HCF Conference, New Orleans, LO, March 8 HCF Conference, New Orleans, LO, March 8 - - 11, 2005 11, 2005 Stochastic Interference and Visualization Stochastic Interference and Visualization Tools for Risk Tools for Risk - - Based In Based In - - Flight Engine Flight Engine Fault Diagnostics and Prognostics Fault Diagnostics and Prognostics Dr. Dan M. Ghiocel Dr. Dan M. Ghiocel Email: dan.ghiocel@ghiocel Email: dan.ghiocel@ghiocel - - tech.com tech.com Phone: 585 Phone: 585 - - 641 641 - - 0379 0379 Ghiocel Predictive Technologies Inc. Ghiocel Predictive Technologies Inc.
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HCF05 Stochastic Inference and Visualization for EHM
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HCF Conference, New Orleans, LO, March 8HCF Conference, New Orleans, LO, March 8--11, 200511, 2005
Stochastic Interference and Visualization Stochastic Interference and Visualization Tools for RiskTools for Risk--Based InBased In--Flight EngineFlight Engine
Fault Diagnostics and PrognosticsFault Diagnostics and Prognostics
Dr. Dan M. GhiocelDr. Dan M. GhiocelEmail: dan.ghiocel@ghiocelEmail: [email protected]
Phone: 585Phone: 585--641641--03790379
Ghiocel Predictive Technologies Inc.Ghiocel Predictive Technologies Inc.
To present innovative stochastic inference and visualization techniques applicable to in-flight engine PHM.
Acknowledgement:Acknowledgement:Collaborative effort with STI Technologies, Inc., a continuationof USAF sponsored StoFIS development (JSF Endorsement)
Objective of the Presentation:Objective of the Presentation:
Presentation ContentPresentation Content
1.1. StochasticStochastic--NeuroNeuro--Fuzzy System (Fuzzy System (StoFISStoFIS) for Engine ) for Engine Fault Diagnostics/PrognosticsFault Diagnostics/Prognostics
4. Visualization Tools for High Dimensional Outputs4. Visualization Tools for High Dimensional Outputs
5. Concluding Remarks5. Concluding Remarks
1. Stochastic1. Stochastic--NeuroNeuro--Fuzzy Inference System Fuzzy Inference System ((StoFISStoFIS) for Engine Fault Diagnostics/Prognostics) for Engine Fault Diagnostics/Prognostics
Fault #7: Drop in High Pressure Compressor Efficiency
-20 -15 -10 -5 0 5 10 15 200
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
NC1%2%3%
-2 -1.5 -1 -0.5 0 0.5 1 1.5 20
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
NC1%2%3%
-10 -8 -6 -4 -2 0 2 4 6 8 100
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
NC1%2%3%
-100 -80 -60 -40 -20 0 20 40 60 80 1000
0.05
0.1
0.15
0.2
0.25
0.3
0.35
NC1%2%3%
Probability Density of Engine Parameter DeviationsProbability Density of Engine Parameter Deviations
Real PHM Problems Are Often in HighReal PHM Problems Are Often in High--Dimensions... Dimensions... Current Practice:Current Practice:
Using 1D Selected Fault Parameters …Using 1D Selected Fault Parameters …Health Index based on subjective data fusion…Health Index based on subjective data fusion…Difficult to understand stochastic fault physics… Difficult to understand stochastic fault physics…
Future Need:Future Need:
Using HighUsing High--Dimensional Parameter Space..Dimensional Parameter Space..Health Index based on High D fault patterns…Health Index based on High D fault patterns…Helps to understand stochastic fault physics…Helps to understand stochastic fault physics…
We need to capture the complex We need to capture the complex stochastic fault patterns:stochastic fault patterns:RESPONSE:RESPONSE:
1) Accurate estimation of the HD 1) Accurate estimation of the HD stochastic inputstochastic input--output relationship output relationship
2) Stochastic pattern mapping in 2) Stochastic pattern mapping in ““2D health visualization maps2D health visualization maps””RISK COMPUTATIONS:RISK COMPUTATIONS:
3) 3) Multidimensional Reliability Model Multidimensional Reliability Model
Data Fusion? Or Stochastic Physics?Data Fusion? Or Stochastic Physics?
