【作者】 赵春晓；

【导师】 王小刚；

【作者基本信息】 东北大学 ， 控制理论与控制工程， 2008， 硕士

【摘要】 在科学、经济、工程等许多应用中都存在着在历史数据的基础上预测未来的问题。时间序列预测是预测领域内的一个重要研究方向。它是一种根据历史数据构造时间序列模型,再把模型外推来预测未来的一种方法。近年来,来自天文、水文、气象等领域如太阳黑子、径流量、降雨量等时间序列都被发现含有混沌特性。面对自然和社会生产中大量存在的混沌时间序列,传统的统计分析方法效果欠佳。支持向量机具有优良的非线性特性,非常适合于混沌序列预测的研究。基于支持向量机的混沌时间序列预测的研究是近几年来的研究热点,受到了特别的重视,本文对此作了较为系统深入的研究。混沌是一个完全确定的系统中出现的一类随机过程的现象,是有序与无序的统一确定性与随机性的统一。近年来,作为一种新兴的研究非周期、复杂和不规则现象的方法,混沌的引入为预测技术的研究注人了新的活力。建立在统计学习理论和结构风险最小原则上的支持向量机在理论上保证了模型的最大泛化能力,它将函数估计最终转化为二次规划问题,理论上可以得到最优解。因此与建立在经验风险最小原则上的神经网络模型相比,理论上更为完善。本文运用支持向量机建立时间序列预测模型,研究影响模型预测精度的相关参数,在分析参数对时间序列预测精度的影响基础上,采用遗传算法优化预测模型参数,从而获取最优参数。通过对太阳黑子时间序列和典型的混沌时间序列的预测,表明改进后的方法具有很好的预测能力和抗噪声能力。最后,用电解铜中铜酸浓度时间序列对本文方法进行了验证。电解铜中铜酸浓度具有明显的混沌特性,本文分别进行了单步预测和多步预测。仿真试验表明,在此模型的参数选取中,与现有某些方法相比,基于遗传算法获取模型参数的方法大大提高了支持向量机对混沌时间序列的预测能力,也说明了支持向量机对混沌时间序列有比较强的拟合能力和比较高的单步和多步预测精度。更多还原

【Abstract】 There is no denying the fact that the method of predicting the future base on historical data is commonly used science, economic and engineering. Time Series Forecasting, which constructs time series model on the basis of historical data and then use the model to forecast the future, is an important research direction in forecasting research area. As far as astronomy, hydrology and meteorological phenomena are concerned, many time series such as sun-spots, amount of runoff, rainfall amount were discovered all including the chaotic character in recent year. In the face of Chaotic Time Series largely existed in nature and social economical phenomena, the traditional method of statistical analysis performed badly. Support Vector Machines possesses excellent non-linear character, which enables it to be extremely suitable to the forecasting research is chaotic array. Based on Support Vector Machines and chaotic theory, the forecasting research has become research hot spot and received special attention at present. This dissertation has done systematic and thorough research on the above mentioned problem.Chaos is a class of random process phenomenon, which appeared in a completely determine dsystem.It is unification of ordered and disorder, deterministic and randomness. Rencently years, it is a new study of non-cycle, complex and irregular phenomenon of method. Chaos prediction of injects new vitality.for theprediction technology.Support Vector Machine (SVM) is based on Statistical Learning Theory (SLT) and Structural Risk Minimization Principle (SRM), and theoretically assures the best model generalization. It changed function estimation to quadratic program, so it can get the optimal solution in theory. Therefore, it is more perfect in theory than Artificial Neural Network (ANN) that is based on Empirical Risk Minimization Principle (ERM).In this paper, SVM is used to establish time series forecasting model, study the parameters that influence forecasting accuracy. On the basis of analyzing model parameters’ influence, a self-adaptive optimizing algorithm for establishing the model parameters based on Genetic Algorithm is put forward. Through predicting the sun-spot time series and tapical chaostic time series, it proved that the method has good prediction capability and anti-noise capability.Finally, the method is probed by predicting the cupric and acid time series. the cupric and acid concentrations are single step and multi-step predicted by the method introduced in the dissertation. It is proved that among the methods of selecting the parameters, the one based on Genetic Algorithm greatly improved the predition ability to Chaotic Time Series. It also proved that SVM has better fitting ability and prediction accuracy to Chaotic Time Series.更多还原