Information Theory-based Approaches for Causality Analysis with Industrial Applications

Abstract

Detection and diagnosis of plant-wide abnormalities and disturbances are major problems in large-scale complex systems. To determine the root cause(s) of specific abnormalities, it is important to capture the process connectivity and investigate the fault propagation pathways, in which causality detection plays a significant and central role. This thesis focuses mainly on information theory-based approaches for causality analysis that are suitable for both linear and nonlinear process relationships. Previous studies have shown that the transfer entropy approach is a very useful tool in quantifying causal influence by inferring material and information pathways in a system. However, the traditional transfer entropy method only determines whether there is causality from one variable to another; it cannot tell whether the causal influence is along a direct pathway or indirect pathways through some intermediate variables. In order to detect and discriminate between direct and indirect causality relationships, a direct transfer entropy concept is proposed in this thesis. Specifically, a differential direct transfer entropy concept is defined for continuous-valued random variables, and a normalization method for the differential direct transfer entropy is presented to determine the connectivity strength of direct causality. A key assumption for the transfer entropy method is that the sampled data should follow a well-defined probability distribution; yet this assumption may not hold for all types of industrial process data. A new information theory-based distribution-free measure, transfer 0-entropy, is proposed for causality analysis based on the definitions of 0-entropy and 0-information without assuming a probability space. For the cases of more than two variables, a direct transfer 0-entropy concept is presented to detect whether there is a direct information and/or material flow pathway from one variable to another. Additionally, estimation methods for the transfer 0-entropy and the direct transfer 0-entropy are also provided. For root cause diagnosis of plant-wide oscillations, comparisons are given between the usefulness of these two information theory-based causality detection methods and other four widely used methods: the Granger causality analysis method, the spectral envelope method, the adjacency matrix method, and the Bayesian network inference method. All six methods are applied to a benchmark industrial data set and a set of guidelines and recommendations on how to deal with the root cause diagnosis problem is discussed.