Enhancing Fault Detection in Stochastic Environments Using Interval-Valued KPCA: A Cement Rotary Kiln Case Study

Fault detection in industrial processes is challenging due to significant data uncertainty, which complicates the accurate modeling of interval-valued data and the quantification of errors necessary for reliable detection. Existing approaches, such as kernel principal component analysis (KPCA), struggle with these challenges because they rely on single-valued data representations and are unable to effectively handle interval-based variability. To address these limitations, this paper introduces the interval-valued model KPCA (IV-KPCA), which extends KPCA by redefining similarity measures and kernel functions to accommodate interval-valued uncertainty. IV-KPCA preserves the interval structure throughout the modeling process, enhancing robustness to dynamic uncertainties and improving fault detection in complex nonlinear systems. Within this framework, fault detection statistics ( $T^{2}$ , Q, and $\Phi $ ) are developed to enable precise error quantification. The proposed method is validated on a cement rotary kiln process, a highly stochastic industrial system characterized by significant uncertainties. Experimental results demonstrate that IV-KPCA reduces false alarms, missed detections, and detection delays by over 100%, 90%, and 95%, respectively, compared to traditional methods. These findings underscore the potential of IV-KPCA in enhancing fault detection performance in complex, uncertain environments.