Adaptive process-knowledge-guided cross-scale graph learning for soft sensing in industrial cyber–physical systems

Accurate acquisition of key quality variables through direct online measurement remains a major issue in complex industrial processes. Soft sensing provides a feasible way to estimate quality information from available process measurements and plays an important role in industrial cyber–physical systems (ICPS). However, high-dimensional measurements in ICPS are distributed across coupled process stages, requiring soft sensors to capture both sensor-level predictive dependencies and process-level contextual information. A central challenge is to integrate sensor-level predictive dependencies with process-zone representations while incorporating known inter-zone relationships. To this end, an adaptive process-knowledge-guided cross-scale graph network (APCG) for soft sensing in ICPS is proposed. The framework combines temporal encoding with dual-sparsity adaptive directed graph learning to encode sensor histories and learn selective predictive dependencies among sensors. Attention pooling constructs representations of predefined process zones from sensor-level features, while a process-knowledge-guided graph attention mechanism restricts inter-zone message passing to known process relationships. Sensor- and process-level representations are subsequently fused for key quality indicator estimation, allowing fine-grained measurements to complement process-level contextual information. Experiments on industrial iron ore pelletizing and sintering processes show that APCG outperforms competitive baselines, reducing RMSE by 23.76% and 10.07% and improving the R 2 score by 13.77% and 6.19%.