A Sparsity-Aware Fault Diagnosis Framework Focusing on Accurate Isolation
Xianchao Xiu, Zhonghua Miao, Wanquan Liu
Abstract
In this article, we propose an efficient fault diagnosis framework to achieve accurate fault isolation. The core is to introduce the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2,0}$</tex-math></inline-formula> -norm sparsity constrained optimization to reduce the variable redundancy and determine the variable number, which is different from the existing sparse variants. In order to illustrate the idea, this article takes principal component analysis (PCA) as an essential step. First, a sparsity-aware PCA is constructed by taking advantage of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2,0}$</tex-math></inline-formula> -norm constrained optimization. Afterward, a two-stage monitoring strategy is designed, including fault detection and fault isolation. Once the fault is detected, the sparsity level is then shrunk to achieve accurate fault isolation. Moreover, an alternating direction method of multipliers-based optimization algorithm is developed with detailed implementation. Finally, the detection improvement and accurate isolation performance are validated by two simulated examples, the Tennessee Eastman benchmark process, and a practical cylinder-piston process.