Online identification of nonlinear system using reduced kernel principal component analysis

Abstract

The Principal Component Analysis (PCA) is a powerful technique for extracting structure from possibly high-dimensional data sets. It is readily performed by solving an eigenvalue problem, or by using iterative algorithms that estimate principal components. This paper proposes a new method for online identification of a nonlinear system modelled on Reproducing Kernel Hilbert Space (RKHS). Therefore, the PCA technique is tuned twice, first we exploit the Kernel PCA (KPCA) which is a nonlinear extension of the PCA to RKHS as it transforms the input data by a nonlinear mapping into a high-dimensional feature space to which the PCA is performed. Second, we use the Reduced Kernel Principal Component Analysis (RKPCA) to update the principal components that represent the observations selected by the KPCA method.

Moving window KPCA with reduced complexity for nonlinear dynamic process monitoring

“…Several solutions have been proposed recently for time varying system. Possible solutions among others consist to find a reduced set of kernel vectors using k-means clustering [36,37] or to build a reduced KPCA (RKPCA) model using reduced training data set [1,20]. In this paper, we improve the use of the RKPCA for handling nonlinear dynamic system, thus the MW-RKPCA method was proposed.…”

“…Also, it can handle a wide range of nonlinearities by the possibility to use different kernels. KPCA has been widely used to solve nonlinear problems [19,20] and it has been applied successfully for process monitoring [1,21,22]. In the field of fault diagnosis, various fault detection indices [7,23,24] have been developed and utilized in practice using the PCA method.…”

Kernel principal component analysis with reduced complexity for nonlinear dynamic process monitoring

“…Also, It should be noted that most computation load is consumed in calculating eigenproblem of the kernel matrix which consumes O(n 3 ) based on standard (SVD) [25] where n is the number of observations in the training data. To overcome this burden, possible solutions among others consist either to use kernel k means for clustering [20,21,26], to use an incremental approach for fast calculation of the kernel PCs [3,17,19], or to search a reduced data set that approach approaches sufficiently the system behavior with and RKPCA model [2] in the offline phase before applying it online [22]. In this section, we improve the use of the RKPCA method for monitoring dynamic system; indeed, we take advantage of lower computation complexity of our proposed method SVD-KPCA for identification of non linear dynamic system [3] to propose the SVD-RKPCA method.…”

“…The main issue with timevarying KPCA is computation time [2,19] and memory demands as training data size increases. Only few methods are available for dimensionality reduction with KPCA, we mention k means clustering [20], [21] and reduced kernel principal component analysis (RKPCA) [18,22].…”

Classifying neuromuscular diseases using artificial neural networks with applied Autoregressive and Cepstral analysis

“…Also, there are lots of studies in the literature [6][7][8]. The principal idea of PCA is reducing the dimensionality of a dataset comprising a multitude of variables related to one another, while maintaining as much as possible of the variation existing in the data set [9].…”