Recursive weighted kernel regression for semi-supervised soft-sensing modeling of fed-batch processes

Soft-sensor techniques have been increasingly applied in chemical industry to establish an online monitor of unmeasured product indices. However, one intrinsic obstacle of soft-sensing modeling is insufficiency of labeled data while unlabeled data is abundant. In this work, a semi-supervised recursive weighted kernel regression (RWKR) method is proposed to model the soft-sensor by leveraging both labeled and unlabeled data. A novel weight strategy is presented to improve the prediction and its recursive algorithm is formulated, which adopts the incremental and decremental learning mechanism to update the soft-sensor model online and control the model complexity. Simulative soft-sensor for penicillin production process indicates that RWKR is superior to both relevance vector machine (RVM) and harmonic functions to model such fed-batch processes. Additionally, it sheds light on more competitive semi-supervised soft-sensing modeling approaches.