a new gas path fault diagnostic method of gas turbine

1 Copyright © 2014 by ASME

A NEW GAS PATH FAULT DIAGNOSTIC METHOD OF GAS TURBINE BASED ON SUPPORT VECTOR MACHINE

Dengji Zhou The key Lab. of power machinery and engineering

of education ministry, Shanghai Jiao Tong University

Shanghai, P.R.China

Jiayun Wang The key Lab. of power machinery and engineering

of education ministry, Shanghai Jiao Tong University

Shanghai, P.R.China

Huisheng Zhang Gas Turbine Research Institute Shanghai Jiao Tong University

Shanghai, P.R.China

Shilie Weng Gas Turbine Research Institute Shanghai Jiao Tong University

Shanghai, P.R.China

ABSTRACT As a crucial section of gas turbine maintenance decision-

making process, to date, gas path fault diagnostic has gained a

lot of attention. However, model-based diagnostic methods, like

non-linear gas path analysis (GPA) and genetic algorithms,

need an accurate gas turbine model, and diagnostic methods

without gas turbine model, like artificial neural networks, need

a large number of experimental data. Both are difficult to gain.

Support vector machine (SVM), a novel computational learning

method with excellent performance, seems to be a good choice

for gas path fault diagnostic of gas turbine without engine

model. In this paper, SVM is employed to diagnose a

deteriorated gas turbine. And the diagnostic result of SVM is

compared to the result of artificial neural networks. The

comparing result confirms that SVM has an obvious advantage

over artificial neural networks method based on a small sample

of data, and can be employed to gas path fault diagnostic of gas

turbine. Additionally, SVM with radial basis kernel function is

the best choice for gas turbine gas path fault diagnostic based

on small sample.

Keywords: gas turbine; gas path fault; diagnostic; support

vector machine; kernel function

NOMENCLATURE R structural risk

Remp empirical risk

RC confidence risk

T training sample / temperature (℃)

xi, yi sample point variables

w, b linear function parameters

αi Lagrange parameters

L Lagrange function

γ kernel parameter

K kernel function

F feature space

PR compressor pressure ratio

qf fuel consumption (kg/s)

PL gas turbine output (MW)

T0 ambient temperature (℃)

T2 compressor outlet temperature (℃)

T4 gas turbine exhaust temperature (℃)

A diagnostic accuracy

nc number of correctly classifying sample

points

ns testing sample size

SVM support vector machine

GPA gas path analysis

INTRODUCTION Gas turbine, with very high power-to-weight ratio,

flexibility for variable working conditions and good emission

performance, is widely used in energy field [1]. Now the

efficiency of combined cycle of gas turbine and steam turbine is

approximately 60%, showing great potential in power

generation. However, the high maintenance cost becomes the

major obstacle of application of gas turbine in energy field [2].

For instance, maintenance cost accounts for about 70% of

Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition IMECE2014

November 14-20, 2014, Montreal, Quebec, Canada

IMECE2014-36367


operating cost of gas turbines for natural gas compressor

station.

Currently, a series of advanced maintenance methods have

been tried to apply for gas turbine maintenance, like condition

based maintenance and reliability-centered maintenance [3].

Diagnostic of gas turbine is one of the key technologies to

support engine these advanced maintenance strategies, with

great potential to reduce maintenance costs, and improve

reliability and availability.

Because of the complexity of gas turbine structure and

working condition, there are a large number of fault modes of

gas turbine. Conclusively, all these fault modes can be divided

into three categories. And each category of faults can be

detected by some special diagnostic techniques.

(1) Gas path fault. This kind of faults always result in the

decrease of engine performance, like output power decrease,

fuel consumption increase, exhaust gas temperature increase,

component efficiency decrease, compressor surge and so on.

They can be detected by gas path analysis (GPA) based on the

monitor of thermal parameters.

(2) Structure strength fault. This kind of faults may cause

very serious consequence, like rupture and damage to the

engine due to insufficient strength, mainly including creep and

fatigue. The diagnostic of this kind of faults needs considering

both vibration parameters and thermal parameters, based on

stress analysis, even some non-destructive testing technology.

