EE392m Fault Diagnostics Systems Introduction Gorinevsky Fault Diagnostics Systems 1 EE392m Fault...

2009Gorinevsky

Fault Diagnostics Systems 1

EE392m EE392m Fault Diagnostics Systems Fault Diagnostics Systems

Introduction Introduction Dimitry Gorinevsky Consulting Professor

Information Systems Laboratory

E392m ● Spring 2009

2009Gorinevsky


Course Subject

• Engineering of fault diagnostics systems • Embedded computer interacting with real world

– Detect abnormal operation – Fault tolerance: more than 80% of critical control code

• Operations and maintenance – More than 50% of the system lifetime costs – Troubleshooting support – Condition-based maintenance – CBM

2009Gorinevsky


Prerequisites and Course Place

• The subject is not covered in other courses• Prerequisites (helpful but not necessary)

– Stat 116; EE263 or Eng 207a; EE278 or Eng 207b

• The course is about technical approaches that are actually used in fault diagnostics applications – Survived demands of real life – Used and supported by BS-level engineers in industry – Should be accessible to a Stanford grad student

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Course Mechanics • Class website: www.stanford.edu/class/ee392M/• Weekly seminars

– Follow website announcements • Guest lecturers from diverse industries

– Co-sponsored by NASA • Travel support for lecturers

– Lecture notes will be posted as available• Attendance • Reference texts

– Isermann; Chiang, Russel, & Braatz; Patton, Clark & Frank– Different coverage – Contact me if you have a specific interest

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On-line (Embedded) Functions

• Embedded system, anomaly warnings – BIT – Built-in-Test– BITE – Built-in-Test Equipment

• FDIR – Fault Detection Identification and Recovery

• FT-RM– Fault Tolerance and Redundancy Management

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Off-line Functions• Reliability

– FMECA- Failure Mode, Effects, and Criticality Analysis – Design time analysis – open loop

• Maintenance and Support – Diagnostics for maintenance– Troubleshooting support– Test equipment – CBM – Condition Based Maintenance– Pre-testing – disk drives

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Fault Diagnostics in Industry• Space systems • Defense systems: aviation, marine, and ground • Commercial aerospace

– Aircraft, jet engines • Ground vehicles

– Locomotives, trucks, cars• High-tech

– Networks and IT systems – Disk drives– Server farms

• Process control– IC Manufacturing– Refineries– Power plants

• Oil and gas drilling

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Guest Lecture Overview

Automotive powertrain

Military aircraft systems

Computing systems

Jet engines

Avionics of commercial aircraft

IC Manufacturing processes

Networks and IT systems

Introduction and overview

Diagnostics Application

2-Jun-0910

FordKolmanovsky26-May-099

LockheedBodden19-May-098

SunUrmanov12-May-097

5-May-096

GE InfrastructureAdibhatla28-Apr-095

HoneywellFelke21-Apr-094

IntelTuv14-Apr-093

VMTurbo (EMC) Rabover7-Apr-092

StanfordGorinevsky31-Mar-091

From LectorDate#

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Diagnostics Methods Overview

• Shewhart chart (Control chart)• Multivariable SPC, T2

• Model-based estimation – Least squares estimation

• Integrated diagnostics – Cascaded design

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Abnormality Detection - SPC

• SPC - Statistical Process Control – monitoring of manufacturing processes– warning for off-target quality

• Main SPC method – Shewhart Chart (1920s)

• Also see – EWMA (1940s)– CuSum (1950s) – Western Electric Rules (1950s)

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SPC: Shewhart Control Chart• W.Shewhart, Bell Labs, 1924• Statistical Process Control (SPC) • UCL = mean + 3·σ• LCL = mean - 3·σ

Walter Shewhart (1891-1967)

sample3 6 9 1212 15

mean

qual

ity v

aria

ble

Lower Control Limit

Upper Control Limit

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Shewhart Chart, cont’d• Quality variable assumed randomly

changing around a steady state value• Detection: y(t) > UCL=mean+3·σ• For normal distribution, false alarm

probability is less than 0.27%

P(e > 3) = 1-Φ(3) = 0.1350·10-2

P(e < 3) = Φ(-3) = 0.1350·10-2

σµ0)()( −

=tyte

UCLLCL

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Shewhart Chart –Hypothesis Test• Null hypothesis

