hcf05 stochastic inference and visualization for ehm

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

2. Stochastic Fault Simulation2. Stochastic Fault Simulation

3. Stochastic Inference Models3. Stochastic Inference Models

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

Overall Engine GPA ModelOverall Engine GPA Model

Generic InGeneric In--Flight Turbofan Engine GPA ModelsFlight Turbofan Engine GPA Models

Pn,Tn = fn(P1,T1, ggm& , ωf, ωgg)Develop Generic GPA Models for Simulating Engine Functional Faults

Upstream HPC Fault

Down-stream HPT Fault

2. Stochastic Fault Simulations 2. Stochastic Fault Simulations

Typical Engine Fault in A 2D ProjectionTypical Engine Fault in A 2D Projection

1800 Brighton-Henrietta Townline Road, Rochester, NY 14623 ♦ www.st i- tech.com

Fault #4: Drop in High Pressure Turbine Capacity

-10 -8 -6 -4 -2 0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

NC1%2%3%

-40 -30 -20 -10 0 10 20 30 400

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

NC1%2%3%

-40 -30 -20 -10 0 10 20 30 400

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

NC1%2%3%

Fault #2: Drop in Low Pressure Turbine Capacity

-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

NC1%2%3%

-30 -20 -10 0 10 20 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

NC1%2%3%

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

Comp. PressureComp. Pressure Comp. PressureComp. Pressure

Functional Variation + Random Variation

Speed Speed

3. Stochastic Inference Models3. Stochastic Inference Models

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

1. Generative Topographic Maps (2D function)1. Generative Topographic Maps (2D function)

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.

Stochastic Generative Topographic Map Stochastic Generative Topographic Map

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



Latent Data Space Means and ModesLatent Data Space Means and Modes



Stochastic GTMStochastic GTM



Log of JPDF in Latent Space Log of JPDF in Latent Space



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

hcf05 stochastic inference and visualization for ehm

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