Signed Directed Graph modeling of industrial processes and their validation by data-based methods

This paper is concerned with the fusion of information from process data and process connectivity and its subsequent use in fault detection and isolation and hazard assessment. The Signed Directed Graph (SDG), as a graphical model for capturing process topology and connectivity to show the causal relationships between process variables by flow and information paths, has been widely used in root cause and hazard propagation analysis. An SDG is usually built based on process knowledge as described by piping and instrumentation diagrams. This is a complex and experience-dependent task, and therefore the resulting SDG should be validated by process data before being used for analysis. This paper introduces two validation methods. The first method is based on cross-correlation analysis of process data with assumed time delays. The resulting correlation coefficients can then be validated by examining the paths in SDGs of all the variable pairs and also comparing the signs with the directions of causal relations. The second method is based on transfer entropy, where the information transfer from one variable to another can be computed to validate the corresponding arcs in SDGs. A case study of an industrial process is presented to illustrate the application of the proposed methods.