Vine Copula-Based Dependence Description for Multivariate Multimode Process Monitoring

A novel vine copula-based dependence description (VCDD) process monitoring approach is proposed. The main contribution is to extract the complex dependence among process variables rather than perform dimensionality reduction or other decoupling processes. For a multimode chemical process, the C-vine copula model of each mode is initially created, in which a multivariate optimization problem is simplified as coping with a series of bivariate copulas listed in a sparse matrix. To measure the distance of the process data from each non-Gaussian mode, a generalized local probability (GLP) index is defined. Consequently, the generalized Bayesian inference-based probability (GBIP) index under a given control limit can be further calculated in real time via searching the density quantile table created offline. The validity and effectiveness of the proposed approach are illustrated using a numerical example and the Tennessee Eastman benchmark process. The results show that the proposed VCDD approach achieves good performance in both monitoring results and computation load.