Investigating the Impact of Perturbations in Chemical Processes on Data-Based Causality Analysis. Part 2: Testing Granger Causality and Transfer Entropy

摘要

In this two-part paper, the impact of perturbations generated by conditions typical to chemical processes is analysed. In the first part, causality analysis techniques intended for fault diagnosis are discussed in order to define the desired characteristics of the techniques. In this second part a simple process simulation was used to introduce oscillatory and step perturbations and perform a sensitivity analysis of their impact on the causality detection ability of transfer entropy and Granger causality. This procedure was repeated for three types of operation: (1) a base case open loop operation with sensor noise added, (2) open loop with process noise added and (3) closed loop operation with only sensor noise. Granger causality and transfer entropy both proved robust at detecting causality under different conditions, with some exceptions where the causal relationship was obscured: very high frequency oscillations resembled random noise; for low frequency oscillations the observation window used by the causality techniques was too small to capture the gradual dynamics; closed loop operation attenuated slow acting oscillations and step inputs; and addition of process noise decreased the apparent strength of the causality. Comparing the two techniques: Granger causality proved more reliable than transfer entropy for oscillatory perturbations; the effect of the controller obscuring the causal connection was less pronounced for transfer entropy; and transfer entropy appeared much more sensitive to the influence of additional process noise.