Batch process monitoring based on just-in-time learning and multiple-subspace principal component analysis

• A new division algorithm of multiple subspace is defined.
• JITL is introduced into MSPCA.
• The current state of process can be well tracked by the JITL method.
• All the local information are sufficiently utilized in MSPCA.
• JITL–MSPCA has better monitoring performance than traditional methods.

Batch or fed-batch process monitoring is a challenging task because of its characteristics such as batch-to-batch variations, inherent time-varying dynamics, and multiple operating phases. Thus, a new batch process monitoring method based on just-in-time learning (JITL) and multiple-subspace principal component analysis (MSPCA) is developed. Based on offline one batch normal data, the division algorithm of multiple subspace is proposed, in which mutual information (MI) and K-means are employed to derive the segmentation rule of variable subspace and then the variables are divided into several subspaces according to the segmentation rule of variable subspace. At online monitoring, the training data set for modeling is obtained by JITL and separated into each subspace according to the segmentation rule of variable subspace. Principal component analysis is employed to build the model in each subspace, and all components are retained to calculate T2 statistics. A unique probability index is obtained by Bayesian inference (BI) as the decision fusion strategy of T2 statistics of all subspaces. A simple numerical example is used to show the advantages of the proposed MSPCA method. The feasibility and effectiveness of JITL–MSPCA is demonstrated by fed-batch penicillin fermentation.