Advanced Methods for Fault Detection

Transcription

1 Advanced Methods for Fault Detection Piero Baraldi Agip KCO Introduction Piping and long to eploration distance pipelines activities Piero Baraldi

2 Maintenance Intervention Approaches & PHM Maintenance Intervention Unplanned Planned Corrective Replacement or repair of failed units Scheduled Replacement or Repair following a predefined schedule Conditionbased Monitor the health of the component and then decide on repair actions based on the degradation level assessed Predictive Predict the Remaining Useful Life (RUL) of the component and then decide on repair actions based on the predicted RUL PHM

3 3 Fault Detection Piero Baraldi 3 Agip KCO Introduction Piping and long to eploration distance pipelines activities 3 Piero Baraldi

4 Fault Detection: objective 4 Equipment Measured signals Piero Baraldi

5 Fault Detection: objective 5 5 f Automatic algorithm Normal condition Equipment f Forcing functions Measured signals Piero Baraldi 5

6 Fault Detection: analogy 6 6 f Automatic algorithm Normal condition Equipment f Forcing functions Measured signals f f Piero Baraldi 6

7 7 Methods for Fault Detection: Limit-based Data-driven Piero Baraldi 7

8 8 Methods for Fault Detection: Limit-based Data-driven Piero Baraldi 8

9 Data & Information for fault detection (I) 9 Normal operation ranges of key signals Eample: Pressurizer of a PWR nuclear reactor Water level. m 3.8 m Abnormal condition Abnormal condition time Normal operation range

10 Methods for fault detection (I) Normal operation ranges of key signals Limit Value-Based Fault Detection Eample: Pressurizer of a PWR nuclear reactor Water level. m 3.8 m Abnormal condition Abnormal condition time Normal operation range

11 Methods for fault detection (I) Normal operation ranges of key signals Limit Value-Based Fault Detection Eample: Pressurizer of a PWR nuclear reactor Water level Drawbacks: comple plant too many signals to monitor no early detection control systems operations may hide small anomalies (the signal remains in the normal range although there is a process anomaly) not applicable to fault detection during operational transients. m 3.8 m Abnormal condition Abnormal condition time Normal operation range

12 Methods for Fault Detection: Limit-based Data-driven

13 Data & Information for fault detection (III) 3 Normal operation ranges of key signals Historical signal measurements in normal condition Eample: Liquid Steam Pressuretemperattemperat ure ure Spray flow Surge line flow Heaters power Level Pressure Water level

14 s The fault detection approach Real measurements MODEL OF COMPONENT BEHAVIOR IN NORMAL CONDITION ŝ ŝ t 4 Signal reconstructions s t Pb. t COMPARISON t s ŝ s ŝ Residuals Pb. t DECISION NORMAL CONDITION: No maintenance ABNORMAL CONDITION: maintenance required Piero Baraldi 4

15 s The fault detection approach Real measurements MODEL OF COMPONENT BEHAVIOR IN NORMAL CONDITION ŝ ŝ t 5 Signal reconstructions s t Pb. t COMPARISON t s ŝ s ŝ Residuals Pb. t DECISION NORMAL CONDITION: No maintenance ABNORMAL CONDITION: maintenance required Piero Baraldi 5

16 6 Data-driven fault detection The approach Modeling the component behaviour in normal condition Model requirements Modeling techniques Principal Component Analysis (PCA) AutoAssociative Kernel Regression (AAKR) Eample of application Analysis of the residuals: Sequential Probability Ratio Test (SPRT) Some Conclusions

17 7 Data-driven fault detection The approach Modeling the component behaviour in normal condition Model requirements Modeling techniques Principal Component Analysis (PCA) AutoAssociative Kernel Regression (AAKR) Eample of application Analysis of the residuals: Sequential Probability Ratio Test (SPRT) Some Conclusions

18 Model Requirements () 8 NORMAL CONDITION Real measurements Signal reconstructions t t M O D E L nc ˆ nc ˆ t t ACCURACY: ˆ nc 8

19 Model Requirements () 9 ABNORMAL CONDITION Real measurements Signal reconstructions t M O D E nc ˆ nc ˆ t OK t L t ROBUSTNESS ˆ nc nc 9

