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1448 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 [22] A. Faure, A. Naldi, C. Chaouiya, and D. Thieffry, “Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle”, Bioinformatics, vol. 22, no. 14, pp. 124–131, 2006. [23] D. Cheng, Y. Zhao, X. Xu, “Matrix approach to boolean calculus”, IEEE Conference on Decision and Control and European Control, pp. 6950–6955, 2011. [24] D. Cheng, H. Qi, Y. Zhao, “Synthesis of Boolean networks via semi-tensor product”, 30th Chinese Control Conference, pp. 6–17, 2011. Jinyu Zhan was born in Heilongjiang Province of China in 1978. She received the Ph.D. degree in computer applications from the University of Electronic Science and Technology of China in 2006. Currently, she is an associate professor at the University of Electronic Science and Technology of China. Her research interests include formal co-verification of SoC, model checking, real time embedded systems, and VLSI design and verification. Shan Lu was born in Hunan Province of China in 1989. He received the Bachelor degree in information and computation science from Chongqing Three Gorges University in 2011. Currently, he is a graduate student at the University of Electronic Science and Technology of China. His research interests include formal verification and model checking. Guowu Yang was born in Hubei Province of China in 1966. He received the Ph.D. degree at Electrical and Computer Engineering department of Portland State University in USA in 2005. He was a research associate at Computer Science department of Portland State University from 2005 to 2006. Currently, he is a professor of College of Computer Science and Engineering at University of Electronic Science and Technololgy of China. His research interests include formal verification and developing corresponding program package, theoretical study of synthesis algorithms in quantum computing, and non-linear control theory. © 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1449 Adaptive Chaotic Prediction Algorithm of RBF Neural Network Filtering Model based on Phase Space Reconstruction Lisheng Yin, Yigang He, Xueping Dong, Zhaoquan Lu School of Electrical and Automation Engineering, Hefei University of Technology, Hefei, China E-mail: yls20000@163.com, hyghnu@yahoo.com.cn, hfdxp@126.com, luzhquan@126.com Abstract—With the analysis of the technology of phase space reconstruction, a modeling and forecasting technique based on the Radial Basis Function (RBF) neural network for chaotic time series is presented in this paper. The predictive model of chaotic time series is established with the adaptive RBF neural networks and the steps of the chaotic learning algorithm with adaptive RBF neural networks are expressed. The network system can enhance the stabilization and associative memory of chaotic dynamics and generalization ability of predictive model even by imperfect and variation inputs during the learning and prediction process by selecting the suitable nonlinear feedback term. The dynamics of network become chaotic one in the weight space. Simulation experiments of chaotic time series produced by Lorenz equation are proceeded by a RBF neural network.The experimental and simulating results indicated that the forecast method of the adaptive RBF neutral network compared with the forecast method of back propagation (BP) neutral network based on the chaotic learning algorithm has faster learning capacity and higher accuracy of forecast.The method provides a new way for the chaotic time series prediction. Index Terms—Chaos Theory, Phase Space Reconstruction, Time Series Prediction, RBF Neural network, Algorithm I. INTRODUCTION Since the phase space reconstruction theory proposed by Packard et al. in 1980, many scholars at home and abroad to set off a climax of chaotic time series prediction. Prediction for chaotic time series is to approximate the unknown nonlinear functional mapping of a chaotic signal. The laws underlying the chaotic time series can be expressed as a deterministic dynamical system. Farmer and Sidorowich suggest reconstructing the dynamics in phase space by choosing a suitable embedding dimension and time delay [1]. Takens’ theorem ensures that the method is reliable, based on the fact that the interaction between the variables is such that every component contains information on the complex dynamics of the system [2]. The neural network [3-6]. not only has the selfadaptive, parallelism and fault tolerance characteristics, but also has the ability to approximate any nonlinear function. Based on these advantages, the neural network model of the nonlinear system has a very wide range of applications [7-10]. In recent years, particular interest has been put into predicting chaotic time series using neural networks because of their universal approximation capabilities. Most applications in this field are based on feed-forward neural networks, such as the Back Propagation (BP) network [11-13], Radial Basis Function (RBF) network [14-15], Recurrent neural networks (RNNs) [16-18], FIR neural networks [19-20] and so on. It is widely used tool for the prediction of time series [21- 23]. The RBF neural network model structure is easy to understand, training process stability, training speed is fast, training result is high accuracy and generalization ability is strong. In this paper, the chaotic algorithm is proposed to a RBF neural network filtering predictive model and the model is proposed to make prediction of chaotic time series. The network system can enhance the stabilization and associative memory of chaotic dynamics and generalization ability of predictive model even by imperfect and variation inputs by selecting the suitable nonlinear feedback term. The dynamics of network become chaotic one in the weight space. The model is tested for the chaotic time series which venerated with Lorentz system by on-line method. The experimental and simulation results indicated that the adaptive filtering has a good self-suitable prediction performance and can be successfully used to predict chaotic time series. II. ESTABLISHMENT OF ADAPTIVE RBF NEURAL NETWORK FILTERING PREDICTIVE MODEL BASED ON CHAOTIC ALGORITHM A. Model of Chaotic Time Series Prediction Takens theorem considers evolution of any component of the system is decided by other components interacting with this component, therefore, the information of relevant component imply in the development process of this component, so the original rules of the system can be extracted and restored from a group of time-series data of a certain component. The one-dimensional time series is embedded to multi-dimensional phase space through reconstruction and the new system with same dynamic characteristics as original system can be obtained through the selection of a suitable embedding dimension m and time delayτ . The usual method of selecting time delay © 2013 ACADEMY PUBLISHER doi:10.4304/jcp.8.6.1449-1455
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Journal of Computers ISSN 1796-203X
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Corn Moisture Measurement using a C
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Call for Papers and Special Issues
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(Contents Continued from Back Cover
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