Change Detection with prescribed false alarm and detection ... Blanke.pdf · Change Detection with...
Transcript of Change Detection with prescribed false alarm and detection ... Blanke.pdf · Change Detection with...
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
DTU, Denmark & CeSOS, NTNU, Norway
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
DTU, Denmark & CeSOS, NTNU, Norway
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)
DTU, Denmark & CeSOS, NTNU, Norway
Model tests at MC-lab in Trondheim
6 mooring lines (nylon) with weights
and submerged buoyancy elements
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Creating repeatable physical faults
Submerged line-breaking:
Mooring line of nylon is melted under water by
electrical heating element
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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 ?
DTU, Denmark & CeSOS, NTNU, Norway
Properties of residuals: loss of MLBE at 580s
H1: fault
H0: no fault
Distribution: Gaussian
Auto-correlation:
Not IID
DTU, Denmark & CeSOS, NTNU, Norway
Properties of residuals: loss of MLBE at 580s
H1: fault
H0: no fault
Distribution: Gaussian
Auto-correlation:
Not IID
DTU, Denmark & CeSOS, NTNU, Norway
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
DTU, Denmark & CeSOS, NTNU, Norway
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
DTU, Denmark & CeSOS, NTNU, Norway
Does the whitening help ?
Not entirely, Not entirely,
and what about the distribution after whitening ?
DTU, Denmark & CeSOS, NTNU, Norway
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
DTU, Denmark & CeSOS, NTNU, Norway
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
DTU, Denmark & CeSOS, NTNU, Norway
Alternative - vector-based GLR test
DTU, Denmark & CeSOS, NTNU, Norway
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
DTU, Denmark & CeSOS, NTNU, Norway
Determine threshold from actual test statistics under H0
Distribution in theory (limit): Chi
square.
Real distribution: Weibull tail.
Determine threshold from
estimated distribution
DTU, Denmark & CeSOS, NTNU, Norway
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 !
DTU, Denmark & CeSOS, NTNU, Norway
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
DTU, Denmark & CeSOS, NTNU, Norway
Detectors and test statistics for Parametric Roll Resonance
• frequency ratio 2:1
• phases synchronize
Pitch/rollconditions
DTU, Denmark & CeSOS, NTNU, Norway
Resonance detectors and test statistic
DTU, Denmark & CeSOS, NTNU, Norway
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
DTU, Denmark & CeSOS, NTNU, Norway
Case 3: UAV diagnosis
Test statistics: no-fault and faults on control fins - 2 cases
Feasible to tune threshold - get good PFA and PD
DTU, Denmark & CeSOS, NTNU, Norway
Case 3: Unmanned aerial vehicle – prognosis and diagnosis
Real data
Real events
Real crashes
Failure with consequences
Real drones
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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
DTU, Denmark & CeSOS, NTNU, Norway
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.
DTU, Denmark & CeSOS, NTNU, Norway
Questionsare
welcome