Fault detection and diagnosis in engineering systems basic concepts with simple examples
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Fault Detection and Diagnosis in Engineering Systems Basic concepts with simple examples. Janos Gertler George Mason University Fairfax, Virginia. Outline. What is a fault What is diagnosis Diagnostic approaches Model - free methods Principal component approach Model - based methods

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Fault detection and diagnosis in engineering systems basic concepts with simple examples

Fault Detection and Diagnosisin Engineering SystemsBasic concepts with simple examples

Janos Gertler

George Mason University

Fairfax, Virginia


Outline

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


What is a fault

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 may affect the symptoms


What is a fault1

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


What is fault diagnosis

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


Model free methods

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


Limit checking

Limit checking

flow

l1 l2 l3

s1 s2 s3

y1 y2 y3

y1 y2 y3

S1 faultoffnormalnormal

Leak3normalnormaloff

Leak2normaloffoff

Leak1offoffoff

High/low flowoffoffoff


Limit checking1

Limit checking

  • Easy to implement

  • Requires no design

    BUT

  • To accommodate “normal” variations, must have limited fault sensitivity

  • Has limited fault specificity (symptom explosion)


Principal component approach

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 to representation space

    - if outside RepS, there are faults

    - if inside RepS but outside thresholds, abnormal operating conditions


Principal component approach1

Principal Component Approach

uflow y1 = u

y2 = u

y1 y2

y2

Representation space

Fault

Normal spread

y1

u


Principal component modeling

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 , kn, belonging to nonzero 1 … k ,, span RepS

1 … k are the variances in the respective directions


Principal components residual space

Principal Components – Residual Space

Residual Space (ResS):

complement of Representation Space, spanned by the e-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)


Fault detection and diagnosis in engineering systems basic concepts with simple examples

Residual Space – Directional Property

uflow

u

y1 y2

y1 y2

y2

residual

observation

Repres. Space

q1

y1

u

on u

q3

q2

on y1 on y2

Residual Space


Residual space structural property

Residual Space – Structural Property

u u u

r2 r3

r1

y1 y2 y1 y2 y1 y2

r1, r2, r3 : residuals obtained by projection

uy1y2 Structure matrix

r1 0 1 1

r2 1 1 0 Fault codes

r3 1 0 1


Model based methods

Model-Based Methods

faults 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


Obtaining models

Obtaining Models

  • First principle models

  • Empirical models

    - “classical” systems identification

    - principal component approach

    - neuronets


Analytical redundancy

Analytical Redundancy

d(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)


Analytical redundancy1

Analytical redundancy

f(t)

d(t)n(t)

u(t) y(t)

PLANT

RESIDUAL

GENERATOR

r(t)


Residual properties

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


Residual properties1

Residual Properties

  • Isolation properties

    - selectively sensitive to faults

     structured residuals perfect

     directional residuals decoupling

     “optimal” residuals


Residual generation

Residual Generation

uflow Model:

u y1 = u + u + y1

y1 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


Fault detection and diagnosis in engineering systems basic concepts with simple examples

Residual Generation

uflow Model:

u y1 = u + u + y1

y1 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

r3

on y1

r2

on u

r1

on y2

Directional residuals


Linear residual generation methods

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


Linear residual generation methods1

Linear Residual Generation Methods

Under identical conditions

(same plant, same response specification)

the various methods lead to

identical residual generators


Dynamic consistency relations

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)]


Dynamic consistency relations1

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


Dynamic consistency realtions

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


Diagnosis via systems identification

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)


Applications

Applications

  • Very large systems

    - Principal Components are widely used in chemical plants

    - reliable numerical package is available

  • An intermediate-size system: rain-gauge network in Barcelona, Spain (structured parity relations)

  • Aerospace: traditionally Kalman filtering


Applications1

Applications

  • Mass-produced small systems:

    on-board car-engine diagnosis

    car-to-car variation (model variation robustness)

    - GM: parity relations

    - Ford: neuronets

    - Daimler: parity relations + identification

  • Many published papers “with application to”

    are just simulation studies


Gm gmu on board diagnosis project

GM – GMU On-Board Diagnosis Project

  • OBD-II: any component fault causing emissions (CH, CO, NOX) go 50% over limit must be detected 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 being gradually introduced on GM cars


Filtered and integrated residual with fault

Filtered and integrated residual with fault


On board report map fault

On-board report – MAP fault


Gm fleet experiment

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 vehicles

    Residual means and variances vary

     increase thresholds (sacrifice sensitivity)

    Only a 50% increase is necessary


Fault sensitivities gm fleet experiment

Fault sensitivities – GM fleet experiment

Critical fault sizes for detection and diagnosis

(fleet experiment)

ThrIacEgrMapMaf

detection 2%10%12% 5% 2%

diagnosis6%20%17% 7% 8%


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