1. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 Fault Prediction with Particle Filters by David Hatfield mentors: Dr. D. Kern & Dr. J. Zalewski

2. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 The Particle Filter is a sequential Monte Carlo algorithm used to estimate the true state of a system given a series of measurements (which are corrupted by error) taken periodically over time. What Is a Particle Filter?

3. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 The Monte Carlo method is an algorithm to conduct computations by random sampling of data to assess results statistically. Example of computing area under a curve: http://chc60.fgcu.edu/EN/HistoryDetail.aspx?c=6 What Is a Monte Carlo Method?

4. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 Essential Steps in the Algorithm

5. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 p(x k |D k-1 ) denotes the Probability Density Function of the state vector given all the measurements up to time k – 1 (denoted by D k-1 ). The following are given by Bayes theorem: Prior distribution: Likelihood function: Posterior distribution: Recursive Bayesian Solution

6. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 Predicting Future States At time k, the pdf of the state at time k + p may be calculated as follows: The set of values the state vector may take may be classified as either normal or faulty states. Once the pdf for a future time is obtained, the probability of a fault occurring may may be calculated by integrating the pdf over the set of all faulty states.

7. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 Robotics: Localization, navigation, and tracking as well as fault detection, prediction, and diagnosis. Image and Audio Enhancement: Reduction of noise in image and audio data. Economics and Finance: Estimation of latent variables in Econometrics. Selected Applications