, which contained: 23 sets of
low-energy discharge (LED, represented by “1”), 45 sets of high-energy discharge (HED, represented
by “2”), 10 sets of low and middle-temperature overheat (LMT, using “3”. Representative), 14 sets of
high temperature overheating (HT, represented by “4”), and 26 sets of normal operation (N,
represented by “5”). The states arrangement of samples is given in Table 2.

Table 2. The states arrangement of IEC TC 118.

Label Quantity
1 23
2 45
3 10
4 14
5 26

The data need to be preprocessed: Normalizing the data follows (19) to eliminate differences
caused by ratio magnitude differences:
xi − xi.min
xi.result = (19)
xi.max − xi.min

where xi.result is the result of normalization, xi is the ratio which needs to be normalized, xi.max and xi.min
are the maximum and the minimum members among entire samples.

4.2. Result of DGA Optimal Feature Selection

4.2.1. Parameter Setting in Three Stage-GA–SA–SVM

Polymers 2018, 10, 1096 12 of 20

In 3-stage GA–SA–SVM optimization, several parameters were specified in Tables 3 and 4. The
maximum iteration number was set at 200. The population scale was determined at 20. The number
of chromosome segments was 3. Both L1 and L2 took 18, which guarantees that the upper bound of
both C and σ is 255 and they can be accurate to 10−4. L3 was 28. In the optimization process, the first
40 generations were fully optimized using the GA-SVM method, 40–180 generations utilized the GA–
SA–SVM algorithm, and the Inverse SA–GA–SVM algorithm was applied in the last 20 generations.

Table 3. Parameters preset in 3-stage GA–SA–SVM.

Max Iteration Population Scale L1 L2 L3

200 20 22 22 28

Table 4. Generation interval of three stages.

GA–SVM GA–SA–SVM Inverse SA–GA–SVM

[0, 40] [20, 180] [180, 200]

4.2.2. Comparison with Other Methods

In order to embody the advantages of 3-stage GA–SA–SVM, we used GA–SVM, GA–SA–SVM,
2-stage GA–SA–SVM, and 3-stage GA–SA–SVM to select feature combinations and obtain the results
of four methods. Each result includes CV accuracy, fitness curve, and optimal feature combination.
CV accuracy and the optimal combination of features for each method are listed in Table 5. The fitness
curve for each method is shown in Figure 9, which also included optimal C and σ. In the following
figures, g is used to represent σ and c is used to represent C. In the meantime, we would like to
emphasize that, in order to overcome the possible accuracy problems caused by insufficient public
sample data of transformers, these results are carefully selected by the author after 50 times of
repeated experiments, and are the closest to the average results.

(a)
Polymers 2018, 10, 1096 13 of 20

(b)

(c)

(d)

Figure 9. Results of four optimal feature selection methods: (a) The result of the GA–SVM method;
(b) The result of the GA–SA–SVM method; (c) The result of the 2-stage GA–SA–SVM method; (d) The
result of the 3-stage GA–SA–SVM method.

Table 5. Result of DGA selections.

CV
Method Selected Combinations
Accuracy
H2/CO, H2/CO2, H2/TH, CO/CO2, CO/C2H2, CO2/CH4, CO2/C2H4,
GA–SVM 88.17%
CH4/TH, C2H4/TH, C2H4/C2H6
Polymers 2018, 10, 1096 14 of 20

H2/CO, H2/CO2, H2/CH4, H2/C2H2, CO/CH4, CO/C2H4, CO/TH,

GA–SA–SVM 89.40%
CO2/CH4, CO2/C2H4, CO2/TH, C2H2/C2H4, C2H2/C2H6
2-stage GA– H2/CO, H2/C2H2, CO/CO2, CO/C2H2, CO2/CH4, CO2/C2H4, CH4/TH,
89.45%
SA–SVM C2H4/TH, C2H4/C2H6
3-stage GA– H2/CO2, H2/C2H2, H2/C2H4, H2/TH, CO2/CH4, CO2/C2H2, CO2/C2H4,
90.36%
SA–SVM CH4/C2H6, C2H6/TH, CH4/TH, C2H2/C2H4, C2H2/C2H6