– given mean and covariance

• Fault hypothesis– a different mean

• Hypothesis testing

),(~)(: 200 σµNtyH

),(~)(: 2011 σµµ ≠NtyH

},{)(

10 HHXtyY

∈=given

find

00 )( pHP =

11)( pHP =

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Bayesian Formulation • Data:

• Bayes rule

• Observation model:• Prior model:• Maximum A posteriori Probability estimate

XY Observation

Underlying State

c XPXYPYXP ⋅⋅= )()|()|()|( XYP

)(XP

( ) ( )( )4444 34444 21

indexposterior log

log|logminarg−−

−−=L

XPXYPX

Rev. Thomas Bayes(1702-1761)

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Hypothesis Testing

• Null hypothesis

• Fault hypothesis

• Log-likelihood ratio

• Declare fault if

( ) ( )20221|log µσ

−=− yXYP ( ) 0loglog pXP −=−

( ) ( ) 02

1|log 212 =−=− µ

σyXYP ( ) 1loglog pXP −=−

( ) ( ) 0log2

110

20210 >−−=−=Λ ppyLL µ

σ

110 )1(log2 ppy −>− σµ

10 1 pp −=

σ30113.01 ⇒=p

100

1

)|()|(log LL

YHPYHP

−==Λ

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Shewhart Chart: Use Examples

• SPC in manufacturing

• Fault monitoring

• Fault tolerance – sensor integrity monitoring

Sensor

Reference-+

Fault

|∆y| < 3σ Normalyes

no

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Multivariable SPC• Univariate process

• Two independent univariate processes

( ))(1)(

)1,(1 222

cccFczP

Φ−+−Φ=−=>

( ) ( ) 22

222 ~22

2

22

21

1

11 χσµ

σµ

321321z

y

z

yz −− +=

22

02 ~ χσµ

⎟⎠⎞

⎜⎝⎛ −

=yz

( ) )2;(1 222 cFczP −=>

Chi-squared CDF

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Multivariable SPC

• Two correlated univariate processes y1(t) and y2(t) cov(y1,y2) = Q, Q-1= LTL

• Uncorrelated linear combinationsz(t) = L·[y(t)-µ]

• Declare fault (anomaly) if ( ) ( ) 2

212 ~ χµµ −−= − yQyz T

⎥⎦

⎤⎢⎣

⎡=

2

1

yy

y

⎥⎦

⎤⎢⎣

⎡=

2

1

µµ

µ

( ) )2;(1 222 cFczP −=>

( ) ( ) 21 cyQy T >−− − µµ

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Multivariate SPC - Hotelling's T2

• Empirical parameter estimates

( )

( )µµµ

µ

−≈−−=

≈=

∑

∑

=

=

ytytyn

Q

XEtyn

Tn

t

T

n

t

cov))()()((1ˆ

)(1ˆ

1

1

• Hotelling's T2 statistics is

• T2 can be trended as a univariate SPC variable

( ) ( )µµ −−= − )(ˆ)( 12 tyQtyT T

Harold Hotelling(1895-1973)

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Least Squares Estimation

• Linear observation model:

• Fault signature model– Columns of C are fault signatures– Could be obtained from physics model

• secant method– Could be identified from data:

• regression, data mining

• Estimate – regularized least squares

vCXY +=

( ) YCrICCX TT 1ˆ −+=

Carl Friedrich Gauss (1777-1855)

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Bayesian Estimation

• Observation model: P(Y|X)

• Prior models: P(X)

• MAP estimate:

vCXY +=

( ) YCQRCQCX TT 1111ˆ −−−− +=

),0(~ QNv

),0(~ RNX

3214434421)(log

221

)|(log

221

11minargˆ

XP

R

XYP

QXCXYX

−−

−− +−=

...)(log 121 +=− − XRXXP T

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Model-based Residuals

Plant Model

input variables

Fault Diagnostics

prediction residual

+-

output variables

Plant Data Collected on-line

Input data

Output data

• Compute model-based prediction residualY = Yraw - f(U,X)

