ABSTRACT

The multi-parameter comprehensive evaluation method of gas

turbine can accurately grasp the state of engine health. Eight

evaluation indicators were chosen from the condition of engine gas

path degradation, the combustion system and the whole machine

vibration. Aimed at the uncertainty of data information, the

objective attribute weights were gotten based on the method of the

combination of fuzzy clustering and information entropy by

calculating the mutual information. In view of the equilibrium of

data, another objective weights were gotten using the entropy

weight method. Then the linear weighted sum method of the two

was used to get the final objective weights of indicators. Subjective

weights were obtained by analytic hierarchy process. Integrating

the subjective and objective weights, multiplication combination

method was used to determine the final weights. The multi-attribute

comprehensive evaluation of gas turbine health status was carried

out combined with a 2,000 hours test. Results show that the method

can integrate the advantages of objective and subjective weighting

methods, evaluation results are in line with the practical experience,

which means it is a feasible way to the gas turbine condition

assessment and maintenance decision.

INTRODUCTION

Safe, reliable, and economical gas turbine operation is of great

concern to the user and manager. Increasing attention is being paid

to relative status monitoring and condition-based maintenance. In

the same operation condition, the change trend of engine

performance parameters can objectively reflect performance

deterioration. Therefore, evaluating the state according to

monitoring information can predict the rate of performance

deterioration and provide a scientific basis for maintenance

decisions. According to the state monitoring information, the

performance of a gas turbine can be determined objectively and

accurately, which is the fundamental guarantee of high safety and

reliability.

Gas turbine performance evaluation indicators include exhaust

gas temperature, thermocouple dispersion, vibration value and so

on. People are used to relying on a single parameter to evaluate an

engine’s performance. This is simple, and it provides some basis for

gas-turbine maintenance decisions. But as performance parameters

often have complex interrelationships, only monitoring one index

cannot fully reflect the performance of a gas turbine, and it can lead

to the wrong decision. A multi-parameter comprehensive evaluation

method is an effective solution to this problem.

There are two kinds of approach to determine the weight

coefficient of a multi-parameter comprehensive assessment:

subjective and objective [1]. The subjective approach is based on

expert prior information on the weight of each attribute to make

evaluations and comparisons. Common approaches of this type

include the analytic hierarchy process (AHP) and Delphi method

[2]. Although this method is quite explicable, there is an obvious

subjective randomness. The objective approach determines the

weight coefficient from objective information reflected in attribute

indices. Examples include the common mean square error method,

the maximum deviation method, and the entropy method [3-4]. This

kind of method strengthens objectivity when determining the

weight, but sometimes the results contradict practical experience,

and they may not provide a reasonable explanation.

Fuzzy mathematics has been proved to be an effective method

to solve uncertain decision-making problems [4]. And many

scholars have applied fuzzy logic to gas turbine fault diagnosis [7-

8]. The advantage of fuzzy mathematics in dealing with uncertain

knowledge is that there is no loss of effective information. But it

cannot determine the importance of various factors, and it needs a

priori information to judge the relative weight. In information

theory, the mutual information derived from entropy need not

provide prior information and can determine the importance of

various factors. Combining these two characteristics, Huang [9]

proposed a multi-factor weight-allocation method based on

objective information on entropy. Using this method, Zhang [10]

calculated the comprehensive weights to analyze the performance

of civil aviation engines.

In this paper, on the basis of above study, gas turbine health

assessment indicators will be chosen from the condition of engine

gas path degradation, the combustion system and the whole

machine vibration, and the comprehensive assessment method of

gas turbine health status integrating the advantages of subjective

and objective weighting will be proposed. Aimed at the uncertainty

and equilibrium of data, two objective attribute weights will be

gotten based on the method of the combination of fuzzy clustering

and information entropy and the entropy weight method. The final

objective weights of indicators will be obtained by the linear

weighted method of the two. Subjective weights will be obtained

by analytic hierarchy process (AHP). Multiplication combination

method integrating the subjective and objective weights will be

used to determine the final weights. The evaluation of gas turbine

health status will be carried out combined with an example.

