Presentation Cdc 2012

8/12/2019 Presentation Cdc 2012

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INSTITUTEFOR SYSTEMS

NDROBOTICS

Fault Detection and Isolation for

Inertial Measurement Units

51stIEEE Conference on Decision and Control

Maui, Hawaii, USA

S. Brs P. Rosa C. Silvestre P. Oliveira

Institute for Systems and Robotics

Instituto Superior Tcnico

Lisbon, Portugal


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Introduction

The navigation system is a critical component in any aircraft or

spacecraft.

In high reliability systems it is not only necessary to detect faults, but

also to isolate the defective sensor.

Objective:

Development of Fault Detection and Isolation (FDI) strategies for

Inertial Measurement Units (IMUs).


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Introduction

Two strategies are proposed, which exploit:

Hardware redundancy by identifying non-compatible redundant

sensor measurements.

Analytical redundancy by using Set-Valued Observers to model

the dynamic relation between measurement of the sensor suite.

It is assumed that the sensor measurements are corrupted by

bounded noise.

The proposed solutions guarantee that there will be no false alarms.

Tuning of a decision rule based on a threshold to declare whether or

not a fault has occurred is not needed.


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Sensor Model

Rate-gyros model

Inertial vector model (such as accelerometers)

Each component of satisfies


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Hardware Redundancy

Measurement model Matrix form


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Hardware Redundancy

(k) (k)

Non-faulty sensors Faulty sensor


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Hardware Redundancy

Fault detection and isolation algorithm:

If Set(MH,m) is empty, a fault is detected.

Then the emptiness of Si=Set(MH\{i},m\{i}) for all sensors

is evaluated.

If only for one i, Siis non-empty, the faulty measurement is

r(i). If not, it is not possible to isolate the fault at this instant.


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Hardware Redundancy

Proposition:

If the magnitude of the fault is greater than , the proposed FDIscheme is able to detect and isolate non-simultaneous faults.

Assumption:

There are at least five sensor measurements.


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Set-Valued Observers

There is uncertainty on the state and on the

measurements.

Uncertainty is described by means of polytopes. The dynamic model may be uncertain.


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Set-Valued Observers

Prediction Update

(model) (measurements)


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Analytical Redundancy

Analytical model of the vector observations:

Solution:

Using the Mean Value Theorem it can be concluded that

Bounds on the transition matrix elements


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Fault detection filter:


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Fault detection and isolation filter:


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Stages of the FDI filter:


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Simulation Results

Angular velocity:

Vector measurements:

Noise bounded by 0.05

Sampling period of all sensors set to T=0.1 s

100 Monte-Carlo runs


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Simulation Results

We assume that one of the following six faults can occur:

1. a stuck at type of fault in rate gyro #1;

2. rate gyro #3 badly damaged generating a null measurement;

3. the maximum amplitude of the noise in the rate gyro #3 increases

fifteen times;

4. the second component of vector #2 is null;

5. a stuck at type of fault in first sensor of vector #1;

6. the maximum amplitude of the noise in the third sensor of vector

#3 increases five times.


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Simulation Results

Five gyros and five sensors per vector

Three gyros and three sensors per vector


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Simulation Results


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Simulation Results


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Conclusions Two novel FDI methodologies for IMUs and vector observations were

proposed.

The first scheme takes advantage of hardware redundancy in the sensor

measurements to detect incoherences between them.

Sufficient conditions have been provided that guarantees isolation of non-

simultaneous faults.

The dynamic relation between the angular velocity and the vector

measurements is exploited in the second methodology, which resorts to the set-

valued state estimates provided by SVOs to validate or falsify different models of

faults.

Neither solution generates false detections, as long as the non-faulty model ofthe system remains valid.

Simulation results show that the detection and isolation of the faults take, in

general, only a few iterations.


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Thank you

Presentation Cdc 2012

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