A matrix analytic approach for Bayesian network modeling and inference of a manufacturing system

Abstract

A shared digital twin of a manufacturing system is valuable to provide maintenance services in a collaborative manner. An accurate analytical model of the Bayesian network is crucial to depict endogenous failure mechanisms in the digital twin. Nodes’ connections in Bayesian networks correspond to a range of linear, bilinear or multilinear mappings over finite-state variables. The conditional probability table (CPT) of a child node can be represented as a k-dimensional tensor if it has (k-1) parent nodes. A new matrix analytic approach is proposed for Bayesian network inference based on the theory of semi-tensor product. The matrix representation of probabilistic networks is firstly studied, and a specific parameter training algorithm is constructed based on the matrix model. Bayesian network inference algorithms, including both forward and backward reasoning, are then presented for reliability analysis and fault diagnosis. A real manufacturing system is applied to verify the proposed approach. This matrix analytic approach helps to study the Bayesian network’s mathematical properties, and it is proved to be convenient and efficient in probability network modeling and inference.