Modeling And Identification Of Nonlinear System Based On Kernel Method

Currently,Intelligent Computing methods such as neural networks and fuzzy systems have been successfully applied in the modeling and identification of nonlinear systems.Comparing with the methods of Intelligent Computing such as neural networks and fuzzy systems etc,Feature Vectors Selection(FVS)and Kernel-based Orthogonal Projections to Latent Structures methods(K-OPLS)which based on ‘kernel trick' will be implemented by mapping the input data to high-dimensional feature space.In the high-dimensional feature space,firstly,considering the geometric features,FVS selects the relevant data subset to form the base vector of the subspace,Secondly,the input data is projected onto the feature subspace,and the final regression model is established by using the MSVM method,MSVM reserve the advantages of compact and sparse under the insensitive loss function.Under the O-PLS framework,the K-OPLS method removes variation from the input variables that is not correlated to the output variables,that is equivalent to removing systematic variation from the description variables that is orthogonal to the response variables,and this realize the predictive and response-orthogonal components are respectively calculated.Therefore,FVS and K-OPLS can effectively reduce the computational load and improve the identification efficiency while having a stronger nonlinear approximation capability.In this paper,the kernel-based learning FVS and K-OPLS methods are used to model and identify the robot systems and chaotic dynamics systems respectively.The main research contents of the thesis include the following aspects:(1)The basic principles and implementation process of the FVS-LR and FVS-SVM methods were studied.In order to verify the effectiveness of the FVS method,it was first applied to the Mackey-Glass time series prediction examples.The experimental results show,comparing with methods such as SVM,KPCA-SVM and LS-SVM etc,the chaos time series based on FVS method has higher prediction accuracy and higher computational efficiency.Further,a method combining FVS and MSVM is proposed to the the inverse kinematics identification of the PUMA 560 industrial robot,and the inverse kinetic modeling of the SARCOS humanoid robot which are MIMO.Under the same conditions,the FVS-MSVM method is compared with SVM,KPCA-MSVM and FVS-linear regression(LR)method etc.The experimental results show that FVS-MSVM method can not only reduce the computational complexity,but also have good identification accuracy and good model promotion.Among them,FVS-MSVM method has higher accuracy.(2)For the identification of the chaotic dynamics system of Duffing-Ueda oscillators,the K-OPLS method is proposed.At the same time,to verify the validity of the K-OPLS method,it is first applied to the identification of Mackey-Glass time series.The result shows thatK-OPLS based chaotic time series prediction has higher prediction accuracy and higher computational efficiency than FVS-LR etc.numerical example of Duffing-Ueda oscillator for chaotic dynamical system based on simulated data,the qualitative and quantitative analysis for various validation tests of the dynamical properties of the original system and the identification model are carried out.A set of qualitative validation criteria is implemented by comparing chaotic attractor i.e.trajectory embedding,computing the corresponding Poincare mapping,the bifurcation diagram as well as plotting the steady-state trajectory i.e.the limit cycle between the original system and the identification model.Meanwhile,the quantitative validation criteria which includes computing the largest positive Lyapunov exponent and the correlation dimension of the chaotic attractors is also done to measure the closeness i.e.the approximation error between the original system and the identification model.the results confirm that the K-OPLS identification method has a better performance of dynamic reconstruction,which can capture the dynamical features of chaotic system,it can produce accurate nonlinear model of process exhibiting chaotic dynamics.Further more,it has been shown that the employed K-OPLS identification model can also accurately reproduce the dynamic invariants which qualitatively and quantitatively characterize the original chaotic system,i.e.the identification model is dynamical equivalent or system approximation to the original system.(3)Considering the real Chua's circuit which is a source of a rich and complex dynamical behavior including chaos,the K-OPLS identification method is further applied to a practical implementation example of Chua's circuit based on the experimental data which are generated by sampling and recording the measured voltage across a capacitor and the inductor current from the double-scroll attractor,the measured voltage across a capacitor from the Chua's spiral attractor.Data filtering technology is used as a preprocessing approach,on the basis of wavelet denoising of measured data with lower signal noise ratio(SNR)which can produce the double-scroll attractor or the spiral attractor,the model validity tests are implemented by comparing chaotic attractor between the original system and the identification model.Experimental results show that the original double-scroll or spiral attractor reconstructed directly from the recorded data and the one generated using the identified model is in excellent agreement.