Sensor degradation seriously hinders the practical application of soft sensors. To reduce the negative effect of sensor degradation, in this article, we propose a robust domain adaptation mixture of Gaussian processes (DA-MGP) for online soft sensor modeling of multimode processes. Based on the decomposition of industrial data into a group of Gaussian domains, Gaussian domain discrepancy (GDD) is designed for domain adaptation and process mode recognition. After recognizing the process mode based on GDD, a Gaussian domain adaptation is presented to correct the drifted online input data by domain mapping, which can significantly improve the robustness of the soft sensor against sensor degradation. Furthermore, the domain mapping matrix is utilized as a transferred basis function for a local transferred Gaussian process component, which is used for robust soft sensor modeling. Additionally, an online block processing framework is adopted when the DA-MGP-based soft sensor is applied in online quality prediction. Finally, the TE benchmark process and a real industrial polypropylene process are employed to verify the effectiveness of the proposed method. In the designed five cases of sensor degradation, the DA-MGP-based soft sensor shows its strong robustness against sensor degradation.

Causality in an industrial process provides insights into how various process variables interact and affect each other within the system. It reveals the underlying mechanisms of industrial processes, which ensures predictive reliability and facilitates physical interpretability. However, existing causality-based techniques have limitations, as they neglect the temporal factor in causal description, introduce spurious causal associations in causal discovery, and fail to consider the spatial-temporal synchronicity in causal utilization. To address these issues, this article proposes a spatial-temporal causality modeling approach. A novel spatial-temporal causal digraph (STCG) is proposed to describe causal dependencies among process variables, which considers both spatial and temporal factors encompassing causal relationships and time delays. The STCG identification procedure is formulated as a Markov decision process, and knowledge-data guided reinforcement learning is developed to acquire the optimal identification policy and avoid spurious causal associations. With the identified STCG, a graph attention gate recurrent unit (GAGRU) is constructed for spatial-temporal process modeling, which is able to capture the synchronous evolution of industrial data in spatial-temporal dimensions. Finally, the effectiveness of the proposed modeling approach is verified by applying to two real industrial cases, including soft sensing for a sulfur recovery unit and anomaly detection for an argon distillation system. The experimental results demonstrate that the STCG-based industrial process modeling outperforms classical and state-of-the-art comparison methods in terms of reliability and interpretability.

In multiunit industrial plant-wide processes (MIPPs), data-driven distributed process monitoring methods have played an important role in ensuring process safety and reliability. However, the existing studies fail to leverage the relational knowledge about the underlying process structure of MIPPs, which may lead to inaccurate process modeling and degradation of the monitoring performance. To tackle these issues, this work proposes a novel knowledge-enhanced distributed graph autoencoder for plant-wide process monitoring. Firstly, a posterior graph structure learning module (PGSL) is designed for relational knowledge discovery, which explicitly characterizes the dependencies between operation units in MIPPs into a directed graph. Prior knowledge is introduced into PGSL as a learning bias that steers the posterior graph to adhere to the underlying physics. Then, a novel distributed graph autoencoder (DGAE) is developed to encode both the local information within each unit and the global information between units for distributed process monitoring. The discovered posterior knowledge is embedded as a relational inductive bias in DGAE to enhance the capability of unsupervised representation learning, thereby improving the monitoring performance. Finally, the effectiveness of the proposed method is demonstrated through the Tennessee Eastman process and a real-world air separation process.