Approximation of Chaotic Dynamics by Using Smaller Number of Data Based upon the Genetic Programming and Its Applications(Special Section on Digital Signal Processing)
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概要
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This paper deals with the identification of system equation of the chaotic dynamics by using smaller number of data based upon the genetic programming (GP). The problem to estimate the system equation from the chaotic data is important to analyze the structure of dynamics in the fields such as the business and economics. Especially, for the prediction of chaotic dynamics, if the number of data is restricted, we can not use conventional numerical method such as the linear-reconstruction of affractors and the prediction by using the neural networks. In this paper we utilize an efficient method to identify the system equation by using the GP. In the GP, the performance (fitness) of each individual is defined as the inversion of the root mean square error of the spectrum obtained by the original and predicted time series to suppress the effect of the initial value of variables. Conventional GA (Genetic Algorithm) is combined to optimize the constants in equations and to select the primitives in the GP representation. By selecting a pair of individuals having higher fitness, the crossover operation is applied to generate new individuals. The crossover operation used here means the replacement of a part of tree in individual A by a part of tree in individual B. To avoid the meaningless genetic operation, the validity of prefix representation of the subtree to be embedded to the other tree is probed by using the stack count. These newly generated individuals replace old individuals with lower fitness. The mutation operation is also used to avoid the convergence to the local minimum. In the simulation study, the identification method is applied at first to the well known chaotic dynamics such as the Logistic map and the Henon map. Then, the method is applied to the identification of the chaotic data of various time series by using one dimensional and higher dimensional system. The result shows better prediction than conventional ones in cases where the number of data is small.
- 社団法人電子情報通信学会の論文
- 2000-08-25
著者
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Tokinaga Shozo
The Graduate School Of Economics Kyushu University
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IKEDA Yoshikazu
the Graduate School of Economics, Kyushu University
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Ikeda Yoshikazu
The Graduate School Of Economics Kyushu University
関連論文
- Controlling the Chaotic Dynamics by Uusing Approximated System Equations Obtained by the Genetic Programming(Special Section on Nonlinear Theory and its Applications)
- Approximation of Chaotic Dynamics by Using Smaller Number of Data Based upon the Genetic Programming and Its Applications(Special Section on Digital Signal Processing)
- Approximation of Multi-Dimensional Chaotic Dynamics by Using Multi-Stage Fuzzy Inference Systems and the GA(Special Section on Nonlinear Theory and its Applications)
- Approximation of Chaotic Dynamics for Input Pricing at Service Facilities Based on the GP and the Control of Chaos
- Prediction of Future Stock Trends by Using Two-Stage Hierarchical Systems Based on the Segment Categorization and Recognition of Series of Category Symbols Using the Genetic Programming