Spectral radius-based interval principal component analysis (SR-IPCA) for fault detection in industrial processes with imprecise data. (June 2022) - Zhang, Shumei; Wang, Sijia
Abstract: Data-driven process monitoring approaches like principal component analysis (PCA) have been widely used in many industrial processes, most of which assume that the data are precise and reliable. However, the data collected from actual processes are usually contaminated with uncertainties due to measurement noise, severe working scenarios and other reasons. Aiming at fault detection in the complex industrial processes with imprecise measurement data, a spectral radius-based interval PCA (SR-IPCA) method is proposed in this work. First, kernel density estimation (KDE)-based measurement error estimation strategy is presented to transform imprecise single-valued data into interval-valued data. Then, a spectral radius based eigen-decomposition method for interval matrix is developed to extract the process features by projecting high-dimensional interval data to low-dimensional space. Moreover, four monitoring statistics are defined to analyze process status and identify the fault. The proposed SR-IPCA method can effectively tackle the uncertainties by defining an interval domain and extract correlation structure with relative low computation complexity. The simulation results on the synthetic data sets and the Tennessee Eastman process (TEP) reveal that SR-IPCA significantly reduces the false alarm rate and the missed detection rate compared with PCA, vertices PCA (V-PCA) and centers PCA (C-PCA). Highlights: A spectral radius-based interval PCA method is developed for fault detection in industrial processes with imprecise data. The interval transformation strategy describes data with uncertainty by estimating the PDF of measurement error using KDE. Spectral radius based eigen-decomposition method for interval matrix is developed to find the transformation matrices. Four monitoring statistics are defined to comprehensively analyze the process operating status.