GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION A. - - PowerPoint PPT Presentation

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

K.

• K. Mathioudakis

Mathioudakis

Professor Professor

Laboratory of Thermal Turbomachines National Technical University of Athens

• A. Kyriazis
• A. Kyriazis

Research Assistant Research Assistant

GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

• Description of the Fusion Method

Description of the Fusion Method

• Aggregation theory

Aggregation theory-

• Probability Consensus

Probability Consensus

• Classification of Consensus

Classification of Consensus

• Application Test Cases

Application Test Cases

• Summary

Summary-

• Conclusions

Conclusions GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

• Description of the Fusion Method

Description of the Fusion Method Aggregation theory-Probability Consensus Classification of Consensus Application Test Cases Summary-Conclusions GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

Two Two-

• Step Fusion Method for Decision Level Fusion

Step Fusion Method for Decision Level Fusion

Individual diagnostic tools-methods (e.g. PNN, BBN, Pattern recognition etc.)

Decision Level Fusion

Probability Distribution Probability Distribution

Black Boxes “EXPERTS”

Aggregation Probability Consensus Classification of Consensus Probability Distribution Probability Distribution

1. All the outputs of the independent diagnostic methods are aggregated deriving the probability consensus. 2. The probability consensus is then classified to a certain fault with the aid of Fuzzy Set Theory and Fuzzy Logic

GENERAL DESCRIPTION

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

Description of the Fusion Method

• Aggregation theory

Aggregation theory-

• Probability Consensus

Probability Consensus Classification of Consensus Application Test Cases Summary-Conclusions GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

AGGREGATION THEORY

m m experts provide a probability distribution over the experts provide a probability distribution over the n n possible faults possible faults

Probability consensus Probability consensus

. . .

p1(aj)

Expert 1

a1 a2 an p2(aj)

Expert 2

pm(aj)

Expert m

. . .

. . . . . . . . . . . . . . .

aj a1 a2 an aj a1 a2 an aj

( )

1 2

( ) ( ), ( ),..., ( )

j j m j

X j f p a p a p a =

. . . . .

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

The probability consensus (combination of the experts The probability consensus (combination of the experts’ ’ opinions)

• pinions)

is derived by application of the is derived by application of the aggregation function aggregation function X

X (weighted average of probability density functions)

(weighted average of probability density functions)

1 1

( ) ( ) , 1,..,

m i i j i m i i

w p a X j k j n w

= =

⋅ = ⋅ =

∑ ∑

PROBABILITY CONSENSUS

• k is a normalization factor (optional)
• When 0≤ wi ≤1 (normalized weights adding up to 1) denominator is omitted

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

Description of the Fusion Method Aggregation theory-Probability Consensus

• Classification of Consensus

Classification of Consensus Application Test Cases Summary-Conclusions

GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

Two different approaches for fuzzy classification Two different approaches for fuzzy classification CLASSIFICATION OF CONSENSUS Appr1

(principles Fuzzy Set Theory)

Appr2

(principles Fuzzy Logic and reasoning) (complete FIS system) 1 1

( ) ( )

m i i j i m i i

w p a X j k w

= =

⋅ = ⋅ ∑

∑

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

Membership functions Membership functions

1.PROBABLE = {x, g2(x) / x A} 2.NOT_PROBABLE = {x, g1(x) / x A} Universe of Discourse:

1

1, 20 1 3 ( ) , 20 60 40 2 0, 60 x g x x x x <= ⎧ ⎪ ⎪ = − + < < ⎨ ⎪ >= ⎪ ⎩

2

0, 40 1 ( ) 1, 40 80 40 1, 80 x g x x x x <= ⎧ ⎪ ⎪ = − < < ⎨ ⎪ >= ⎪ ⎩

X-axis Y-axis

20 40 50 60 80 100 1

g2(x) g1(x)

A = x [0,100] ∈

∈ ∈

Appr1

CLASSIFICATION OF CONSENSUS Fuzzy sets Fuzzy sets

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

Appr1

CLASSIFICATION OF CONSENSUS

X-axis Y-axis

20 40 50 60 80 100 1

g2(x) g1(x)

2 1

( ( )) ( ( )) g X i g X i −

( ) X i

( )

