Mixture of D-Vine copulas for chemical process monitoring

- D-vine copulas combined with the finite mixture model are used for the statistical modeling.
- The probability distribution model is built by describing complex dependencies without dimensionality reduction.
- The HDR and DAQ are used to achieve the HDRP index for nonlinear and non-Gaussian process monitoring.
- The TE process and a real industrial process show the good performance in chemical process fault monitoring.

Complex dependence structures often exist in chemical process multivariate data. Although they are difficult to capture, vine copula shows good performance and stronger flexibility in depicting the highly nonlinear dependencies. To identify and fully understand the complex dependence patterns in multivariate data, a mixture of D-vine copulas (MDVC) is proposed. By using the expectation-maximization (EM) algorithm and stepwise semi-parametric (SSP) estimation for parameter estimation, the proposed model can depict the complex dependence structures in multivariate data. The highest density region (HDR) and the density quantile approach (DQA) are both used to construct the highest density region distance-based probability (HDRP) index to achieve a real-time process fault monitoring. The effectiveness and benefits of the proposed model are illustrated with a numerical example, the Tennessee Eastman (TE) benchmark process and a real acetic acid dehydration distillation system for fault detection. The results show that the proposed mixture of D-vine copulas can achieve good performance in chemical process fault monitoring.