(3) Auxiliary system fault. This kind of faults is caused by

the consumable parts damage in auxiliary system for engine,

like inlet air filter block, valve leak and so on. These faults will

reduce the performance of engine [2].

The second kind of faults has gained a lot of attention and

has entered the stage of products, because of the hazardous

consequence. And the third kind of faults is usually prevented

easily by periodical inspection and comparing the monitoring

parameters with their threshold. This paper focuses on the first

kind of fault modes and shows a new diagnostic method for this

kind of faults.

GAS PATH FAULT DIAGNOSTIC OF GAS TURBINE Gas path fault, caused by the degradation of gas path

components, leads to gas turbine performance deterioration.

The most common causes of the degradation are compressor

fouling, blade tip clearance increase due to wearing and

erosion, labyrinth seal damage, foreign and domestic object

damage, hot end component damage, corrosion, etc [4]. These

physical faults result in the thermodynamic performance

changes of gas turbine compressor and turbine, which reflected

from efficiency and flow capacity of compressor and turbine.

Thus, the objective of gas path fault diagnostic is to detect these

faults and determine the extent of them, based on observable

engine parameters such as temperature, pressure, rotational

speed and fuel flow rate [5]. In other word, gas path fault

diagnostic is the inverse process of the real engine working

process, in which degradation of component performance is

calculated based on monitoring parameters and the fault modes

and extent are estimated based on the calculated degradation of

component performance, Fig. 1.

Output

Working condition

Degradation of component performance

Fault modes and extent

Gas turbine

Monitoring parameters

...

Real working process

Diagnostic process

Fig. 1 Gas turbine gas path fault diagnostic theory

Since Urban introduced a linear model based GPA analysis

method in 1967, six kinds of methods have been presented, in

Table 1 [6].

Table 1 Comparison of current gas path fault diagnostic

methods [7]

Diagnostic methods

Earliest

year of

use

Model

based

Model

complexity

Computation

speed

Coping

with

noise

Coping

with

bias

Linear

model-

base method

Linear GPA 1967 Yes Low High No No

Optimal estimates

1980 Yes Fairly low High Yes Yes

Non-

linear

model-based

methods

Non-linear

GPA 1992 Yes Low Fairly high No No

Conventional

optimization 1990 Yes Medium Low Yes Yes

Neural Networks 1965 No Fairly high High Yes Yes

Genetic algorithms 1999 Yes Fairly high Low Yes Yes

Rule-based expert systems Early 1980’s

No High High Yes Yes

Rule-based fuzzy expert

systems 1997 No High Fairly high Yes Yes

Expert system needs the knowledge database from experts,

whose acquisition has been recognized the “bottleneck”

problem; Linear GPA, non-linear GPA and genetic algorithms

methods need accurate gas turbine model which is difficult to

obtain. Neural networks method can diagnose without gas

turbine model, based on historical monitoring parameters and

fault data, seeming to be potential. However, the number of

these data is always small. Thus how to make full use of these

data is a key knowledge.

SVM FOR GAS TURBINE GAS PATH FAULT DIAGNOSTIC

Support Vector Machine (SVM) is a set of related methods

for supervised learning, applicable to both classification and

regression problems [8-10]. Its classification function can be

applied to gas turbine gas path fault diagnostic. Since the

introduction of the SVM classifier decades ago (Cortes and

Vapnik, 1995), SVM gained popularity due to its solid

theoretical foundation [11, 12]. It has been proved a useful tool

which has a good performance to solve nonlinear and small

sample problems, seeming to make full use of limited data.

Following is the basis theory of SVM.


SVM basic theory

SVM method is based on VC (Vapnik–Chervonenkis)

dimension from the statistical learning theory, a measure of the

capacity of a statistical classification algorithm, and structural

risk minimization principle, to find the best compromise

between the limited sample complexity of the model (i.e. the

accuracy of a particular learning training samples) and learning

ability (i.e. the ability to identify any error in the sample)

according to the information, in order to obtain the best

generalization ability (or generalization).

