Uneven-length phase data of batch processes directly affect phase modeling accuracy of data-driven multivariate statistical analysis

resulting in reduced process monitoring performance. A trajectory synchronization method of lifting wavelet package transform (LWPT) and dynamic time warping (DTW) was proposed for the uneven-length phase data of batch process. First

LWPT was used to decompose trajectories of uneven-length phase data at multiple levels of high and low frequency and extract complete time-frequency domain information. Secondly

DTW was used to synchronize coefficient matrices at different frequency bands. Finally

inverse LWPT was used to integrate synchronized coefficient matrices

to obtain the even-length phases

and to reduce the impact of the Gibbs phenomenon on data trajectory synthesis. The simulation results of penicillin fermentation batch process show that the new method calculates fast and stable with better accuracy of synchronization

which can provide reliable process data for data-driven phase modeling of batch processes.