Data-Driven Incipient Fault Detection via Canonical Variate Dissimilarity and Mixed Kernel Principal Component Analysis

Abstract

Incipient fault detection plays a crucial role in preventing the occurrence of serious faults or failures in industrial processes. In most industrial processes, linear, and nonlinear relationships coexist. To improve fault detection performance, both linear and nonlinear features should be considered simultaneously. In this article, a novel hybrid linear-nonlinear statistical modeling approach for data-driven incipient fault detection is proposed by closely integrating recently developed canonical variate dissimilarity analysis and mixed kernel principal component analysis (MKPCA) using a serial model structure. Specifically, canonical variate analysis (CVA) is first applied to estimate the canonical variables (CVs) from the collected process data. Linear features are extracted from the estimated CVs. Then, the canonical variate dissimilarity (CVD) which quantifies model residuals in the CVA state-subspace is calculated using the estimated CVs. To explore the nonlinear features, the nonlinear principal components are extracted as nonlinear features through performing MKPCA on CVD. Fault detection indices are formed based on Hotelling's T 2 as well as Q statistics from the extracted linear and nonlinear features. Moreover, kernel density estimation is utilized to determine the control limits. The effectiveness of the proposed method is demonstrated by the comparisons with other relevant methods via simulations based on a closed-loop continuous stirred-tank reactor process. Index Terms-Canonical variate analysis (CVA), dissimilarity analysis, incipient fault detection, kernel principal component analysis (KPCA), mixed kernel.

Nonlinear Dynamic Process Monitoring Using Canonical Variate Kernel Analysis

“…These faults are obvious and can be easily detected using DKPCA. Faults 5,6,10,13,16,17,19 and 20 form the second category. These faults are not so obvious but still can be detected most of the time using DKPCA.…”

“…However, it can only extract linear features for linear processes. Nonlinear features usually occur in the residuals of the linear model [10] and nonlinear features cannot be distinguished from noise in the residual. Therefore, CVA performs poorly in nonlinear dynamical systems, showing a low detectability for small faults.…”

“…However, in reality, dynamic industrial processes account for most processes. Different from PCA, CVA takes time correlation into consideration [10]. Although DPCA can detect some dynamic information, Russell et al [11] extensively tested the effectiveness of DPCA and CVA in process monitoring for dynamic industrial processes.…”

Nonlinear Dynamic Process Monitoring Based on Ensemble Kernel Canonical Variate Analysis and Bayesian Inference

“…Researchers have used various forms of CSTRs for process monitoring in a variety of studies. 22 , 39 , 47 A simplified diagram of the three-state closed-loop CSTR process is depicted in Figure 4 . The following equations primarily describe the mechanism of the CSTR process: …”

“…To determine the upper control limits, the widely used kernel density estimation (KDE) is employed in this study. In KDE, a smoothed peak function (kernel) is used to estimate the probability density functions (PDF) from the observed data points curve. ,, Thus, the Gaussian distribution assumption of process data is not necessary. Taking the T 2 as an example, the PDF of the calculated N T 2 ( k ), k = 1, ..., N statistics is estimated as where d is the kernel bandwidth, and is the kernel function.…”