Generalized matrix-based Bayesian network for multi-state systems

To achieve a resilient society, the reliability of core engineering systems should be evaluated accurately. However, this remains challenging due to the complexity and large scale of real-world systems. Such complexity can be efficiently modelled by Bayesian network (BN), which formulates the probability distribution through a graph-based representation. On the other hand, the scale issue can be addressed by the matrix-based Bayesian network (MBN), which allows for efficient quantification and flexible inference of discrete BN. However, the MBN applications have been limited to binary-state systems, despite the essential role of multi-state engineering systems. Therefore, this paper generalizes the MBN to multi-state systems by introducing the concept of composite state. The definitions and inference operations developed for MBN are modified to accommodate the composite state, while formulations for the parameter sensitivity are also developed for the MBN. To facilitate applications of the generalized MBN, three commonly used techniques for decomposing an event space are employed to quantify the MBN, i.e. utilizing event definition, branch and bound (BnB), and decision diagram (DD), each being accompanied by an example system. The numerical examples demonstrate the efficiency and applicability of the generalized MBN. The supporting source code and data can be download at https://github.com/jieunbyun/Generalized-MBN-multi-state.