Deriving prognostic continuous time Bayesian networks from D-matrices

Probabilistic graphical models are widely used in the context of fault diagnostics and prognostics, providing a framework to model the relationships between faults and tests in complex systems. Bayesian networks have sufficient representational power as a model for system-level diagnosis but are inadequate for domains involving prognosis. In order to perform fault prognostics, a model must have the capability to perform probabilistic reasoning over time. One model well suited to this problem is the continuous time Bayesian network (CTBN). In this paper, we propose a method of constructing a continuous time Bayesian network from a D-matrix, a common matrix representation of a diagnostic model. Additionally, we provide procedures for parameterizing the CTBN using reliability information such as the mean time between failures, as well as the false alarm and non-detect probabilities. Through experiments on two different datasets, we demonstrate the correctness of our parameterization process. We also explore the ways in which applying evidence impacts the query results over the network. Finally, we demonstrate the real-world applicability of this approach by performing incremental tests for the purpose of diagnosing and prognosing a fault in the system.