In the industrial process situation, principal component analysis (PCA) is ageneral method in data reconciliation. However, PCA sometime is unfeasible to nonlinear featureanalysis and limited in application to nonline...In the industrial process situation, principal component analysis (PCA) is ageneral method in data reconciliation. However, PCA sometime is unfeasible to nonlinear featureanalysis and limited in application to nonlinear industrial process. Kernel PCA (KPCA) is extensionof PCA and can be used for nonlinear feature analysis. A nonlinear data reconciliation method basedon KPCA is proposed. The basic idea of this method is that firstly original data are mapped to highdimensional feature space by nonlinear function, and PCA is implemented in the feature space. Thennonlinear feature analysis is implemented and data are reconstructed by using the kernel. The datareconciliation method based on KPCA is applied to ternary distillation column. Simulation resultsshow that this method can filter the noise in measurements of nonlinear process and reconciliateddata can represent the true information of nonlinear process.展开更多
This paper presents a classifier named kernel-based nonlinear representor (KNR) for optimal representation of pattern features. Adopting the Gaussian kernel, with the kernel width adaptively estimated by a simple tech...This paper presents a classifier named kernel-based nonlinear representor (KNR) for optimal representation of pattern features. Adopting the Gaussian kernel, with the kernel width adaptively estimated by a simple technique, it is applied to eigenface classification. Experimental results on the ORL face database show that it improves performance by around 6 points, in classification rate, over the Euclidean distance classifier.展开更多
Presents the iterative method of solving Cauchy problem with reproducing kernel for nonlinear hyperbolic equations, and the application of the computational technique of reproducing kernel space to simplify, the itera...Presents the iterative method of solving Cauchy problem with reproducing kernel for nonlinear hyperbolic equations, and the application of the computational technique of reproducing kernel space to simplify, the iterative computation and increase the convergence rate and points out that this method is still effective. Even if the initial condition is discrete.展开更多
In this article, we present approximate solution of the two-dimensional singular nonlinear mixed Volterra-Fredholm integral equations (V-FIE), which is deduced by using new strategy (combined Laplace homotopy perturba...In this article, we present approximate solution of the two-dimensional singular nonlinear mixed Volterra-Fredholm integral equations (V-FIE), which is deduced by using new strategy (combined Laplace homotopy perturbation method (LHPM)). Here we consider the V-FIE with Cauchy kernel. Solved examples illustrate that the proposed strategy is powerful, effective and very simple.展开更多
In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM...In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.展开更多
An accurate short-term wind speed prediction algorithm based on the efficient kernel ridge pseudo inverse neural network （KRPINN） variants is proposed in this paper. The use of nonlinear kernel functions in pseudo i...An accurate short-term wind speed prediction algorithm based on the efficient kernel ridge pseudo inverse neural network （KRPINN） variants is proposed in this paper. The use of nonlinear kernel functions in pseudo inverse neural networks eliminates the trial and error approach of choosing the number of hidden layer neurons and their activation functions. The robustness of the proposed method has been validated in comparison with other models such as pseudo inverse radial basis function （PIRBF） and Legendre tanh activation function based neural network, i.e., PILNNT, whose input weights to the hidden layer weights are optimized using an adaptive firefly algorithm, i.e., FFA. However, since the individual kernel functions based KRPINN may not be able to produce accurate forecasts under chaotically varying wind speed conditions, a linear combination of individual kernel functions is used to build the multi kernel ridge pseudo inverse neural network （MK-RPINN） for providing improved forecasting accuracy, generalization, and stability of the wind speed prediction model. Several case studies have been presented to validate the accuracy of the short-term wind speed prediction models using the real world wind speed data from a wind farm in the Wyoming State of USA over time horizons varying from 10 minutes to 5 hours.展开更多