Comprehensive assessment of gas turbine health condition

based on combination weighting of subjective and objective

Fang You-long1,2,Liu Dong-feng1,2,Liu Yong-bao2 and Yu Liang-wu2

1 Unit NO.91663, Qingdao 266012,CHINA 2 College of Power Engineering, Naval University of Engineering, Wuhan 430033, CHINA

International Journal of Gas Turbine, Propulsion and Power Systems April 2020, Volume 11, Number 2

Copyright © 2020 Gas Turbine Society of Japan

Manuscript Received on May 16, 2019 Review Completed on April 1, 2020

56

CHOICE OF GAS TURBINE HEALTH STATUS

EVALUATION INDICATORS

Gas turbine health status evaluation index selection should

satisfy the principle of the comprehensive, independence,

comparability and operability, etc. For this reason, this paper

choices evaluation index from the aspects of gas path degradation

condition, the combustion system state and the whole machine

vibration state. Take a certain type of marine three-shaft gas turbine

as an example. The schematic diagram is shown in figure 1.In figure

1 and paper below, LC, HC, B, HT, LT, PT respectively represent

low pressure compressor, high pressure compressor, combustion

chamber, high pressure turbine, low pressure turbine and power

turbine. Each subscript number of letters in this paper represent

corresponding section noted in figure 1.

4321 5 6 70

LC HC

B

HT LT PT

0

Fig. 1: Schematic representation of a three-shaft gas turbine

Gas Path Degradation Condition Indicators of Whole Engine

The engine gas path degradation state assessment indexes can be

made of heat loss index [11-12], power deficit index [11], exhaust

gas temperature margin, thermal efficiency ratio [13].

The heat loss index hlI is defined as the ratio of the

6T rise with

respect to the design point:

hl 6 6 exp 6d/I T T T ， , (1)

where 6T is measured value of low pressure turbine outlet

temperature, 6 expT ，

is expectancy obtained by the health gas turbine

model in the same environment parameters and control conditions,

and 6dT is design point temperature of rated condition.

The power deficit index pdI is defined as the ratio of the power

deficiency to the design point power [11]:

pd exp d/I Ne Ne Ne , (2)

where Ne is the actual output power, expNe is the theoretical output

power obtained by measured value 6T ,

dNe is the designed point

power of rated condition.

The thermal efficiency ratio teR is defined [13] as

te r mR , (3)

where r is thermal efficiency obtained by measured values, m

is the thermal efficiency predicted by the model at the same running

conditions.

The exhaust gas temperature margin egtM of gas generator is

defined as

egt 6,thres 6

aM T T , (4)

where 6,thresT is the threshold of

6T ,0= 288.15T ,

0T is ambient

temperature, and a is an experiential index to eliminate the

influence of environment temperature described in [14].

Gas Path Degradation Condition Indicators of Components

Gas path degradation condition of components can be

characterized by degradation factors (defined as translation of

characteristic curves caused by degradation) [15], such as low

pressure compressor flow degradation factor LCG , high pressure

compressor flow degradation factor HCG , high pressure turbine

efficiency degradation factor HT , low pressure turbine

efficiency degradation factor LT and so on. The degradation

factors can be solved by the method of linear or nonlinear Kalman

filter.

Combustion System Status Indicators

There are 16 thermocouples temperature sensors along the

circumference between the low-pressure turbine and power turbine

in this type engine. The 1 # thermocouple temperature dispersion

1S is defined as the difference between the highest and the lowest

thermocouple temperature reading; the 2 # dispersion 2S is defined

as the difference between the highest with the second lowest

reading; and the 3 # dispersion 3S the difference between highest

and the third lowest reading. To eliminate the influence of

environment temperature, corrected dispersion is defined as

c = aS S , (5)

where 0= 288.15T , a is the same as Eq.(4). Thermocouple

temperature dispersions reflect comprehensively the condition of

the combustion chamber, fuel supply system and high temperature

gas path.

Vibration State Indicators

The vibration acceleration sensors are set at the case of LC and

HC and PT parts of the gas turbine. The vibration severity sV is

defined as the root mean square value of LC vibration velocity

effective value lcv , HC vibration velocity effective value hcv and

power turbine vibration velocity effective value ptv , i.e.,

2 2 2

s lc hc pt 3V v v v . Select the vibration intensity to

characterize the gas turbine vibration condition.

WEIGHT ASSIGNMENT METHOD

Objective Weight Assignment Method Based on Information

Entropy and Fuzzy Clustering

In this method, objective weights for each indicator are assigned

combined with fuzzy clustering analysis and relative importance in

the principle of rough set theory. Let’s clear a few concepts first.

