LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION A. Kyriazis K. Mathioudakis Mathioudakis A. Kyriazis K. Research Assistant Research Assistant Professor Professor Laboratory of Thermal Turbomachines National Technical University of Athens Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion 1 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION � 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 2 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION � 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 3 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS GENERAL DESCRIPTION Two- -Step Fusion Method for Decision Level Fusion Step Fusion Method for Decision Level Fusion Two Individual diagnostic tools-methods Black Boxes (e.g. PNN, BBN, Pattern recognition “EXPERTS” etc.) Probability Probability Probability Probability Distribution Distribution Distribution Distribution Aggregation Probability Consensus Decision Level Fusion Classification of Consensus 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 Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion 4 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION � 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 5 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS AGGREGATION THEORY m m experts provide a probability distribution over the experts provide a probability distribution over the n n possible faults possible faults Expert Expert Expert . . . 1 2 m p 1 (aj) p 2 (aj) p m (aj) . . . . . . . . . . . . . . . . . . a 1 a 2 a j a n a 1 a 2 a j a n a 1 a 2 a j a n . . . . . ( ) = X j f p a p a p a ( ) ( ), ( ),..., ( ) j j m j 1 2 Probability consensus Probability consensus Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion 6 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS PROBABILITY CONSENSUS The probability consensus (combination of the experts The probability consensus (combination of the experts’ ’ opinions) opinions) is derived by application of the is derived by application of the aggregation function X X (weighted average of probability density functions) (weighted average of probability density functions) aggregation function m ∑ ⋅ w p a ( ) i i j = ⋅ = = X j k i j n 1 ( ) , 1,.., m ∑ w i = i 1 • k is a normalization factor (optional) • When 0 ≤ w i ≤ 1 (normalized weights adding up to 1) denominator is omitted Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion 7 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION � 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 8 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS CLASSIFICATION OF CONSENSUS Two different approaches for fuzzy classification Two different approaches for fuzzy classification m ⋅ ∑ ⋅ w p a ( ) i i j = = X j k i 1 ( ) m ∑ w i = i 1 Appr1 Appr2 (principles Fuzzy Set Theory) (principles Fuzzy Logic and reasoning) (complete FIS system) Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion 9 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS CLASSIFICATION OF CONSENSUS Appr1 Fuzzy sets Fuzzy sets Membership functions Membership functions Y-axis ∈ 1.PROBABLE = {x, g2(x) / x A} 1 ∈ g 1 (x) g 2 (x) 2.NOT_PROBABLE = {x, g1(x) / x A} <= <= ⎧ x ⎧ x 1, 20 0, 40 ⎪ ⎪ ⎪ ⎪ 1 3 1 = − + < < = − < < g x x x g x x x ⎨ ⎨ ( ) , 20 60 ( ) 1, 40 80 1 2 ⎪ 40 2 ⎪ 40 ⎪ >= ⎪ >= x x ⎩ 0, 60 ⎩ 1, 80 X-axis 0 20 40 50 60 80 100 Universe of Discourse: ∈ A = x [0,100] Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion 10 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS Y-axis CLASSIFICATION OF CONSENSUS 1 g 1 (x) g 2 (x) Appr1 − g X i g X i ( ( )) ( ( )) 2 1 X-axis 0 20 40 50 60 80 100 X i ( ) Diagnostic criterion Diagnostic criterion ( ) ( ) ( ) ( ) , ( ) ( ) ( ) ( ) ⎡ ⎤ ⎡ ⎤ ≠ j: g Χ j -g Χ j > g Χ i -g Χ i i j ⎣ ⎦ ⎣ ⎦ 2 1 2 1 Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion 11 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS CLASSIFICATION OF CONSENSUS Appr2 ⎧ = X j (1) , 1 = ⎨ X j '( ) SCALING PROCEDURE: ⎩ − • + = j X j j N [( 1) 100] ( ) , 2, 3,..., Prob X(1) Two Fuzzy Sets Not-Prob X(1) Prob X(2) Not-Prob X(2) 1 (for each element of X ΄ ): 1.ProbX i 2.Not-ProbX i Universe of Discourse: 0 = ∈ A x N i [0, 100] 100 200 300 MFs for the first two elements of X ΄ Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion 12 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS Appr2 CLASSIFICATION OF CONSENSUS: • 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 Diagnostic criterion Diagnostic criterion [ ] [ ] − ⋅ < ≤ ⋅ j j crisp value j : ( 1) 100 _ 100 Gas Turbine Fault Diagnosis Using Fuzzy-based Decision Fusion 13 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
LABORATORY OF THERMAL TURBOMACHINES NATIONAL TECHNICAL UNIVERSITY OF ATHENS GAS TURBINE FAULT DIAGNOSIS USING FUZZY-BASED DECISION FUSION � 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 14 XVIII ISABE Conference, September 2-7, 2007, Beijing, China
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