【作者】 王洪波；

【导师】 崔宝同； 朱启兵；

【作者基本信息】 江南大学 ， 检测技术与自动化装置， 2008， 硕士

【摘要】 基于时间序列模型的预测作为定量预测的主要方法,在实际中的应用几乎遍及预报活动的所有领域。传统的时间序列建模主要针对线性或弱非线性时间序列,但是面对现实生活中大量的复杂非线性时间序列(甚至混沌)时则显得力不从心。基于统计学习理论的支持向量机是一种新型的学习方法,它采用结构风险最小化原则,为解决小样本、非线性、高维数等学习问题提供了一个框架。近年来,支持向量机已开始应用于非线性时间序列预测中。本文以提高支持向量机预测模型的精度为主要目的,研究了非线性时间序列的降噪、非平稳化处理和模型参数优化等问题。局部投影降噪算法已广泛应用于非线性时间序列的分析中,但其邻域选取具有主观性,严重影响到降噪的性能。本文研究了一种按照自适应方式选取邻域大小的局部投影降噪算法。首先用时间延迟方法将一维时间序列重构到高维相空间。然后逐步增大每个待分析相点的领域大小,在领域最大主方向变化过程中,自适应地确定该相点的最优领域。最后再用局部几何投影的方法去除噪声成分。实验结果表明,自适应邻域选取方法,提高了局部投影算法的降噪能力。非平稳时间序列具有一定的周期性和随机性的,难以用单一的方法进行精确的预测。本文提出将经验模式分解(EMD)和最小二乘支持向量机(LS-SVM)相结合的预测方法。首先,运用EMD将趋势时间序列自适应地分解成一系列不同尺度的本征模式分量;其次,对每个本征模式分量,采用合适的核函数和超参数构造不同的LS-SVM进行预测;最后对各分量的预测值进行拟合得到最终的预测值。并将此方法成功应用于机械振动非平稳趋势序列的预测。重构相空间和支持向量机的参数优化是提高预测性能的两个重要方面,传统上这两个问题是分开解决的。本文提出采用混合粒子群算法实现二者的联合优化。联合优化方法融合了离散粒子群和实数值粒子群算法,同时对空间重构的参数和支持向量机的参数设置进行优化。仿真试验表明,此方法可以提高预测精度。更多还原

【Abstract】 As the main technique of the quantitative forecast, the method of time series prediction is used almost in all fields of forecast. The traditional methods of time series prediction mainly focus on linear time series and weak nonlinear time series, so they lack effectiveness when they face complex nonlinear time series (even chaos time series). Support Vector Machine (SVM) is a kind of novel machine learning methods, theoretically based on statistic learning theory. It employs the criteria of structural risk minimization and provides a framework for the small samples, nonlinearity and high dimension problems. SVM has been applied in nonlinear time series prediction in recent years. Focusing on raising accuracy of SVM prediction model, this paper studies noise-reduction, non-stationary processing and model parameters optimization of nonlinear time series.Although widely applied in nonlinear time series analysis, the noise reduction method via local projection has the subjectivity of selecting the neighborhood, which greatly affects the performance. A new method by local projection using adaptive neighborhood selection is studied. First, one dimensional time series are embedded into a high dimensional phase space according to time-delay theory. The neighborhood size for each candidate phase point in phase space is increased by adding neighboring point one by one. The optimal neighborhood size for the phase point is determined during the direction’s variation of the most significant eigenvector of neighborhood as size increasing, and then the noise is eliminated through local geometric projection. Experiment results show that adaptive neighborhood selection can improve the noise reduction performance of local projection method.Non-stationary time series has periodicity and randomness so that it is difficult to construct the model of accurate forecast with single method. A hybrid forecasting method based on Empirical Mode Decomposition (EMD) and Least Square Support Vector Machine (LS-SVM) is presented in this paper. Firstly, the non-stationary time series is adaptively decomposed into a series of stationary intrinsic mode functions (IMF) in different scale space using EMD. Then the right parameter and kernel functions are chosen to build different LS-SVM respectively to every IMF. Finally, these forecasting results of each IMF are combined to obtain final forecasting result. This method is successfully applied to non-stationary trend prediction of mechanical vibration.Phase space reconstruction and SVM parameters optimization are two important aspects for improving prediction performance and are solved separately traditionally. This paper proposes a joint optimization algorithm based on Hybrid PSO. This method combines the discrete PSO with the continuous-valued PSO to simultaneously optimize the phase space reconstruction and the SVM parameters setting. The experimental results showed the proposed approach can raise prediction accuracy.更多还原