(1) Information entropy. In the probabilistic approximation

space , ,U X P , 1 2, , , nX X X X is a classification exported

from the domain of discourse (i.e., the equivalence relation), and

iP X is the probability in approximate space (that is the ratio of

the cardinalities between each equivalent classification set and the

domain). Then the uncertainty of the system can be represented by

the information entropy, i.e.,

2

1

logn

i i

i

H X P X P X

. (6)

(2) Conditional entropy. If 1 2, , , mY Y Y Y is another

classification exported from the domain of discourse, the

uncertainty of X when is obtained is the conditional entropy, Y

JGPP Vol. 11, No. 2

57

2

1 1

| | log |m n

i j i j i

i j

H X Y P Y P X Y P X Y

,

(7)

where |j i

j i

i

X YP X Y

Y

, and denotes the number of

elements in the set , 1,2, ,i m , .

(3) Mutual information. The mutual information between X

and Y is defined as

; | |I X Y H X H X Y H Y H Y X . (8)

It denotes the information of X obtained when Y is observed.

The method of multi-attribute weight distribution based on

information entropy and fuzzy clustering is as follows.

(1) Determine the decision matrix. Identify samples and factor

indicators that must be addressed. Let 1 2, , , nX X X X be a

set of n samples to be processed, and represent each sample by m

indicators 1 2, , ,j j j mjX x x x . Then the samples required to be

clustered can be represented by the decision matrix ij m nx

.

(2) Data normalization processing. The indices of a decision

matrix usually relate to efficiency or cost type. The dimensions of

indicators may differ, and indicators often vary in magnitude. To

avoid the phenomenon that large numbers cover small numbers, the

data must first be mapped into a certain range before clustering,

which is called normalization processing. The normalized

processing method is as follow [16]: for the cost type indicators (the

smaller the better), 1

1 01

j ij

ij

j j

z xr

z z

, (9)

for the efficiency type indicators (the bigger the better), 0

1 01

ij j

ij

j j

x zr

z z

, (10)

where 1

1maxj ij

i mz x

and 0

1minj ij

i mz x

. To avoid an element

taking a value of zero after normalization, an equilibrium factor

in the range [0,1] is introduced, and is set to 0.9 in this paper.

After normalization, the decision matrix becomes a fuzzy matrix,

.

(3) Construct fuzzy similarity matrix. Using the maximum

minimum method, the fuzzy matrix R is turned into the fuzzy

similarity matrix :

1 1

m m

ij ik jk ik jk

k k

s r r r r

. (11)

(4) Construct fuzzy equivalent matrix. The transitive closure

t S of fuzzy similarity matrix S is solved by the equivalent

closure method [17], whose result is the fuzzy equivalent matrix

E .

(5) Classification. The fuzzy equivalent matrix is truncated by

the appropriate threshold k , and the cut set matrix is obtained.

The equivalent classifications can be obtained from the cut set

matrix [17], and these are labeled as 1,2, ,k

C k p . It does

not take into account that the total is one class and each element is

one class.

After one factor is deleted from all the indicators, repeat steps

(3)-(5). The equivalent classifications corresponding to each

threshold k are labeled as .

(6) Search for mutual information. Determine the mutual

information at each threshold after removing the various factors.

When the classification is changed from the set C to the set D as a

certain factor is removed, the influence on the positive domain of

the object classification can be represented by the mutual

information at each threshold, i.e.,

; |k

I C D H C H C D . (12)

Eq.(12) expresses information on set C when set D is observed.

The smaller ;k

I C D is, the more important the removed factor

is. From the meaning of mutual information, after deleting one

factor, if you can get more information from the initial classification,

then the removed attribute contains less information for

classification. Conversely, if you get less information from the

initial classification, the information contained in the deleted

attribute is greater. Therefore, the amount of mutual information

obtained from the initial classification after deleting a factor is

inversely proportional to the amount of information contained in

the deleted factor. So, the reciprocal of mutual information can be

used to indicate the relative amount of information contained in the

deleted factor.

