Fault Detection Using Structured Joint Sparse Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is an efficient dimension reduction technique, which has been extensively used in the fields, such as image processing, automatic control, and machine learning. The application to fault detection (FD) is still not investigated sufficiently. To improve the performance of NMF-based FD approaches, this article proposes a novel FD approach using the structured joint sparse NMF (SJSNMF) for non-Gaussian processes. The basic idea of SJSNMF is to incorporate the graph Laplacian to preserve the relationship between process variables and operation units and introduce the joint sparsity to exploit row-wise sparsity of the latent variables. Technically, an optimization algorithm based on the alternating direction method of multipliers (ADMM) is established. To detect the fault, two test statistical metrics are adopted and the kernel density estimation (KDE) is calculated to estimate the control limit. The effectiveness of the proposed SJSNMF is verified on the benchmark Tennessee Eastman process (TEP) and the cylinder-piston assembly of diesel engines.