Reduced complexity rao-blackwellised particle


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The presentation I gave at ISPAC 2011 Chiang Mai. It is a Reduced-Complexity technique for Rao-Blackwellised Particle Filters.

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Reduced complexity rao-blackwellised particle

  1. 1. Reduced-Complexity Rao-Blackwellised Particle Filtering for Fault Diagnosis Assoc.Prof.Dr. Peerapol Yuvapoositanon Centre of Electronic Systems Design and Signal Processing (CESdSP), Department of Electronic Engineering, Mahanakorn University of Technology, 140 Chemsampan Rd., Nong-Chok, Bangkok 10530, ThailandISPACS 2011 Reduced-Complexity Rao-Blackwellised 1 Particle Filtering for Fault Diagnosis
  2. 2. What is a Fault?• “A fault is an unpermitted deviation of at least one characteristic property (feature) of the system from the acceptable, usual standard condition.” 1• In short, a fault is an undesired state within the system.• A fault is meant to be promptly diagnosed. 1 R.Isermann, Fault-Diagnosis Applications Model-Based Condition Monitoring: Actuators, Drives, Machinery, Plants, Sensors, and Fault tolerant Systems. Springer- Verlag Berlin Heidelberg, 2011.ISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 2 Filtering for Fault Diagnosis
  3. 3. Example: Industrial Dryer Faulty fan Faulty grill Rub´en Morales-Men´endez, Nando de Freitas and David Poole, Real-time monitoring of complex industrial processes with particle filters, in Neural Information Processing Systems, 2002, pp. 1433–1440.ISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 3 Filtering for Fault Diagnosis
  4. 4. Discrete States Assignment• Normal operation corresponds to low fan speed, open air-flow grill and clean temperature sensor.• Normal discrete state:• Three types of faults : Faulty fan Faulty grill Faulty fan and grillISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 4 Filtering for Fault Diagnosis
  5. 5. State and Measurement ModelISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 5 Filtering for Fault Diagnosis
  6. 6. The Dynamic Bayesian Network Hidden Part Control Part Observable PartISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 6 Filtering for Fault Diagnosis
  7. 7. PF and RBPF• Particle Filters (PFs) is a powerful state distribution estimation methodology for nonlinear-non Gaussian distribution.• However, for discrete-state estimation like in fault diagnosis, the variance of PF is too high.• Rao-Blackwellised Particle Filter (RBPF), a class of PFs that stems from the Rao- Blackwellised factorisation theorem, enjoys much less variance than PFs.ISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 7 Filtering for Fault Diagnosis
  8. 8. Rao-Blackwellised Factorisation Analytical Density Reduced Space Density (Continuous state) (Discrete state) Kalman Filtering Particle FilteringISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 8 Filtering for Fault Diagnosis
  9. 9. ISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 9 Filtering for Fault Diagnosis
  10. 10. RBPF AlgorithmISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 10 Filtering for Fault Diagnosis
  11. 11. Reduced-Complexity RBPF• RBPF uses Kalman filtering method in updating the mean and the covariance of every survived particle, which in turn requires enormous computational power.• However, the particles in the same group have exactly the same statistical mean and covariance.• Updating only one particle and using the results for all of the rest in the group is possible and is then proposed for RC-RBPF.ISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 11 Filtering for Fault Diagnosis
  12. 12. Proposition 1• Let TRC−RBPF and TRBPF be the time consumption required to complete each recursion t for the RC-RBPF and RBPF algorithms respectively. For any number of particles N,ISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 12 Filtering for Fault Diagnosis
  13. 13. RC-RBPF AlgorithmISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 13 Filtering for Fault Diagnosis
  14. 14. ISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 14 Filtering for Fault Diagnosis
  15. 15. Simulation• We investigated the time usages and predic- tion errors of the three algorithms over the range of one to 1,000 particles.• Xeon CPU Dual Core 2.40 GHz with 8 GB RAM• 64-bit Windows Server 2007 operating system.• Each test was averaged over 100 Monte Carlo runs.ISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 15 Filtering for Fault Diagnosis
  16. 16. Three-state Markovian transition matrixISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 16 Filtering for Fault Diagnosis
  17. 17. Three-state: Time UsageISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 17 Filtering for Fault Diagnosis
  18. 18. Three-state: Prediction ErrorsISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 18 Filtering for Fault Diagnosis
  19. 19. Six-state Markovian transition matrixISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 19 Filtering for Fault Diagnosis
  20. 20. Six-state: Time UsageISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 20 Filtering for Fault Diagnosis
  21. 21. Six-state: Prediction ErrorsISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 21 Filtering for Fault Diagnosis
  22. 22. Prediction percentage errors comparison for three states (nz = 3)ISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 22 Filtering for Fault Diagnosis
  23. 23. Prediction percentage errors comparison for six states (nz = 6)ISPACS 2011 Reduced-Complexity Rao-Blackwellised Particle 23 Filtering for Fault Diagnosis
  24. 24. Conclusions• RC-BBPF is exactly RBPF.• RC-RBPF has lower computational complexity.• RC-RBPF is reverted to RBPF when the number of particles is small.• The main point: Kalman updating step is performed to only one representative particle of a group particles gathering in a particular state. Reduced-Complexity Rao-Blackwellised Particle 24ISPACS 2011 Filtering for Fault Diagnosis