(7) Solve index information. The weighted reciprocal of mutual

information at a different threshold is used to represent the index

information contained in the deleted factor, i.e.,

1

1

;k

p

i k

k

MI C D

. (13)

(8) Distribute index weights. The index information is

normalized to obtain the weight of each index, i.e.,

1

m

iIEFC i i

i

w M M

. (14)

Objective Weight Assignment Based on Entropy Weight

Method

The greater an indicator fluctuation is, the greater amount of

information the indicator provides for comprehensive evaluation.

Entropy weight method (EW) is based on each index fluctuation

degree, using the relative strength entropy of the index value to

calculate the weight of each index. The meaning of the relative

strength entropy is as follows: take the proportion of the j th

indicator of the sample iX as the probability in information

entropy formula, i.e.,

1

m

ij ij ij

i

p r r

. If the j th index values of

the samples are the same, i.e., 1 2j j mjr r r , 1ijp m ,

it means the data are the most equalizing, and this index provides

the least amount of information. So its weight is the least. The

relative strength entropy of j th index is defined as

1

1

1

ln1

ln1 1 ln

ln

m

ij ij mi

j ij ijmi

i

p p

e p pm

m m

. (15)

As 0

lim ln 0x

x x

, lnij ijp p is set 0 when 0ijp . The most

value of je is 1. 1 je denotes the numerical difference of j th

indicator. The bigger the numerical difference is, the bigger the

weight is. The method process is as follow:

(1) Normalize the data of decision matrix, and we get fuzzy

decision matrix .

(2) Calculate the proportion of the j th indicator of samples, i.e.,

1

m

ij ij ij

i

p r r

.

(3) Calculate the relative strength entropy je of j th index.

1,2, ,j n

ij m nR r

S

1,2, ,k

D k p

/U C

ij m nR r

JGPP Vol. 11, No. 2

58

(4) Calculate the weight

1

1 j

jH n

j

j

ew

n e

.

(16)

Determine Ultimate Objective Weights by Weighted Sum

Method

We get two kinds of objective weights from the uncertainty and

the equilibrium of data above. As the two have the compensatory,

we could obtain comprehensive objective weights by weighted sum

method, i.e.,

1jOb jIEFC jHw w w , (17)

where 0,1 , and 1,2, ,j n . We set 0.5 in this

paper.

Determine Final Weights by Multiplication Combination

Method

Objective weighting method does not consider the importance

of the index itself, and the evaluation results are lack of convincing,

while subjective weighting method (take AHP as an example) is

difficult to avoid the influence of subjective randomness on the

evaluation results. To make up for the defect of the two methods,

we can combine the two kinds of weights. There are addition and

multiplication in the combination weighting methods. Addition

combination applies only on the occasions that there is linear

compensability between indexes, while multiplication combination

applies also when there is no compensability between indexes. So

the multiplication combination method is adopted, i.e.,

1

jOb jAHP

j n

jOb jAHP

j

w ww

w w

,

(18)

where jObw is objective weight, and jAHPw is subjective weight

obtained by AHP. Limited by space, the process of AHP is not

expounded in this paper.

The fuzzy decision matrix R multiplied by the index weight

vector, the utility value of each sample can be obtained, i.e.,

Y R W , (19)

where jW w , and 1,2, ,j n .

INSTANCE ANALYSIS

A reliability test for the three-shaft marine gas turbine was

carried out over 2,000 hours, during which three off-line cleanings

were conducted. There are 16 thermocouples along the

circumference between the low-pressure turbine and power turbine,

so as to monitor the combustion chamber flame indirectly.

Monitoring parameters include ambient temperature, atmospheric

pressure,2P ,

3P ,6P ,

6T ,7T , low pressure shaft speed, high pressure shaft

speed, power turbine speed, power Ne and fuel flow rate, etc.

Using gas turbine health state model [12] and test data, we get the

indicators of the thermocouple dispersions1CS ,

2CS ,3CS , the

vibration intensity sV , heat loss index

hlI , power deficit index

pdI , exhaust temperature margin of gas generator egtM , thermal

efficiency ratio teR , low pressure compressor flow degradation

factor LCG , high pressure compressor flow degradation factor

HCG , high pressure turbine efficiency degradation factor HT

and low pressure turbine efficiency degradation factor LT at

rated working conditions, as shown in figures 2-5.