• If X = 0 (nominal case) we should have Y = 0. • Residuals Y reflect faults

– Sensor fault model - additive output change– Actuator fault model - additive input change

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Example: Jet Engine Model

• Nonlinear jet engine model– static map

• Residuals

• Linearized model

vCXY += ⎥⎦

⎤⎢⎣

⎡=

driftsensor EGTleak band Bleed

iondeteriorat TurbineX

),( XUfYY raw −=

XXUfC

∂∂

−=),(

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Example: Fault Estimates• Maintenance decision support tool

HoneywellLF507 EngineFleet

Estimates of (fault)performance parameter deterioration

1550 1600 1650 1700 1750 1800 1850 1900-1

-0.50

0.51

1.52

2.53

HP

Spo

ol D

eter

iora

tion

(%)

Sample No.

1550 1600 1650 1700 1750 1800 1850 1900-10-505

1015202530

Ble

ed B

and

Leak

age

(%)

Sample No.

1550 1600 1650 1700 1750 1800 1850 1900-40

-20

0

20

40

60

EG

T S

enso

r Offs

et (d

eg C

)

Sample No.

6-10-03

Ganguli, Deo, & Gorinevsky, IEEE CCA’04

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Cascaded Design

• Increasing complexity and integration of system

• Slower time scale • Simple inner loop models• Examples

– Control systems – Estimation and data fusion – Fault diagnostics systems

Unit

Subsystem

System

UnitUnit

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Integrated System Diagnostics• Complex integrated systems • Examples

– Aerospace vehicle, e.g. B777– Large scale computer network– Medical equipment

Subsystem 1 Diagnostics

Subsystem nDiagnostics

Integrated Diagnostic System

Decision Support Interface

Subsystem 2 Diagnostics …

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Discrete Fault Signatures

0000000

#0Null

001011#7011000#6010001#5000001#4100101#3010110#2100110#1

#6#5#4#3#2#1Root Cause Symptom Code

kk BY =Model of root cause fault k :

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Estimation Algorithm

• Diagnosis problem:Given data Y, diagnose root cause k

• Solution:

• Minimal Hamming distance• Justifications

– Case-based reasoning (table of fault cases)– Model-based reasoning (fault signature model)– Bayesian

1minarg kBYk −=

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Bayesian Justification

• Data

• Observation model

{ }nn BHBHHXY :,,:,0: 1

10 K=

11)|( pHbyP kkjj −==

)|( XYP1)|( pHbyP k

kjj =≠

( )444 3444 21

2/1for ,0

110

1

1

)1log(log||)1log(<>=

−−⋅−−−⋅− ∑p

n

j

kjj ppbypn

1)|(log k

k bywcHYP −+=−

yj follows the model

deviates from the model

=−+−−=− ∑∑≠= k

jjkjj byby

k ppHYP 11 log)1log()|(log

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Bayesian Justification

• Prior model

• MAP Estimate

)(XP ( )11)( += nHP k

( )dbywck k

k+−+=

1minarg

dHP k =− )(log

( ) ( )( )kk HPHYPk log|logminarg −−=

1minarg k

kbyk −=

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Conclusions

• Basic diagnostics estimation methods – Are known for long time – Used in on-line systems for less time– Can be explained in several ways, e.g., Bayesian

• Engineering of fault diagnostics systems– Is new and current – Will be discussed in guest lectures– Not just diagnostics algorithms

2009Gorinevsky


Guest Lectures: Approaches

Automotive

Aircraft

Computing

Jet Engines

Aircraft

IC Manufacture

Network

Application

Model-basedFordKolmanovsky26-May-099

Fault toleranceLockheedBodden19-May-098

Multivariate SPC, MLSunUrmanov12-May-097

Multivariate estimationGE InfraAdibhatla28-Apr-095

Integrated diagnostics HoneywellFelke21-Apr-094

Fault signature IDIntelTuv14-Apr-093

Integrated diagnostics EMCRabover7-Apr-092

ApproachFrom LectorDate#

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