Learning Multihierarchical Spatiotemporal Dependence of Complex Industrial Flowsheets and Its Soft Sensor Applications

Abstract

Online prediction of key quality variables is essential for the real-time optimization and stable operation of complex industrial processes. However, with the increasing scale of modern industrial flowsheets, production systems are usually organized into multiple interconnected subprocesses. These subprocesses exhibit relatively independent local dynamic behaviors due to different equipment units and operating mechanisms while remaining globally coupled through material transfer and energy exchange. Such local independence and global interdependence make it difficult for existing soft sensor models to comprehensively characterize multihierarchical spatiotemporal dependencies, thereby posing significant challenges for accurate quality prediction. To address these issues, this article proposes a novel multihierarchical spatial–temporal dependence-aware graph convolutional network (MHSTA-GCN) for online quality prediction in large-scale industrial processes. In particular, an integrated graph topology learning method is designed by combining correlation-based prior knowledge with adaptive parameter learning to construct coupled spatial relationships among variables, thereby enhancing structural reliability while uncovering latent dynamic dependencies. Subsequently, a mix-hop graph convolutional network (GCN) is developed to selectively propagate critical information through multihop operations and is incorporated into the spatial–temporal dependence-aware feature extraction module to capture multiscale sequential patterns and dynamic variations, thereby modeling complex spatiotemporal interactions. Furthermore, a multihierarchical feature extraction framework is introduced to jointly exploit global and local process information, enabling a comprehensive multihierarchical feature representation. Extensive experiments on two real-world large-scale industrial process datasets validate the effectiveness of the proposed method.