【作者】 汤岩；

【导师】 王福林；

【作者基本信息】 东北农业大学 ， 管理科学与工程， 2007， 硕士

【摘要】 时间序列分析是动态数据分析处理的一种重要的方法，以概率统计学作为理论基础来分析随机数据序列(或称动态数据序列)，并对其建立数学模型，以及进一步应用于预测、自适应控制等诸多方面，是一个具有相当高的实际价值的应用研究领域。随着时间序列分析方法的日趋成熟，其应用领域越来越广泛，对模型的精度提出了更高的要求。由于时间序列建模过程中的各种参数估计方法最终都会归结为高度非线性函数的优化问题，传统的优化方法估计出的参数可信度较低，因此本文将模拟生物进化过程的遗传算法作为求解复杂优化问题的手段应用时间序列模型的参数估计中来。遗传算法作为一种全局的优化算法，在处理高度非线性函数的优化问题中有着传统优化方法不可比拟的优越性，但在实际应用中也存在一定的缺陷，主要表现在算法的早熟现象、局部寻优能力差、收敛速度慢等，因此本文应用了改进的实数遗传算法(1RGA)对时间序列模型中的参数进行估计。本文主要做了以下四方面的研究工作：(1)论述了研究时间序列分析的背景和意义，总结了目前的学科发展以及参数估计方法的研究现状：(2)讨论了时间序列分析建模的理论方法；(3)阐述了遗传算法的发展和研究状况，给出了改进的实数遗传算法的原理和运算流程；(4)在时间序列分析和遗传算法的理论指导下，将遗传算法引入时间序列建模过程中，进行深入的讨论与研究。研究内容及成果主要包括以下几个方面：1．介绍了时间序列及其相关的基本概念，分析了随机时间序列的特性、研究中的方法性工具以及时间序列的特征函数，分析并讨论了ARIMA模型体系。介绍了拟合模型参数估计的常用方法，对目前模型参数估计方法存在的不足作了一定的探讨。介绍了Box-Jenkins建模的理论和流程，以及线性最小方差预测的理论方法。2．对遗传算法作了概述，简要介绍了基本遗传算法(SGA)的构成要素、运算流程和实现。阐述了实数遗传算法(RGA)研究的发展和研究状况，讨论了实数遗传算法特点，比较全面地描述了目前实数编码遗传算法中常用的选择、交叉、变异算子及适应度函数，给出了改进的实数遗传算法(IRGA)的原理和运算流程。3．进行实证分析，将基本遗传算法和改进实数遗传算法分别应用到时间序列模型参数辨识中，并与传统随机时间序列分析所辨识的模型精度进行比较，得出结论：在选定的误差指标下，应用本文中的改进实数遗传算法辨识参数后得到的时间序列模型拟合精度最高。4．提出了IRGA-ARIMA建模方法，并将研究的成果应用于电力系统负荷时间序列的建模和预测上，验证了模型的适用性，并取得了较好的预测效果。更多还原

【Abstract】 Time series analysis is the important approach to solve and analyze the dynamic data. It is actual value to applied research study, which is basic on the probability statistics to analyze random data series (or called dynamic data series), develop the mathematic model, and further apply to forecast, adaptive control, and so on.With the development of the method of time series analysis, the applied field is more and more wide, thus the precision of the model is required to higher level. Various method of parameter estimation is come down to solve the optimization problem of the highly nonlinear function, and the confidence about parameter estimation by the traditional optimization approach is lower, therefore, in the paper, the complex optimization problem is solved by applying genetic algorithm (GA) to the parameter estimation of the time series model. GA which is an universal algorithm is more advantageous than the traditional optimization approach when the optimization problem of the highly nonlinear function is achieved. But this algorithm exists some limitation in practice, which appears the phenomena of the prematurity, the bad capability to obtain the local solution of the optimization problem and the slowly converge rate, and so on.. Hence the modified method of GA when we estimate parameters of the time series model by GA is provided.In this thesis four aspects are studied. Firstly, illustrate the background and the meaning to analyze the time series, and provide the research actuality of the development and the approach of parameter estimation. Secondly, analyze the theory method of modeling the time series analysis. Thirdly, illustrate the research actuality of the development and the approach of GA and capture the theory and the operator flow of improved real coding based genetic algorithm (IRGA). The last one, according to the theory of the time series analysis and GA, the GA is introduced in the process of modeling the time series, which is discussed and studied. The following conclusions are achieved:1. The concepts of time series and the related concepts are provided. It is analyzed which is the characteristics of time series , the research tool and the eigenfunction of time series. ARIMA model system is analyzed and discussed. The usual approach of fitting of model parameter estimation is introduced and the limitation of parameter estimation is probed. The theory and the flow of the Box-Jenkins modeling are introduced, and the theory method of the linear minimum variance forecast is introduced. 2. GA is illustrated in this paper, some are also simple introduced, thus the components, algorithm flow and the realization of simple genetic algothm (SGA). Contemporarily, the research development and the characteristics of RGA are illustrated and selection operator, crossover operator、mutation operator and fitness function of RGA is captured. The principle and the algorithm flow of IRGA are provided.3. By the demonstration, the precision of SGA and IRGA, which are respectively applied to the parameter estimation of the time series model, are contrasted with the precision of the approach of the traditional time series analysis. In the end, the conclusion is achieved. In the case of the selected error index, the fitting of precision of the time series model, which is obtained by the parameter estimation used IRGA, is the highest.4. the research result is applied on modeling and forecasting time series about the electric power system load. The applicability is tested and the forecast effect is obtained.更多还原