基于Lorenz系统的多维时间序列突变检测方法研究

发布时间：2018-02-22 04:01

  本文关键词： Lorenz系统 多维时间序列 突变检测　出处：《西北民族大学》2017年硕士论文　论文类型：学位论文

【摘要】：自从ThOms提出突变理论后,它被广泛应用于各个方面,也包括气象方面。其中气象的影响因素是多重的,即用数值形式表示气象的变幻时,为一个多维的时间序列,而现有的检测方法只能用于检测单点时间序列,因此论文旨在提供一种方法,即用现有的检测方法去检测气象变幻所形成的多维时间序列。在文中主要以Lorenz系统为研究对象。在第二章,首先给出了Lorenz方程的数值解,其中初始值为(12,23,56),积分步长为0.01,积分区间为[0,10],而数值解便为之后用于突变检测的多维时间序列,又给出了 Lorenz轨线真实的突变时间节点,后续用于与突变检测方法检测的突变时间作对比,查看检测结果的优劣性。在第三章,论文给出了两大类方法来处理第二章中的多维时间序列。方法一为向量内积法,选用了四组基础的参考向量(1,0,0)、(0,1,0)、(0,0,1)、(1,1,1)与多维时间序列作内积,便可得到四组相应的单点时间序列,用滑动T-检验法对其进行检测,将检测到的突变时间与第二章中真实的突变时间节点作对比,得知当参考向量为(1,0,0)时,检测结果最为良好。方法二为范数法,选用三种基础范数1-范数、2-范数、∞-范数对多维时间序列进行处理,得到三组相应的单点时间序列,同样用滑动T-检验法对其进行检测,将检测到的突变时间与第二章中真实的突变时间节点作对比,得知用1-范数、2-范数、∞-范数处理多维时间序列,检测结果较为低劣。在第四章,论文选取了三组不同的初始值、相同的积分区间、相同的积分步长下Lorenz方程的数值解与参考向量(1,0,0)作内积,得到三组不同的单点时间序列,用滑动T-检验法对其进行检测,并将检测到的突变时间与相应的真实突变时间节点作对比,得知,总体而言,检测结果较为良好。
[Abstract]:Since ThOms put forward the catastrophe theory, it has been widely used in many fields, including meteorology, in which the factors affecting meteorology are many, that is, when the change of meteorology is expressed in numerical form, it is a multidimensional time series. But the existing detection methods can only be used to detect single point time series, so this paper aims to provide a method. In this paper, we mainly take Lorenz system as the research object. In the second chapter, we give the numerical solution of the Lorenz equation. The initial value is 1 / 12 / 23 / 56 / 1, the integral step is 0. 01 and the integral interval is [0 / 10]. The numerical solution is then a multidimensional time series for abrupt detection, and the real abrupt time node of the Lorenz trajectory is given. In the third chapter, two kinds of methods are presented to deal with the multi-dimensional time series in chapter two. The first method is vector inner product method. Four groups of basic reference vectors are selected for internal product with multidimensional time series, and four groups of corresponding single point time series are obtained, and the sliding T- test method is used to detect them. By comparing the detected mutation time with the real mutation time node in Chapter 2, it is found that the detection results are the best when the reference vector is 1 / 0 / 0). The second method is the norm method, and three basic norms (1- norm / 2- norm) are selected. 鈭，

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