Statistical study introduces the concept of generalization

error bound, which means the real risk characterization should

be composed of two parts: one is empirical risk, on behalf of

the classifier on a given error in the sample; the other one is

confidence risk, representing the extent of our classifier can be

trusted on the unknown text classification results [11].

Obviously, the second part cannot be accurately calculated, and

can only be given an estimate of the range, so that the accurate

values cannot be calculated. For structural risk:

R ≤ Remp + RC (1)

Formula R is the real risk, Remp is the empirical risk, RC is

the confidence risk. The goal of statistical learning is to seek

the minimization of structural risk, which is the sum of

experience risk and confidence risk

SVM is such a structural risk minimization algorithm. It is

characterized by small sample, nonlinear, high dimensional

pattern recognition.

SVM solving process

It is assumed that there is the training sample

T = *(𝐱𝟏, y1), ⋯ , (𝐱𝐧, yn)+ ∈ (X × Y)n

𝒙𝒊 ∈ 𝑋 = 𝑅𝑛 , 𝑦 ∈ 𝑌 = *1, ⋯ , 𝑀+, 𝑖 = 1, ⋯ , 𝑛 (2)

This sample can be separated by a hyperplane, and the

function of the hyperplane can be assumed as [13]:

((𝐰 ∙ 𝐱) + b) = 0

𝒘 ∈ 𝑅𝑛 , 𝑏 ∈ 𝑅 (3)

The optimal hyperplane is affected by a small number of

sample points (support vectors) close to it, and having nothing

to do with other sample points. Thus the optimal problem

should be [14]

Min*w.b+

1

2‖𝐰‖2

(4)

Subjtect to yi ∙ ((𝐰 ∙ 𝐱𝐢) + b) ≥ 1, i = 1, … , n (5)

Based on the quadratic Programming in optimization

theory, this problem can be transformed to Wolfe dual of the

optimization problem. Introducing Lagrange function:

L(𝐰, b, α) =

1

2‖𝐰‖2 − ∑ αi(yi ∙ ((𝐰 ∙ 𝑥𝑖) + b) − 1)

n

i=1

(6)

Where, Lagrange multipliers αi > 0. Thus,

∂L

∂b= 0 (7)

∂L

∂𝐰= 0

(8)

Thus, the Wolfe dual of the optimization problem for the

multipliers can be arrived:

maxα

∑ αi −1

2∑ αiαjyiyj(𝐱𝐢 ∙ 𝐱𝐣)

n

i,j=1

n

i=1

(9)

Subject to αi ≥ 0, i = 1, … , n, ∑ αiyi = 0

n

i=1

(10)

Then, based on equation (2), the hyperplane decision

function can be presented as:

f(x) = sign (∑ αiyi(𝐱 ∙ 𝐱𝐢) + b

n

i=1

) (11)

where, b =

1

|I|∑ (yi − ∑ αjyj(𝐱𝐢 ∙ 𝐱𝐣)

n

j=1

)

i∈I

,

𝑖 ∈ 𝐼 ≡ *𝑖: 𝛼𝑖 ≠ 0+

(12)

Kernel Trick

The linear classify function is chosen to introduce SVM

theory, (3). Using the kernel trick for SVM makes the

maximum margin hyperplane be fit in a feature space F. The

feature space F is a non-linear map Φ : RN → F from the

original input space, usually of much higher dimensionality

than the original input space. Four most commonly used kernel

function is chosen in this paper, Table 2.

