CeSOS Workshop NTNU May 27-29 2013 Change Detection with prescribed false alarm and detection probabilities Mogens Blanke Adjunct 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)
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 Prognosis Fault detection, isolation (FDI), change detection, hypothesis eff Supervision C diag P diag Known input u(t) Measured output y(t) sens fus ctrl actu Residual generator Controlled Process Residual r(t) Decision system Hypothesis about fault, detection, isolation: H 0 : normal, H 1 :fault Research Topics 3
Analytical residuals follow from structural analysis and insertion in constraints Residual R 1 R 2 R 3... R 9 Physical meaning linear acceleration balance (x-component is the one relevant for the model basin test) angular acceleration balance (horizontal) 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 Time-histories of residuals and distributions before and after a fault (at t= 580s) Looks OK but is this enough?
Properties of residuals: loss of MLBE at 580s H1: fault H0: no fault Autocorrelation: Not IID Distribution: Gaussian
Properties of residuals: loss of MLBE at 580s H0: no fault H1: fault Autocorrelation: Not IID Distribution: Gaussian
Why IID condition? (independent and identical distributions) Statistical test makes an average of a test quantity z(i): probability density of each sample is pz ( i ). For the generalized likelihood ratio (GLR) test : 1 k Sk zi k j1i j p( z ) p( z z p iff i j) pz ( j1 j)... ( k k1 IID: p( z ) p( z ) i k i j i 2 z z... z ) j Difficult to impossible for non-gaussian process Possible also for several non-gaussian processes Textbook assumption!
Whitening of residuals E: white noise sequence R i : residual C 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, 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 Distribution of test statistics iff IID: p ( g) p( g ) GLR k km 2 distribution for large m and g is IID p p( g H ) dg where is threshold FA g 0 i i The IID assumption is clearly violated Theoretical threshold can not be used
Determine threshold from actual test statistics under H 0 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) Statistical test makes an average of a test quantity z(i): probability density of each sample is pz ( i). For the generalized likelihood ratio (GLR) test : S k 1 k j 1 k i j 2 p( z ) p( z ) pz ( z )... p( z z... z ) iff i IID: j z i j1 j k 2 ( i) ( i) Sk (asymptotic result) i j p z p z p k k1 j 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 Pitch/roll conditions frequency ratio 2:1 phases synchronize
Resonance detectors and test statistic
Threshold selection two detectors Joint probability of two detectors: Significantly enhance P FA P ( A, B) P ( A) P ( B A) FA FA FA Detectors: Uncorrelated under H 0 Highly correlated under H 1
Case 3: UAV diagnosis Test statistics: no-fault and faults on control fins - 2 cases Feasible to tune threshold - get good P FA and P D
Case 3: Unmanned aerial vehicle prognosis and diagnosis Real drones Real data Real events Failure with consequences Real crashes
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
References Fang, 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 on Ships. Chapter 2 in Parametric Resonance in Dynamical Systems. Eds:T.I.Fossen and H. Nijmeijer. Springer, Jan. 2012 Galeazzi, R., M. Blanke and N. K. Poulsen: Early Detection of Parametric Roll Resonance on Container Ships. IEEE Transactions on Control Systems Technology 2013, 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.
Questions are welcome