Deriving Prognostic Continuous Time Bayesian Networks from Fault Trees

Abstract

Probabilistic graphical models have been applied successfully to a number of Prognostic and Health Management (PHM) applications. Continuous time Bayesian networks (CTBNs) are one such model, and they are capable of representing discrete systems that evolve in continuous time. In this work, we propose a method for constructing a CTBN from a fault tree, a model often used for evaluating system reliability. Additionally, we provide a method for reducing the number of required CTBN parameters by pruning unnecessary portions of the fault tree. Furthermore, we take advantage of the information encoded in the remaining gates of the tree and make use of the Noisy-OR model, offering additional reductionsin the number of parameters needed to specify the CTBN model. We show how a CTBN derived from a fault tree can be combined with a CTBN derived from a D-matrix to form a unified model. This allows for a description of faults and effects that evolve in continuous time based on test outcomes. We demonstrate the derivation and parameterization processes using a running example, and show how the resulting model can be queried to obtain information about the state of the system over time.