In Table 5, 3-stage GA–SA–SVM has the highest CV accuracy among all algorithms. In Figure
9a, GA–SVM’s fitness reaches the highest value within 20 generations and takes the shortest time,
which is only about 200 s, to end the iteration. However, due to the fitness curve no longer climbing
after reaching a platform, the GA algorithm is more likely to be trapped in the local optimal solution,
making the result unstable. Also, the accuracy of the GA–SVM is slightly lower than that of other
algorithms. The GA–SA–SVM algorithm made some improvements based on the GA algorithm. In
Figure 9b, the fitness of the GA–SA–SVM changed after arriving at a local optimization platform,
which means that it is easier for the GA–SA–SVM to jump out of the local optimal solution. Therefore,
the result of the GA–SA–SVM looks more stable and accurate. However, the weakness of the GA–
SA–SVM is marked. The GA–SA–SVM’s fitness reaches the platform period at around the 40th
generation and requires a long running time of more than 600 s. The adoption of the 2-stage GA–SA–
SVM has already made some improvements to this problem. In Figure 9c, the 2-stage GA–SA–SVM
was able to jump out of the local optimal solution and merely required 474 s to complete the
optimization, and 20 generations to reach the local optimal platform. The shortcoming that remains
in the 2-stage GA–SA–SVM is that the fitness may jump out of the global optimal solution at the end
of the optimization. This situation is due to the temperature T in the SA algorithm is already very
low within the last ten generations, and the probability of accepting a positive-direction-mutation
(which makes the fitness grow) is quite low. In contrast, the probability of receiving a negative-
direction-mutation is 100%. For example, maximum fitness in the 194th generation of Figure 9c
decreased during accepting a negative-direction-mutation. This generation was very close to the
maximum number of iterations. At this moment, it was a risk that the result may return to the local
optimal solution and never grow again until the end of the iteration. This is a typical defect of the SA
algorithm when the maximum number of iterations is set in the first place. A similar situation also
occurs in the GA–SA–SVM hybrid algorithm: At the 190th generation in Figure 9b, fitness returns to
the local optimal solution until the end of the iteration. The 3-stage GA–SA–SVM was intended to
overcome this shortage. In Figure 9d, the 3-stage GA–SA–SVM retains all of the benefits of the 2-stage
GA–SA–SVM, except that the solution takes a little longer—up to 506 s. After the 180th generation,
the inverse SA algorithm not only eliminated the decrease in fitness that might occur in the SA
algorithm, but also provided two opportunities for the fitness to raise. The 3-stage GA–SA–SVM is
therefore more stable and accurate than the 2-stage GA–SA–SVM method.
Based on the high accuracy and stability of the 3-stage GA–SA–SVM, the selection results of the
3-stage GA–SA–SVM are considered to be the most reasonable OFC. DGA ratio components of the
OFC are set out in Table 6.

Table 6. Optimal feature combination.

Ratios
H2/CO2, H2/C2H2, H2/C2H4, H2/TH, CO2/CH4,
CO2/C2H2, CO2/C2H4, CH4/C2H6, C2H6/TH,
CH4/TH, C2H2/C2H4, C2H2/C2H6

4.3. ABC Diagnostic Results

4.3.1. Parameter Setting in Three ABC–SVM

Polymers 2018, 10, 1096 15 of 20

Based on the LpO CV, 118 sets of IEC TC 10 samples were divided into two groups. Among
these, 93 sets were for training and 25 sets for testing. The states arrangement of testing samples is
listed in Table 7.

Table 7. The states arrangement of the testing sample.

Label Quantity
1 5
2 10
3 3
4 3
5 4

In the ABC algorithm, we set the scale of the bee colony to 20. The number of honey sources
(solutions) is set to half of the scale, that is, 10. In each generation, the maximum number of extra
honey sources that can be found are 100. That is, if the reconnaissance bees discover more than 100
fresh honey sources and the quality of the honey sources does not increase, reinitialize the honey
sources. This setting is to prevent ABC from being trapped in the local optimal solution. The
maximum number of loops is 10 and the dimension of the vector to be optimized is 2. The parameters
are arranged as shown in Table 8.