Table 2 Four kernel functions used in this paper

Kernel K(x, xi)

Linear 𝑥𝑇 ∙ 𝑥𝑖 (13)

Polynomial (𝑥𝑇 ∙ 𝑥𝑖) + η)𝑑 (14)

Radial Basis exp(−γ‖x − 𝑥𝑖‖2) (15)

Sigmoidal tanh (γ(𝑥𝑇 ∙ 𝑥𝑖) + η) (16)

Several applications of SVM for diagnostics have been

finished. L.B. Jack and A.K. Nandi diagnosed motor bearings

faults with the help of SVM [15]; B. Samanta used SVM to

detect bearing faults with the SVM optimized by genetic

algorithm [16]; G.Y. Lv employed SVM combined with

dissolved gas analysis to isolate common transfer faults [17];

H.X. Cui used SVM combined with information entropy for

reciprocating compressor diagnosis [18]. However, the

application of SVM for gas turbine gas path fault diagnostic

cannot be found in the published papers.

For gas turbine gas path fault diagnostic, the process and

function of the application of SVM method seems similar to

application of neural networks method. Both employ acquired

sensor data, fault mode and extent information to build a

model, used for determining the fault mode and fault extent

based on sensor data. For diagnostic process, in Fig. 1, the step

of calculating degradation of component performance can be

deleted. Conclusively, the relationship between monitoring

parameters and fault modes and extent can be built directly.

SVM DIAGNOSTIC FOR A SINGLE-SHAFT INDUSTRY GAS TURBINE

A single-shaft industry gas turbine is cited as an instance to

validate the application of SVM for gas turbine gas path fault


diagnostics. The design point performance of this gas turbine is

as follows, Table 3.

Table 3 Single-shaft industry gas turbine design point

performance parameters [19]

Pressure ratio 17.02

Power output 260 MW

Exhaust gas temperature 635.32 ℃

Fuel consumption 15.06 kg/s

Application of SVM consists of two sub-processes,

training process and testing process, based on training sample

and testing sample, in Fig.2. Both of the two samples consist of

some sets of data, sample points. And each sample point

consists of sensor data and gas turbine fault modes and extent.

These data should be accumulated by operation and

maintenance of real engine. For example, fault modes and

extent should be determined by the borescope inspection in

overhaul, and sensor data should be the data recorded before

the overhaul shutdown. In this paper, a deteriorated gas turbine

simulation model is employed, instead of the real gas turbine.

After acquiring these two samples based on the simulation

model, training sample can be the input to build a SVM

diagnostic model based on SVM methods. Then testing sample

can be used to validate the accuracy of the diagnostic model. In

the testing process, the monitoring parameters of each sample

point should be the input, and the output of SVM diagnostic

model and the real fault modes and extent should be compared.

Then the accuracy of the SVM diagnostic model should be

A =nc

ns

(17)

Where, A is the accuracy of diagnosis; nc is the number of

correctly classifying sample points; ns is testing sample size.

Deteriorated gas turbine simulation model Real gas turbine

Training sample

Testing sample

SVM diagnostic model

SVM diagnostic model accuracy

Sensor data

Fault modes and extent

Training process

Testing process

Fig. 2 Application process of SVM for gas path diagnostic

The number of states of gas turbine may greatly affect the

accuracy of SVM model. Based on operating and maintenance

experience of this type of single-shaft industry gas turbine, 8

fault modes and 8 common health states are taken into

consideration in this paper, in Table 4 and Table 5. For each

health state, the extent of every fault mode is listed in Table 5.

Table 4 Eight main fault modes of gas turbine

Fault Item Fault name

Fault A Compressor blades fouling

Fault B Compressor blade tip clearance increase

Fault C Compressor blades erosion and corrosion

Fault D Compressor foreign object damage

Fault E Turbine nozzles corrosion

Fault F Turbine blades fouling

Fault G Turbine blades erosion

Fault H Turbine foreign object damage

Table 5 Eight health states of gas turbine State

Number A B C D E F G H

1 - - - - - - - -

2 50% - - - - - - -

3 100% - - - - - - -

4 50% - 50% - 50% 50% 50% -

5 100% - 50% - 50% 50% 50% -

6 100% 50% 50% - 50% 50% 50% -

7 - - - 100% - - - -

8 - - - - - - - 100%

For each health state, several sample points can be

acquired based on the deteriorated gas turbine performance

simulation model. In the simulating process, ambient

temperature is set as between 0 and 30 ℃, and gas turbine

output is set as between 80% and 100% of the rated power

output. Thus, each sample point is generated randomly under

the normal working environment and condition for gas turbine.

