Transfer Zero-Entropy and Its Application for Capturing Cause and Effect Relationship Between Variables

Detection of causality is an important and challenging problem in root cause and hazard propagation analysis. It has been shown that the transfer entropy approach is a very useful tool in quantifying directional causal influence for both linear and nonlinear relationships. A key assumption for this method is that the sampled data should follow a well-defined probability distribution; yet this assumption may not hold for some industrial process data. In this paper, a new information theory-based measure, transfer 0-entropy (T0E), is proposed for causality analysis on the basis of the definitions of 0-entropy and 0-information without assuming a probability space. For the cases of more than two variables, a direct T0E (DT0E) concept is presented to detect whether there is a direct information and/or material flow pathway from one variable to another. Estimation methods for the T0E and the DT0E are addressed. The effectiveness of the proposed method is illustrated by two data sets, one based on data from a pilot scale process and a second evaluation based on data from a benchmark industrial case study.