Kernel Vertices PCA: A Novel Interval-Valued PCA Approach for Fault Detection in Nonlinear Complex Systems

Interval-valued data techniques are widely utilized in fault detection to enhance robustness against uncertainty. Among these, Vertices Principal Component Analysis (VPCA) is one of the most commonly applied methods. Constructing a VPCA model involves transforming the interval data matrix into a vertices matrix. This study introduces a novel data-driven approach for fault detection in uncertain nonlinear processes called Kernel VPCA (K-VPCA), which extends the VPCA method to handle nonlinear interval data. Specifically, the data are mapped into a high-dimensional kernel feature space before applying VPCA, allowing nonlinear relationships to be effectively modeled. The K-VPCA approach maintains robustness against false alarms without compromising fault detection performance. The proposed method is validated using data from a cement rotary kiln, confirming its effectiveness in fault detection. 

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