An approach for batch processes monitoring and fault detection based on multiway kernel partial least squares(MKPLS) was presented.It is known that conventional batch process monitoring methods,such as multiway partia...An approach for batch processes monitoring and fault detection based on multiway kernel partial least squares(MKPLS) was presented.It is known that conventional batch process monitoring methods,such as multiway partial least squares(MPLS),are not suitable due to their intrinsic linearity when the variations are nonlinear.To address this issue,kernel partial least squares(KPLS) was used to capture the nonlinear relationship between the latent structures and predictive variables.In addition,KPLS requires only linear algebra and does not involve any nonlinear optimization.In this paper,the application of KPLS was extended to on-line monitoring of batch processes.The proposed batch monitoring method was applied to a simulation benchmark of fed-batch penicillin fermentation process.And the results demonstrate the superior monitoring performance of MKPLS in comparison to MPLS monitoring.展开更多
基金This project is supported by Special Foundation for Major State Basic Research of China (Project 973, No.G1998030415)
文摘In the industrial process situation, principal component analysis (PCA) is ageneral method in data reconciliation. However, PCA sometime is unfeasible to nonlinear featureanalysis and limited in application to nonlinear industrial process. Kernel PCA (KPCA) is extensionof PCA and can be used for nonlinear feature analysis. A nonlinear data reconciliation method basedon KPCA is proposed. The basic idea of this method is that firstly original data are mapped to highdimensional feature space by nonlinear function, and PCA is implemented in the feature space. Thennonlinear feature analysis is implemented and data are reconstructed by using the kernel. The datareconciliation method based on KPCA is applied to ternary distillation column. Simulation resultsshow that this method can filter the noise in measurements of nonlinear process and reconciliateddata can represent the true information of nonlinear process.
文摘This paper presents a classifier named kernel-based nonlinear representor (KNR) for optimal representation of pattern features. Adopting the Gaussian kernel, with the kernel width adaptively estimated by a simple technique, it is applied to eigenface classification. Experimental results on the ORL face database show that it improves performance by around 6 points, in classification rate, over the Euclidean distance classifier.
文摘Presents the iterative method of solving Cauchy problem with reproducing kernel for nonlinear hyperbolic equations, and the application of the computational technique of reproducing kernel space to simplify, the iterative computation and increase the convergence rate and points out that this method is still effective. Even if the initial condition is discrete.
文摘In this article, we present approximate solution of the two-dimensional singular nonlinear mixed Volterra-Fredholm integral equations (V-FIE), which is deduced by using new strategy (combined Laplace homotopy perturbation method (LHPM)). Here we consider the V-FIE with Cauchy kernel. Solved examples illustrate that the proposed strategy is powerful, effective and very simple.
文摘In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.
文摘An accurate short-term wind speed prediction algorithm based on the efficient kernel ridge pseudo inverse neural network （KRPINN） variants is proposed in this paper. The use of nonlinear kernel functions in pseudo inverse neural networks eliminates the trial and error approach of choosing the number of hidden layer neurons and their activation functions. The robustness of the proposed method has been validated in comparison with other models such as pseudo inverse radial basis function （PIRBF） and Legendre tanh activation function based neural network, i.e., PILNNT, whose input weights to the hidden layer weights are optimized using an adaptive firefly algorithm, i.e., FFA. However, since the individual kernel functions based KRPINN may not be able to produce accurate forecasts under chaotically varying wind speed conditions, a linear combination of individual kernel functions is used to build the multi kernel ridge pseudo inverse neural network （MK-RPINN） for providing improved forecasting accuracy, generalization, and stability of the wind speed prediction model. Several case studies have been presented to validate the accuracy of the short-term wind speed prediction models using the real world wind speed data from a wind farm in the Wyoming State of USA over time horizons varying from 10 minutes to 5 hours.
基金National Natural Science Foundation of China (No. 61074079)Shanghai Leading Academic Discipline Project,China (No.B504)
文摘An approach for batch processes monitoring and fault detection based on multiway kernel partial least squares(MKPLS) was presented.It is known that conventional batch process monitoring methods,such as multiway partial least squares(MPLS),are not suitable due to their intrinsic linearity when the variations are nonlinear.To address this issue,kernel partial least squares(KPLS) was used to capture the nonlinear relationship between the latent structures and predictive variables.In addition,KPLS requires only linear algebra and does not involve any nonlinear optimization.In this paper,the application of KPLS was extended to on-line monitoring of batch processes.The proposed batch monitoring method was applied to a simulation benchmark of fed-batch penicillin fermentation process.And the results demonstrate the superior monitoring performance of MKPLS in comparison to MPLS monitoring.
