Abstract:

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.

Key words: uneven-length phase data, trajectory synchronization, lifting wavelet package transform, dynamic time warping, batch process

摘要：

间歇过程不等长时段数据直接影响数据驱动的多元统计分析时段建模精度，导致间歇过程的监控性能降低。针对间歇过程不等长时段数据问题，提出一种基于提升小波包变换（LWPT）和动态时间规整（DTW）算法的间歇过程不等长时段数据同步化方法。该方法引入LWPT对间歇过程不等长时段数据轨迹进行高低频的多级分解，充分提取数据轨迹的所有时频域信息；采用DTW算法对不同频段的系数矩阵进行同步化，并利用提升小波包逆变换对同步化后的系数矩阵进行合成，降低吉布斯现象对数据轨迹合成的影响，获得等长的时段轨迹，实现了间歇过程不等长时段数据同步化。青霉素发酵过程仿真实验表明，所提出的方法运算速度快、稳定，不等长时段数据的同步化结果具有较高的准确性，为间歇过程时段建模提供了可靠的过程数据。

关键词: 不等长时段数据, 同步化, 提升小波包变换, 动态时间规整, 间歇过程