Global-local structure analysis for fault detection

Abstract

In this paper a new dimensionality reduction technique named global-local structure analysis (GLSA) is proposed. It constructs a dual-objective optimization function, which exploits the underlying geometrical manifold and keeps the global information for dimensionality reduction simultaneously. This combines the advantages of locality preserving projections (LPP) and principal component analysis (PCA) under a unified framework. Besides, GLSA successfully avoids the singularity problem in LPP and shares the orthogonal property with PCA. A further contribution of this paper is to propose a strategy for determining the parameter η which is used to balance the subobjectives corresponding to global and local structure preservings. For fault detection purpose, two traditional statistics 2 T and SPE are constructed based on the new proposed GLSA method. Case studies on a numerical example and Tennessee Eastman process demonstrate the efficiencies of GLSA in feature extraction and fault detection.

LGSPP-Bayes for Fault Detection and Diagnosis

“…The low-dimension space after PCA has the same outer shape with the original space, for they have the same direction to ensure the data variance maximal [5,6]. But PCA ignores the inner local structure of different samples.…”