Uncertainty Quantification Kernel PCA: Enhancing Fault Detection in Interval-Valued Data

The interval-valued kernel PCA (UQ-KPCA) is a variation of the kernel PCA (KPCA) designed for interval-valued data, designed to handle data uncertainty by defining specific similarity measures and kernel functions for interval data. This paper introduces Uncertainty Quantification KPCA (UQ-KPCA) as a novel method to address uncertainties in data. UQ-KPCA converts the traditional KPCA model from single-valued to interval-valued representations, allowing for accurate error and uncertainty quantification. The process modeling using KPCA is then performed on data based on the interval model, followed by the computation of fault detection statistics such as T-2, Q, and Phi. The method's effectiveness is evaluated in the context of the cement rotary kiln process, and compared with the KPCA demonstrating superior performance in accurately identifying faults within a stochastic setting with unknown uncertainties.