Monitoring of Nonlinear Time-Delay Processes Based on Adaptive Method and Moving Window

Mathematical Problems in Engineering, Jul 2014

A new adaptive kernel principal component analysis (KPCA) algorithm for monitoring nonlinear time-delay process is proposed. The main contribution of the proposed algorithm is to combine adaptive KPCA with moving window principal component analysis (MWPCA) algorithm, and exponentially weighted principal component analysis (EWPCA) algorithm respectively. The new algorithm prejudges the new available sample with MKPCA method to decide whether the model is updated. Then update the KPCA model using EWKPCA method. And also extend MPCA and EWPCA from linear data space to nonlinear data space effectively. Monitoring experiment is performed using the proposed algorithm. The simulation results show that the proposed method is effective.

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Monitoring of Nonlinear Time-Delay Processes Based on Adaptive Method and Moving Window

Monitoring of Nonlinear Time-Delay Processes Based on Adaptive Method and Moving Window Yunpeng Fan, Wei Zhang, and Yingwei Zhang State Laboratory of Synthesis Automation of Process Industry, Northeastern University, Shenyang, Liaoning 110819, China Received 2 June 2014; Accepted 17 June 2014; Published 21 July 2014 Academic Editor: Ligang Wu Copyright © 2014 Yunpeng Fan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract A new adaptive kernel principal component analysis (KPCA) algorithm for monitoring nonlinear time-delay process is proposed. The main contribution of the proposed algorithm is to combine adaptive KPCA with moving window principal component analysis (MWPCA) algorithm, and exponentially weighted principal component analysis (EWPCA) algorithm respectively. The new algorithm prejudges the new available sample with MKPCA method to decide whether the model is updated. Then update the KPCA model using EWKPCA method. And also extend MPCA and EWPCA from linear data space to nonlinear data space effectively. Monitoring experiment is performed using the proposed algorithm. The simulation results show that the proposed method is effective. 1. Introduction Fault detection and diagnosis are very important aspects in modern industrial processes because they concern the execution of planned operations and process productivity. In order to meet the need of production, data-based methods have been deeply developed, such as principal component analysis (PCA), partial least squares (PLS), and independent component analysis (ICA) [1–5]. PCA as a multivariable statistical method is widely used for damage detection and diagnosis of structures in industrial systems [6–8]. Because PCA is an orthogonal transformation of the coordinate system, it is a linear monitoring method. However, most industrial processes have strong-nonlinearity characteristics [9, 10]. Document [11] shows that application of linear monitoring approaches to nonlinear processes may lead to unreliable process monitoring, because a linear method is inappropriate to extract the nonlinearities within the process variables. To solve the nonlinear problem, several nonlinear methods have been proposed in the past decades [12–17]. Kernel principal component analysis (KPCA), as a nonlinear version of PCA method which is developed by many researchers, is more proper in nonlinear process monitoring [18–20]. KPCA can efficiently compute principal components (PCs) by nonlinear kernel functions in a high-dimensional feature spaces. The main advantages of KPCA are that it only solves an eigenvalue problem and does not involve nonlinear optimization [21]. However, a KPCA monitoring model requires kernel matrix, whose dimension is given by the number of reference samples. In addition, the KPCA with fixed model may lead to large error because of the gradual change of parameters with the operation of process [22–26]. Because the old samples are not representative of the current process status, the adaptation of KPCA model is necessary. To date, MWPCA algorithm and EWPCA algorithm are two representative adaptive methods [27–31]. Performing a moving window approach, which was proposed by Hoegaerts et al., overcomes this problem and produces a constant scale of the kernel matrix and a fixed speed of adaptation [32, 33]. Choosing a proper weighting factor is an important issue, which determines the influence that the older data has on the model [31]. Paper [34] has proposed a moving window KPCA formulation, which has some advantages such as using the Gram matrix instead of the kernel matrix, incorporation of an adaptation method for the eigendecomposition of the Gram matrix. In this paper, a new algorithm combining these two representative methods is proposed. The proposed algorithm mapped the sample set in feature space and prejudges the new available sample with MKPCA method to decide whether the model is updated. Then update the KPCA model using EWKPCA method. The proposed algorithm can reduce negative impact of outliers on model; the updating after prejudgment can reduce computational complexity and be more efficient. The remaining sections of this paper are organized as follows. The KPCA method based on loss function and the online monitoring strategy are introduced in Section 2. The iterative KPCA algorithm with penalty factor is presented in Section 3. The proposed adaptive KPCA method combining two representative methods is described in Section 4. The simulation results are presented in Section 5. Finally, the conclusion is given in Section 6. 2. Kernel Principal Component Analysis Based on Loss Function2.1. Kernel Principal Component Analysis KPCA is an extension of PCA, and it can be solved as an eigenvalue problem of its kernel matrix. KPCA algorithm makes use of the (...truncated)


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Yunpeng Fan, Wei Zhang, Yingwei Zhang. Monitoring of Nonlinear Time-Delay Processes Based on Adaptive Method and Moving Window, Mathematical Problems in Engineering, 2014, 2014, DOI: 10.1155/2014/546138