Online Condition Assessment of Wind Turbine Based On
Integrated Fuzzy Theory and Evidence Theory
GUO Peng*, CHI Bing †
*North China Electric Power University, Bei Jing,China,102206
1572647494@qq.com
Keywords: wind turbines; condition assessment; evidence
theory; fuzzy theory.
Abstract
For the purpose of optimizing the maintenance strategy, the
wind turbine real-time condition needs to be assessed
accurately. Based on SCADA system data, this paper put
forward the wind turbine running condition assessment model
integrating the Fuzzy Theory with Evidential Theory. Firstly,
the index system of wind turbines running condition
assessment was constructed in this paper. The active curve of
temperature indicators was obtained under bin method, and
then the indicators were quantified under degradation degree
concept; Secondly, the wind turbine running condition
assessment model integrating the fuzzy theory with evidential
theory was proposed as a resolution to the fuzzy uncertainty
of wind turbines condition assessment indicators. In this
model, concept of fuzzy sets and membership functions of the
fuzzy theory were imported into the evidence theory to build
reasonable belief function assignment. Finally, the proposed
assessment model and method were proved to be correct and
effective by the practical operational results based on the
actual monitoring data of a 1.5MW WTGS within a certain
period of time.
1 Introduction
As a typical representative of new energy sources, wind
power is getting people's attention with the intensification of
energy crisis and the upgrading of human environmental
awareness. However, the operating environment of wind
turbine is harsh. The wind velocity is not controllable and the
external environment of wind turbine has a large temperature
difference. That harsh environment leads to the costs of
operation and maintenance of the wind turbine up to 10% to
15%[1]. Therefore, wind turbine failure could be avoided
effectively by monitoring and evaluating the unit timely and
accurately. In the meantime, it provides a reliable basis for the
state maintenance. It has an important practical significance
for wind turbine operation.
Large-scale grid-connected wind turbines start relatively late
in China. Test Data of wind turbine unit is relative lack, such
as the pre-test data during manufacturing or operation, etc. In
recent years, most studies focus on an additional sensors or
special online monitoring device. Assess the state of the
subsystem of wind turbine such as generator, gearbox, pitch
system and drive chain[2-4]. However, this state assessment
method is only directed against a single component. It does
not consider the coupling and interaction between the various
components or subsystems so it is not possible to assess the
operational status of the unit from the overall perspective [5].
Therefore, it is necessary to find an effective way to do the
wind turbine operating state assessment by using the SCADA
system data instead of unduly relying on other data.
At present, there have been some research developed several
wind turbine state assessment models based on neural
networks, probability and statistics, matter element analysis
or fuzzy comprehensive evaluation, etc. The basic idea is
divided into two ways. One way is to extract fault
characteristics by digging the related fault information from
SCADA historical data[6,7]. The second way is to establish a
healthy running wind turbine unit model by handling
historical SCADA system data. The former way requires a
great amount of fault data supportive so it is hard to achieve
for those units whose running time is short. The latter way
could avoid the above shortcomings. But if using intelligent
algorithms such as neural networks, it is short for training
samples as the lacking of studies on the state assessment of
the overall operation wind turbine in the existing literature.
Based on the above characteristics, this paper presents a wind
turbine state assessment model based on fuzzy theory and
evidential theory.
2 The index system established based on
SCADA data
Wind Turbine Generator System (WTGS) is a complex
system. It can be divided into many subsystems and
components in terms of different function and structure. Then,
evaluation index system can be established for each part. It is
shown in Figure 1.
3 Calculate of the degradation degree
3.1 Monitoring data processing
The indicators Xijk in FIG.1 are divided into two categories.
The first one is the type of the smaller the better indicators,
taking temperature as a representative, which is expressed by
g(1)Xijk. The second one is the type of intermediate indicators.
It is other indicators except temperature, which is expressed
with g(2)Xijk . It should be noted that the index of environment
temperature is included in the second category indicators, and
the index of active power is included in the first category
indicators.
Grid frequency
Grid factors
Reactive power
Active power
Fig 3 Curve of gearbox oil temperature
Phase current
Environmental
factors
Temp. of environment
Control cabinet
Temp. of IGBT
Wind speed
Temp. of control cabinet
Therefore, the polynomial function of wind speed vs gearbox
bearings temperature can be described with the following
expression:

