Continual Semisupervised Learning of Echo State Network for Quality Prediction of Multimode Processes

The successive switching nature of multimode processes, coupled with data scarcity, challenges traditional quality prediction models. Specifically, the difficulty of simultaneously collecting abundant labeled datasets from all modes forces the model to update its parameters as modes switch. This leads to the forgetting of historical mode knowledge and hinders the aggregation of knowledge, thereby degrading generalization across modes. To this end, we propose a novel continual semisupervised graph echo state network ($\text{CS}^{2}$GESN). First, a semisupervised graph echo state network ($\text{S}^{2}$GESN) is designed based on the graph smoothing assumption to extract dynamic information from unlabeled samples within each mode. The $\text{S}^{2}$GESN model then evolves into a continual model, $\text{CS}^{2}$GESN, employing an elastic weight consolidation strategy for parameter importance estimation derived from pseudoinverse parameter optimization, facilitating the accumulation of historically learned knowledge. This manner alleviates performance deterioration from data scarcity and information forgetting, and enables more flexible modeling of successive arriving operating modes. The superiority and feasibility of the proposed method are demonstrated through its application to the Tennessee Eastman process and the three-phase flow facility process.