Real-time synchronization of batch trajectories for on-line multivariate statistical process control using Dynamic Time Warping

Abstract

This paper addresses the real-time monitoring of batch processes with multiple different local time trajectories of variables measured during the process run. For Unfold Principal Component Analysis (U-PCA)-or Unfold Partial Least Squares (U-PLS)-based on-line monitoring of batch processes, batch runs need to be synchronized, not only to have the same time length, but also such that key events happen at the same time. An adaptation from Kassidas et al.'s approach [1] will be introduced to achieve the on-line synchronization of batch trajectories using the Dynamic Time Warping (DTW) algorithm. In the proposed adaptation, a new boundaries definition is presented for accurate on-line synchronization of an ongoing batch, together with a way to adapt mapping boundaries to batch length. A relaxed greedy strategy is introduced to avoid assessing the optimal path each time a new sample is available. The key advantages of the proposed strategy are its computational speed and accuracy for the batch process context. Data from realistic simulations of a fermentation process of the Saccharomyces cerevisae cultivation are used to illustrate the performance of the proposed strategy.

Using warping information for batch process monitoring and fault classification

“…Before the multivariate modeling is carried out, the synchronization of NOC batches must be performed. In order to establish the proper parameters of the RGTW algorithm, the cross-validation procedure proposed in [11] was run. Firstly, the basic parameters of the off-line DTW algorithm were assessed.…”

“…Hence, a study of the set of warping profiles obtained from the off-line and on-line synchronization is highly desired. Some authors have emphasized the importance of not discarding the information derived from the synchronization [10] and others have used this warping information as an extra variable in the multivariate analysis [11,14]. Nevertheless, there is no sound study on the use of the warping information for: i) unsupervised (i.e.…”

“…The RGTW algorithm [11] is used in this paper for batch synchronization due to its versatility both for end-of-batch and real-time applications. This algorithm synchronizes trajectories of a test batch…”

“…The optimal warping path f * new (also called warping profile, or warping information) is assessed by obtaining the path that minimizes the cumulative distance. This synchronization procedure is carried out within a moving window ζ with a defined width, which is optimized by cross-validation [11].…”

“…The approaches for synchronizing batch data can be roughly classified into three categories: i) methods based on compressing/expanding the raw trajectories using linear interpolation either in the batch time dimension [3,4] or in an indicator variable dimension (the so-called Indicator Variable-based synchronization, IV) [5]; ii) methods based on features extraction [6,7,8,9]; and iii) methods based on stretching, compressing and translating pieces of trajectories, such as Dynamic Time Warping (DTW) [10] and Relaxed Greedy Time Warping (RGTW) [11].…”