Graph convolutional network soft sensor for process quality prediction

The nonlinear time-varying characteristics of the process industry can be modeled using numerous data-driven soft sensor methods. However, the intrinsic relationships among the variables, especially the localized spatial–temporal correlations that shed light on model behavior, have received little attention. In this study, a soft sensor based on a graph convolutional network is constructed by introducing the concept of graph to process modeling. The focus is on obtaining localized spatial–temporal correlations that aid in comprehending the intricate interactions among the variables included in the soft sensor. The model is trained by considering the regularization terms and it learns distinctive localized spatial–temporal correlations in an end-to-end manner. Furthermore, long-term dependence is established via temporal convolution. Thus, both the localized spatial–temporal correlations and time-series properties are captured. The feasibility of the proposed soft sensor is illustrated using two fermentation processes. The localized spatial–temporal correlations of this case study are visualized, and they demonstrate that the soft sensor is not a black-box model; instead, it is consistent with process knowledge.