Reduced complexity rao-blackwellised particle
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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, Thailand ISPACS 2011 1 Reduced-Complexity Rao-Blackwellised Particle Filtering for Fault Diagnosis
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Transcript of Reduced complexity rao-blackwellised particle
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 1Reduced-Complexity Rao-Blackwellised
Particle Filtering for Fault Diagnosis
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.
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1 R. Isermann, Fault-Diagnosis Applications Model-Based Condition Monitoring: Actuators, Drives, Machinery, Plants, Sensors, and Fault tolerant Systems. Springer-Verlag Berlin Heidelberg, 2011.
Example: Industrial Dryer
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.
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Faulty fan
Faulty grill
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 grill4Reduced-Complexity Rao-Blackwellised Particle
Filtering for Fault DiagnosisISPACS 2011
State and Measurement Model
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The Dynamic Bayesian Network
Hidden Part
Observable Part
Control Part
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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.
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Rao-Blackwellised Factorisation
Particle FilteringKalman Filtering
Analytical Density(Continuous state)
Reduced Space Density(Discrete state)
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RBPF Algorithm
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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.
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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,
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RC-RBPF Algorithm
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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.
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Three-state Markovian transition matrix
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Three-state: Time Usage
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Three-state: Prediction Errors
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Six-state Markovian transition matrix
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Six-state: Time Usage
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Six-state: Prediction Errors
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Prediction percentage errors comparison for three states (nz = 3)
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Prediction percentage errors comparison for six states (nz = 6)
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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.
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