20 Model Requirements (3) ABNORMAL CONDITION Real measurements Signal reconstructions t t M O D E L nc ˆ nc ˆ t t NO OK NO SPILL-OVER

21 Data-driven fault detection The approach Modeling the component behaviour in normal condition Model requirements Modeling techniques Principal Component Analysis (PCA) AutoAssociative Kernel Regression (AAKR) Eample of application Analysis of the residuals: Sequential Probability Ratio Test (SPRT) Some Conclusions

22 PRINCIPAL COMPONENT ANALYSIS (PCA) ˆ t t MODEL OF COMPONENT BEHAVIOR IN NORMAL CONDITIONS ˆ t t Piero Baraldi

23 PCA for fault detection Auto-associative model n Auto- Associative Model nc ˆ nc ˆ nc ˆn nc ˆ i f,,, i,, n n Piero Baraldi

24 PCA for fault detection Auto-associative model n Auto- Associative Model nc ˆ nc ˆ nc ˆn nc ˆ i f,,, i,, n n Empirical model built using training patterns = historical signal measurements in normal plant condition Signal X nc k N nc nc j kj Nj nc n kn nc Nn Observation Piero Baraldi

25 PCA for fault detection 5 Training pattern Test pattern: input Test pattern: output X nc k N nc nc nc ˆ ( ˆ j kj Nj (,, ) nc,, ˆ X nc n n ) nc nc n kn nc Nn = historical signal measurements in normal plant condition = measured signals at current time = signal reconstructions (epected values of the signals in normal condition) n PCA nc ˆ nc ˆ nc ˆn Piero Baraldi

26 What is PCA? 6 PCA: space transformation from an n-dimensional space to a λ-dimensional space (λ<n) Retaining most of the information (loosing the least information). 3 Piero Baraldi

27 PCA Eample 7 B (,) A (,) X C (, ) Piero Baraldi

28 PCA Eample 8 B (,) ' A (,) X C (, ) ' U Piero Baraldi

29 PCA Eample 9 B (,) ' A (,) X C (, ) ' U Piero Baraldi

30 Basic Concepts 3 Two signals are highly correlated or dependent One is enough! u s s Piero Baraldi

31 Basic Concepts 3 Two signals are highly correlated or dependent key underlying phenomena One is enough! Areas of variance in data Focus on directions along which the ervations have high variance u 8 6 s - -. s s s Piero Baraldi

32 What does PCA do? 3 ) Find Principal Components: PC is the direction of maimum variance PC,, PC n are orthogonal to PC and describe maimum residual variance s PC PC s - Piero Baraldi

33 What does PCA do? 33 ) Find Principal Components: PC is the direction of maimum variance PC,, PC n are orthogonal to PC and describe maimum residual variance 3 Piero Baraldi

34 What does PCA do? 34 Step ) Find Principal Components: PC is the direction of maimum variance PC,, PC n are orthogonal to PC and describe maimum residual variance s PC PC Step ) PCA approimation: ignore the PCs of lower significance s Lost small information number of dimensions from n= to = 4 Piero Baraldi

35 How does PCA works? (step ) 35 ) Find principal components: V Compute the covariance matri of X nc 8 V nc nc T nc nc X X X X Empirical mean matri N i i i V Piero Baraldi

36 How does PCA works? (step ) 36 ) Find principal components: V Compute the covariance matri of X nc V nc nc T nc nc X X X X N i i i V Piero Baraldi

37 Piero Baraldi PCA Eample : Variance Matri 37 X X X X X X V T T A (,) ), ( C (,) B X X

38 How does PCA works? (step ) 38 8 ) Find principal components: V Compute the covariance matri of nc X, p,, p n n Find the n eigenvectors of and the corresponding eigenvalues : p V Vp p Piero Baraldi

