Supervised probabilistic dynamic-controlled latent-variable model for quality pattern prediction and optimisation

A supervised probabilistic dynamic-controlled latent-variable (SPDCLV) model is proposed for online prediction, as well as real-time optimisation of process quality indicators. Compared to existing probabilistic latent-variable models, the key advantage of the proposed method lies in explicitly modelling the dynamic causality from the manipulated inputs to the quality pattern. This is achieved using a well-designed, dynamic-controlled Bayesian network. Furthermore, the algorithms for expectation-maximisation, forward filtering, and backward smoothing are designed for learning the SPDCLV model. For engineering applications, a framework for pattern-based quality prediction and optimisation is proposed, under which the pattern-filtering and pattern-based soft sensor are explored for online quality prediction. Furthermore, quality optimisation can be realised by directly controlling the pattern to the desired condition. Finally, case studies on both an industrial primary milling circuit and a numerical example illustrate the benefits of the SPDCLV method in that it can fully model the process dynamics, effectively predict and optimise the quality indicators, and monitor the process.