Combining Particle Filters and Consistency-based Approaches for Monitoring and Diagnosis of Stochastic Hybrid Systems

Fault detection and isolation are critical tasks to ensure correct operation of systems. When we consider stochastic hybrid systems, diagnosis algorithms need to track both the discrete mode and the continuous state of the system in the presence of noise. De- terministic techniques like Livingstone cannot deal with the stochas- ticity in the system and models. Conversely Bayesian belief up- date techniques such as particle filters may require many computa- tional resources to get a good approximation of the true belief state. In this paper we propose a fault detection and isolation architec- ture for stochastic hybrid systems that combines look-ahead Rao- Blackwellized Particle Filters (RBPF) with the Livingstone 3 (L3) diagnosis engine. In this approach RBPF is used to track the nominal behavior, a novel n-step prediction scheme is used for fault detection and L3 is used to generate a set of candidates that are consistent with the discrepant observations which then continue to be tracked by the RBPF scheme. fault is diagnosed by ensuring particles enter the true fault mode and then the observation function would keep increasing the weight of these particles. If there are a large number of fault modes then this requires a lot of computational resources since particles need to be put in all fault modes to make sure no fault is missed. On the other hand consistency-based approaches like Livingstone (12, 6) hand use structural and behavioral models (as opposed to tran- sition models) to diagnose the faults. The system is modeled in ab- stracted form and the observations are also converted to this form ("monitors" for Livingstone). When the predictions from the model are not consistent with the observations, then the discrepancies are used to identify conflicts which are then used to identify possible fault candidates. These candidates can be tracked by comparing the predictions under these fault conditions against the observations. In this approach, rather than blindly guessing the faults, the constraints in the model are used to limit the candidates to be considered. How- ever these approaches tend to be deterministic in nature (in some cases prior probabilities are used) and hence cannot deal with uncer- tain transitions and noise in the sensors and system. In this paper, we combine these two approaches in an effort to reduce the computational complexity associated with proba- bilistic approaches while extending Livingstone-like approaches to handle stochasticity. Our approach combines the look-ahead Rao- Blackwellized Particle Filter (RBPF) (2, 5) and Livingstone 3 (L3) systems to provide a diagnosis architecture for stochastic hybrid sys- tems. Section 2 describes the RBPF and L3 algorithms and also de- scribes the unified modeling framework used by both diagnostic sys- tems. In Section 3 we present the combined architecture and explain the different components of this architecture: the nominal observer, the fault detector, the fault observer and the candidate generator.