混沌系统中参数估计的演化建模方法

借助于演化算法的自组织、自适应和自学习特征,本文提出了基于演化算法的参数辨识方案,并利用经典的Lorenz方程进行了数值仿真试验,研究了参数辨识方案对于单参数、双参数以及Lorenz系统三个参数完全未知时的性能.数值试验结果表明,新方法能够很好的对未知参数进行较为快速、准确的辨识,但存在对多个参数同时搜索时速度较慢的缺陷.鉴于此,将演化算法变异操作中的参数变异范围附加一种约束机理,试验结果表明,这一约束机理有效地提高了多参数估计中算法的收敛速度.

Evolutionary modeling for parameter estimation for chaotic system

On the basis of evolutionary algorithm, a novel method for parameter estimation of nonlinear dynamic equations is given in the present paper. Numerical tests indicate that the unknown parameters all can be estimated quickly and accurately whether the partial parameters are unknown or all parameters are unknown in the classic Lorenz equation. However, it is found that the convergence rate of the new algorithm is relatively slow when multiple unknown parameters are estimated simultaneously. To solve this problem, a corresponding improvement of measure is proposed, namely, a constraint mechanism is taken during the variation operation of evolutionary algorithm. The improvement is mainly based on the characteristic that the longer the running time of the evolutionary algorithm, the smaller the range of variation of the estimated parameters. Results indicate that the searching speed of the algorithm is greatly improved by using the improved estimation parameter project.