A mixture of variational canonical correlation analysis for nonlinear and quality-relevant process monitoring

Proper monitoring of quality-related variables in industrial processes is nowadays one of the main worldwide challenges with significant safety and efficiency implications.Variational Bayesian mixture of canonical correlation analysis (VBMCCA)-based process monitoring method was proposed in this paper to predict and diagnose these hard-to-measure quality-related variables simultaneously. Use of Student's t-distribution, rather than Gaussian distribution, in the VBMCCA model makes the proposed process monitoring scheme insensitive to disturbances, measurement noises, and model discrepancies. A sequential perturbation (SP) method together with derived parameter distribution of VBMCCA is employed to approach the uncertainty levels, which is able to provide a confidence interval around the predicted values and give additional control line, rather than just a certain absolute control limit, for process monitoring. The proposed process monitoring framework has been validated in a wastewater treatment plant (WWTP) simulated by benchmark simulation model with abrupt changes imposing on a sensor and a real WWTP with filamentous sludge bulking. The results show that the proposed methodology is capable of detecting sensor faults and process faults with satisfactory accuracy.