A Novel Causality Method for Reconstruction of Process Topology in Multivariable LTI Dynamical Systems

Abstract

Reconstruction of process topology from cause-effect analysis of measurements finds applications in root-cause analysis, identification of disturbance propagation pathways, estimation of fault propagation times, and interaction assessment. A widely used technique based on the notion of Granger causality (GC), but is well-suited only for stationary stochastic processes. The GC-based measures and methods, while being useful in certain cases, can be highly restrictive and produce misleading results in engineering applications since changes in process variables are frequently deterministic. The lack of sufficient excitation and presence of measurement errors further restricts their applicability. In this respect, we present (i) a new definition of direct causality for deterministic linear time-invariant (LTI) dynamical systems, and (ii) a novel causality detection method based on delay estimation from noisy multivariable measurements. Efficient estimates of time delays are obtained from recently developed non-parametric frequency domain method based on partial coherence and Hilbert transform relations. In addition to the ability of handling deterministic variations, the proposed causality detection method is well-suited to handle low excitation signals and does not require the specification of any model structure. Case studies involving data from synthetic and benchmark processes are presented to illustrate the utility and efficacy of the proposed method.