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Estimation of Disturbance Propagation Path Using Principal Component Analysis (PCA) and Multivariate Granger Causality (MVGC) Techniques

ABSTRACT

Process monitoring and fault diagnosis using the multivariate statistical methodologies has been extensively used in the process and product development industries for the last several decades. The fault in one process variable readily affects all the other associated variables, which makes the fault detection process not only more difficult but also time-consuming. In this study, principal component analysis (PCA)-based fault amplification algorithm is developed to detect both the root cause of fault and the fault propagation path in the system. The developed algorithm projects the samples on the residual subspace (RS) to determine the disturbance propagation path. Usually, the RS of the fault data is superimposed with the normal process variations, which should be minimized to amplify the fault magnitude. The RS-containing amplified fault is then converted to the covariance matrix, followed by singular value decomposition (SVD) analysis, which, in turn, generates the fault direction matrix corresponding to the largest eigenvalue. The fault variables are then rearranged according to their magnitude of contribution toward a fault, which, in turn, represents the fault propagation path using an absolute descending order function. Moreover, the multivariate Granger causality (MVGC) algorithm is used to analyze the causal relationship among the variables obtained from the developed algorithm. Both the methodologies are tested on the LNG fractionation process train and distillation column operation, where some fault case scenarios are assumed to estimate the fault directions. It is observed that the hierarchy of variables obtained from fault propagation path algorithm are in good agreement with the MVGC algorithm. Therefore, fault amplification methodology can be used in industrial systems for identifying the root cause of fault, as well as the fault propagation path.

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