An effective MW-PCP-based intermittent fault detection method via sparse matrix factorization and noise reduction

Intermittent faults (IFs) usually have significant impact on systems, and the detection of IFs is faced with challenges because of their short duration and randomness. At present, IFs detection has received widespread attention, but few studies have focused on leveraging IFs’ unique characteristics. IFs exhibit sparsity in the process data matrix due to its short and limited duration. This paper proposes an effective Moving Window-Principal Component Pursuit (MW-PCP)-based IFs detection method aiming at utilizing the sparsity of IFs to accurately detect them. Firstly, PCP method is used to decompose the process data matrix and resulting in a sparse matrix that encompasses IFs and sparse process noise. Secondly, MW technique is combined with PCP to lower the interference of noise and accurately capture fault information. And then Hotelling’s $T^2$ statistic is used to achieve efficient IFs detection. Especially, we provide the detectability analysis of IFs under the proposed method with detailed proof, including its definition and the necessary and sufficient conditions. Finally, several experiments show that the MW-PCP-based method outperforms existing methods, including Principal Component Analysis (PCA), MW-PCA, PCP, etc. Specifically, it achieved Fault Detection Rates (FDRs) of 97.3$\text{\%}$, 85.8$\text{\%}$, and 75$\text{\%}$ in numerical simulation, the CSTR process, and the Cranfield Multiphase Flow Facility dataset, respectively.