Abstract
For decades, soft sensors have been extensively renowned for their efficiency in real-time tracking of expensive variables for advanced process control. However, despite the diverse efforts lavished on enhancing their models, the issue of label sparsity when modeling the soft sensors has always posed challenges across various processes. In this paper, a fledgling technique, called co-training, is studied for leveraging only a small ratio of labeled data, to hone and formulate a more advantageous framework in soft sensor modeling. Dissimilar to the conventional routine where only two players are employed, we investigate the efficient number of players in batch processes, making a multiple-player learning scheme to assuage the sparsity issue. Meanwhile, a sliding window spanning across both time and batch direction is used to aggregate the samples for prediction, and account for the unique 2D correlations among the general batch process data. Altogether, the forged framework can outperform the other prevalent methods, especially when the ratio of unlabeled data is climbing up, and two case studies are showcased to demonstrate its effectiveness.