Particle Filters for Real-Time Fault Diagnosis in Hybrid Systems M. H. REFAN 1 , MAHDI BASHOOKI 2 , SAREH BAHMANPOUR 2 1 S. Rajaee University, Lavizan, Tehran 16788, IRAN 2 MAPNA Electrical and Control Company (MECO), Karaj, IRAN refan@mapnaec.com , mehdibashooki@yahoo.com , sarehbahmanpour@hotmail.com Abstract: - Embedded systems are composed of a large number of components that interact with the physical world via a set of sensors and actuators, have their own computational capabilities, and communicate with each other via a wired or wireless network. Diagnostic systems for such applications must address new challenges caused by the distribution of resources, the networking environment, and the tight coupling between the computational and physical worlds. Our approach is to move from centralized, discrete or continuous techniques toward a distributed, hybrid diagnosis architecture. Monitoring and diagnosis of any dynamical system depend crucially on the ability to estimate the system state given the observations. Estimation for hybrid systems is particularly challenging, because it requires keeping track of multiple models and the transitions between them. This paper presents a particle filtering based on estimation algorithm that addresses the challenge of the interaction between continuous and discrete dynamics in hybrid systems. Keywords: - State estimation, Fault diagnosis, Hybrid systems, Particle filtering, JMLG model. 1 Introduction In Embedded systems, the physical plant is composed of a large number of distributed nodes, each of which performs a moderate amount of computation, collaborates with other nodes via a wired or wireless network, and is embedded in the physical word via a set of sensors and actuators. Such systems can be best represented by hybrid models and present a number of interesting new challenges for diagnostic systems. The diagnosis problem is to determine the current state of a system given a stream of observations of that system. In traditional model-based diagnosis systems such as Livingstione [1], diagnosis performes by maintaining a set of candidate hypotheses about the current state of the system, and using the model to predict the expected future state of the system given each candidate. The predicted states are then compared with the observations of what actually occurred. If the observations are consistent with a particular state that is predicted, that state is kept as a candidate hypothesis. If they are inconsistent, the candidate is discarded. In the hybrid model, the task is to determine the best action to perform the given current estimate of actual state of the system. This estimate, referred to as the belief state, is exactly what we would like to determine in the diagnosis problem, and the problem of keeping the belief state update is well understood in the decision theory literature. Unfortunately, maintaining an exact belief state is computationally intractable for the type of problem we are interested in. Since our model contains both discrete and continuous variables, the belief state is a set of multidimensional probability distributions over the continuous state variables, with one such distribution for each mode of the system. These distributions may not even be unimodal, so just representing the belief state is a complex problem, but updating it when new observations are made is intractable for hybrid models in all but the simplest model of models. Therefore, an approximation needs to be made. A particle filter represents a probability distribution using a set of discrete samples, referred to as particles, each of which has an associated weight. The set of weighted particles constitutes an Proceedings of the 7th WSEAS International Conference on Robotics, Control & Manufacturing Technology, Hangzhou, China, April 15-17, 2007 295