39 Piero Baraldi PCA Eample : Eigenvalue 39 V Eigenvalues from: 4 ) det( 4 4 det det ) det( I V I V p Vp

40 PCA Eample: Eigenvectors 4 Vp p V 4 First eigenvector: p p p Vp p p p p 4 p p p p p 4 p 4 p p p p p p Piero Baraldi

41 Piero Baraldi PCA Eample: Eigenvectors 4 Second eigenvector: V p Vp p p p p p p p p p p p p p p Vp p p p 4

42 How does PCA works? (step ) 4 8 ) Find principal components: V Compute the covariance matri of nc X, p,, p n n Find the n eigenvectors of and the corresponding eigenvalues : p V Vp p p p T.8 T 9.5 highest.4 smallest Piero Baraldi

43 Eample: the trasformed basis p p p p T.8 T Piero Baraldi

44 How does PCA works? (step ) 44 8 ) Find principal components: V Compute the covariance matri of nc X, p,, p n n Find the n eigenvectors of and the corresponding eigenvalues : p V Vp p p p T.8 T 9.5 highest.4 smallest P p p, Piero Baraldi

45 How does PCA works? (step ) 45 ) Find principal components: V Compute the covariance matri of Find the n eigenvalues of and the corresponding eigenvectors p, p,, p n P represents an orthonormal basis: pi p i p PP T I j i j X n nc V Piero Baraldi

46 Piero Baraldi PCA Eample: P 46 V p Vp 4 p p P

47 Piero Baraldi PCA eample: P is an orthonormal basis 47 i i i p p p p p I PP T p p p p p

48 How does PCA works? (step ) 48 ) Find principal components: V Compute the covariance matri of V nc nc nc T nc nc X X X X P ( n, n) Find the n eigenvectors of and the corresponding eigenvalues : X V n P represents an orthonormal basis U the projection of X -nc on the new basis is given by: U X nc P The inverse relation is: nc T X UP Piero Baraldi

49 PCA Eample : projection of X 49 B (,) A (,) C (, ) X Piero Baraldi

50 PCA Eample : projection of X 5 C B (,) (, ) p p PC A (,) PC Piero Baraldi

51 PCA Eample : projection of X 5 PC PC C B (,) (, ) p A (,) p C ( ) A ( ) B (,) PC PC U XP Piero Baraldi

52 X Eample: projection of on the new basis 5 nc X nc U X nc P PC p p PC Piero Baraldi

53 X Eample: projection of on the new basis 53 nc U X nc P PC p p nc T X UP PC Piero Baraldi

54 Properties of the PCs 54 PCs are uncorrelated p i p j Data can be transformed from the original to the trasformed bases and viceversa without any loss of information (multiplication for P and P T ) PCs are ordered the first few retains the most of the variation present in the data. % Var PC i i i,, n i Piero Baraldi

55 Why does PCA work? () 55 PC arg w ma Var X nc w Var w ma T X w X w X w T X nc nc T X T T Var X w L( w, ) w Vw w w nc nc nc w w T Vw nc Lagrange multiplier To be maimized! L( w, ) Vw w Eigenvectors T w are solutions of Which eigenvector is maimizing the variance w T Vw? Piero Baraldi L( w, )

56 Why does PCA work? () 56 Eigenvectors w T are solutions of Vw w Which eigenvector is maimizing the variance w T Vw? T T w Vw w w The eigenvector associated to the largest eigenvalue Piero Baraldi

57 How does PCA work? (Step ) 57 ) PCA approimation = ignore the PCs of lower significance map the ervations in a subspace identified by the first eigenvectors p n,, p XP 8 nc X nc X P PC 8.8 X nc P PC PC P p p p Piero Baraldi

58 How does PCA work? (Step 3) 58 ) PCA approimation = map the ervations in a subspace n identified by the first n eigenvectors p,, p XP ) Antitrasform: XP P T PC Piero Baraldi

59 Piero Baraldi 59 PCA for fault detection: Historical data nc Nn Nj nc N kn kj k nc n j nc nc X P nc X Find from

60 PCA for fault detection: 6 Historical data nc k N nc nc Measured signals at present time: X j kj Nj nc n kn nc Nn Find (,, n ) P from X nc Trasform and project P I m looking at the measurements considering only the directions that are most meaningful in normal condition (directions of maimum variance) Antitrasform ˆ nc P P T Signal reconstructions ˆ ˆ nc normal condition nc abnormal condition Piero Baraldi I loose only the irrelevant noise The process is changed

