Structured Joint Sparse Principal Component Analysis for Fault Detection and Isolation

Principal component analysis (PCA) has been widely applied in process monitoring of modern industrial systems. PCA performs fault detection by mapping the process data into a low dimensional subspace and tracking the process behavior using T
²
and SPE statistics, whilst in fault isolation, it heavily relies on contribution plot or reconstruction based approaches. However, conventional methods based on contribution plot and reconstruction suffer from insufficient fault isolation capabilities. In order to improve the fault isolation performance, this article proposes a novel fault detection and isolation approach based on the Structured Joint Sparse PCA (SJSPCA). The objective function of SJSPCA involves two regularization terms: l
2,1
norm and the graph Laplacian. By imposing the l
2,1
norm term, SJSPCA is able to achieve row-wise sparsity, introducing the graph Laplacian regularization term can incorporate structured variable correlation information. In fault detection, conventional T
²
and SPE statistics are constructed to detect abnormal situations. Once a fault is detected, a two stage fault isolation strategy is considered and a score index is calculated for each variable. The row-sparsity property of l
2,1
norm ensures that the score indices associated to normal variables approach zero and the graph Laplacian constraint helps isolation of correlated faulty variables. The validity of SJSPCA in fault detection and isolation is illustrated by a process fault observed in an industrial blast furnace iron-making process.