Synchronization of batch trajectory based on multi-scale dynamic time warping

Based on dynamic time warping (DTW), this paper proposes MSDTW (multi-scale DTW) to synchronize batch trajectory. DTW is a method for flexible pattern-matching scheme. It translates, compresses, and expands a pairs of patterns so that similar features within the two patterns are matched. DTW is used in spoken word recognition widely. Similarly, DTW has the ability to synchronize two trajectories from batch process and provides an elegant solution to the synchronization of batch trajectories. MSDTW is combination of DTW and wavelet, and is used for synchronization more precise than DTW. MSDTW firstly decomposes original trajectories into approximations and details at different scales. Contributions from each scale are collected in separate matrices, and data are synchronized at each level based on DTW respectively. Then synchronized separate matrices are reconstructed to form new synchronized trajectories. Application to industrial process making process illustrates the MSDTW is valid and precise.