Optimal Indicator-Variable Approach for Trajectory Synchronization in Uneven-Length Multiphase Batch Processes

Partial least-squares regression models assessing the end-point product quality in batch processes require that all of the measured variable trajectories across the historical batches have the same length. Most of the conventional and advanced methodologies for batch synchronization need some prior knowledge about the process to carry out one or more of the following activities: partitioning of the batches into phases, selection of an appropriate indicator variable that is then used to synchronize the batches, or selection of a reference batch to which all other batches are matched. We present an optimal indicator-variable approach for phase partitioning and trajectory synchronization in uneven-length multiphase batch processes. The main advantages are that partitioning into phases and selection of the most appropriate indicator variable within each phase are performed automatically rather than manually and are carried out simultaneously rather than disjointly based on a surrogate optimization framework that maximizes the performance of the product quality assessment model under development. Therefore, differently from conventional and advanced synchronization methodologies currently available, the proposed method is completely process-agnostic, which enhances applicability to complex batch processes. Also, in terms of computational times, it scales favorably with the calibration data set size. An industrial fed-batch process for the manufacturing of a specialty chemical and a simulated fed-batch process for the manufacturing of penicillin are used as test beds and demonstrate that the new indicator-variable approach has a superior performance than models built using other synchronization strategies.