Laplacian Sparse Dynamic Slow Feature Analysis for Process Monitoring and Fault Isolation

The process monitoring and fault isolation are essential for ensuring operational safety and maintaining product quality in the industrial processes. This study introduces a novel approach to process monitoring and fault isolation based on the Laplacian sparse dynamic slow feature analysis (LSDSFA). To simultaneously account for sparsity, dynamics, and global structural information, a new optimization framework for LSDSFA is proposed. This framework incorporates the ${l}_{{1}}$ norm and a Laplacian graph into dynamic slow feature analysis (SFA), with enhancements to process variable representation. The optimization problem is addressed using the alternating direction method of multipliers (ADMMs). The proposed method decomposes the process variable space into latent and residual subspaces. In addition, three monitoring statistics are developed to facilitate effective process monitoring, while fault isolation is achieved through a two-level contribution plot. Specifically, the intrinsic structure of the process data is captured by employing a graph Laplacian operator to explore intervariable correlations. Simultaneously, the incorporation of the graph Laplacian operator and ${l}_{{1}}$ norm into dynamic SFA (DSFA) reduces variable redundancy, thereby exploiting the intrinsic structure of the process data more effectively and improving interpretability through the sparsity. Experimental evaluations conducted on the widely adopted Tennessee Eastman Process (TEP) benchmark and a real-world blast furnace ironmaking process (BFIP) demonstrate the superior performance of the proposed LSDSFA-based method in comparison with related techniques.