Process Monitoring Method Based on Double-Model and Multi-Subspace Vine Copula

Abstract

A process monitoring method based on double-model and multi-subspace vine copula (DMVC) is proposed in this paper. To improve the fault detection performance, process variables are divided into two sets according to their correlation, in which C-vine and D-vine are used to build models, respectively. The variables with stronger correlation are selected to build the C-vine model, and those with weak correlation are used for the D-vine model. In addition, the two models individually establish three different subspaces according to different training data information, including marginal distribution subspace (MDS), dependent structural subspace (DSS), and joint distribution subspace (JDS). Highest density region (HDR) and generalized local probability (GLP) are also introduced to establish a robust control domain and detection index, which makes the method more sensitive to data. The effectiveness of the proposed method in the field of process monitoring is verified by numerical simulation and the Tennessee Eastman (TE) process. Compared with classical multivariate statistical methods, the DMVC displays superior monitoring performance.

Process Monitoring and Fault Diagnosis Based on a Regular Vine and Bayesian Network

“…Each copula pair has a different correlation character, and it is because of these correlations of individual variables that vine copula exhibits better flexibility in describing tail correlations, asymmetry, conditional correlations, and other characteristics of complex variables. 45 As was previously noted, the most classical vine copula is C vine and D vine. These two forms are only special cases of R vine.…”

“…Vine copula transforms the multivariate copula into a combination of binary copula, which also results in vine copula containing a series of copula pairs that are optimal for the current variables. Each copula pair has a different correlation character, and it is because of these correlations of individual variables that vine copula exhibits better flexibility in describing tail correlations, asymmetry, conditional correlations, and other characteristics of complex variables . As was previously noted, the most classical vine copula is C vine and D vine.…”

Nonlinear Non-Gaussian and Multimode Process Monitoring-Based Multi-Subspace Vine Copula and Deep Neural Network

“…In conclusion, the CDS method considers not only the random behavior of multivariate variables but also variables from marginal deviation and dependency relations. Detailed explanations can be found in refs and .…”