Fault Detection and Identification Based on Explicit Polynomial Mapping and Combined Statistic in Nonlinear Dynamic Processes

Abstract

Single traditional multivariate statistical monitoring methods, such as principal component analysis (PCA) and canonical variate analysis (CVA), are less effective in nonlinear dynamic processes. Monitoring approaches based on radial basis kernel function have been intensively applied. However, an infinite dimension nonlinear mapping is redundant and inefficient. To improve the efficiency of traditional methods and consider the nonlinearity and dynamics simultaneously, this paper proposes canonical variate nonlinear principal component analysis (CV-NPCA) based on explicit polynomial mapping and combined statistic for detecting and identifying faults in nonlinear dynamic processes. There are two main contributions of the proposed method. First, explicit second-order polynomial mapping is introduced to combine CVA with PCA to simultaneously decrease the adverse effects of nonlinearity and dynamics. Second, the $Q_{c}$ statistic combining residual vectors with residual components is proposed, and a two-dimensional (2D) contribution plot and the variable with the largest contribution based on the $Q_{c}$ statistic are given for fault identification in the simulation study. Compared with the results of PCA, CVA, kernel principal component analysis (KPCA), nonlinear dynamic principal component analysis (NDPCA) and kernel entropy component analysis (KECA), the proposed method not only has relatively higher fault detection rates and identification rates but also has lower false alarm rates in the numerical simulation process and the benchmark Tennessee Eastman process.

Keywords

• Canonical variate
• combined statistic
• explicit polynomial mapping
• fault detection
• fault identification
• principal component analysis