Global–Local Structure Analysis Model and Its Application for Fault Detection and Identification
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Abstract
In this paper, a new fault detection and identification scheme that is based on the global–local structure analysis (GLSA) model is proposed. By exploiting the underlying geometrical manifold and simultaneously keeping the global data information, the GLSA model constructs a dual-objective optimization function for dimension reduction of the process dataset. It combines the advantages of both locality preserving projections (LPP) and principal component analysis (PCA), under a unified framework. Meanwhile, GLSA can successfully avoid the singularity problem that may occur in LPP and shares the orthogonal property of the PCA method. In order to balance the two subobjectives (corresponding to global and local structure preservings), a tuning parameter is introduced, and an energy-function-based strategy is proposed to determine the value of the introduced tuning parameter. For the purpose of fault detection, two statistics are constructed, based on the GLSA model. Furthermore, the Bayesian inference algorithm is introduced upon the two monitoring statistics for fault identification. Two case studies are provided to demonstrate the efficiencies of the GLSA model.