Table 8. Parameters preset in ABC.

Number of Honey Scale of The Bee Max Number of New Sources in Max Number of
Source Colony One Generation Loops
10 20 100 10

4.3.2. Diagnostic Result

The final results of the 25 testing sample diagnoses and the accuracy of the diagnosis are given
in Figure 10. The blue circle in the upper half of the diagram represents the correct label status of the
testing data, and the red dot is the diagnostic result from the diagnostic system. When the red dot
coincides with the blue circle, it means that the result of diagnosis is accurate. The lower half figure
depicts the distribution of the diagnostic deviation of the diagnostic system. Results showed that
diagnostic accuracy amounts to 92% (23/25); errors only occurred at points 16 and 17.

Figure 10. Diagnosis result of ABC–SVM.

Polymers 2018, 10, 1096 16 of 20

4.3.3. Result of Comparison

We divided the comparison into two parts: Self-comparing and comparison with standard
algorithms and other wrapper algorithms.
• Self-comparing
Since that the task of ABC algorithm is to search the optimal value of C and the σ, we simulated
the diagnostic accuracy of each point of C and the σ to demonstrate the superiority of ABC. The σ and
C are both on a [0, 200] × [0, 200] square plane. Their values correspond to the X axis and the Y axis
on the plane, respectively. The Z axis perpendicular to the plane represents the accuracy of diagnosis.
The detailed results of the simulation are presented in Figure 11, which depicted that the highest
precision obtained by the SVM classifier was 91.96%. The diagnostic result of the ABC–SVM has
reached the global highest point. The self-comparison verified that ABC has excellent performance
under given data and operating conditions.

(a) (b)

(c)

Figure 11. Testing accuracies for all the points (c, σ) (a) Cross-sections of the points at (100, 90.19); (b)
Cross-sections of the points at (100, 90.72); (c) is a 3D visualization of all the points.

• Comparison with Standard Algorithms and other Wrapper Algorithms

We compared the results obtained by ABC–SVM with the results originating from standard
algorithms based methods: SVM, and back propagation neural networks (BPNN) and wrapper
algorithms: GA–SVM and PSO–SVM. These methods shared the same sample, based on the optimal
feature combination in Table 6. The diagnostic result of each method is listed in Figure 12. To compare
with other wrapper algorithms, fitness curves of wrapper algorithms are shown in Figure 13. In the
meantime, we would like to emphasize that, in order to overcome the possible accuracy problems
caused by insufficient public sample data of transformers, these diagnostic results are carefully
Polymers 2018, 10, 1096 17 of 20

selected by the author after 50 times of repeated experiments, and are the closest to the average
results.
The advantages of the ABC–SVM in terms of accuracy can be clearly seen from the comparison
between Figures 10 and 12. The ABC–SVM is the only one of all algorithms with a precision of over
90%. The diagnostic accuracy of ABC–SVM is obviously improved compared to that of standard
SVM, and it is better than that of BPNN. The accuracy of ABC–SVM is also higher than that of other
wrapper algorithms.
In addition, it can be seen that the ABC algorithm has better convergence characteristics when
compared to other optimization algorithms, which guarantees that ABC–SVM performs better than
other wrapper algorithms. It runs steadily, has fewer iterations, and has a rapid convergence time
and a high termination fitness. Unlike GA or PSO, which require hundreds of generations of
calculations, ABC reached the optimal platform within five iterations. Besides, as seen in Figure 13,
termination fitness of ABC exceeded 95%, which is almost 10% higher than that of the GA and the
PSO. This shows the ABC’s outstanding preferment in convergence.

