New online kernel method with the Tabu search algorithm for process monitoring

Kernel principal component analysis (KPCA) is a method for performing a nonlinear form of principal component analysis (PCA). It involves nonlinear mapping of the input data onto a high dimensional feature space and performing PCA there. Through KPCA, nonlinear relations in the input space are detected as linear relations in the feature space. Furthermore, explicit computation of the mapping is not necessary in KPCA. Only dot products of the mapped data items in the feature space are required which are obtained directly from the input data using a kernel function. Moreover, control limits of traditional statistical process monitoring indices are usually determined under assumption of normal (Gaussian) distribution. Although, it is recognized that this is inappropriate in nonlinear processes, the impact of using kernel density estimation (KDE), which is a nonparametric method, to determine control limits in KPCA-based process monitoring has not been reported. This paper seeks to bridge this gap. The KPCA with KDE approach is applied to the Tennessee Eastman process for the detection of faults. The results confirm that associating KPCA with kernel density estimated control limits provides better monitoring performance than using control limits based on the normal probability density function.

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

This paper presents a novel algorithm - robust kernel principal component analysis (robust KPCA), on the basis of the research of kernel principal component analysis (KPCA) and robust principal component analysis (RPCA). First, this algorithm sets the radius of the images of the training samples in the feature space using kernel tricks, then determines whether the samples are outliers or not, and finally analyzes the training samples which have eliminated the outliers using KPCA algorithm. The improved KPCA algorithm not only retains the non-linearity property of KPCA algorithm but also gets better robustness. Because the effects of outliers are eliminated, robust KPCA algorithm gets higher accuracy than KPCA algorithm for data analysis. The simulation experiments show that the robust KPCA algorithm developed is better than the KPCA algorithm.

Kernel principal component analysis (KPCA) has become a popular technique for process monitoring in recent years. However, the performance largely depends on kernel function, yet methods to choose an appropriate kernel function among infinite ones have only been sporadically touched in the research literatures. In this paper, a novel methodology to learn a data-dependent kernel function automatically from specific input data is proposed and the improved kernel principal component analysis is obtained through using the data-dependent kernel function in traditional KPCA. The learning procedure includes two parts: learning a kernel matrix and approximating a kernel function. The kernel matrix is learned via a manifold learning method named maximum variance unfolding (MVU) which considers underlying manifold structure to ensure that principal components are linear in kernel space. Then, a kernel function is approximated via generalized Nystrom formula. The effectiveness of the improved KPCA model is confirmed by a numerical simulation and the Tennessee Eastman (TE) process benchmark.

Data-driven techniques have been receiving considerable attention in the industrial process monitoring field due to their major advantages of easy implementation and less requirement for the prior knowledge and process mechanism. Principal component analysis (PCA) method is known as a popular method for monitoring and fault detection in industrial systems but as it is basically a linear method. However, most practical systems are nonlinear. To make the extension to nonlinear systems, kernel PCA (KPCA) method has been proposed for process modeling and monitoring. We present in this paper an online reduced rank optimized KPCA (RR-KPCA) technique for fault detection in order to extend the advantages of the KPCA models to online processes. Following the fault detection, the identification of the variables correlated to the fault occurred is of great importance. For this purpose, it is proposed to extend the approaches of localization by partial PCA and by elimination in the linear case to the nonlinear case, by exploiting the solution of reduction of the dimension of the kernel matrix in the feature space. The partial RR-KPCA and the elimination sensor identification (ESI-RRKPCA) are generated based on the static RR-KPCA and the online RR-KPCA methods. The idea of these approaches is to generate partial RR-KPCA models with reduced sets of variables. In other words, their goal is to generate indices of fault detection sensitive to certain faults and insensitive to others. The proposed fault isolation methods are applied for monitoring an air quality monitoring network (AIRLOR) data.

