Fault Detection and Isolation of an Aircraft using

Set-Valued Observers

Paulo Rosa (ISR/IST)!

Dynamic Stochastic Filtering, Prediction,!and Smoothing – July 7th – 2010!

Introduction!

Plant Control input

Measurement output

Disturbances Time-varying parameters Sensors noise

Model

FDI Filter Estimated

output

Fault?

Introduction (cont.’d)!•  Standard approaches for Fault Detection (FD):

•  Compute estimated output •  Generate a residual using the actual output

•  Compare it with a given threshold

•  Main drawback: the exact value of the threshold is highly dependent on the exogenous disturbances, measurement noise, and model uncertainty!

Fault Detected Fault Not Detected

Yes No r(k) > �

r(k) = ytrue(k)� yestimated(k)

Model Falsification!•  Main idea:

•  Set of plausible models for the plant •  Discard models that are not compatible with the input/output sequences

•  Model falsification for FD •  A fault is detected when the model of the non-faulty plant is invalidated

But… How can we invalidate models?

Robust Set-Valued Observers!

•  Problem formulation: •  Dynamic system with no disturbances

•  Dynamic system with disturbances, unknown initial state and uncertain model

x(k + 1) = f(x(k), u(k))

x(k + 1) � F (x(k), u(k), d(k), �(k))

solution is a set, rather than a point!

Robust Set-Valued Observers (cont.’d)!

X(k)X(k � 1)

x(k � 1)

x(k)X(k)

Y (k)

Prediction Update

Using Set-Valued Observers in Model Falsification!

•  Main idea: •  Design a Set-Valued Observer (SVO) for each plausible model the plant •  If the set-valued estimate of SVO #n is empty

Model #n is invalidated!

Unknown PlantSVO

u(k) y(k)SensornoisePlantdisturbancesd(k) n(k)

LogicX(k)^

X(k)= ?^ YesNoNo FaultDetected FaultDetected

FD signal

FD Filter w/SVO

Fault Detection and Isolation using SVOs!

•  Architecture: •  Example for an aircraft FDI filter

Uncertain Aircraft Modelu(k) y(k)SensornoisePlantdisturbancesd(k) n(k)

FDI signals

FDI Filter w/SVOs

FDI Pitch Angle SensorNominal FD Filter

FDI Forward Airspeed SensorFDI Angle-of-attack Sensor

FDI Elevator

Fault Detection and Isolation using SVOs (cont.’d)!

•  Main properties •  No false alarms •  No need to compute a decision threshold •  Model uncertainty and bounds on the disturbances and measurement noise are explicitly taken into account •  Applicable to LTI and LPV systems

•  Shortcomings •  Computationally heavier than the classical FDI methods

Simulations!

•  Longitudinal dynamics of an aircraft •  Described by a linear parameter-varying (LPV) model

•  5 models considered: •  Non-faulty model •  Fault on the forward airspeed sensor •  Fault on the pitch angle sensor •  Fault on the angle-of-attack sensor •  Fault on the elevator (actuation fault)

Simulations (cont.’d)!Fault: Elevator stuck (loss-of-effectiveness)

Hard fault

Soft fault

0 5 10 15 20 25 30 35 40

0

0.5

1

Elev

ator

effe

ctiv.

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FD F

ilter

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Elev

ator

effe

ctiv.

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FDI #

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ator

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ctiv.

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FDI #

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ctiv.

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1FD

I #3

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ctiv.

Time (s)0 5 10 15 20 25 30 35 40

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FDI #

4

Fault detected

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0.5

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Elev

ator

effe

ctiv.

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FD F

ilter

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0.5

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Elev

ator

effe

ctiv.

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FDI #

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Elev

ator

effe

ctiv.

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FDI #

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Elev

ator

effe

ctiv.

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FDI #

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evat

oref

fect

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Time (s)0 5 10 15 20 25 30 35 40

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FDI #

4

Fault isolated

Fault detected

Fault isolated

Conclusions!•  A fault detection and isolation (FDI) technique using set-valued observers (SVOs) was introduced

•  The method handles model uncertainty and exogenous disturbances

•  It is guaranteed that there are no false alarms

•  The detection and isolation of faults usually requires only a few iterations

•  Unlike the classical approach in the literature, the computation of residuals and thresholds is avoided •  Main drawback: computationally heavier than the classical solution

Thank You!

Questions/Comments?