Fault Diagnostics Based on the Analysis of Probability Distributions Estimated Using a Particle Filter
Abstract
:1. Introduction
 We provide a set of indicators to evaluate the probability distribution of the states estimated using the particle filter.
 This study investigates the homogeneity of probability distributions generated with a particle filter using probabilistic and informationtheoretic metrics.
 The evolution of the correlation structure of estimated distributions over time is monitored.
 The consistency between modelpredicted distributions and measurements is monitored.
 The proposed indicators are demonstrated through a vehicle dynamics example.
 The effectiveness of the proposed metrics is examined using sensor and actuator failure scenarios.
2. Monitoring the Operation of the Particle Filter and Its Estimated Distributions
 the heterogeneity of the estimated state distributions is examined over time;
 the correlation pattern between the state variables is monitored;
 the consistency between model predictions and measurements is also qualified.
2.1. State Estimation with Particle Filter
Algorithm 1 The particle filter algorithm 
Input: A set of measurements (mostly in realtime defined as streaming data, but the whole time series may be already available) ${\mathbf{y}}^{(0:t)}$, a set of control inputs (as streaming data or whole time series) ${\mathbf{u}}^{(0:t)}$, the model is defined by the f and h functions, and the parameters of the algorithm $(\mathbf{R},\mathbf{Q},{N}_{s},\u03f5)$ Output: Set of state samples ${\mathbf{x}}_{i}^{\left(t\right)}$ and the associated weights ${w}_{i}^{\left(t\right)}$

2.2. Monitoring the Behavior of a Particle Filter
2.2.1. Evaluation of the Compactness and Heterogeneity of the Posterior Distribution
2.2.2. Investigating Correlations between the State Variables of Particles
2.2.3. Investigation of the Weight Update Process to Infer the Consistency between the Model and Observations
3. Application to the Diagnosis of the Sensor and Actuator Faults of Vehicles
3.1. The Applied Model
3.2. Simulation Scenarios
 Actuator fault: This fault is in the steering angle command. The effective steering angle differs from the commanded steering angle by a constant $0.4$ degrees.
 Sensor fault: The measured yaw rate does not correspond to the actual yaw rate, due to a positive 0.02 rad/s offset.
3.3. Applied Estimator Parameters
3.4. Results and Discussion
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Darányi, A.; Abonyi, J. Fault Diagnostics Based on the Analysis of Probability Distributions Estimated Using a Particle Filter. Sensors 2024, 24, 719. https://doi.org/10.3390/s24030719
Darányi A, Abonyi J. Fault Diagnostics Based on the Analysis of Probability Distributions Estimated Using a Particle Filter. Sensors. 2024; 24(3):719. https://doi.org/10.3390/s24030719
Chicago/Turabian StyleDarányi, András, and János Abonyi. 2024. "Fault Diagnostics Based on the Analysis of Probability Distributions Estimated Using a Particle Filter" Sensors 24, no. 3: 719. https://doi.org/10.3390/s24030719