(a) (b)

(c) (d)
Figure 12. Fault diagnosis results and the spatial distribution of the optimal solution using different
methods (a) PSO–SVM; (b) GA–SVM; (c) SVM; (d) BPNN.
Polymers 2018, 10, 1096 18 of 20

(a)

(b)

(c)
Figure 13. Average fitness and best fitness of SVM based methods (a) ABC method; (b) PSO method;
(c) GA–SVM.

5. Conclusions and Future Directions

This paper combines the traditional DGA method and intelligent algorithms and proposes a
complete online monitoring and diagnostic system for power transformers. Inheriting the advantages
of traditional DGA online technology, the novel diagnostic method has sound economic
characteristics and alleviates the pressure brought by the allowable-time problem effectively. The
diagnostic process includes: (1) An extracted DGA feature combination based on 3-stage GA–SA–
SVM and (2) using the ABC–SVM classification model to diagnose transformer faults based on the
optimal feature combination. The results are shown to be highly accurate and reliable. The system
has strong anti-noise ability, so it requires less attention in the working environment condition.
In subsequent studies, we will concentrate on two research directions: (1) Developing an
improved ABC algorithm to link SVM mode, and (2) designing an algorithm (ABC–SVR) that
combines support vector regression (SVR) with ABC.

Author Contributions: In this research activity, all the authors were involved in the data collection and
preprocessing phase, model constructing, empirical research, results analysis and discussion, and manuscript
preparation. All authors have approved the submitted manuscript.

Acknowledgments: The authors acknowledge the National Natural Science Foundation of China (Grant No.
51867003), the National Basic Research Program of China (973 Program, 2013CB228205), the National High-tech
R & D Program of China (863 Program, 2015AA050204), the Natural Science Foundation of Guangxi
(2015GXNSFBA139235), the Foundation of Guangxi Science and Technology Department (AE020069), the
Foundation of Guangxi Education Department (T3020097903), and the National Key Research and Development
Program of China (2016YFB0900101) in support of this work.

Conflicts of Interest: The authors declare no conflict of interest.

References
1. Li, J.S.; Zhou, H.W.; Meng, J.; Yang, Q.; Chen, B. Carbon emissions and their drivers for a typical urban
economy from multiple perspectives: A case analysis for Beijing city. Appl. Energy 2018, 226, 1076–1086.
2. Liu, J.; Zheng, H.; Zhang, Y.; Zhou, T.; Zhao, J.; Li, J.; Liu, J.; Li, J. Comparative Investigation on the
Performance of Modified System Poles and Traditional System Poles Obtained from PDC Data for
Diagnosing the Ageing Condition of Transformer Polymer Insulation Materials. Polymers 2018, 10, 191.
3. Zhang, Y.; Liu, J.; Zheng, H.; Wei, H.; Liao, R.; Sciubba, E. Study on Quantitative Correlations between the
Ageing Condition of Transformer Cellulose Insulation and the Large Time Constant Obtained from the
Extended Debye Model. Energies 2017, 10, 1842.
Polymers 2018, 10, 1096 19 of 20