61 Eercise Measured signals at present time: Signal reconstructions? Normal or abnormal condition? (, ) available historical signal measurements in normal plant condition Piero Baraldi

62 Eercise : Solution Measured signals at present time: p Step : find principal components:, (, p ) p p available historical signal measurements in normal plant condition Piero Baraldi

63 Eercise : Solution Measured signals at present time: p Step : find principal components, p (, ) p p PC Piero Baraldi

64 Eercise : Solution Measured signals at present time: p Step : find principal components, (, Step (PCA approimation): keep only PC of p ),i.e. p p p PC Piero Baraldi

65 Eercise : Solution Measured signals at present time: Step : find principal components (, Step (PCA approimation): keep only PC of Step 3 (antitrasform): 8 6 measuraments reconstruction ˆ nc P P T ),i.e. p ˆ Piero Baraldi nc normal condition

66 Eercise Measured signals at present time: Signal reconstructions? Normal or abnormal condition? (, ) available historical signal measurements in normal plant condition Piero Baraldi

67 Eercise : Solution Measured signals at present time: Step : find principal components p (, p Step (PCA approimation): keep only PC of ),i.e. p p p PC Piero Baraldi

68 Eercise : Solution Measured signals at present time: Step : find principal components p (, p Step (PCA approimation): keep only PC of ),i.e. p p p PC Piero Baraldi

69 Eercise : Solution Measured signals at present time: Step : find principal components (, Step (PCA approimation): keep only PC of Step 3 (antitrasform): 8 ˆ nc P P T ),i.e. p 6 4 measuraments reconstruction ˆ Piero Baraldi nc Abnormal condition

70 PCA remarks 7 Computational time: Training time = computational time necessary to find the Principal Components is proportional to the number of measured signals (n) Eecution time: very short (only matri multiplications) OK for online applications Piero Baraldi

71 PCA remarks 7 Performance: Accuracy = satisfactory t t M O D E L ˆ t t Piero Baraldi

72 PCA remarks 7 Performance: Accuracy = satisfactory Low robustness and spillover effects on highly correlated signals t t M O D E L ˆ t t Unsatisfactory for dataset characterized by highly non linear relationships. Piero Baraldi

73 73 Data-driven fault detection The approach Modeling the component behaviour in normal condition Model requirements Modeling techniques Principal Component Analysis (PCA) AutoAssociative Kernel Regression (AAKR) Eample of application Analysis of the residuals: Sequential Probability Ratio Test (SPRT) Some Conclusions

74 Auto Associative Kernel Regression (AAKR)

75 What is AAKR? Auto-associative model n Auto- Associative Model ˆ ˆ ˆn ˆ i f,,, i,, n n Empirical model built using training patterns = historical signal measurements in normal plant condition Signal nc nc j n nc X k kj kn nc nc N Nj Nn Observation 75

76 76 How does AAKR work? Training pattern Test pattern: input Output X nc k N nc nc j kj Nj (,, n ) nc nc nc ˆ ( ˆ,, ˆ ) X n nc nc n kn nc Nn = historical signal measurements in normal plant condition = measured signals at current time = signal reconstructions (epected values of the signals in normal condition) nc ˆ n AAKR nc ˆ nc ˆn 76

77 77 How does AAKR work? Training pattern X Test pattern: input Test pattern: output nc k N nc nc j kj Nj (,, n ) nc nc nc ˆ ( ˆ,, ˆ ) n nc n kn nc Nn = historical signal measurements in normal plant condition = measured signals at current time = weighted sum of the training patterns: 77

78 78 How does AAKR work? Training pattern X Test pattern: input Test pattern: output nc k N nc nc j kj Nj (,, n ) nc nc nc ˆ ( ˆ,, ˆ ) n nc n kn nc Nn = historical signal measurements in normal plant condition = measured signals at current time = weighted sum of the training patterns: On all the training pattern ˆ nc j N k w( k) N k w( k) nc kj 78

