Ilyes Elaissi

Online identification of nonlinear system using reduced kernel principal component analysis

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.

Online prediction model based on the SVD-KPCA method.

This paper proposes a new method for online identification of a nonlinear system modelled on Reproducing Kernel Hilbert Space (RKHS). The proposed SVD-KPCA method uses the Singular Value Decomposition (SVD) technique to update the principal components. Then we use the Reduced Kernel Principal Component Analysis (RKPCA) to approach the principal components which represent the observations selected by the KPCA method.

Identification of Non Linear Multivariable Processes Modelled on Reproducing Kernel Hilbert Space: Application to Tennessee Process

Abstract Abstract In this paper we extend the results obtained in Reproducing Kernel Hilbert Space (RKHS) modelling in the case of Single Input Single Output (SISO) processes to the multivariable (MIMO) ones. Once the model structure is established the model parameters are identified. The validation of the identified model is built on the Tennessee Eastman Process (TE) which is a highly non linear multivariable and non minimum phase chemical process. This process which is unstable in open loop is handled as closed loop controlled process

Online prediction model based on Reduced Kernel Principal Component Analysis

This paper proposes a new technique for online identification of a nonlinear system modeled on Reproducing Kernel Hilbert Space (RKHS) using kernel method. This new method uses the Reduced Kernel Principal Component Analysis (RKPCA) to update the principal component which represent the observations selected by the Kernel Principal Component Analysis method (KPCA). The KPCA is a nonlinear extension of Principal Component Analysis (PCA) to RKHS as it transforms the input data by a nonlinear mapping from the input space into a high dimensional feature space to which the PCA is performed. The proposed technique may be very helpful to design an adaptive control strategy of nonlinear systems.

Dimensionality reduction of RKHS model parameters.

This paper proposes a new method to reduce the parameter number of models developed in the Reproducing Kernel Hilbert Space (RKHS). In fact, this number is equal to the number of observations used in the learning phase which is assumed to be high. The proposed method entitled Reduced Kernel Partial Least Square (RKPLS) consists on approximating the retained latent components determined using the Kernel Partial Least Square (KPLS) method by their closest observation vectors. The paper proposes the design and the comparative study of the proposed RKPLS method and the Support Vector Machines on Regression (SVR) technique. The proposed method is applied to identify a nonlinear Process Trainer PT326 which is a physical process available in our laboratory. Moreover as a thermal process with large time response may help record easily effective observations which contribute to model identification. Compared to the SVR technique, the results from the proposed RKPLS method are satisfactory.

Nonlinear process monitoring based on new reduced Rank-KPCA method

Kernel Principal Component Analysis (KPCA) is an efficient multivariate statistical technique used for nonlinear process monitoring. Nevertheless, the conventional KPCA suffers high computational complexity in dealing with large samples. In this paper, a new kernel method based on a novel reduced Rank-KPCA is developed to make up for the drawbacks of KPCA. The basic idea of the proposed novel approach consists at first to construct a reduced Rank-KPCA model that describes properly the system behavior in normal operating conditions from a large amount of training data and after that to monitor the system on-line. The principle of the proposed Reduced Rank-KPCA is to eliminate the dependencies of variables in the feature space and to retain a reduced data from the original one. The proposed monitoring method is applied to fault detection in a numerical example, Continuous Stirred Tank Reactor and air quality-monitoring network AIRLOR and is compared with conventional KPCA and Moving Window KPCA methods.

Identification of non linear system modeled in Reproducing Kernel Hilbert Space using a new criterion

This paper proposes a new algorithm to estimate the required number of parameters in the models developed in Reproducing Kernel Hilbert Space (RKHS). The proposed method considers models with growing complexities and calculates for each a given matrix, such that these matrices tend to singularity. The required number of parameters is given by verifying a criterion on the determinants of these matrices.

Comparative study of minimal value parameters and RKPCA in RKHS

This paper aims to compare two RKHS models used for describing nonlinear process behaviour. The first model is issued from the estimation of the minimal value of the learning set cardinal and the second results from the complexity reduction of an RKHS model built using arbitrary learning set cardinal. Both models have been tested on non linear dynamic system used as a benchmark and the results were successful.

Online identification of nonlinear system in the Reproducing Kernel Hilbert Space using SVDKPCA method

This paper proposes a new method for online identification of a nonlinear system modelled on Reproducing Kernel Hilbert Space (RKHS). The proposed SVD-KPCA method uses the SVD technique to update the principal components. Then we use the Reduced Kernel Principal Component Analysis (RKPCA) to approach the principal components which represent the observations selected by the KPCA method.