[Image: see text]-Norm-Based Robust Feature Extraction Method for Fault Detection

[Image: see text] Industrial data are in general corrupted by noises and outliers, which do not meet the application assumptions in feature extraction. Many existing feature extraction algorithms are not robust, overly consider the less important features of the data, and cannot capture the key features of the data. To this end, the two-level feature extraction method (TFEM) based on [Image: see text]-norm is proposed in this study. Compared with single-projection feature extraction algorithms, TFEM consists of two projections: the nonreduced and reduced dimensionality projections. The nonreduced dimensionality projection can remove the parts of less important features that are unrelated to the key features of the data. The reduced dimensionality projection can reduce the dimensionality of the data and further extract the features of the data. In addition, [Image: see text]-norm is used to make the algorithm more robust. Finally, the convergence of the proposed algorithm is analyzed. Extensive experiments have been conducted on the Tennessee Eastman and Penicillin Fermentation processes to demonstrate that the proposed method is more effective than other state-of-the-art fault detection methods.