基于非线性动力系统的时间序列预测技术研究

发布时间：2018-06-08 07:48

本文选题：相空间重构 + 遗传算法　；参考：《天津理工大学》2017年硕士论文

【摘要】：非线性动力系统是由确定的动力系统产生的复杂行为。对于结构已知的非线性动力系统,可以根据动力特性建立非线性动力系统模型。大部分的非线性动力系统很难建立一个精确的数学模型。但是,根据观测到的时间序列值,可以近似的拟合出一个非线性动力系统模型。本文对结构已知与结构未知的非线性动力系统模型进行研究。首先对非线性动力系统进行分析,包括系统稳定性、倍周期分岔性、混沌特性进行研究。重点研究了相空间重构理论,分别使用互信息法和饱和关联维数法来确定相空间重构的参数。相空间重构理论为建立非线性预测模型奠定基础。对于结构已知的非线性动力系统,根据动力系统特性,建立非线性动力系统模型。对于可以求出解析式的非线性动力系统模型,采用粒子群方法求解最优模型参数,仿真实验表明,该方法比传统的求解方法具有更高的预测精度。对于难以求出解析式的非线性动力系统模型,采用Newmark和Wilson计算方法,求解非线性动力系统模型的瞬态解析,仿真实验表明,当积分步长很短时,该方法具有很高的预测精度。对于结构未知的非线性动力系统,对常用的自适应预测模型和局域预测模型进行研究。在相空间中,构建Volterra自适应预测模型。为了提高Volterra自适应预测模型预测精度,采用群体智能的遗传算法,通过交叉、变异、选择等方法求解模型最优参数,实验表明该方法改进模型的学习能力,加快收敛速度,提高了预测精度。在相空间中,构建基于粒子滤波优化的局域线性预测模型。在局域线性预测模型中,使用欧氏距离和相关系数结合的方法来选择邻近点,根据邻近点构建局域线性预测模型,并采用粒子滤波方法求解最优模型参数,实验表明该方法较局域线性表模型和局域神经网络模型,具有更高的预测精度。
[Abstract]:Nonlinear dynamic system is a complex behavior produced by a definite dynamic system. For the known nonlinear dynamic system, the nonlinear dynamic system model can be established according to the dynamic characteristics. It is difficult for most nonlinear dynamic systems to establish an accurate mathematical model. However, according to the observed time series, we can approximate fit a nonlinear dynamic system model. In this paper, the nonlinear dynamic system model with known structure and unknown structure is studied. Firstly, the nonlinear dynamical system is analyzed, including system stability, period doubling bifurcation and chaos characteristics. The theory of phase space reconstruction is mainly studied. Mutual information method and saturation correlation dimension method are used to determine the parameters of phase space reconstruction. The theory of phase space reconstruction lays a foundation for the establishment of nonlinear prediction model. According to the characteristics of the dynamic system, the nonlinear dynamic system model is established for the known nonlinear dynamic system of the structure. The particle swarm optimization (PSO) method is used to solve the optimal model parameters for the analytical nonlinear dynamic system model. The simulation results show that the proposed method has higher prediction accuracy than the traditional method. For the nonlinear dynamic system model which is difficult to be solved, Newmark and Wilson calculation methods are used to solve the transient analysis of the nonlinear dynamic system model. The simulation results show that the method has a high prediction accuracy when the integral step is very short. For nonlinear dynamical systems with unknown structures, adaptive prediction models and local prediction models are studied. Volterra adaptive prediction model is constructed in phase space. In order to improve the prediction accuracy of Volterra adaptive prediction model, the genetic algorithm of swarm intelligence is used to solve the optimal parameters of the model by means of crossover, mutation and selection. The experiments show that this method improves the learning ability of the model and accelerates the convergence speed. The prediction accuracy is improved. A local linear prediction model based on particle filter optimization is constructed in phase space. In the local linear prediction model, the Euclidean distance and the correlation coefficient are combined to select the adjacent points, the local linear prediction model is constructed according to the adjacent points, and the particle filter method is used to solve the optimal model parameters. Experiments show that this method has higher prediction accuracy than local linear table model and local neural network model.
【学位授予单位】：天津理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O19

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