Complex Fault Patterns
Single Fault Parameter
Severe Fault
Incipient Fault
Fault
FaultBasin
Fault Basin
Usage Trajectory
Stochastic Fault Basin Concept
High Severity
LowSeverity
HighSeverity
LowSeverity
Parameter i
Parameter j
Type A Type B
MeasurementEllipsoid
FaultLocation Ellipsoids
Note: Need to scan all the Fault Basins
Critical FaultDiagnosed Fault
Diagnosed Fault
Reliability Index Reliability Index
Cumulative Fault Progression Index Cumulative Fault Progression Index
0
100
200
300
400
500
600
60% 65% 70% 75% 80% 85% 90% 95% 100%
P3 (P
SIA
)
0
20
40
60
80
100
120
140
160
180
60% 65% 70% 75% 80% 85% 90% 95% 100%
P3 (P
SIA
)
GroundGround--test datatest data InIn--flight dataflight dataInIn--Flight vs. Ground Parameter Variations Flight vs. Ground Parameter Variations
Stochastic Approximation in HighStochastic Approximation in High--DimensionsDimensionsOneOne--Dimensional Function Dimensional Function Multidimensional Function Multidimensional Function
2L and 3L Hierarchical Approximation Models2L and 3L Hierarchical Approximation Models
1L denoted one computational layer ( stochastic FEA)
1L 1L 1L
Symbolic Representation
Input Output
∑=k
kkji )h(fw)x,x(f
jxix1h
2h
jxix1h
2h
∑=k
kklji )h(fw)x,x,x(f3D
2DLocal JPDF ModelsLocal JPDF Models
HO Stochastic Field Approximation Using Local JPDF Models HO Stochastic Field Approximation Using Local JPDF Models
Data Space State Space
Comparison of 2L and 3L (Bayesian) HM ModelsComparison of 2L and 3L (Bayesian) HM Models
2L HM 10 2L HM 10 ClustClust BFBF 3L HM (10 3L HM (10 ClustClust BF with Point BF) BF with Point BF)
2L HM Point BF 2L HM Point BF ANFIS 10 Subs ANFIS 10 Subs ClustClust BFBF
InnovativeInnovative
- If the posterior JPDF in latent space is unimodal and symmetric, then the mean and mode are closely-spaced, i.e. the map is uniformly colored. - If the posterior JPDF is more complex, i.e. the mapping manifold is locally twisted or highly curved near a data point the posterior mean and mode are well separated, i.e. the map is non-uniformly colored. -- Magnification factors (measure of local nonlinear distortion ofMagnification factors (measure of local nonlinear distortion of the mapping the mapping surface) shows the data clustering structure.surface) shows the data clustering structure.
4. Visualization Tools for High4. Visualization Tools for High--Dimensional ReponsesDimensional Reponses
2. JPDF Map in Latent Space (2D function)2. JPDF Map in Latent Space (2D function)-- This is a powerful tool totally new for describing highThis is a powerful tool totally new for describing high--dimensional, complex dimensional, complex stochastic patterns. Statistical moments can be used as stochaststochastic patterns. Statistical moments can be used as stochastic fault features ic fault features for fault diagnosis. The use of KL expansion as a synthetic clasfor fault diagnosis. The use of KL expansion as a synthetic classifier.sifier.
Sample Data in the 3D Original Space Data in 2D Latent Space
Responsibility of Data Point 297 Magnification Factor Map (MFM)
Uniform Random Points in 3D Data Space Mean and Mode in the 2D Latent Space
MFM (2D Visualization Map) Uniform vs. Gaussian Data Points PDF
Stochastic Map Applied to Random Data Stochastic Map Applied to Random Data HyperplaneHyperplane
Simulated Fault # 1 Simulated Fault # 2
Simulated Fault # 3
Normal Conditions
Fault #1 - HPT
Fault #2 – HPC & LPT
Fault #3 - LPC
Normal Conditions Fault #1 - HPT
Fault #2 – HPC & LPT Fault #3 - LPC
Data Points in Latent Space Data Points in Latent Space
Normal Conditions Fault #1 - HPT
Fault #2 – HPC & LPT Fault #3 - LPC
Latent Data Space Means and ModesLatent Data Space Means and Modes
Normal Conditions Fault #1 - HPT
Fault #2 – HPC & LPT Fault #3 - LPC
Stochastic GTMStochastic GTM
Normal Conditions Fault #1 - HPT
Fault #2 – HPC & LPT Fault #3 - LPC
Log of JPDF in Latent Space Log of JPDF in Latent Space
Normal Conditions Fault #1 - HPT
Fault #2 – HPC & LPT Fault #3 - LPC
Log of JPDF in Latent SpaceLog of JPDF in Latent Space
Identification of Incipient Faults KLE Mode ClassifierIdentification of Incipient Faults KLE Mode ClassifierKL Classifier for Anomaly Detection
KL Vector Mode Classifier for Fault Diagnostics
Simple Fault Index
5. Concluding Remarks5. Concluding Remarks
1.1. Need to use accurate stochastic approximation tools for measuredNeed to use accurate stochastic approximation tools for measuredoutputs that are highoutputs that are high--dimensional stochastic functions of engine dimensional stochastic functions of engine parameters.parameters.
We recommend the use of 3We recommend the use of 3--level hierarchical stochastic approximation level hierarchical stochastic approximation models. They proposed models train much faster than standard NN.models. They proposed models train much faster than standard NN.
2.2. 2D Visualization Maps are extremely useful tools for complex2D Visualization Maps are extremely useful tools for complexfault diagnostic and prognostic problems.fault diagnostic and prognostic problems.
We recommend the output pattern visualization using (i) GeneratiWe recommend the output pattern visualization using (i) Generative ve Topographic Maps and (ii) JPDF Map in latent spaceTopographic Maps and (ii) JPDF Map in latent space