100 / 2025-04-17 11:20:18

Interval Principal Component Analysis for Fault Detection of Wastewater Treatment Processes with Uncertainty

Uncertainty, fault detection, interval principal component analysis, characteristic decomposition

In practical industrial processes, measurement data collected from various sensors are often contaminated by uncertainty due to measurement noise and unknown disturbances. These uncertainties introduce undesirable spikes into the process data, which can significantly impact subsequent fault detection. To address this issue, this paper proposes an improved interval principal component analysis (PCA) fault detection model to handle uncertainty. First, imprecise single-valued measurement data are transformed into interval-valued form to more effectively capture the underlying characteristics of the data. Second, the traditional PCA method is extended to the interval-valued domain, and an improved computational approach is proposed to solve the characteristic decomposition problem for interval covariance matrices. The obtained interval eigenvalues and eigenvectors are then used to project high-dimensional interval data into a lower-dimensional space for feature extraction. Finally, four monitoring statistics are constructed to analyze process states and detect faults. Simulation experiments conducted on the BSM1 benchmark demonstrate that the proposed method effectively addresses uncertainty issues. Compared with PCA, central PCA (CPCA), and midpoint-radius PCA (MRPCA) methods, the fault detection approach presented in this paper significantly reduces both FAR and MDR.