A semi-supervised stochastic configuration network with ordered incremental self-training and pseudo-label confidence evaluation for industrial soft sensor

Modern industrial processes are characterized by nonlinearity, multiple variables, and a scarcity of labeled data, posing significant challenges for accurate modeling of key performance indicators. To address these difficulties, a novel incremental self-training algorithm is proposed to efficiently leverage unlabeled data for semi-supervised learning of stochastic configuration network (SCN)-based soft sensors. Firstly, a weighted Gaussian mixture model clustering method is developed to rank unlabeled samples. These samples are then sequentially labeled according to their proximity to existing labeled samples in the feature space, thereby lowering the likelihood of inaccurate labeling in early training stages. Secondly, a pseudo-label confidence evaluation algorithm is proposed to quantify the reliability of pseudo-labels, enabling selective inclusion of high-confidence samples into the augmented training dataset. Finally, a semi-supervised learning framework is introduced by integrating the unlabeled sample ranking and the pseudo-label confidence evaluation into the iterative self-training process of SCN. This approach augments the training dataset through ordered and quality-controlled increments to enhance model performance. Experimental validation on both a public case and an actual industrial case demonstrates that the proposed algorithm outperforms existing state-of-the-art methods. In the industrial case, our approach reduced the mean absolute error by 26.3% and 25.0%, the mean squared error by 14.5% and 14.6%, while improving the correlation coefficient by 9.9% and 9.1%, compared to the state-of-the-art self-training and generative model methods, respectively. Additionally, ablation studies are conducted to evaluate the contribution of different techniques on the model performance.