Each sample point consists of the health state No. and the

monitoring parameters, including ambient temperature, output,

compressor pressure ratio, fuel consumption, compressor outlet

temperature and exhaust gas temperature. Table 6 is an example

of part of the sample points of training sample or testing sample

to show the format of every sample points.

Table 6 Part of sample points of training sample or testing

sample State No. T0 PL PR qf T2 T4

1 27.5 240.5 16.61 14.25 439.70 636.10

1 5.0 234.0 16.62 13.56 386.48 563.44

2 27.5 260.0 16.52 15.32 442.66 695.26

2 5.0 253.5 16.57 14.68 389.64 624.09

3 25.0 253.5 16.06 15.10 435.57 708.92

5 27.5 247.0 15.85 15.45 443.08 747.35

⋯

5 5.0 240.5 15.89 14.80 389.62 673.09

6 5.0 240.5 16.82 14.24 408.05 600.59

6 7.5 240.5 16.80 14.28 414.11 608.01

7 27.5 253.5 17.24 16.18 446.72 736.65

8 22.5 240.5 15.56 15.09 428.01 738.65


RESULTS AND DISCUSSION Firstly, two sets of training samples are generated by the

deteriorated gas turbine simulation model. Sample size of

Sample set 1 is 400, and sample size of Sample set 2 is 144.

Both of the two sample sets are very small. Then the two

sample sets are adopted for gas turbine gas path fault diagnostic

by five different methods, i.e. SVM with linear kernel function,

SVM with polynomial kernel function, SVM with sigmoidal

kernel function, SVM with radial basis kernel function and

neural networks. Then two testing samples are generated to test

the diagnostic accuracy. The size of both samples is 48. The

result is shown in Table 7. The optimal kernel parameter for

every kernel function is suggested. However, it should be noted

that the best γ value may not be unique because of the small

size of testing sample.

Table 7 Result of SVM gas path diagnostic

Set No. Kernel

function Optimal γ

Accuracy

(%)

Support vector

Number

Sample 1

Linear 0.25 89.58 217

Polynomial 1 93.75 122

Radial Basis 1.2 93.75 199

Sigmoidal 0.1 66.67 230

Sample 2

Linear 0.32 70.83 91

Polynomial 1 64.58 82

Radial Basis 1.2 91.67 88

Sigmoidal 0.1 43.75 95

The effect of training sample size and monitoring

parameters number on diagnostic accuracy is taken into

consideration. And the accuracies of SVM and neural networks

are compared.

Effect of training sample size

Though SVM is suitable for solving small sample problem,

it is obvious that the increase of sample size will increase the

accuracy of SVM diagnostic model. Two training samples with

different sample size are generated to judge the extent of this

effect. The only difference between these two samples is the

number of sets of data. In addition, all of the four common

kernel functions are adopted in the diagnostic process.

Fig. 3 Effect of sample size and kernel function on SVM

diagnostic accuracy

The result, in Fig.3 shows that sigmoidal kernel function is

not suitable for gas turbine gas path fault diagnostics.

The accuracies of all kernel functions increase with the

increase of sample size. And Radial Basis kernel function

seems to be the most suitable one for gas turbine gas path fault

diagnostic, especially for small training sample. When the

training sample size is just 144, the accuracy of Radial Basis

SVM can be 89.6%. That is to say, a power company, with 24

gas turbines which will be inspected every half year, can

diagnose nearly 90% faults and their extent for their gas

turbines engine, after three years’ data accumulation.

Sample size has more critical effect on SVM diagnostic

accuracy with other kernel function than that with radial basis

kernel function. It means that the choice of suitable kernel

gradually becomes less important with the increase of sample

size.

