Change Detection with prescribed false alarm and detection ... Blanke.pdf · Change Detection with prescribed false alarm and detection probabilities. DTU, Denmark & CeSOS, NTNU,

Mogens BlankeAdjunct Professor at Centre for Ships and Ocean Structures, NTNU, Norway

Professor in Automation and Control, Dept. of Electrical Engineering, DTU, Denmark

Collaborators: Roberto Galeazzi, (CeSOS & DTU), Niels K. Poulsen (DTU), Shaoji Fang (CeSOS), Søren Hansen (DTU), Bernt J. Leira (NTNU)

CeSOS Workshop – NTNU May 27-29 2013

Change Detection with prescribed false alarm and detection probabilities

DTU, Denmark & CeSOS, NTNU, Norway

Position Mooring – essential in offshore

Mooring lines provide energy-free positioning

They are anchored to the bottom (200-1500 m)

Buoys are attached along mooring lines

Position Mooring (PM) means thrusters alleviate low frequency dynamic wave and wind loads

Top deflection max 4-6 % of depth

Abortion is extremely critical


Diagnosis and PrognosisFault detection, isolation (FDI), change detection, hypothesis

3Research Topics

Known input u(t) Measured output y(t)

Residual r(t)

Hypothesis about fault, detection, isolation: H0: normal, H1:fault

Residual generator

Decision system

sens fus ctrl actu

Controlled Process

P diagC diageff

Supervision


Analytical residuals follow from structural analysis and insertion in constraints

Residual Physical meaningR1 linear acceleration balance

(x-component is the one relevant for the model basin test)

R2 angular acceleration balance (horizontal)

R3 ... R9 balance measured line tension – calculated for each mooring line (6 in experiment)


Model tests at MC-lab in Trondheim

6 mooring lines (nylon) with weights

and submerged buoyancy elements


Creating repeatable physical faults

Submerged line-breaking:

Mooring line of nylon is melted under water by

electrical heating element


Properties of residuals: loss of MLBE at 580s

histories of residuals and Time-histories of residuals and distributions before and after

a fault (at t= 580s)

Looks OK but is this enough ?



H1: fault

H0: no fault

Distribution: Gaussian

Auto-correlation:

Not IID



H1: fault

H0: no fault

Distribution: Gaussian

Auto-correlation:

Not IID


Why IID condition ?(independent and identical distributions)

Difficult to impossible for non-Gaussian

process

Possible also for several non-Gaussian

processes

Textbook assumption !

1

2

Statistical test makes an average of a test quantity z(i):probability density of each sample is ( ).For the generalized likelihood ratio

) ( | )..

(GLR) test :

11

. (( ) (

k

i

ki

j

j

i

i

j j

p z

S

p z

zk j

p z p z z p

1| ... )

IID:

( ) )(

j

k

i

k

i j

k

ip z p

z z z

i

z

ff


Whitening of residuals

E: white noise sequenceRi: residualC and F: polynomials

Method: determine C and F from autocorrelation of residual

Apply recursive on data in real-time – C(q) must be stable


Does the whitening help ?

Not entirely, Not entirely,

and what about the distribution after whitening ?


Nonlinear compression needed to regain Gaussian distribution of whitened residuals

Adopt a result from robust statistics, the “Huber” transformation.

Gives a Gaussian distribution

Reasonably preserves the “whiteness”

This formulation gives adaptation to the variance as the signal develops over time


Time histories of test statistics for scalar GLR tests

Scalar GLR test

Choice of test: CUSUM or GLR

CUSUM fine for complete loss of buoy

GLR better to determine partial loss of buoyancy & less sensitive to mooring

system parameters


Alternative - vector-based GLR test


Test statistics and threshold selection -vector residual

The IID assumption is clearly violated

Theoretical threshold can not be used

2

0

Distribution of test statistics iff IID:

( ) ( )

distribution for large m and is IID

( ) where is threshold

k

GLR ik m

i

FA g

p g p g

g

p p g H dg


Determine threshold from actual test statistics under H0

Distribution in theory (limit): Chi

square.

Real distribution: Weibull tail.

Determine threshold from

estimated distribution


IID condition is violated in practice(independent and identical distributions)

1

2

Statistical test makes an average of a test quantity z(i):probability density of each sample is ( ).For the generalized likelihood ratio

) ( | )..

(GLR) test :

11

. (( ) (

k

i

ki

j

j

i

i

j j

p z

S

p z

zk j

p z p z z p

1

2

| ... )

IID:

)( ) ( (asymptotic result)

k k

i

j

k

i ki j

p z p z p

z z z

iff

S

Our alternative: Estimate p(g) from

data !


Case 2: Parametric Roll Resonance Detection

Roberto Galeazzi will present the details in session S17

Here are the highlights related to estimation of distribution of test statistics


Detectors and test statistics for Parametric Roll Resonance

• frequency ratio 2:1

• phases synchronize

Pitch/rollconditions


Resonance detectors and test statistic


Threshold selection – two detectors

Joint probability of two detectors:

Significantly enhance PFA

Detectors:

Uncorrelated under H0

Highly correlated under H1

( , ) ( ) ( | )FA FA FAP A B P A P B A


Case 3: UAV diagnosis

Test statistics: no-fault and faults on control fins - 2 cases

Feasible to tune threshold - get good PFA and PD


Case 3: Unmanned aerial vehicle – prognosis and diagnosis

Real data

Real events

Real crashes

Failure with consequences

Real drones


Conclusions

Fault diagnosis investigated in different applications

Whitening and signal compression discussed

Self-tuning of threshold possible from data

Demonstrated on model tests and on real data See papers for details


ReferencesFang, S., B. J. Leira and M. Blanke: Position Mooring Control Based on a Structural Reliability Criterion. Structural Safety. Vol. 41 (2013), 97-106

Blanke, M., S. Fang, R. Galeazzi and B. J. Leira: Statistical Change Detection for Diagnosis of Buoyancy Element Defects on Moored Floating Vessels. IFAC Safeprocess 2012, Mexico, pp 462-467

Fang, S., M. Blanke and B. J. Leira: Mooring System Diagnosis and Structural Reliability Based Control for Position-moored Vessels. Control Engineering Practice. Conditionally Accepted. Under revision

R. Galeazzi, M. Blanke and N. K. Poulsen: Early Detection of Parametric Roll onShips. Chapter 2 in Parametric Resonance in Dynamical Systems. Eds: T. I. Fossenand H. Nijmeijer. Springer, Jan. 2012

Galeazzi, R. , M. Blanke and N. K. Poulsen: Early Detection of Parametric RollResonance on Container Ships. IEEE Transactions on Control Systems Technology2013, vol. 21 (2), 489-503

S. Hansen and M. Blanke: Diagnosis of Airspeed Measurement Faults for Unmanned Aerial Vehicles. IEEE Trans. Aerospace and Electronic Systems. 2013 In print.

S. Hansen and M. Blanke: Control Surface Fault Diagnosis with Specified Detection Probability - Real Event Experiences. Proc. IEEE ICUAS’2013 Symposium, May 29-31, 2013, Atlanta, Georgia.


Questionsare

welcome

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Change Detection with prescribed false alarm and detection ... Blanke.pdf · Change Detection with prescribed false alarm and detection probabilities. DTU, Denmark & CeSOS, NTNU,