Average trajectory calculation for batch processes using Dynamic Time Warping

This paper proposes a method for fault detection of batch processes. The method utilizes Dynamic Time Warping (DTW) which has been used to synchronize batch trajectories, making all batch data equal in length, as a preprocessing tool of Multi-way Principal Component Analysis (MPCA). When DTW is used, an adjustment window condition, within which the synchronization is allowed in the time axis, should be defined beforehand. It is difficult to define the adjustment window appropriately, especially when the window needs to be changed dynamically throughout the process. Conventional DTW uses too simple formulations to define the window. The proposed method firstly calculates an "average trajectory", which includes information of elapsed time of normal trajectories. Then the method can automatically define the adjustment window appropriately when DTW between the average trajectory and new trajectories is done according to the information.