For most nonlinear problems, polynomial kernel function

has better performance than linear kernel function. However, it

is interesting that linear kernel function is better than

polynomial kernel function when sample size is small, in this

instance. When the sample size is large (Sample 1, sample size

= 400), polynomial kernel function is as good as Radial Basis

kernel function.

Effect of monitoring parameters number

For many gas turbine power stations, especially some old

gas turbine stations, compressor outlet temperature is not

monitored. Thus, the effect of reducing this sensor on SVM

diagnostic model accuracy is taken into consideration in this

paper. Because of sigmoidal kernel function’s poor

performance for this issue, it is not considered in the further

research.

Fig. 4 Effect of monitoring parameters number on SVM

diagnostic accuracy (sample size = 400)

0

20

40

60

80

100

Linear Polynomial Radial Basis Sigmoidal

Acc

ura

cy (

%)

Sample 1 (400) Sample 2 (144)

0

20

40

60

80

100

Linear Polynomial Radial Basis

Acc

ura

cy (

%)

With T2 Without T2


Fig. 5 Effect of monitoring parameters number on SVM

diagnostic accuracy (sample size = 144)

The result, in Fig. 4 and Fig. 5, shows that the sensor of

compressor outlet air temperature has great effect on diagnostic

accuracy. Thus the application of diagnostic system for old gas

turbines without T2 information may benefit from the

installation of T2 sensor.

For all of the three kinds of kernel function, radial basis

shows the steadiest performance. It can get the accuracy more

than 80% for both samples. Polynomial function can get higher

accuracy than radial basis when sample size is big. However, it

accuracy is the lowest of three when the sample size is small.

Linear function seems to be affected very lightly by the

removal of this sensor when sample size is small. However,

more research should be done to validate this conclusion.

In general, radial basis function is also the suggested kernel

function of gas path fault diagnostic for old gas turbines

without compressor outlet air temperature sensor.

Comparison of SVM and neural networks

The diagnostic accuracies of SVM with three different

kernel functions and neural networks are compared in this

section, based on Sample set 1 (sample size =400) and Sample

set 2 (sample size =144). A 4-1-1 BP neural network is adopted

in this comparison.

Fig. 6 Diagnostic accuracy comparison of SVM and neural

networks

In Fig. 6, the result shows that SVM with radial basis

kernel function is better than neural networks for both sample

sets. When sample size is very small, neural networks has better

performance than SVM without suitable kernel function. It

means that if the suitable kernel function of SVM is unknown,

neural networks may be a better choice than SVM. However,

SVM method with unsuitable kernel function may have better

diagnostic accuracy than neural networks when having a larger

sample size.

Thus, it may be the greatest drawback of SVM that the

suitable kernel function must be known before application. So

much theoretical investigation has to be done before the real

application of SVM.

CONCLUSIONS SVM has been firstly introduced for gas turbine gas path

fault diagnostic in this paper. It seems quite suitable for solving

this problem with very small sample size and without gas

turbine accurate model. Four different kernel functions of SVM

have been employed in this paper, and the optimal kernel

parameters of every kernel function are suggested. The

following conclusions can be drawn:

(1) Radial basis kernel function is the best one to solve gas

turbine gas path diagnostic problem, especially when the

sample size is very small. When sample size is just 144, its

diagnostic accuracy can reach 91.67%.

(2) The sensor of compressor outlet air temperature has

great effect on diagnostic accuracy. Radial basis function is also

the suggested kernel function of gas path fault diagnostic for

old gas turbines without compressor outlet air temperature

sensor.

(3) SVM with Radial Basis kernel function shows better

performance than neural networks for gas turbine gas path fault

diagnostics. However, neural networks method seems to be a

choice for this problem when the suitable kernel function of

SVM function is unknown.

ACKNOWLEDGMENTS This work was supported by Program of Science and

Technology Committee of Shanghai Municipal (09DZ1200702)

and Program of Economy and Information Committee of

Shanghai Municipal.

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a new gas path fault diagnostic method of gas turbine

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