( )

( )

( )

( )

( )

( )

( ) ,

2 1 2 1

j: g Χ j

• g

Χ j > g Χ i

• g

Χ i i j ⎡ ⎤ ⎡ ⎤ ≠ ⎣ ⎦ ⎣ ⎦

Diagnostic criterion Diagnostic criterion

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

SCALING PROCEDURE:

Two Fuzzy Sets (for each element of X΄): 1.ProbXi 2.Not-ProbXi Universe of Discourse:

MFs for the first two elements of X΄

Appr2

(1) , 1 '( ) [( 1) 100] ( ) , 2, 3,..., X j X j j X j j N = = −

• +

=

⎧ ⎨ ⎩

[0, 100] A x N = ∈ i

CLASSIFICATION OF CONSENSUS

1 100 200 300 Prob X(1) Not-Prob X(1)

Prob X(2) Not-Prob X(2)

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

• A set of fuzzy “if-then” rules equal to number of faults are defined over the

membership functions

• For the FIS, the Mamdani Model of implication

and the max-min method of composition have been considered.

• For the deffuzification process mean of maximum (mom) method has been selected
• Output is a crisp_value

Appr2

[ ] [ ]

: ( 1) 100 _ 100 j j crisp value j − ⋅ < ≤ ⋅

CLASSIFICATION OF CONSENSUS:

Diagnostic criterion Diagnostic criterion

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

Description of the Fusion Method Aggregation theory-Probability Consensus Classification of Consensus Application Test Cases Summary-Conclusions GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

TEST CASE APPLICATIONS

• Two cases have been examined:

Two cases have been examined:

• The case of a

The case of a radial radial compressor compressor

• The case of an

The case of an axial axial compressor compressor

• In both cases the goal is to detect deliberately implemented

In both cases the goal is to detect deliberately implemented mechanical faults mechanical faults

• The available information is two sets of measurements, in each

The available information is two sets of measurements, in each case: case:

• A set of fast response data (vibrations, sound pressures, etc

A set of fast response data (vibrations, sound pressures, etc… …) )

• A set of performance data (pressures, temperatures, etc

A set of performance data (pressures, temperatures, etc… …) )

• In each case two independently acting diagnostic methods

In each case two independently acting diagnostic methods have been applied: have been applied:

• The method of PNN for diagnosis over fast response data

The method of PNN for diagnosis over fast response data

• The method of PNN for diagnosis over performance data

The method of PNN for diagnosis over performance data

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

The case of radial compressor

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

Examined faults Examined faults

Impeller Fouling-M2 Inlet Distortion-M3 Diffuser Fault-M1

The case of radial compressor

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

PNN Architecture for radial compressor case

Probabilistic Neural Network (PNN) for Fast Response Data

Features of the Probabilistic Neural Network

• Input Layer:

Inputs are the available fault

• signatures. Each node represents an

element of the vector consisting the fault signature.

• Hidden Layer:

Training patterns are the reference fault signatures.

• Output Layer:

Each node (class) represents a certain mechanical fault.

VR

M1

M1 VR

M2

VR

M3

Input layer Output layer VR

Mi : Reference signature

• f fault Mi

Hidden layer

Fast_Response Data Input Vector (47 elements)

M3 M2

The case of radial compressor

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

PNN Architecture for radial compressor case

Probabilistic Neural Network (PNN) for Performance Data

Features of the Probabilistic Neural Network

• Input Layer:

Inputs are the 7 deviations (deltas) of aerothermodynamic measurements according to type: where is the value of a measurement for the ith fault and is the value for a “healthy” engine

• Hidden Layer:

Training patterns are the mean averages of deviations, each corresponding to a specific fault

• Output Layer:

Each node (class) represents a certain mechanical fault.