Fig.2 Variation trend of corrected thermocouple

dispersion

Fig.3 Variation trend of vibration severity

(a) Heat loss index

(b) Power deficit index

0 500 1000 1500 200020

30

40

50

60

70

80

90

100

working hours/h

corr

ecte

d t

her

mo

cou

ple

dis

per

sio

n/K

S1c

S2c

S3c

0 500 1000 1500 20002

3

4

5

6

7

8

9

10

working hours/h

Vs/m

m/s

original data

linear regression data

0 500 1000 1500 20000.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

working hours/h

I hl

original data

exponential smoothing data

linear regression data

0 500 1000 1500 20000

0.02

0.04

0.06

0.08

0.1

working hours/h

I pd

original data

exponential smoothing data

linear regression data

JGPP Vol. 11, No. 2

59

(c) Exhaust gas temperature margin

(d) Thermal efficiency ratio

Fig.4 Variation trend of overall engine performance

degradation indexes

(a) Flow capacity degradation factors of low pressure

compressor

(b) Flow capacity degradation factors of high pressure

compressor

(c) Efficiency degradation factors of high pressure turbine

(d) Efficiency degradation factors of low pressure turbine

Fig.5 Variation trend of degradation indexes of gas path

components

The mean indicators data of the rated working conditions during

the eight periods in the experiment are selected. Time periods are

shown in table 1.

Table 1: Time periods

NO. Periods (h) remarks

Ⅰ 0-25 initial run

Ⅱ 576-595 before 1st cleaning

Ⅲ 625-650 after 1st cleaning

Ⅳ 960-986 before 2nd cleaning

Ⅴ 995-1,002 after 2nd cleaning

Ⅵ 1,268-1,275 before 3rd cleaning

Ⅶ 1,348-1,355 after 3rd cleaning

Ⅷ 1,993-2,000 ending

The decision matrix is

71.5 54.4 36.2 5.84 0.06 0.04 136 0.97 0.009 0.010 0.005 0.010

88.4 46.2 39.9 5.49 0.08 0.05 101 0.96 0.019 0.016 0.004 0.130

59.7 55.7 53.1 7.34 0.04 0.02 127 0.98 0.016 0.012 0.021 0.114

50.3 44.7 32.6 6.87 0.06 0.04 110 0.9=

7 0.045X

0.053 0.013 0.125

64.9 64.4 53.3 6.48 0.05 0.05 120 0.96 0.016 0.026 0.011 0.105

76.8 50.4 46.4 5.90 0.08 0.06 102 0.96 0.049 0.040 0.010 0.094

47.8 38.7 35.6 4.18 0.06 0.03 120 0.98 0.037 0.031 0.017 0.109

45.8 42.5 40.3 3.91 0.

06 0.04 102 0.97 0.054 0.048 0.053 0.140

.

The front six columns are cost type indicators, and the back six

columns are efficiency type indicators, so they are normalized

according to Eq.(9) and (10) separately, and the fuzzy decision

matrix is

0 500 1000 1500 200080

90

100

110

120

130

140

150

working hours/h

Megt/K

original data

exponential smoothing data

linear regression data

0 500 1000 1500 20000.94

0.96

0.98

1

1.02

working hours/h

Rte

original data

exponential smoothing data

linear regression data

JGPP Vol. 11, No. 2

60

0.46 0.45 0.85 0.49 0.54 0.55 1.00 0.54 1.00 1.00 0.80 1.00

0.10 0.74 0.68 0.59 0.10 0.17 0.10 0.17 0.59 0.63 0.79 0.17

0.71 0.40 0.11 0.10 1.00 1.00 0.77 1.00 0.65 0.69 1.00 0.28

0.90 0.79 1.00 0.22 0.50 0.65 0.33 0.65 0.22 0.10 0.58 0.20

0.60 0.R

10 0.10 0.33 0.91 0.16 0.59 0.15 0.64 0.49 0.60 0.34

0.35 0.59 0.40 0.48 0.18 0.10 0.11 0.10 0.16 0.29 0.62 0.42

0.96 1.00 0.87 0.93 0.56 0.96 0.58 0.96 0.34 0.41 0.54 0.31

1.00 0.87 0.67 1.00 0.45 0.58 0.12 0.61 0.10 0.17 0.10 0.10

.

