Real-time alignment of batch process data using COW for on-line process monitoring

For the purpose of enabling real-time monitoring of a batch process with multiple traditional process parameters, time-alignment using correlation optimized warping (COW) was investigated. In the proposed procedure, subsequent to data acquisition, COW was applied as a preprocessing tool prior to, e.g., multivariate batch model prediction. The batches forming the multivariate process model used in this study were all warped using COW. The time-aligning information contained in the warping paths was added to the process data after matrix unfolding. For real-time monitoring, the following procedure is proposed: (1) a library is constructed with incremental process parameter trajectory segments and a search is performed to determine batch progress, (2) the batch in progress is warped with the matching library trajectory segment as reference and (3) model predictions are obtained. The outcome from (2) was evaluated by calculating the correlation between the warped trajectory segment from the batch in progress and the library match, and the outcome from (3) was investigated by studying the predicted Hotelling's T2 and the predicted residuals. The results showed that time-aligning algorithms such as COW could be applied in real-time for on-line monitoring applications, be it univariate control charts or, as in this case, multivariate batch model predictions.