Directed Acyclic Graphs With Tears
This work addresses incremental improvements in structure learning for Bayesian networks, making it more practical for industrial process fault detection and diagnosis.
The paper tackled the challenge of learning directed acyclic graphs (DAGs) for Bayesian networks in industrial fault detection, where existing methods face issues like infeasible solutions and truncation for acyclicity, and proposed a novel DAGs with Tears method based on mix-integer programming to address these problems, demonstrating superiority in numerical and industrial case studies.
Bayesian network is a frequently-used method for fault detection and diagnosis in industrial processes. The basis of Bayesian network is structure learning which learns a directed acyclic graph (DAG) from data. However, the search space will scale super-exponentially with the increase of process variables, which makes the data-driven structure learning a challenging problem. To this end, the DAGs with NOTEARs methods are being well studied not only for their conversion of the discrete optimization into continuous optimization problem but also their compatibility with deep learning framework. Nevertheless, there still remain challenges for NOTEAR-based methods: 1) the infeasible solution results from the gradient descent-based optimization paradigm; 2) the truncation operation to promise the learned graph acyclic. In this work, the reason for challenge 1) is analyzed theoretically, and a novel method named DAGs with Tears method is proposed based on mix-integer programming to alleviate challenge 2). In addition, prior knowledge is able to incorporate into the new proposed method, making structure learning more practical and useful in industrial processes. Finally, a numerical example and an industrial example are adopted as case studies to demonstrate the superiority of the developed method.