gertler talk

8/12/2019 Gertler Talk

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Fault Detection and Diagnosis

in Engineering SystemsBasic concepts with simple examples

Janos Gertler

George Mason University

Fairfax, Virginia


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Outline

What is a fault

What is diagnosis

Diagnostic approaches

Model - free methods

Principal component approach

Model - based methods

Systems identification

Application example: car engine diagnosis


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What is a fault

Fault: malfunction of a system component

- sensor fault - bias

- actuator fault - parameter change

- plant fault - leak, etc.

Symptom: an observable effect of a fault

Noise and disturbance: nuissances that mayaffect the symptoms


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What is a fault

actuator command

actuator leak sensor faults

fault

sensor readings

Sensor fault: reading is different from true value

Actuator fault: valve position is different from command

Plant fault: leak


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What is fault diagnosis

Fault detection: indicating if there is a fault

Fault isolation: determining where the fault is

Detection + Isolation = Diagnosis

Fault identification:

Determining the size of the fault

Determining the time of onset of the fault


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Model-free methods

Fault-tree analysis

- cause-effect trees analysed backwards

Spectrum analysis

- fault-specific frequencies in sound, vibration, etc

Limit checking

- checking measurements against preset limits


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flow

l1 l2 l3

s1 s2 s3

y1 y2 y3

Limit checking

y1 y2 y3

S1 fault off normal normal

Leak3 normal normal off

Leak2 normal off off

Leak1 off off off

High/low flow off off off


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Limit checking

Easy to implement

Requires no design

BUT

To accommodate normal variations, must have

limited fault sensitivity

Has limited fault specificity (symptom explosion)


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Principal Component Approach

Modeling phase: based on normal data

- determine the subspace where normal data exists(representation space, RepS)

- determine the spread (variances) of data in the RepS

Monotoring phase: compare observations torepresentation space

- if outside RepS, there are faults

- if inside RepS but outside thresholds, abnormaloperating conditions


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Principal Component Approach

u flow y1 = u

y2 = u

y1 y2

y2

Representation space

Fault

Normal spread

y1

u


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Principal component modeling

Centered normalised measurementsx(t) = [x1(t) xn(t)]

Data matrix: X = [ x(1) x(2) x(N)]

Covariance matrix: R = XX/N

Compute eigenvalues 1 n and eigenvectors q1 qn

q1 qk , kn, belonging to nonzero 1 k ,, span RepS

1 k are the variances in the respective directions


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Principal Components Residual Space

Residual Space (ResS):

complement of Representation Space, spanned by thee-vectors qk+1 qn , belonging to (near) - zero e-values

Residual= (Observation) (Its projection on RepS)

Residuals exist in ResS

ResS provides isolation information

- directional property (fault-specific response directions)

- structural property (fault-specific Boolean structures)


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Residual Space Directional Property

u flow

uy1 y2

y1 y2

y2

residualobservation

Repres. Space

q1y1

u

on u

q3q2

on y1 on y2

Residual Space


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Residual Space Structural Property

u u u

r2 r3r1

y1 y2 y1 y2 y1 y2

r1, r2, r3 : residuals obtained by projection

u y1 y2 Structure matrix

r1 0 1 1r2 1 1 0 Fault codes

r3 1 0 1


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Model-Based Methodsfaults f(t)

disturbances d(t) noise n(t)

outputs y(t)

inputs u(t) parameters

Complete model: y(t) = f[u(), f(), d(), n(), ]

Nominal model: y^(t) = f[u(), ]Models are: static/dynamic

linear/nonlinear


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Obtaining Models

First principle models

Empirical models

- classical systems identification

- principal component approach

- neuronets


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Analytical Redundancyd(t) f(t) n(t)

u(t) y(t)

PLANT

+

e(t) RESIDUAL r(t)

PROCESSING

-MODEL y^(t)

Primary residuals: e(t) = y(t) y^(t)

Processed residuals: r(t)


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Analytical redundancyf(t)

d(t) n(t)

u(t) y(t)PLANT

RESIDUAL

GENERATOR

r(t)


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Residual Properties

Detection properties

- sensitive to faults- insensitive to disturbances (disturbance decoupling)

