Causality in Control Systems Based on Data-Driven Oscillation Identification

This paper addresses the subject of causality analysis using simulation data and data collected from a real control system. Simulated data includes Gaussian and Cauchy noise signals. Real-time series include various, mostly unknown distortions, like trends, oscillations, and noises. Presented research focuses on the oscillatory component in data and its propagation in multi-loop control systems. Oscillation identification is based on a deep decomposition process for control error time series. Identified periodic signals are used for further causality processing. The analysis uses the Transfer Entropy approach. This method belongs to the group of model-free methods. The determination of information pathways is conducted without any model or a priori process knowledge. The research investigates the impact of the oscillation time-series component on the Transfer Entropy causality analysis. The summary shows the observations obtained for given simulated datasets and those collected from real processes. The obtained results show that simulated analysis works properly. On the contrary, the direct application of the oscillation decomposition in real industrial cases may be misleading. Large datasets demand modification in the methodology. Different variants are tested. They show that oscillation propagation is biased in real systems and, therefore, the decomposition should be applied with caution. Furthermore, it is important to remember that the algorithm transition from simulated data to real industrial ones is demanding and should be done with the utmost care.