4. Liu, J.; Zheng, H.; Zhang, Y.; Wei, H.; and Liao, R. Grey Relational Analysis for Insulation Condition
Assessment of Power Transformers Based Upon Conventional Dielectric Response Measurement. Energies
2017, 10, 1526.
5. Borutzky, W. Bond Graph Modelling of Engineering Systems. Springer: New York, NY, USA, 2011; pp. 105–
135, 978-1-4419-9367-0.
6. Djeziri, M.A.; Ananou B.; Ouladsine M. Data driven and model based fault prognosis applied to a
mechatronic system. In Proceedings of Fourth International Conference on Power Engineering, Energy and
Electrical Drives. IEEE, Istanbul, Turkey, 13–17 May 2013.
7. Sun, H.-C.; Huang, Y.-C.; Huang, C.-M. A Review of Dissolved Gas Analysis in Power Transformers.
Energy Procedia 2012, 14, 1220–1225.
8. Sica, F.C.; Guimarães, F.G.; Duarte, R.d.O.; Reis, A.J.R. A cognitive system for fault prognosis in power
transformers. Electr. Power Syst. Res. 2015, 127, 109–117.
9. Bengtsson, C. Status and trends in transformer monitoring. IEEE Trans. Power Deliv. 1996, 11, 1379–1384.
10. Yang, M.-T.; Hu, L.-S. Intelligent fault types diagnostic system for dissolved gas analysis of oil-immersed
power transformer. IEEE Trans. Dielectr. Electr. Insul. 2013, 20, 2317–2324.
11. Singh, S.; Bandyopadhyay, M.N. Dissolved gas analysis technique for incipient fault diagnosis in power
transformers: A bibliographic survey. IEEE Electr. Insul. Mag. 2010, 26, 41–46.
12. Duval, M.; Pablo, A.D.; Atanasova-Hoehlein, I.; Grisaru, M. Significance and detection of very low degree
of polymerization of paper in transformers. IEEE Electr. Insul. Mag. 2017, 1, 31–38.
13. Peischl, S.; Walker, J.P.; Ryu, D.; Kerr, Y.H. Analysis of Data Acquisition Time on Soil Moisture Retrieval
from Multiangle L-Band Observations. IEEE Trans. Geosci. Remote 2017, 56, 966–971.
14. Unsworth, J.; Mitchell, F. Degradation of electrical insulating paper monitored with high performance
liquid chromatography. IEEE Trans. Electr. Insul. 1990, 25, 737–746.
15. Verma, H.C.; Baral, A.; Pradhan, A.K.; Chakravorti, S. A method to estimate activation energy of power
transformer insulation using time domain spectroscopy data. IEEE Trans. Dielectr. Electr. Insul. 2017, 24,
3245–3253.
16. Saha, T.K.; Purkait, P.; Muller, F. An attempt to correlate time &amp; frequency domain polarisation
measurements for the insulation diagnosis of power transformer. In Proceedings of Power Engineering
Soc. General Meeting, Denver, CO, USA, 6–10 June, 2004.
17. Bakar, N., A.; Abu-Siada, A.; and Islam, S. A review of dissolved gas analysis measurement and
interpretation techniques. IEEE Electr. Insul. Mag. 2014, 30, 39–49.
18. Gómez, N.A.; Wilhelm, H.M.; Santos, C.C.; Stocco, G.B. Dissolved gas analysis (DGA) of natural ester
insulating fluids with different chemical compositions. IEEE Trans. Dielectr. Electr. Insul. 2014, 21, 1071–
1078.
19. Rogers, R.R. IEEE and IEC Codes to Interpret Incipient Faults in Transformers, Using Gas in Oil Analysis.
IEEE Trans. Electr. Insul. 1978, EI-13, 349–354.
20. Duval, M.; Depabla, A. Interpretation of gas-in-oil analysis using new IEC publication 60599 and IEC TC
10 databases. IEEE Electr. Insul. Mag. 2001, 31–41.
21. Irungu, G.K.; Akumu, A.O. Munda, J.L. A new fault diagnostic technique in oil-filled electrical equipment;
the dual of Duval triangle. IEEE Trans. Dielectr. Electr. Insul. 2016, 23, 3405–3410.
22. Irungu, G.K.; Akumu, A.O.; Munda, J.L. Comparison of IEC 60599 gas ratios and an integrated fuzzy-
evidential reasoning approach in fault identification using dissolved gas analysis. In Proceedings of
International Universities Power Engineering Conference (UPEC), Coimbra, Portugal, 6–9 Sept 2016.
23. Barbosa, T.M.; Ferreira, J.G.; Finocchio, M.A.F.; Endo, W. Development of an Application Based on the
Duval Triangle Method. IEEE Latin Am. Trans. 2017, 15, 1439–1446.
24. Benmahamed, Y.; Teguar, M.; Boubakeur, A. Application of SVM and KNN to Duval Pentagon 1 for
transformer oil diagnosis. IEEE Trans. Dielectr. Electr. Insul. 2017, 24, 3443–3451.
25. Faiz, J.; Soleimani, M.; Dissolved gas analysis evaluation in electric power transformers using conventional
methods a review. IEEE Trans. Dielectr. Electr. Insul. 2017, 24, 1239–1248.
26. Islam, S.M.; Wu, T.; Ledwich, G. A novel fuzzy logic approach to transformer fault diagnosis. IEEE Trans.
Dielectr. Electr. Insul. 2000, 7, 177–186.
27. Miranda, V.; Castro, A.R.G. Improving the IEC table for transformer failure diagnosis with knowledge
extraction from neural networks. IEEE Trans. Power Deliv. 2005, 20, 2509–2516.
Polymers 2018, 10, 1096 20 of 20

