Nonlocal structure constrained neighborhood preserving embedding model and its application for fault detection

• Nonlocal structure constrained neighborhood preserving embedding is proposed for linear dimensionality reduction.
• Data relation among the neighborhoods is preserved, while the relation outside the neighborhoods is also considered.
• A dual-objective optimization function is constructed to preserve the local and nonlocal characteristics simultaneously.
• The new method can characterize the whole data structure and discriminate the remote data points effectively.

In this paper, an unsupervised dimensionality reduction technique named nonlocal structure constrained neighborhood preserving embedding (NSC-NPE) is developed and applied for fault detection. To exploit the underlying geometrical structure, NSC-NPE constructs a global information-based dual-objective optimization function for modeling the process data. Besides the local variance information refined by the neighborhood preserving embedding algorithm, NSC-NPE also considers to utilize the meaningful nonlocal variance information via maximizing the Euclidean distance between the points outside the neighbors. The objective that having the local and nonlocal characteristics preserved in the low-dimensional space is achieved by minimizing the local scatter and maximizing the nonlocal scatter simultaneously. The proposed method is applied to fault detection based on the Hotelling’s T2 and squared prediction error (SPE) statistics. Three case studies are provided to demonstrate the efficiency of the proposed method.