Optimizing manipulated trajectory based on principal time-segmented variables for batch processes

Non-unitized loading cosine similarity A recursive optimization method that updates fewer parameters of the manipulated trajectory determined by principal time-segmented variables (PTVs) for batch processes with multi-stage characteristics is presented. First, the correlation analysis between time-segmented variables and the controlled product quality index variable is carried out in a non-unitized orthogonal latent variable space. Next, the parameters of the manipulated trajectory and the PTVs of each stage are determined according to the correlation and trend characteristics of the trajectory. Then, the parameters of the manipulated trajectory are recursively updated according to the cosine similarity between PTVs and the controlled quality index variable. Finally, performance of the proposed optimization technique is evaluated using the Bisphenol A (BPA) crystallization process to verify the effectiveness and advantages of the methods.