Quality prediction and quality-relevant monitoring with multilinear PLS for batch processes

• Two new multilinear PLS models named HOPLS-CP and HOPLS-RTucker are developed.
• Batch process monitoring methods are proposed based on multilinear PLS.
• Multilinear PLS is used for the quality prediction in batch processes.
• Multilinear PLS has better monitoring and prediction abilities than unfold-PLS.

The multilinear regression method is applied for quality prediction and quality-relevant monitoring in batch processes. Four multilinear partial least squares (PLS) models are investigated, including three higher-order PLS (HOPLS) models, termed as HOPLS-Tucker, HOPLS-RTucker and HOPLS-CP, and the N-way PLS (N-PLS) model. These multilinear PLS methods have two advantages as compared to the unfold-PLS method. Firstly, they retain the inherent three-way representation of batch data and avoid the disadvantages caused by data unfolding, resulting in more stable process models. Secondly, they summarize the main information on each mode of data and describe the three-way interactions between them, and therefore have better modeling accuracy and intuitive interpretability. Online quality prediction and quality-relevant monitoring methods are developed by combining multilinear PLS with the moving data window technique. These methods are tested in a fed-batch penicillin fermentation process. The results indicate that the multilinear PLS method has higher predictive accuracy, better anti-noise capability and monitoring performance than the unfold-PLS method.