Research On Prediction And Identification Of Chaotic Systems Using Support Vector Machines

Prediction and identification of chaotic systems are the basis of chaos synchronization and control. At present, computation intelligent methods such as neural network and fuzzy system have been widely used in prediction and identification of chaotic system, what’s more, these methods obtain good results. In this thesis, Support Vector Machine (SVM) is applied to single-step and multi-step prediction of chaotic time series, and the prediction result is pretty good. Partical swarm optimization is also introduced to optimize the parameters of SVM. In the other hand, SVM is used in the identification of typical chaotic systems, and the performance of identification model is analysed and compared, and the result shows that the proposed methods are effective.The main contents of the thesis are as follows.Firstly, by virtue of the theory of phase space reconstruction of chaotic time series, mutual information method used to determine the the delay time of the chaotic time series is studied, then the Cao method to determine the embedding dimension is used, on the basis, Least Square Support Vector Regression (LS-SVR) method is adopted to complete the single-step prediction of three typical chaotic time series, including Mackey-Glass, Santa Fe and Monthly Sun Spots time series etc. the performance of the prediction model is also analysed. In order to verify the validity of the method, the performance of prediction model using LS-SVR with RBF kernel, multi-layer perception kernel and poly kernel is compared. Moreover, the performance of the prediction model using ε-SVR and v-SVR with the different kernels is analyzed and compared furtherly. Modified PSO algorithm is used to optimize the parameters of LS-SVR, and it gives the better performance. The predictive method based on SVR and LS-SVR used in chaotic time series with gaussian whiten noise is also studied.Secondly, the prediction method of LS-SVR used in iterative and direct multi-step prediction of chaotic time series is given. Compared to the ε-SVR and v-SVR method, the experiment results show that the corresponding predictive method using LS-SVR is effective for muti-step prediction of chaotic time series.Finally, the LS-SVR is used to build the identification model of typical chaotic systems such as one-dimensional Logistic map, two-dimensional Henon map and three-dimensional Lorenz system etc. Reconstruction of chaotic attractor and calculation of Lyapunov exponents are used to the qualitative and quantitative evaluation of the identification model performance. Compared to the identification model using Back-Propagation and RBF neural network, experiment results show that the built identification model by LS-SVR give the better performance in approximation of the three typical chaotic systems.