, 1,2,...7

i i i i

Y Y d i Y − = =

i

Y

i

Y

V1

VR

M1

M1 VR

M2

VR

M3

Input layer Output layer Hidden layer

Performance Data Input Vector (7 elements)

V2 V3 V4 V5 V6 V7

M3 M2

VR

Mi : Reference signature

• f fault Mi

The case of radial compressor

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

Classification Probabilities for radial compressor faults

Fault classification from fast response data

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1 2 3 4 5 6 7 8 9 10 11 12

Probability (%) of test-case

M1 M2 M3

M1 M2 M3

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1 2 3 4 5 6 7 8 9 10 11 12

Probability (%) of test-case

M1 M2 M3

M1 M2 M3

Fault classification from performance data

1 1

( ) ( )

m i i j i m i i

w p a X j k w

= =

⋅ = ⋅ ∑

∑

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

Aggregation Aggregation – – Probability consensus results Probability consensus results

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1 2 3 4 5 6 7 8 9 10 11 12

Probability (%) of test-case M1 M2 M3

M1 M2 M3

The case of radial compressor

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

Fuzzy classification regarding Appr1 Fuzzy classification regarding Appr1

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8 9 10 11 12

M1 M2 M3

M1 M2 M3

The case of radial compressor

2 1

( ( )) ( ( )) g X i g X i −

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

Overall Results Overall Results

test-cases of incorrect classification / total test-cases

1/12 0/12 Appr2 1/12 0/12 Appr1 1/12 1/12 PNN_Performance 1/12 3/12 PNN_Fast Response Set A2 + Performance Set A1 + Performance Fast Response data + Performance data Radial compressor

The case of radial compressor

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

The case of axial compressor

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

• F-2: Fouled Rotor of Stage 2
• F-3: Two blades of Rotor 1 fouled
• F-4: Twisted blade of Rotor 1
• F-53: Three mistuned stator vanes

Examined faults Examined faults

The case of axial compressor

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

PNN Architecture for axial compressor case

Probabilistic Neural Network (PNN) for Fast Response Data

Features of the Probabilistic Neural Network

• Input Layer:

Inputs are the available fault

• signatures. Each node represents an

element of the vector consisting the fault signature.

• Hidden Layer:

Training patterns are the reference fault signatures.

• Output Layer:

Each node (class) represents a certain mechanical fault.

V1

VR

F-2

F-2 VR

F-3

VR

F-4

VR

F-i : Reference signature

• f fault F-i

Fast_Response Data Input Vector (36 elements)

V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18 V19 V20 V21 V22 V23 V24 V25 V26 V27 V28 V29 V30 V31 V32 V33 V34 V35 V36

F-4 F-3

Input layer Output layer Hidden layer

VR

F-53

F-53

The case of axial compressor

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

PNN Architecture for axial compressor case

Probabilistic Neural Network (PNN) for Performance Data

Features of the Probabilistic Neural Network

• Input Layer:

Inputs are the 7 deviations (deltas) of aerothermodynamic measurements according to type: where is the value of a measurement for the ith fault and is the value for a “healthy” engine

• Hidden Layer:

Training patterns are the mean averages of deviations, each corresponding to a specific fault

• Output Layer:

Each node (class) represents a certain mechanical fault.

, 1,2,...7

i i i i

Y Y d i Y − = =

i

Y

i

Y

V1

VR

F-2

F-2

VR

F-3

VR

F-4

VR

Fi : Reference signature

• f fault F-i

Performance Data Input Vector (7 elements)

V2 V3 V4 V5 V6 V7

F-4 F-3

Input layer Output layer Hidden layer

VR

F-53

F-53

The case of axial compressor

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China 0/16 0/16 0/16 2/16 Appr2 0/16 0/16 0/16 2/16 Appr1 4/16 4/16 4/16 4/16 PNN Performance 0/16 0/16 0/16 1/16 PNN_Fast Response PT2+ Performance ACC3+ Performance ACC2+ Performance ACC1+ Performance Fast Response data + Performance data Axial compressor

Overall Results Overall Results

The case of axial compressor

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

Description of the Fusion Method Aggregation theory-Probability Consensus Classification of Consensus Application Test Cases Summary-Conclusions GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION

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LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS

Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion

XVIII ISABE Conference, September 2-7, 2007, Beijing, China

A new approach for information fusion by combining data of different nature has been demonstrated It utilizes the concepts of Aggregation Theory, Fuzzy Set theory and Fuzzy Logic principles PNN networks act as first level diagnostic techniques (“experts”). Improvement to the final diagnostic decision by the proposed fusion method has been presented by application to test-cases of faults from a radial compressor and an axial compressor

GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION