Structured Pattern Discovery Using Dictionary Learning for Incipient Fault Detection and Isolation

To address the challenges encountered by dictionary learning-based monitoring, this article presents a novel pattern discovery scheme for detection and isolation of incipient faults that involves structured sparse coding and sequential dictionary augmentations. Through learning a basic dictionary for normal pattern and augmenting the low-dimensional sparse dictionaries for analyzing different fault patterns, the process signals can be decomposed into fault-free and fault-related components. To guarantee the in-statistical-control status of the fault-free part and improve detection sensitivity, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2}$</tex-math></inline-formula>-penalty is imposed on the sum of coefficient vectors to ensure that the monitoring statistic related to the fault-free part will not exceed the control limit. In addition, two Frobenius norm penalties are imposed on the zero centered coefficient matrix and atom matrix to improve the robustness of signal decomposition. Instead of imposing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{1}$</tex-math></inline-formula>-sparsity constraint on the atoms, a hard sparsity constraint is used to correctly select fault-related feature variables, so that fault patterns can be better revealed. The informative dictionaries are then incorporated into the moving window-based monitoring strategy, yielding a fault detection and isolation scheme suitable for incipient faults. The superior performance of our proposed approach is validated by application studies involving a numerical example and two practical industrial processes.