Data-driven causal inference based on a modified transfer entropy
Introduction
Elucidation of the cause-and-effect relationships among variables or events is the central aim of many studies in physical, social, behavioral and biological sciences (Pearl, Pearl, 2009). In the chemical process industry, knowing the cause-and-effect relationships means knowing the propagation path of fault or disturbance, which is critical for alarm management, fault diagnosis, and incident/accident investigations. As a result, it is of great significance to develop an effective and reliable method of causal inference and root cause analysis.
There exists some techniques that are to some extent similar to causal inference and root cause analysis, like HAZOP analysis (Dunjó, Dunjó et al., 2010), and signed digraph (SDG)-based methods (Maurya, Maurya et al., 2004). But methods that rely on only process knowledge are often difficult to use because of the increasing complexity and size of modern industrial processes. Meanwhile, data-driven methods like cross-correlation function (Bauer, Bauer et al., 2008), and transfer entropy (Schreiber, Schreiber, 2000, Bauer, Bauer et al., 2007) can overcome such difficulties. However, data-driven methods needs to be improved to avoid mbiguities or false results. This paper is focused on causal inference based on an improved transfer entropy.
Section snippets
Introduction to transfer entropy
Based on the concept of information theory and information entropy (Shannon and Weaver, 1948), Schreiber proposed the concept of transfer entropy in 2000 to measure the asymmetric interactions in a system. Unlike mutual information, transfer entropy is in an asymmetric form, which makes it possible to measure cause-and-effect relationships. To consider time delay, which is common in many practical situations, Bauer in Shannon and Weaver, 1948 incorporated h, the prediction horizon, and rewrote
Causal inference based on the modified transfer entropy
To obtain a causal map based on the time series of process variables, the following four steps are proposed based on the modified transfer entropy.
Case study
The chemical process with 14 process variables simulated by UniSim Design R390.1 includes two CSTRs in series where cold water and hot water are mixed. All of the control loops are proportional controls. The Process Flow Diagram (PFD) is shown in Fig. 3.
200 samples with 0.5 second sampling interval are collected for the case study. A significance threshold of 0.1 is chosen to decide whether a transfer entropy can represent the existence of a cause-effect relationship.
With k = 1, the generated
Conclusion
Causal inference is of great value for alarm management, fault diagnosis, and incident investigation. Due to the increasing size and complexity of modern industrial process, data-driven methods of causal inference show its advantage over knowledge-based ones. This paper modifies the Bauer's form of transfer entropy proposed and improves its performance in estimating time delay of causal relations. A causal inference approach based on transfer entropy is also proposed in this paper. A case study
Acknowledgements
The authors gratefully acknowledge financial support from the National Basic Research Program of China (973 Program, Grant No. 2012CB720500).