The similarity matrix is obtained from Eq.(11), and is 1.00 0.49 0.56 0.51 0.49 0.42 0.55 0.41

0.49 1.00 0.38 0.44 0.44 0.59 0.45 0.41

0.56 0.38 1.00 0.49 0.59 0.32 0.58 0.36

0.51 0.44 0.49 1.00 0.41 0.45 0.70 0.66

0.49 0.44 0.59 0.41 1.00 0.46 0.45 0.30

0.42 0.59 0.32 0.45 0.46 1.00 0.42 0.41

0.55 0.

S

45 0.58 0.70 0.45 0.42 1.00 0.66

0.41 0.41 0.36 0.66 0.30 0.41 0.66 1.00

.

The corresponding fuzzy equivalence matrix is calculated by the

equivalent closure method, and is 1.00 0.49 0.56 0.56 0.56 0.49 0.56 0.56

0.49 1.00 0.49 0.49 0.49 0.59 0.49 0.49

0.56 0.49 1.00 0.58 0.59 0.49 0.58 0.58

0.56 0.49 0.58 1.00 0.58 0.49 0.70 0.66

0.56 0.49 0.59 0.58 1.00 0.49 0.58 0.58

0.49 0.59 0.49 0.49 0.49 1.00 0.49 0.49

0.56 0.

E

49 0.58 0.70 0.58 0.49 1.00 0.66

0.56 0.49 0.58 0.66 0.58 0.49 0.66 1.00

.

The classification of the fuzzy equivalent matrix can be

determined at different thresholds as follows:

If 0.56 , then the samples are divided into two classes:

1,3,4,5,7,8 , 2,6 ;

if 0.58 , then they are divided into three classes: 1 , 2,6 ,

3,4,5,7,8 ;

if 0.59 , then they are divided into four classes: 1 , 2,6 ,

3,5 , 4,7,8 ;

if 0.66 , then they are divided into five classes: 1 , 2 , 3 ,

4,7,8 , 5 , 6 ;

if 0.70 , then they are divided into six classes: 1 , 2 , 3 ,

4,7 , 5 , 6 , 8 .

In the same way, the clustering of the fuzzy equivalent matrix is

as follows when the first factor, 1CS , is deleted:

If 0.56 , then the samples are divided into three classes: 1 ,

2,6 , 3,4,5,7,8 ;

if 0.58 , then they are divided into five classes: 1 , 2,6 ,

3,5 , 4,7,8 ;

if 0.59 , then they are divided into five classes: 1 , 2,6 ,

3,5 , 4,7,8 ;

if 0.66 , then they are divided into six classes: 1 , 2 , 3 ,

4,7 , 5 , 6 , 8 ;

if 0.70 , then they are divided into seven classes: 1 , 2 , 3 ,

4 , 5 , 6 , 7 , 8 .

The initial information entropy of the system H C is 0.8113

when 0.56 , according to Eq.(6). The conditional entropy

1|H C D is 0 according to Eq.(7) when the parameter 1CS is

deleted at the same threshold. The mutual information at the same

threshold is 0.56 1, 0.8113I C D , according to Eq.(12). Similarly,

0.58 1, 1.2988I C D ， 0.59 1, 1.9056I C D ， 0.66 1, 2.4056I C D ，

0.7 1, 2.75I C D . The information for index 1 (i.e., 1CS ) from

Eq.(13) is 1 1.9802M .

Repeating the process above, we get 2 1.9802M ,

3 2.4748M , 4 1.9802M ,

5 1.9802M ,6 1.9802M ,

7 1.9802M ,8 1.9802M ,

9 1.9802M ,10 1.9802M ,

11 1.9802M and 12 2.0873M . The weight distribution of

each index is gotten by Eq.(14).

Objective weights obtained by the method of information

entropy and fuzzy clustering (IEFC),objective weights by entropy

weight method (EW), ultimate objective weights by weighted sum

method (Ob), subjective weights by AHP and the final weights by

multiplication combination method (Com) are all shown in Table 2.

The utility values and sorts of engine health conditions during 8

periods obtained the single and comprehensive assessment methods

are shown in table 3 (A represents utility value, B represents sort).

The final utility values of the comprehensive evaluation based on

multiplication combination method are

0.82,0.28,0.71,0.40,0.53,0.21,0.61,0.34combY .