- insensitive to model errors (model-error robustness)

perfect decoupling under limited circumstances optimal decoupling

- insensitive to noise

noise filtering statistical testing


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Residual Properties

Isolation properties

- selectively sensitive to faults

structured residuals perfect

directional residuals decoupling optimal residuals


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Residual Generation

u flow Model:

u y1 = u + u + y1y1 y2

y1 y2 y2 = u + u + y2

Primary residuals:e1 = y1 u = u + y1 u y1 y2

e2 = y2 u = u + y2 r1 1 1 0

Processed residuals: r2 1 0 1

r1 = e1 = u + y1 r3 0 1 1

r2 = e2 = u + y2

r3 = e2 e1 = y2 y1 Structured residuals


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Residual Generation

u flow Model:

u y1 = u + u + y1y1 y2

y1 y2 y2 = u + u + y2

Primary residuals:

e1 = y1 u = u + y1

e2 = y2 u = u + y2

Processed residuals:r1 = e1 = u + y1

r2 = e2 = u + y2

r3 = e1 e2 = y1 y2

r3on y1

r2

on ur1

on y2

Directional residuals


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Linear Residual Generation Methods

Perfect decoupling

- direct consistency relations- parity relations from state-space model

- Luenberger observer

- unknown input observer

Approximate decoupling

- the above with singular value decomposition

- constrained least-squares

- H-infinity optimization


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Linear Residual Generation Methods

Under identical conditions

(same plant, same response specification)

the various methods lead to

identical residual generators


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Dynamic Consistency Relations

System description:

y(t) = M(q)u(t) + Sf(q)f(t) + Sd(q)d(t)

q : shift operator

Primary residuals:e(t) = y(t) M(q)u(t) = Sf(q)f(t) + Sd(q)d(t)

Residual transformation:

r(t) = W(q)e(t) = W(q)[Sf(q)f(t) + Sd(q)d(t)]


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Dynamic Consistency Relations

Response specification:

r(t) = f(q)f(t) + d(q)d(t)

f(q) : specified fault response (structured or directional)

d(q) : specified disturbance response (decoupling)

W(q)[Sf(q) Sd(q)] = [f(q) d(q)] Solution for square system:

W(q) = [f(q) d(q)] [Sf(q) Sd(q)] -1


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Dynamic Consistency Realtions

Realization:

The residual generator W(q) must be causal and stable;

[Sf(q) Sd(q)]-1 is usually not so

Modified specification:

W(q) = [f(q) d(q)] (q) [Sf(q) Sd(q)] -1(q) : response modifier, to provide causality and

stability without interfering with specification

Implementation:

inverse is computed via the fault system matrix


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Diagnosis via Systems Identification

Approach:

- create reference model by identification- re-identify system on-line

discrepancy indicates parametric fault

Difficulty: discrete-time model parameters are nonlinear

functions of plant parameters

for small faults, fault-effect linearization continuous-time model identification (noise

sensitive or requires initialization)


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Applications

Very large systems

- Principal Components are widely used inchemical plants

- reliable numerical package is available

An intermediate-size system: rain-gauge

network in Barcelona, Spain (structured parity

relations)

Aerospace: traditionally Kalman filtering


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Applications

Mass-produced small systems:

on-board car-engine diagnosiscar-to-car variation (model variation robustness)

- GM: parity relations

- Ford: neuronets

- Daimler: parity relations + identification

Many published papers with application toare just simulation studies


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GM GMU On-Board Diagnosis Project

OBD-II: any component fault causing emissions

(CH, CO, NOX) go 50% over limit must bedetected on-line

Pilot project: intake manifold subsystem (THR,

MAP, MAF, EGR) Structured parity relations based on direct

identification

After more in-house development, this is beinggradually introduced on GM cars


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Filtered and integrated residual with fault


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On-board report MAP fault


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GM fleet experiment

Fleet of identical vehicles (Chevy Blazer) available at GM

Collect data from 25 vehicles

Identify models from combined data from 5 vehicles

Test on data from 25 vehiclesResidual means and variances vary

increase thresholds (sacrifice sensitivity)

Only a 50% increase is necessary


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Fault sensitivities GM fleet experiment

Critical fault sizes for detection and diagnosis

(fleet experiment)

Thr Iac Egr Map Maf

detection 2% 10% 12% 5% 2%

diagnosis 6% 20% 17% 7% 8%

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