In this paper, we develop an improved fault detection (FD) technique in order to enhance the monitoring abilities of nonlinear biological processes. Generalized likelihood ratio test (GLRT)-based kernel principal component analysis (KPCA) (called also kernel GLRT) is an effective data-driven technique for monitoring nonlinear processes. However, it is well known that the data collected from complex and multivariate processes are multiscale due to the variety of changes that could occur in process with different localization in time and frequency. Thus, to enhance the process monitoring abilities, we propose to combine the advantages of kernel GLRT and multiscale representation using wavelets by developing a multiscale kernel GLRT (MS-KGLRT) detection chart. The proposed fault detection approach is addressed so that the KPCA is used to compute the model in the feature space and the MS-KGLRT chart is applied to detect the faults. The detection performance of the new chart is studied using two examples, one using synthetic data and the other using biological process representing a Cad System in E. Coli (CSEC) model for detecting small and moderate shifts (offset or bias and drift). The MS-KGLRT chart is used to enhance fault detection of the CSEC model through monitoring some of the key variables involved in this model such as enzymes, lysine, and cadaverine.

Kernel principal component analysis (KPCA) has gained much attention for capturing nonlinear image features which is particularly important for clustering high-dimensional multi-class features. We introduce KPCA in this paper for detecting and classifying moving vehicles from its viewpoint images. The KPCA extracts non-linear features of multi-class moving vehicles by mapping input space to a higher dimensional feature space through a nonlinear map. The results provide us a clustered feature space of the car and non-car for classifying them by separating the dimensional space or eigenvector. The experimental results show the robustness of the KPCA's feature separation in our car database that lead to the cars' classification. Extended experiments on various vehicles detection have also shown the remarkable performance of the proposed method

Improved kernel principal component analysis for fault detection

Conventional principal component analysis (PCA) performs poorly in nonlinear process monitoring due to it only can capture the linear structure of the process variables. To overcome this nonlinear problem, a new nonlinear process monitoring technique based on kernel principal component analysis (KPCA) is proposed. In order to enhance the ability of capturing the nonlinear feature for KPCA, a marr wavelet kernel is constructed and proved. Then the proposed method is applied to the fault detection in the Tennessee Eastman process (TEP). The simulation results showed superior process monitoring performance compared with PCA.

An adaptive non-parametric model (ANPM) has been developed for condition monitoring and applications within prognostics. The ANPM has the ability to monitor systems while adapting to expanded conditions. This ability is useful in uncertain systems where the range of the model could be exceeded by the system when under non-fault conditions. Differentiating between expanded and fault conditions is essential to the ANPM. A method for differentiating between expanded and a fault condition for use in an adaptive model is described. Statistical process monitoring methods using principal component analysis (PCA) have been extensively studied and heavily applied within the chemical industry. A thorough literature review is given on the past applications of such methods, highlighting the applications strengths and weaknesses. A comparison between traditional fault detection and monitoring techniques and the newly proposed expanded process differentiation technique is discussed. Adaptive modeling requirements in a dynamic environment are shown to extend beyond the traditional modeling requirements. The basic approach to PCA is described, with a detailed description of the differentiation method. The Hotelling's T 2 statistic and the squared prediction error, also known as the Q statistic, are used as indicators of the condition of the system. Dependence on the internal linear relationships of the data is discussed, and kernel principal component analysis is described as a solution to difficulties posed by nonlinear relationships. This multivariate differentiation technique is applied to a simulated data set and is shown to correctly differentiate between expanded operating conditions and faulted conditions in an adaptive environment.

Viewing to monitoring the continuous casting process, a nonlinear fault detection method based on kernel principal component analysis (KPCA) was introduced. KPCA can efficiently compute principal components in high-dimensional feature spaces by means of integral operators and nonlinear kernel functions, which is to first map the input space into a feature space via nonlinear mapping and then to compute the principal components in that feature space. Based on T2 and SPE charts in feature space, principal component analysis(PCA)can be used to detect faults.. The simulation results show that the proposed approach effectively captured the nonlinear relationship in the process variables and showed superior process monitoring performance compared to linear PCA.

