Structure Function Learning Of Hierarchical Multi-State Systems With Incomplete Observation Sequences

Structure function, which quantitatively represents the relation between system states and unit states, is essential for system reliability assessment and oftentimes may not be known in advance due to complicated interactions among units. In this article, a dynamic Bayesian network (DBN) model is put forth to leverage incomplete observation sequences of hierarchical multi-state systems for structure function learning. To achieve a consistent structure function at different time instants, a customized Expectation-Maximization (EM) algorithm with parameter modularization is proposed and executed by two steps: (1) filling the missing values in the incomplete observation sequences with their expectations to break the dependencies among nodes; (2) decomposing the graphical network into V-shape structures, and then integrating the identical V-shape structures at different time slices to learn the parameters in the DBN model. Based on the learned DBN model, system state distribution and reliability function over time can be readily assessed. Two illustrative examples are presented and the results demonstrate that the structure function of a hierarchical multi-state system can be accurately learned despite the incompleteness of observation sequences.