54. 6,

3 5
2 4
3
1. 6  10   6. 78  10   1. 0873

( 1) '
2
gXi j (  )  8. 1015  25. 7974  83. 7263,
2. 9  103 3  0. 1438 2  2. 2891

75. 8789,
3
3    10

( 1)
10
Where, g (  ) is the temperature of calculated gearbox
bearing; ω is the wind speed.
( 1) '
Xi j
Cabin vibration acceleration
Cabin
Framework for condition assessment of WTG
Phase voltage
Cabin location
Gearbox
Temp. of gearbox oil
Temp. of gearbox bearing2
Temp. of gearbox bearing1
Generator
Temp. of generator winding
Generator rotational speed
Temp. of generator bearing
Figure1 Wind turbine index system of operation data
Bin method is used for reference to draw the curve of
indicators which belongs to the first kind. Then each index’s
fitting function changing with wind speed is obtained by
polynomial curve fitting. It is illustrated by the case of
gearbox oil temperature and gearbox bearing temperature in
Figure 2, 3.
3.2 Calculate of the degradation degree
The temperature deviation between actual monitoring value
and normal temperature can be used as basis for judging
whether failure in one certain wind speed. The deviation
degree can be expressed by formula (2):
gX
ij
 gX  gX
ij
'
( 2)
ij
The concept of degradation degree is introduced to
characterize the relative degradation between normal running
state and fault condition for a wind turbine. Its range is from 0
to 1. Different state evaluation indicators values reflect the
degree of deterioration. The closer to 1 means the more
serious degradation. The degradation degree of assessment
indicators for the first category is represented by the formula
(3):
0

 g(X1)  
( 1)
ij
m( gX )  
ij
  
1

Where, m
( gX
( 1)
ij

gX
ij
  gX
ij
gX
ij
 
( 3)

) is the degradation degree of indicators
which belongs to the first category, αis the ideal value of the
indicator, β is the limit value of the index.
The indicators of the second category, taking engine room
location, environment temperature, engine vibration
acceleration as example, is calculated by formula (4) as
follows:
Fig 2 Curve of gearbox bearing temperature
1
gX
1
ijk

  g( 2)
Xi j
 2
1  g Xi j
2
  2  1

m( g(X2) )  0
 2  g Xi j  2
( 4)
ij
 ( 2)
 g Xi j  2
2
g x  1

ij
 1  2
1
gX
1

ij
Where, mg
( (X2) ) is the degradation degree of indicators which
ij
belong to the second category, α1 is the upper limit value of
the index, β1 is the lower limit value of the index; α2 , β2 are
permitted value under normal working conditions. They’re
determined by wind farm’s inspection records, fault manual.
4 WTGS online assessment model based on
Fuzzy Theory and Evidence Theory
The assessment indicators are divided into six sub-body of
evidence according to the indicators layer established in
Section 1. They are generator (sub-evidence1), gearbox (subevidence2), cabin (sub-evidence3), control cabinet (subevidence4), power factor (sub- evidence5) and environmental
factors (sub-evidence6). Each sub-body of evidence is
constituted by a number of evaluation indicators (FIG. 1).
The steps of establishing WTGS online assessment model
based on Fuzzy Theory and Evidence Theory are as follows:
1) to get the actual value of each evaluating index and
calculate the degree of degradation; 2) to calculate the
membership of each level status for sub-body of evidence; 3)
Evidence Theory is used to testify each son-body of evidence.
Then an overall assessment of the wind turbine is obtained.
The flow chart of WTGS Assessment Model is shown in
Figure 4.
g>0.9
Y
ridge is selected in this paper to determine the level of
evaluation indicators. The membership function is defined as
follows:

1

 
a  a2 
1 1
v 1( g )    si n 
(g  1
)
2
 a2  a1

2 2

0

1
 
a  a2 
1
(g  1
)
  si n 
2
2
 a2  a1

2

v 2( g )  
1

a  a4 
 1  1 si n  
(g  3
)

2 2
a

a
2
3
 4


1

1
  si n 
2
 a4
2

v 3( g )  