Conventional kernel principal component analysis (KPCA) may not function well for nonlinear process monitoring, since the Gaussian assumption of the method may be violated through nonlinear and kernel transformation of the original process data. To overcome this deficiency, a statistical local approach has been incorporated into KPCA. Through this method, a new score variable which was called improved residual in the statistical local approach is constructed. This new variable approximately follows Gaussian distribution, in spite of which distribution the original data follow. Like the traditional method, two statistics can be constructed for process monitoring, with their corresponding confidence limits determined by a $${{\chi }^{2}}$$ distribution. Besides of the improvement made on KPCA, the joint local approach-KPCA method also shows superiority on detection sensitivity, especially for small faults slow changes of the process.KeywordsKernal principal component analysisNonlinear process monitoringNon-GaussianLocal approach

As a valid statistical tool, principal component analysis (PCA) has been widely used in industrial process monitoring. But due to its intrinsic linear character, it performs badly in nonlinear process monitoring. Kernel PCA (KPCA) can extract useful information in nonlinear data. However KPCA-based monitoring is not suitable for on-line monitoring because of large calculation and much memory occupation. The paper introduces an on-line monitoring method based on KPCA and neural network (NN), where KPCA is used to extract nonlinear principal components (PCs) and then NN approximates the relationship between process data and nonlinear PCs. We can obtain nonlinear PCs by NN to compute the monitoring indices and then achieve the on-line monitoring. The case study shows the validity of the method.KeywordsNeural NetworkKernel Principal Component AnalysisMonitoring IndexMemory OccupationComplex Industrial ProcessThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Principal component analysis (PCA) has been proven to be an efficient method in dimensionality reduction, feature extraction and pattern recognition. Kernel principal component analysis (KPCA) can be considered as a natural nonlinear generalization of PCA, which performs linear PCA in a high dimensional space implicitly by using kernel trick. However, both conventional PCA and KPCA suffer from the deficiency of being sensitive to outliers. Existing robust KPCA has to eigen-decompose the gram matrix directly in each step and is much more computationally infeasible due to the large size of the matrix when the number of training samples is large. By extending existing robust PCA algorithm using kernel methods, we present a novel robust adaptive algorithm for calculating the kernel principal components. The proposed method not only preserves the characteristic of capturing underlying nonlinear structure of KPCA but also is robust against outliers by restraining the effect of outlying samples. Compared with existing robust KPCA methods, our method is performed without having to store the kernel matrix, which can reduce significantly the storage burden. In addition, our method shows the potential of expansibility to the incremental learning version. Experimental results on synthetic data indicate that our improved algorithm is effective and promising.

Outlier detection is the task of classifying test data that differ in some respect from the data that are available during training. This may be seen as one-class classification, in which a model is constructed to describe normal training data. In wireless sensor networks (WSNs), the outlier detection process is a necessary step in building sensor network systems to assure data quality for perfect decision making. For this case, the task amounts to create a useful model based on kernel principal component analysis (KPCA) to recognize data as normal or outliers. Recently, KPCA has used for nonlinear case which can extract higher order statistics. KPCA mapping the data onto another feature space and using nonlinear function. On account of the attractive capability, KPCA-based methods have been extensively investigated, and it have showed excellent performance. Within this setting, we propose KPCA-based Mahalanobis kernel as a new outlier detection method using Mahalanobis distance to implicitly calculate the mapping of the data points in the feature space so that we can separate outlier points from normal pattern of data distribution. The use of KPCA-based Mahalanobis kernel on real-word data obtained from Intel Berkeley are reported showing that the proposed method performs better in finding outliers in WSNs when compared with the original reconstruction error-based variant and the one-class support vector machine detection approach. All computation are done in the original space, thus saving computing time using Mahalanobis kernel.