A Novel Framework for Causality Analysis of Deterministic Dynamical Processes

Reconstruction of process networks from data through the detection of cause-effect relationships between process variables is of great importance in the analysis of multivariable processes, especially in determining the root cause of faults, plant-wide abnormalities, and disturbances. Among the prevalent definitions of causality, one of the most widely used is the prediction-based Granger causality (GC), which has its origins in econometrics. However, the concept of GC is devised only for stochastic processes. Application of GC-based measures and methods for engineering processes produces spurious results since changes in process variables are frequently deterministic. Further, the presence of measurement errors greatly restricts their applicability. In this work, we present a novel definition and method for discovering causal relations in deterministic dynamical systems. The causal discovery problem is formulated, for the first time, as a constraint identification problem. Further, we show, for the first time, that the widely used principal component analysis (PCA)-based approach can be used to infer causal relations from measurements corrupted with Gaussian white noise. The specific contributions of this work are (i) a novel constraint-based framework for causality analysis of deterministic linear time-invariant dynamical processes, (ii) three useful forms of network representations, namely, source flow, bivariable, and multivariable causal networks, and (iii) data-driven causal inference and network reconstruction methods based on the dynamic iterative PCA. The proposed methods effectively handle deterministic variations and unequal measurement error variances, making them well-suited for engineering processes. Case studies are presented to demonstrate the efficacy of the proposed methods.