New Adaptive Kernel Principal Component Analysis for Nonlinear Dynamic Process Monitoring (original) (raw)
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Adaptive kernel principal component analysis for nonlinear dynamic process monitoring
2013 9th Asian Control Conference (ASCC), 2013
In this paper a new algorithm for adaptive kernel principal component analysis (AKPCA) is proposed for dynamic process monitoring. The proposed AKPCA algorithm combine two existing algorithms, the recursive weighted PCA (RWPCA) and the moving window kernel PCA algorithms. For fault detection and isolation, a set of structured residuals is generated by using a partial AKPCA models. Each partial AKPCA model is performed on subsets of variables. The structured residuals are utilized in composing an isolation scheme, according to a properly designed incidence matrix. The results for applying this algorithm on the nonlinear time varying processes of the Tennessee Eastman shows its feasibility and advantageous performances.
Adaptive kernel principal component analysis for nonlinear time-varying processes monitoring
On-line control using multivariate statistical methods has been widely used for largescale nonlinear industrial processes monitoring. Kernel principal component analysis (KPCA) is a nonlinear monitoring method that cannot be employed for dynamic systems. The adaptive KPCA (AKPCA) is developed for nonlinear and time varying processes based on moving window KPCA (MWKPCA) and weighted PCA (WPCA) to update online the KPCA model and its corresponding control limits. In the proposed AKPCA the model of history data is used to build new model after the new sample is obtained. The results for applying this algorithm on the nonlinear time varying processes of the Tennessee Eastman benchmark shows its feasibility and advantageous performances. Key-words : adaptive kernel principal component analysis, multivariate statistical methods, nonlinear time-varying processes, moving window and weighted principle component analysis.
Brazilian Journal of Chemical Engineering, 2021
Timely detection and diagnosis of process abnormality in industries is crucial for minimizing downtime and maximizing profit. Among various process monitoring and fault detection techniques, principal component analysis (PCA) and its different variants are probably the ones with maximum applications. Because of the linearity constraint of the conventional PCA, some non-linear variants of PCA have been proposed. Among different non-linear variants of PCA, the kernel PCA (KPCA) has gained maximum attention in the field of industrial fault detection. This article revisits the basic KPCA algorithm along with different limitations of KPCA and the crucial open issues in design of KPCA based monitoring system. Different modifications proposed by different researchers are reviewed. Strategies adopted by various researchers for optimal selection of kernel parameter and number of principal components are also presented.
Nonlinear process monitoring using kernel principal component analysis
Chemical Engineering Science, 2004
In this paper, a new nonlinear process monitoring technique based on kernel principal component analysis (KPCA) is developed. KPCA has emerged in recent years as a promising method for tackling nonlinear systems. KPCA can e ciently compute principal components in high-dimensional feature spaces by means of integral operators and nonlinear kernel functions. The basic idea of KPCA is to ÿrst map the input space into a feature space via nonlinear mapping and then to compute the principal components in that feature space. In comparison to other nonlinear principal component analysis (PCA) techniques, KPCA requires only the solution of an eigenvalue problem and does not entail any nonlinear optimization. In addition, the number of principal components need not be speciÿed prior to modeling. In this paper, a simple approach to calculating the squared prediction error (SPE) in the feature space is also suggested. Based on T 2 and SPE charts in the feature space, KPCA was applied to fault detection in two example systems: a simple multivariate process and the simulation benchmark of the biological wastewater treatment process. The proposed approach e ectively captured the nonlinear relationship in the process variables and showed superior process monitoring performance compared to linear PCA. ?
Fault identification for process monitoring using kernel principal component analysis
2005
In this research, we develop a new fault identification method for kernel principal component analysis (kernel PCA). Although it has been proved that kernel PCA is superior to linear PCA for fault detection, the fault identification method theoretically derived from the kernel PCA has not been found anywhere. Using the gradient of kernel function, we define two new statistics which represent the contribution of each variable to the monitoring statistics, Hotelling's T 2 and squared prediction error (SPE) of kernel PCA, respectively. The proposed statistics which have similar concept to contributions in linear PCA are directly derived from the mathematical formulation of kernel PCA and thus they are straightforward to understand. The main contribution of this work is that we firstly suggest a fault identification method especially applicable to process monitoring using kernel PCA. To demonstrate the performance, the proposed method is applied to two simulated processes, one is a simple nonlinear process and the other is a non-isothermal CSTR process. The simulation results show that the proposed method effectively identifies the source of various types of faults.