79 79 How does AAKR work? Output nc ˆ ( ˆ nc,, ˆ nc n ) = weighted sum of the training patterns: On all the training pattern ˆ nc j N k w( k) k nc kj weights w(k) = similarity measures between (the test and the k-th training pattern): n w N w( k) d ( k ) h ( k) e h and nc k nc with d ( k) ( j ) Euclidean distance between and j kj low weight nc k high weight h = bandwidth parameter 79

80 Bandwidth parameter d= w=.4/h d=h w=.4/h d=h w=.5/h d=3h w=.4/h w d h w( d 3h) w 4 w 8 6 h=. h= d 8

81 Eample Signal values at current time: Signal reconstructions? Normal or abnormal condition? (,, n ) available historical signal measurements in normal plant condition 8

82 Eample : Solution Signal values at current time: ( ˆ nc nc ˆ,, (,, n nc ˆ n ) Signal reconstructions: based on the available historical signal measurements in normal plant condition ) ˆ nc normal condition 8

83 Eample Signal values at current time: Signal reconstructions? Normal or abnormal condition? (,, n ) available historical signal measurements in normal plant condition 83

84 84 Eample : Solution Signal values at current time: ( ˆ nc nc ˆ,, (,, n nc ˆ n ) Signal reconstructions: based on the available historical signal measurements in normal plant condition ) ˆ nc abnormal condition available historical signal measurements in normal plant condition 84

85 85 AAKR: Computational Time Computational time: No training of the model Test: computational time depends on the number of training patterns (N) and on the number of signals (n) d ( k) n j ( j nc kj ) 85

86 86 AAKR Performance: Accuracy Accuracy: depends on the training set: N Accuracy 86

87 87 AAKR Performance: Accuracy () Accuracy: depends on the training set: N Accuracy Few patterns and not well distributed in the training space Inaccurate reconstruction 87

88 AAKR Robustness and resistance to the spill-over effect 88

89 Case study: Monitoring a Turbine for Energy Production 89 6 Temperature Sensors in different position Highly Correlated Signals Abnormal conditions occur on the first.95 signal

90 Residual Residual Case study: Traditional AAKR Traditional AAKR Simulated abnormal residuals conditions Time Traditional AAKR Simulated abnormal residuals conditions Time DELAY IN THE DETECTION IMPOSSIBILITY TO IDENTIFY THE SIGNALS TRIGGERING THE ABNORMAL BEHAVIOR

91 Our Contribution: A modified AAKR method 9 Ԧ - Δ Ԧ Fault Detection Fault No Fault Modified AAKR Ԧ nc Ԧ Pre-processing ψ Ԧ Kernel-Based Reconstruction Ԧ nc Projecting the measurement and the historical data in a new space Ԧ, Ԧ hist k ψ Ԧ, ψ Ԧ hist k Ԧ hist Ԧhist Ԧ Malfunctions causing variations of a small number of signals are more frequent than those causing variations of a large number of signals ψ Ԧ ψ Ԧ hist ψ Ԧ hist Ԧ Ԧ hist Ԧ hist Dilatation matri ψ Ԧ hist = D Ԧp P perm Ԧ hist Permutation matri Modification of the loci of equisimilarity points

92 Residual Residual Results Modified AAKR Traditional AAKR Simulated abnormal conditions Time Modified AAKR Traditional AAKR Simulated abnormal conditions Time Early Detection 3 Correct Diagnosis of the signal that triggers the alarms More Accurate 4 5 6

93 Application to a real case study 93

94 Application to a real case study 94

95 Application to a real case study 95

96 Visual Comparison with historical normal condition values 96

97 Visual Comparison with historical normal condition values 97

98 Correlation coefficients 98 Historical Values Modified AAKR reconstruction Traditional AAKR reconstruction

99 Modified AAKR 99 Traditional AAKR Modify AAKR Loci of equisimilarity points Ԧ Ԧ hist Ԧ hist Ԧ Ԧ hist Ԧ hist Accuracy OK! OK! Robustness NO! Especially with correlated signals. Robust reconstruction of the values epected in normal conditions. Correct identification of signals affected by abnormal condition 3. Good performance with correlated signals

