This paper proposed a quality-related online monitoring strategy based on time and batch two-dimensional evolution information for batch processes. In the direction of time, considering the difference between each phase and the steady part and the transition part in the same phase, the change trend of the regression coefficient of the PLS model is used to divide each batch into phases, and each phase into parts. The phases, the steady parts, and the transition parts are finally distinguished and dealt with separately in the subsequent modeling process. In the batch direction, considering the slow time-varying characteristics of batch evolution, sliding windows are used to perform mode division by analyzing the evolution trend of the score matrix T in the PLS model on the base of phase division and within-phase part division. Finally, an online monitoring model that comprehensively considers the evolution information of time and batch is obtained. In a typical batch operation process, injection molding is used as an example for experimental analysis. The results show that the proposed algorithm takes advantage of mixing the time-batch two-dimensional evolution information. Compared with the traditional methods, the proposed method can overcome the shortcomings caused by the single dimension analysis and has better monitoring results.

A PLS-based quality prediction method is proposed for batch processes using two-dimensional extended windows. To realize the adoption of information in the direction of sampling time and batch, a new definition region of support (ROS), k-i-back-extended region of support (KIBROS), is proposed to establish the extended window, which including the data of the previous sampling times in the same batch, the data of the same sampling time in the historical batches, the data of the previous sampling times in the historical batches and the data of the later sampling times in the historical batches. According to these regions of support, extended windows are established, and different models are proposed based on the extended windows for batch processes quality prediction. Further, using a typical batch process as an example, the injection molding process, the proposed quality prediction method is experimentally verified, proving that the proposed methods have higher prediction accuracy than the traditional method and the prediction stability is also improved.

A PLS-based quality prediction method is proposed for batch processes using two-dimensional extended windows. To realize the adoption of information in the directions of sampling time and batch, a newly defined region of support (ROS), called the k-i-back-extended region of support (KIBROS), is proposed; it establishes an extended window by adding two regions of data to the traditional ROS to include all possible important data for quality prediction. Based on the new ROS, extended windows are established, and different models are proposed using the extended windows for batch process quality prediction. Furthermore, using the typical injection molding batch process as an example, the proposed quality prediction method is experimentally verified, proving that the proposed methods have higher prediction accuracy than the traditional method and that the prediction stability is also improved.