Computers & Industrial Engineering, 2011
On-line control of nonlinear nonstationary processes using multivariate statistical methods has recently prompt a lot of interest due to its industrial practical importance. Indeed basic process control methods do not allow monitoring of such processes. For this purpose this study proposes a variable window real-time monitoring system based on a fast block adaptive Kernel Principal Component Analysis scheme. While previous adaptive KPCA models allow only handling of one observation at a time, in this study we propose a way to fast update or downdate the KPCA model when a block of data is provided and not only one observation. Using a variable window size procedure to determine the model size and adaptive chart parameters, this model is applied to monitor two simulated benchmark processes. A comparison of performances of the adopted control strategy with various Principal Component Analysis (PCA) control models shows that the derived strategy is robust and yields better detection abilities of disturbances.
Online reduced kernel principal component analysis for process monitoring
Journal of Process Control, 2018
Kernel principal component analysis (KPCA), which is a nonlinear extension of principal component analysis (PCA), has gained significant attention as a monitoring method for nonlinear processes. However, KPCA cannot perform well for dynamic systems and when the training data set is large. Therefore, in this paper, an online reduced KPCA algorithm for process monitoring is proposed. The process monitoring performances are studied using two examples: a numerical example and Tennessee Eastman Process (TEP). The simulation results demonstrate the effectiveness of the proposed method when compared to the online KPCA method.
Chemometrics and Intelligent Laboratory Systems, 2013
Traditional 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.
IEEE Access, 2019
Statistical local kernel principal component analysis (SLKPCA) has demonstrated its success in incipient fault detection of nonlinear industrial processes by incorporating the statistical local analysis (SLA) technology. However, the basic SLKPCA method builds the statistical model only based on the normal data and neglects the utilization of the prior fault information, which is often available in many industrial cases. To take full advantage of the prior fault information, this paper proposes an enhanced SLKPCA method, called primary-auxiliary SLKPCA (PA-SLKPCA), for better incipient fault monitoring. The contribution of the proposed method includes three aspects. First, one primary-auxiliary statistical monitoring framework is designed, by which not only the normal training data are applied to develop a primary SLKPCA model, but also the prior fault data are used to build the auxiliary SLKPCA models. Second, a double-block modeling strategy is developed to construct the auxiliary SLKPCA model for each fault case, where a variable grouping strategy based on Kullback-Leibler divergence is applied to divide the process variables into the fault-relevant group and fault-independent variable group, and the sub-model is developed for each group. Third, the Bayesian inference is used to combine the statistical results of each variable group, and one weighted fusion strategy is further designed to integrate the monitoring results from the primary and auxiliary models. Lastly, two case studies including one numerical system and the simulated continuous stirred tank reactor (CSTR) system are used for method evaluation and the simulations show that the proposed method can detect the incipient faults effectively and outperform the traditional SLKPCA method. INDEX TERMS Incipient fault, fault detection, kernel principal component analysis, statistical local analysis, prior fault information.
Nonlinear Process Fault Diagnosis Based on Serial Principal Component Analysis
IEEE transactions on neural networks and learning systems, 2016
Many industrial processes contain both linear and nonlinear parts, and kernel principal component analysis (KPCA), widely used in nonlinear process monitoring, may not offer the most effective means for dealing with these nonlinear processes. This paper proposes a new hybrid linear-nonlinear statistical modeling approach for nonlinear process monitoring by closely integrating linear principal component analysis (PCA) and nonlinear KPCA using a serial model structure, which we refer to as serial PCA (SPCA). Specifically, PCA is first applied to extract PCs as linear features, and to decompose the data into the PC subspace and residual subspace (RS). Then, KPCA is performed in the RS to extract the nonlinear PCs as nonlinear features. Two monitoring statistics are constructed for fault detection, based on both the linear and nonlinear features extracted by the proposed SPCA. To effectively perform fault identification after a fault is detected, an SPCA similarity factor method is buil...