Synchronization of batch trajectories using dynamic time warping

The application of dynamic time warping (DTW) to the analysis and monitoring of batch processes is presented. This dynamic-programming-based technique has been used in the area of speech recognition for the recognition of isolated and connected words. DTW has the ability to synchronize two trajectories by appropriately translating expanding, and contracting localized segments within both trajectories to achieve a minimum distance between the trajectories. Batch processes often are characterized by unsynchronized trajectories, due to the presence of batch-to-batch disturbances and the existence of physical constraints. To compare these batch histories and apply statistical analysis one needs to reconcile the timing differences among these trajectories. This can be achieved using DTW with only a minimal amount of process knowledge. The combination of DTW and a monitoring method based on Multiway PCA/PLS is used for both off-line and on-line implementation. Data from an industrial polymerization reactor are used to illustrate the implementation and the performance of this method.