An improved method for nonlinear parameter estimation: a case study of the Rössler model

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• 作者：Wen-Ping He ; Liu Wang ; Yun-Di Jiang ; Shi-Quan Wan
• 刊名：Theoretical and Applied Climatology
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：125
• 期：3-4
• 页码：521-528
• 全文大小：3,165 KB
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Meteorology and Climatology
  Atmospheric Protection, Air Quality Control and Air Pollution
  Climate Change
  Waste Water Technology, Water Pollution Control, Water Management and Aquatic Pollution
  
• 出版者：Springer Wien
• ISSN：1434-4483
• 卷排序：125

文摘

Parameter estimation is an important research topic in nonlinear dynamics. Based on the evolutionary algorithm (EA), Wang et al. (2014) present a new scheme for nonlinear parameter estimation and numerical tests indicate that the estimation precision is satisfactory. However, the convergence rate of the EA is relatively slow when multiple unknown parameters in a multidimensional dynamical system are estimated simultaneously. To solve this problem, an improved method for parameter estimation of nonlinear dynamical equations is provided in the present paper. The main idea of the improved scheme is to use all of the known time series for all of the components in some dynamical equations to estimate the parameters in single component one by one, instead of estimating all of the parameters in all of the components simultaneously. Thus, we can estimate all of the parameters stage by stage. The performance of the improved method was tested using a classic chaotic system—Rössler model. The numerical tests show that the amended parameter estimation scheme can greatly improve the searching efficiency and that there is a significant increase in the convergence rate of the EA, particularly for multiparameter estimation in multidimensional dynamical equations. Moreover, the results indicate that the accuracy of parameter estimation and the CPU time consumed by the presented method have no obvious dependence on the sample size.