100 Data-driven fault detection The approach Modeling the component behaviour in normal condition Model requirements Modeling techniques Principal Component Analysis (PCA) AutoAssociative Kernel Regression (AAKR) Eample of application Analysis of the residuals: Sequential Probability Ratio Test (SPRT) Some Conclusions

101 Problem Statement (EdF): hundreds of signals Grouping AUTO-ASSOCIATIVE MODEL OF PLANT BEHAVIOR IN NORMAL CONDITION MEASURED SIGNALS COMPARISON MODEL MODEL MODEL m

102 Challenge: Optimal Grouping MEASURED SIGNALS COMPARISON HOW TO GROUP SIGNALS? MODEL MODEL MODEL m

103 Case Study (EdF) 3 COMPONENT TO BE MONITORED Reactor Coolant Pumps of a PWR Nuclear Power Plant 4 MEASURED 94 signals, 48 of which considered SIGNALS as most important by EdF eperts RECONSTRUCTION Auto-Associative Kernel Regression MODEL (AAKR) historical measurements test measurements reconstruction

104 Approaches to signal grouping 4 HOW TO SPLIT THE SIGNALS INTO SUBGROUPS? A-PRIORI CRITERIA (signals divided on the basis of ) location in the power plant correlation physical homogeneity others

105 Results 5 BEST A-PRIORI GROUPING: correlation signals WHITE: high correlation (.7 ] 33 GREY: medium correlation (.4.7] BLACK: low correlation [.4] signal belonging to group signal belonging to group signal belonging to group 3 signal belonging to group 4 signal belonging to group 5 4 signals CRITICALITY: how to group the signals which have a low degree of correlation with all the others?

106 Approaches to Signal Grouping 6 HOW TO SPLIT THE SIGNALS INTO SUBGROUPS? A-PRIORI CRITERIA (signals divided on the basis of ) location in the power plant correlation physical homogeneity others WRAPPER APPROACH n SIGNALS SEARCH ENGINE SEARCH ALGORITHM CANDIDATE GROUPS AAKR PERFORMANCE EVALUATION OPTIMAL GROUPING

107 The Wrapper Approach: Genetic Algorithms 7 SEARCH ENGINE Genetic Algorithms CHROMOSOME n genes = n signals GENE signal signal signal 3 signal i signal n GROUP LABEL (integer number) PERFORMANCE EVALUATION fitness = Accuracy Robustness

108 Results 8 OBTAINED GROUPINGS correlation GA MAIN DIFFERENCE: signals which have a low degree of correlation are divided in groups and/or mied with signals with a high degree of correlation

109 Results 9 correlation GA Accuracy = = Robustness NO Spill-Over = =

110 Results: Wrapper Approach AUTO-ASSOCIATIVE MODEL OF PLANT BEHAVIOR IN NORMAL CONDITIONS ŝ t COMPARISON MEASURED SIGNALS s s ŝ (SEAL OUTCOMING FLOW) t DECISION t ABNORMAL CONDITION: seal deterioration NORMAL CONDITION ABNORMAL CONDITION

111 Conclusions groups of correlated signals accurate AAKR reconstructions; big groups robust AAKR reconstructions; the wrapper GA search finds the optimal groups also for those signals with low degree of correlation with all the others.

112 Data-driven fault detection The approach Modeling the component behaviour in normal condition Model requirements Modeling techniques Principal Component Analysis (PCA) AutoAssociative Kernel Regression (AAKR) Eample of application Analysis of the residuals: Sequential Probability Ratio Test (SPRT) Some Conclusions

113 Model based fault detection 3 SIGNAL RECONSTRUCTIONS ŝ MEASURED SIGNALS s MODEL OF COMPONENT BEHAVIOR IN NORMAL CONDITIONS ŝ t t t s COMPARISON t RESIDUALS Pb. s ŝ s ŝ t DECISION t NORMAL CONDITION: No maintenance ABNORMAL CONDITION: maintenance required 3

114 Abnormal condition detection: decision Basics of the decision: residual analysis r ˆ r r Normal condition Abnormal condition Methods Threshold-based approaches Stochastic approaches 4

