A Graph Neural Network With Dual-Stage Feature Aggregation for Industrial Soft Sensors

Soft sensing, as a key engineering methodology, leverages readily accessible information from auxiliary variables to estimate hard-to-measure targets. Deep learning frameworks have significantly advanced intelligent data-driven modeling in this field. However, most multivariate data reside in structured spaces, where the interactions among different variables are accompanied by scale disparities, posing significant challenges to conventional neural networks. In response, we propose a novel graph neural network (GNN) with dual-stage feature aggregation (DA-GNN) for soft sensor modeling. Initially, multivariate time spans associated with graph nodes are chronologically segmented to build small-scale node subareas, which serve as the basic units for graph state updates. Subsequently, in the first stage, an attention mechanism is adopted to select subregion states of adjacent nodes guided by their importance scores. In the second stage, a gated recurrent module is embedded in the graph architecture to aggregate temporal features of the subregions based on the evolution orders of the industrial process. As a result, this dual-stage mechanism reconciles the scale differences while capturing local dependencies within the structured multivariate space, leading to enhanced performance. The proposed framework is applied to soft sensing of chemical oxygen demand (COD) in a real-world wastewater treatment process. Its effectiveness is validated through comparative studies with some classical and advanced algorithms.