Modified kernel principal component analysis based on local structure analysis and its application to nonlinear process fault diagnosis

Abstract

a b s t r a c t a r t i c l e i n f oTraditional kernel principal component analysis (KPCA) concentrates on the global structure analysis of data sets but omits the local information which is also important for process monitoring and fault diagnosis. In this paper, a modified KPCA, referred to as the local KPCA (LKPCA), is proposed based on local structure analysis for nonlinear process fault diagnosis. In order to extract data feature better, local structure analysis is integrated within the KPCA, and this results in a new optimisation objective which naturally involves both global and local structure information. With the application of usual kernel trick, the optimisation problem is transformed into a generalised eigenvalue decomposition on the kernel matrix. For the purpose of fault detection, two monitoring statistics, known as the T 2 and Q statistics, are built based on the LKPCA model and confidence limit is computed by kernel density estimation. In order to identify fault variables, contribution plots for monitoring statistics are constructed based on the idea of sensitivity analysis to locate the fault variables. Simulation using the Tennessee Eastman benchmark process shows that the proposed method outperforms the traditional KPCA, in terms of fault detection performance. The results obtained also demonstrate the potential of the proposed fault identification approach.

Monitoring Nonlinear and Non-Gaussian Processes Using Gaussian Mixture Model-Based Weighted Kernel Independent Component Analysis

“…The Tennessee Eastman (TE) industrial process [35] is a well-known benchmark process for testing process monitoring methods [1], [5], [7]- [10], [14], [17], [19], [20], [22]. The flowchart of the TE process is depicted in Fig.…”

“…Based on the idea of sensitivity analysis [25], we develop a novel nonlinear contribution plots method for fault identification. Specifically, define [10], while its sign is unimportant. Secondly, the contributions of different process variables have different means and variances.…”

“…To decrease the risk of false alarm, a fault is detected only when eight consecutive monitoring statistic values exceed the confidence limit, and the fault detection time is then defined as the first sample at which the confidence limit is exceeded. The fault detection rate is defined as the ratio of the fault samples whose monitoring statistic values exceed the confidence limit to all the fault samples [7], [10], [14], [16], [19]. The hyper-dimension a, the number of dominant KICs d, and the kernel width c were found according to the empirical rule suggested in [14].…”

“…It projects the original high-dimensional process variables onto a low-dimensional space that retains most of the original variance to obtain a smaller set of the uncorrelated latent variables called principal components (PCs). Many extensions [10]- [12] of PCA have been developed to improve process monitoring performance by taking different process characteristics into consideration. However, PCA only considers the second-order statistic and cannot make use of the higher-order statistical information in non-Gaussian process data [13], [14].…”

Fault discriminant enhanced kernel principal component analysis incorporating prior fault information for monitoring nonlinear processes

“…However, industrial data have highly complex characteristics and they may not obey these assumed distributions. Therefore, we use a data-driven confidence limit computation method based on the well-known kernel density estimation (KDE) method [25,44,45,46]. Specifically, the normal operation data are first projected onto the statistical models and the monitoring statistics T…”