Table 2: Weight distribution

IEFC EW Ob AHP Comb

1cS 0.081 0.091 0.071 0.075 0.061

2cS 0.081 0.056 0.067 0.033 0.025

3cS 0.102 0.056 0.094 0.014 0.015

sV 0.081 0.066 0.080 0.057 0.052

hlI 0.081 0.079 0.078 0.129 0.115

pdI 0.081 0.077 0.091 0.070 0.073

egtM 0.081 0.078 0.101 0.283 0.326

teR 0.081 0.078 0.092 0.040 0.043

LCG 0.081 0.122 0.087 0.140 0.139

HCG 0.081 0.118 0.082 0.080 0.074

HT 0.081 0.078 0.063 0.022 0.016

LT 0.086 0.100 0.094 0.056 0.060

Table 3: Utility values and sorts of engine health conditions during

8 periods

IEFC EW Ob AHP Comb

A B A B A B A B A B

Ⅰ 0.73 1 0.75 1 0.74 1 0.80 1 0.82 1

Ⅱ 0.41 7 0.36 7 0.39 7 0.29 7 0.28 7

Ⅲ 0.63 3 0.64 3 0.64 3 0.71 2 0.71 2

Ⅳ 0.52 4 0.49 4 0.50 4 0.41 5 0.40 5

Ⅴ 0.41 6 0.41 6 0.41 6 0.53 4 0.53 4

Ⅵ 0.32 8 0.28 8 0.30 8 0.23 8 0.21 8

Ⅶ 0.70 2 0.69 2 0.70 2 0.62 3 0.61 3

Ⅷ 0.48 5 0.45 5 0.47 5 0.36 6 0.34 6

From table 2, the weight of exhaust temperature margin of gas

generator is bigger based on multiplication combination method.

Considering the thermocouple dispersions, the vibration intensity,

heat loss index, power deficit index, exhaust temperature margin of

gas generator and thermal efficiency ratio, the comprehensive states

sort, from superior to inferior, is:

1 3 7 5 4 8 2 6y y y y y y y y , and only considering

exhaust temperature margin, the sort is

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1 3 7 5 4 6 2 8y y y y y y y y . So, the two are not

consistent. In general, the state of the gas turbine after a single

cleaning is better than that before cleaning, and the state after three

cleaning is better than that before cleaning as a whole. According

to multiple indexes, the state at the beginning of the test is the best,

and the state before the third cleaning (i.e. period Ⅵ) is the worst.

Compared with period Ⅵ, although the indexes such as power

deficit index pdI , exhaust temperature margin of gas generator

egtM , thermal efficiency ratio teR , low pressure compressor flow

degradation factor LCG , high pressure compressor flow

degradation factor HCG , high pressure turbine efficiency

degradation factor HT and low pressure turbine efficiency

degradation factor LT , are worse at the end of the test (i.e. period

Ⅷ), corrected thermocouple dispersions 1cS and

2cS and

vibration intensity index sV are better at the end of the test, so the

comprehensive evaluation of period Ⅷ is better than period Ⅵ.

CONCLUSION

This paper studies the comprehensive evaluation method of gas

turbine state based on the combination of subjective and objective

weights. Evaluation indicators of thermocouple dispersions,

vibration intensity, heat loss index, power deficit index, exhaust

temperature margin of gas generator, thermal efficiency ratio,

compressor flow degradation factors and turbine efficiency

degradation factors are chosen from the gas path degradation

condition of whole engine and components and the whole machine

vibration state. These indicators describe different aspects to grasp

the state of engine health, certainly not always correlated with each

other. Aimed at the uncertainty of data information, the objective

attribute weights are obtained based on the method of the

combination of fuzzy clustering and information entropy by

calculating the mutual information. In view of the equilibrium of

data, another objective weights are gotten using the entropy weight

method. Then the linear weighted sum method of the two is used to

get the final objective weights. Subjective weights are obtained by

AHP method. Integrating the subjective and objective weights,

multiplication combination method is used to determine the final

weights. The multi-attribute comprehensive evaluation of gas

turbine health status is carried out combined with a 2,000 hours test.

Results show that the method can integrate the advantages of

objective and subjective weighting methods, and evaluation results

are in line with the practical experience, which means it is a feasible

way to the gas turbine multi-index state-assessment and

maintenance decision when the weight information is unknown.

ACKNOWLEDGEMENTS

We thank Accdon for its linguistic assistance during the

preparation of this manuscript.

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