With the increase in scale and complexity of process operations, the detection and diagnosis of plantwide abnormalities and disturbances are major problems in the process industry. Because of the high degree of interconnections among different parts in the system, a simple fault may easily propagate along information and material flow pathways and affect other parts of the system. To determine the root cause(s) of certain abnormality, it is important to capture the process connectivity and find the connecting pathways.

For a large-scale industrial process, connectivity-based process topology provides a qualitative overview and a schematic structure. This topology can be described mathematically and electronically by a signed directed graph (SDG) which is usually built based on process knowledge as described by piping and instrumentation diagrams (P&IDs). This graphical model has been widely used in root cause and hazard propagation analysis, in which both material flow and information flow are considered and expressed. Following is an example of a P&ID and the corresponding SDG of a real industrial process. Validated SDGs can be used in fault detection and isolation, hazard assessment, and correlative alarm analysis by inferencing. One can search the upstream and downstream nodes based on graph traversal to find the possible reasons and consequences of the current or assumed symptom; consistent paths describe the fault propagation. If the model is described as an ontology using RDF and OWL, then query language such as SPARQL can be used for this inferencing and more interesting results can be obtained automatically by specific queries on the ontological model.

Besides model-based methods, data-driven causality analysis provides another way to capture process connectivity and investigate information and/or material flow pathways. Granger identified two components of the statement about
causality: (1) the cause occurs before the effect; and (2) the cause contains information about the effect that is unique, and is in no other variable. These statements intuitively mean that the causal variable can help to forecast the effect variable. Although a causal relationship between two variables, X and Y , can be detected using causality analysis techniques, it is difficult to distinguish whether the causal influence is direct or indirect because it is possible that there is an intermediate variable or some intermediate variables which transfer information from X to Y . A direct causality from X to Y is defined as X directly causes Y , which means there is a direct information and/or material flow pathway from X to Y without any intermediate variables. We proposed a direct transfer entropy (DTE) concept to discriminate between direct and indirect causality between two variables. After direct causality is detected between variables, a causal map can be easily constructed, from which we can investigate the information and/or material flow pathways and further used for root cause and fault propagation analysis. Following is a 3-tank system and its causal map obtained via the DTE approach. We can see that the causal map correctly indicates the connectivity of the system.

SDG modeling is a complex and experience-dependent task, and thus the resulting SDG should be validated by process data before being used for further analysis. Two validation methods have been taken into account. 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. Similarly, the results from a data-based method should be combined with the qualitative process information in root cause diagnosis. For example, the results of the causality analysis should be validated by the P&IDs or process flow diagrams (PFDs) of the process.

Plant-wide disturbances detection and diagnosis remain an off-line method so far and cannot utilize process information automatically. Qualitative models of processes will become almost as readily available as historical data in the future. A future research direction can be related to integrating data-based causality analysis techniques with automatic information extraction from process models. In this way, a powerful diagnostic tool for isolating the root causes of plant-wide abnormalities can be developed.