 1  1 si n 

2 2
 a6

g  a1
g  a2
a1
g
a2
a1
g  a2
a2
g  a3
a3
g  a4
a3
g  a4
1
a4
g  a5
a  a6 
(g  5
)
 a5
2

a5
g  a6

 a3
(g 
a3  a4 
)
2



0


a  a6 
1

1
v 4( g )    si n 
(g  5
)
2
2
a

a
2
5
 6



1

( 5)
( 6)
( 7)
g  a5
g  a6
a5
g
( 8)
a6
In formula (5)-(8), g is the shorthand of degradation degree,
v1 (g) ~ v4 (g) are membership of evaluation index X r for levels
of l1 ~l4 , a1 ~a 6 are the boundary values between the different
status levels. The level of wind turbines operation is
represented as L={l1 l2 l3 l4 }={ Good Qualified Attention
Serious}. Since there is no a priori knowledge, so the
membership degree boundary for different states adopt
differentiation processing method in this article. The range of
state l1 ~l4 are from 0~0.3, 0.1~0.6, 0.4~0.9, 0.7~1, so a1~a6
take values of 1/10, 3/10, 4/10, 6/10, 7/10 and 9/10, as shown
in Fig5.
1
0.5
Evaluation Result
is “Serious”
N
Monito
ring
Data
Deterioratio
n Degree
Weight
Each Index
Membership
Confidence
Coefficient
Membership of
Each Evidence
Corre
cted
Credit
Assign
ment
Values
Corre
cted
Credit
Assign
ment
Values
0
Assess
ment
Results
Fig 4 Flow chart of WTGS Assessment Model
4.1 Membership degree of indicators
In this paper, Fuzzy Evaluation Method is used to determine
the status of each index. Compared with other method, Fuzzy
Evaluation Method can deal with state evaluation of boundary
treatment hardening too much. Fuzzy Evaluation Method is
used to overcome the problem that. According to the theory
of fuzzy mathematics, the information of different status
levels can be described by the membership functions. The
membership function which combined half ladder with half
0
0.2
0.4
0.6
0.8
1
Fig 5 Membership degree of valuation indicators
4.2 Membership degree of sub-evidences
By formula (5) ~ (8), it can determined evaluation index
Xr for the membership of four different state levels v1 (g)
~ v4 (g). The mathematical expression of sub-evidence’s
membership is shown as follows:
v i ( Ej ) 
Where, v i ( Ej
m
v ( g
r 1
i
r
)( x r )
( 9)
) is membership degree of state level i for
sub-evidence j ; v i ( g r ) is membership degree of state level
i
about assessment indicator for sub-evidence j ; ( x r ) is
the weight of evaluation indicators 𝑋𝑟 .
The Experts-decision Method is used to determine the weight
of indicators. WTGS states are divided into four levels.
Therefore, the value of i is from 1 to 4. In the same way, there
are six sub-evidences in the assessment model. Therefore, the
value of j is from 1 to 6. “m” is the amount of indicators in six
sub-evidences. We can obtain that the values of m is 3, 3, 2,
2, 2, 5from Figure 1. Weights are obtained by expert scoring.
Weights of evidence are shown in Table 1.
4.3 Evidence Synthesis Theory
Evidence Synthesis Theory is also called DS Theory. It is a
kind of uncertainty reasoning and processing method. The
merger of evidences and the update of trust function are the
basis of Evidence Synthesis Theory. Its uncertainty is
described by the concept of identifying the framework, basic
trust, trust function, true degree, and the reliability interval.
4.3.1 Basic definition
DS evidence theory is an extension method of Bayes, it can
make the information clear in the case of the lack of
information. It has stronger decision-making process
capability.
DS evidence theory define the frame of discernment Θ. All
the possible sets of Θ can be described by power-set 2Θ . If
polar function m: 2Θ → [0, 1], satisfy m(f) = 0 and
∑A⊆Θ m(A) = 1 , function m is called the basic probability
assignment on Θ. ∀A ⊆ Θ, m(A) is called Mass function or
basic credibility of A .
For two evidences, the combine rule of Dempster is shown as
follows:

0,


[ m1 m2 ] ( A)    m1( Ai )m2( Bj )
 Ai  Bj  A
,


1 K
A  f;
( 10)
A  f .
4.3.2 Evidence synthesis
The concept of confidence degree α is introduced to correct
the credit assignment considering that different importance of
sub-evidences.
m'( A)   mA
( )
 ,
m( )  1  
( 11)
Where, m( A) is belief function value with corrected; m( )
is reliability allocation of uncertain evidence.
'
,