28. Zheng, H.; Zhang, Y.; Liu, J.; Wei, H.; Zhao, J.; Liao, R. A novel model based on wavelet LS-SVM integrated
improved PSO algorithm for forecasting of dissolved gas contents in power transformers. Electr. Power Syst.
Res. 2018, 155, 196–205.
29. Zhang, Y.; Wei, H.; Liao, R.; Wang, Y.; Yang, L.; Yan, C. A New Support Vector Machine Model Based on
Improved Imperialist Competitive Algorithm for Fault Diagnosis of Oil-immersed Transformers. J. Electr.
Eng. Technol. 2017, 12, 830–839.
30. Dai, J.; Song, H.; Sheng, G.; Jiang, X. Dissolved gas analysis of insulating oil for power transformer fault
diagnosis with deep belief network. IEEE Trans. Dielectr. Electr. Insul. 2017, 24, 2828–2835.
31. Mirowski, P.; LeCun, Y. Statistical Machine Learning and Dissolved Gas Analysis: A Review. IEEE Trans.
Power Deliv. 2012, 27, 1791–1799.
32. Huang, Y.C. A new data mining approach to dissolved gas analysis of oil-insulated power apparatus. IEEE
Trans. Power Deliv. 2003, 18, 1257–1261.
33. Chen, W.; Pan, C.; Yun, Y.; Liu, Y. Wavelet Networks in Power Transformers Diagnosis Using Dissolved
Gas Analysis. IEEE Trans. Power Deliv. 2008, 24, 187–194.
34. Zhou, J.; Yang, Y.; Ding, S., X.; Zi, Y.; Wei, M. A Fault Detection and Health Monitoring Scheme for Ship
Propulsion Systems Using SVM Technique. IEEE Access 2018, 6, 16207–16215.
35. Zhang, Y.; Zheng, H.; Liu, J.; Zhao, J.; Sun, P. An Anomaly Identification Model for Wind Turbine State
Parameters. J. Clean. Prod. 2018, 195, 1214–1227.
36. Qin, L.; Wang, J.; Li, H.; Sun, Y.; Li, S. An Approach to Improve the Performance of Simulated Annealing
Algorithm Utilizing the Variable Universe Adaptive Fuzzy Logic System. IEEE Access 2017, 5, 18155–18165.
37. Xin, F.; Ni, S.; Li, H.; Zhou, X. General Regression Neural Network and Artificial-Bee-Colony Based General
Regression Neural Network Approaches to the Number of End-of-Life Vehicles in China. IEEE Access 2018,
6, 19278–19286.
38. Tang, W.H.; Goulermas, J.Y.; Wu, Q.H.; Richardson, Z.J.; Fitch, J. A Probabilistic Classifier for Transformer
Dissolved Gas Analysis with a Particle Swarm Optimizer. IEEE Trans. Power Deliv. 2008, 23, 751–759.
39. Kim, S., W.; Kim, S., J.; Seo, H.D.; Jung, J.R.; Yang, H.J.; Duval, M. New methods of DGA diagnosis using
IEC TC 10 and related databases Part 1: Application of gas-ratio combinations. IEEE Trans. Dielectr. Electr.
Insul. 2013, 20, 685–690.
40. Karaboga, D.; Akay, B. A survey: Algorithms simulating bee swarm intelligence. Artif. Intell. Rev. 2009, 31,
61.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).