Semi-supervised graphical autoencoder regression modeling for soft sensors

For soft sensor in chemical processes, process variables are usually measured at a higher frequency while quality variables are often measured at a lower rate. This discrepancy in measurement frequencies results in a large number of unlabeled data points. In addition, there are instances where the daily recorded component variables are more readily available, contrasting with the difficulty in obtaining data for the quality variable data. To address these issues, this paper proposes a novel semi-supervised learning framework, TGAE-STN(Transfer entropy based Graph Autoencoder-Spatiotemporal Networks), which employs an encoder-decoder architecture to efficiently handle both unlabeled and labeled data. For unlabeled data, transfer entropy is computed from the original sampling data to facilitate the conversion into graph data and subsequent reconstruction of graph structure. For labeled data, the latent variable obtained from the reconstruction process of the codec is used as the input to the prediction model, and the adjacency matrix is dynamically constructed during the training process. The prediction network uses a spatiotemporal graph model to extract features across both temporal and spatial dimensions. Moreover, the encoder part is updated asynchronously based on the performance of the decoder and the prediction network, facilitating effective utilization of the information from both unlabeled and labeled data. The effectiveness of the proposed method is verified through a numerical case and a chemical process. The results show that the proposed TGAE-STN method provides a promising solution for soft sensor technology under semi-supervised conditions.