Multiway elastic net (MEN) for final product quality prediction and quality-related analysis of batch processes

• The variable regularization technique is incorporated into batch process modeling.
• The cumulative effect of the variable trajectories on product quality is modeled.
• The time-varying effect of the process variables on product quality is modeled.
• kNN-based future data estimation is utilized to achieve better online prediction.
• Better model interpretation is achieved, which is useful for process understanding.

In batch processes, the final product quality is determined by the trajectories of the process variables throughout each batch. Consequently, there are two important issues that should be considered in the quality-related modeling. First, the process variable trajectories usually contribute to the final product quality cumulatively along the operation time within each batch. Such effect is named as the cumulative effect. Second, each process variable may have different impacts on the product quality at different time intervals, which is denoted as the time-varying effect. In order to model both two effects reasonably, a multiway elastic net (MEN) method is proposed in this paper. Accordingly, a quality prediction and process analysis scheme is presented. MEN integrates variable selection and regression in batch process modeling, where the regression coefficients are regularized in an automatic manner. With proper data pre-treatment, MEN can provide both accurate prediction and good interpretation. For online prediction, a future data estimation approach is proposed based on the k-nearest neighbor technique. The application of the proposed scheme to an injection molding process shows that MEN is not only effective in the online quality prediction but also enhance the understanding of the process.