A novel self-training framework for semi-supervised soft sensor modeling based on indeterminate variational autoencoder

In modern industrial processes, the high acquisition cost of labeled data can lead to a large number of unlabeled samples, which greatly impacts the accuracy of traditional soft sensor models. To this end, this paper proposes a novel semi-supervised soft sensor framework that can fully utilize the unlabeled data to expand the original labeled data, and ultimately improve the prediction accuracy. Specifically, an indeterminate variational autoencoder (IVAE) is first proposed to obtain pseudo-labels and their uncertainties for unlabeled data. On this basis, the IVAE-based self-training (ST-IVAE) framework is further naturally proposed to expand the original small labeled dataset through continuous circulation. Among them, a variance-based oversampling (VOS) strategy is introduced to better utilize the pseudo-label uncertainty. By determining similar sample sets through the comparison of Kullback-Leibler (KL) divergence obtained by the proposed IVAE model, each sample can be independently modeled for prediction. The effectiveness of the proposed semi-supervised framework is verified on two real industrial processes. Comparable results illustrate that the ST-IVAE framework can still predict well even in the presence of missing input data compared to state-of-the-art methodologies in addressing semi-supervised soft sensing challenges.