A stable soft sensor based on causal inference and graph convolutional network for batch processes

Data-driven soft sensor techniques play a crucial role in process control, which can ensure process safety, and improve product quality by measuring key variables that are challenging to measure in batch processes. Batch processes are characterized by periodic batch production. Insufficient utilization of spatiotemporal information and causal relationships between variables in batch process data limits the accuracy of soft sensors, leading to significant intra-batch and inter-batch errors in the models. Accurate and stable soft sensors in batch processes are in great need. In this work, a stable soft sensor based on causal inference and graph convolutional networks is proposed for batch processes. Specifically, a graph structure learning module based on causal inference is employed in order that the network can learn the causal relationships from both global and local causal effects among process variables. Moreover, a causal graph convolutional network is constructed to capture spatial and temporal information and aggregate causal features for soft sensor modeling. Furthermore, the stable soft sensor model is trained end-to-end using a joint loss function. Experimental results from two batch processes demonstrate the feasibility and effectiveness of stable soft sensor, and the learned causal relationships between variables closely correspond to the fundamental principles of the process.