Constrained selective dynamic time warping of trajectories in three dimensional batch data

Three dimensional data structures such as batch process data or infra-red spectral measurements usually contain inconsistent trajectories of various durations and quality. In the case of batch process data, most modeling methods require the data from all batches to be of same duration. For spectral data, peaks might be shifted from one sample to another due to unaccounted sources of variation. These inconsistencies are usually resolved through trajectory alignment (or synchronization) methods. In this paper, we first review the deficiencies of existing approaches. Next, a Constrained selective Derivative Dynamic Time Warping (CsDTW) method is proposed to perform automatic alignment of trajectories. Different from conventional methods, CsDTW preserves key features that characterizes the batch and only apply warping to regions of least impact to trajectory characterization. The proposed warping technique is applied to both industrial and simulated datasets to demonstrate its effectiveness.