115 Abnormal condition detection: decision Basics of the decision: residual analysis r ˆ r r Normal condition Abnormal condition Methods Threshold-based approaches Stochastic approaches 5

116 Threshold-based approaches r Abnormal condition detection t r Too small thresholds high false alarm rates (α) Normal conditions t Too large thresholds high missing alarm rates (β) r Abnormal conditions t 6

117 Stochastic approaches Residual (r)= random variable described by a probability law The probability law is different in case of normal/abnormal condition.5 Normal condition.5 Abnormal condition r r ~ N(, ) r r~ N(, ) 7

118 Stochastic approach: Sequential Probability Ratio Test (SPRT) R r r,, sequence of residuals at time t,t,,t N n, r N Binary hypothesis test: Null hypothesis (H ) Normal condition ~ i i, r N(, ) f r, N r Alternative hypothesis (H ) Abnormal condition ~ i i, r N(, ) f r, N r 8

119 SPRT: the decision L n P P R R n n H H is true is true f f r fr frn r fr frn ln L n H is true B Not enough information A H is true 9

120 SPRT Theorem False alarm B A ln ln P P D H is true D H is true Missing alarm

121 SPRT for the positive mean test Null hypothesis (H ) Normal condition Alternative hypothesis (H ) Abnormal condition ), N( r ~ ), ( N r ~ Sequential Formula! = ) ln( ln n n n n k k n k k n r L r r r L. ),,, ( ),,, ( n k k n k r k r n n n e e H r r r P H r r r P L

122 Eample: SPRT B ln ln L n H is true L ln ln ln( L L lnl L lnl ) r r 3 Not enough information Not enough information t A ln H is true

123 SPRT: parameters to be set the residual variance in normal condition (σ ) the epected offset amplitude (μ ) the maimum acceptable false alarm rate (α) the maimum acceptable missing alarm rate (β) 3

124 Signal value Eample: Reactor Coolant Pumps in a PWR Time interval Offset [-] No [-4] Yes (amplitude =.) [4-6] Yes (amplitude =.3) [6-8] Yes (amplitude =.34) [8-] Yes (amplitude =.46) erved True signal value Reconstruction Time 4

125 Residuals Eample: residuals Time No offset Maimum offset 5

126 L ln ln Eample: SPRT Parameter Value α. Β. μ μ.46 σ. L L L L r r H B ln is true SPRT inde Upper Threshold Lower Threshold SPRT value A ln H is true Time No offset Maimum offset 6

127 SPRT: performance Average Sample Number (ASN) necessary to deliver a decision Time interval Offset Estimated ASN Number of times in which a normal condition has been detected Number of times in which an abnormal condition has been detected [-] No. 5 [-4] amplitude = [4-6] amplitude = [6-8] amplitude = [8-] amplitude =

128 8 Data-driven fault detection The approach Modeling the component behaviour in normal condition Model requirements Modeling techniques Principal Component Analysis (PCA) AutoAssociative Kernel Regression (AAKR) Eample of application Analysis of the residuals: Sequential Probability Ratio Test (SPRT) Some Conclusions

129 9 Fault detection challenges Fault detection systems are currently used to monitor component of comple industrial plants (e.g. electric power plants, transportation systems, process plants) Commercial software for fault detection is available A Challenge: Adaptability 9

130 Fault Detection challenge: adaptability of the methods 3 Eample: monitoring the turbine of an electric power plant t Identify historical signal measurements in normal plant operation P P Develop the model False alarm rate Plant operations slowly change with time T T t t time A New Model is necessary 3

131 Fault Detection challenge: adaptability of the methods 3 Eample: monitoring the turbine of an electric power plant t Identify historical signal measurements in normal plant operation P P Develop the model False alarm rate Plant operations slowly change with time T T t t time t Identify recent historical signal measurements in normal plant operation P Develop the new model P A New Model is necessary False alarm rates T T t t time Periodic Human Interventions for developing new models! high costs! 3

132 Fault detection challenge: adaptability of the methods 3 The detection model should be able to follow the process changes: Incremental learning of the new data that gradually becomes available No necessity of human intervention for: selecting recent normal operation data building the new model New data are coming P P T T Automatic updating of the model P T 3