Hybrid variable dictionary learning for monitoring continuous and discrete variables in manufacturing processes

The fusion of industrial artificial intelligence with the Industrial Internet of Things (IIoT) can attain a heightened level of process monitoring in modern manufacturing processes. In general, the state variables of industrial processes collected through the IIoT encompass not only continuous variables but also numerous discrete variables. Owing to potential coupling factors, these variables frequently exhibit strong correlations. However, most existing methods deal only with continuous variables, which results in breaking the integrity of the state information and being incompetent to extract the useful information carried by discrete variables. To effectively address the joint monitoring challenges of continuous and discrete variables under the IIoT framework, hybrid variable dictionary learning (HVDL) is proposed in this paper. Specifically, considering that the values of discrete variables are finite sets, a specific discrete dictionary is built for data reconstruction. Besides, in order to consider the correlation between continuous and discrete variables, the alignment of them in the time dimension is achieved by sharing labels. The HVDL method can judiciously learn data dictionaries to extract multifaceted valid features across diverse data types, free from prior assumptions on data distributions. Finally, extensive experiments are conducted to demonstrate the superiority of the proposed method, including a numerical simulation case, a closed-loop continuous stirred tank reactor benchmark, and a real zinc smelting roaster. Experimental results indicate that the proposed method can fully consider the correlation between continuous and discrete variables, thus it is conducive to identifying early anomalies and mismatch anomalies.