本文關(guān)鍵詞： Lorenz系統(tǒng) 多維時間序列 突變檢測　出處：《西北民族大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：自從ThOms提出突變理論后,它被廣泛應(yīng)用于各個方面,也包括氣象方面。其中氣象的影響因素是多重的,即用數(shù)值形式表示氣象的變幻時,為一個多維的時間序列,而現(xiàn)有的檢測方法只能用于檢測單點(diǎn)時間序列,因此論文旨在提供一種方法,即用現(xiàn)有的檢測方法去檢測氣象變幻所形成的多維時間序列。在文中主要以Lorenz系統(tǒng)為研究對象。在第二章,首先給出了Lorenz方程的數(shù)值解,其中初始值為(12,23,56),積分步長為0.01,積分區(qū)間為[0,10],而數(shù)值解便為之后用于突變檢測的多維時間序列,又給出了 Lorenz軌線真實的突變時間節(jié)點(diǎn),后續(xù)用于與突變檢測方法檢測的突變時間作對比,查看檢測結(jié)果的優(yōu)劣性。在第三章,論文給出了兩大類方法來處理第二章中的多維時間序列。方法一為向量內(nèi)積法,選用了四組基礎(chǔ)的參考向量(1,0,0)、(0,1,0)、(0,0,1)、(1,1,1)與多維時間序列作內(nèi)積,便可得到四組相應(yīng)的單點(diǎn)時間序列,用滑動T-檢驗法對其進(jìn)行檢測,將檢測到的突變時間與第二章中真實的突變時間節(jié)點(diǎn)作對比,得知當(dāng)參考向量為(1,0,0)時,檢測結(jié)果最為良好。方法二為范數(shù)法,選用三種基礎(chǔ)范數(shù)1-范數(shù)、2-范數(shù)、∞-范數(shù)對多維時間序列進(jìn)行處理,得到三組相應(yīng)的單點(diǎn)時間序列,同樣用滑動T-檢驗法對其進(jìn)行檢測,將檢測到的突變時間與第二章中真實的突變時間節(jié)點(diǎn)作對比,得知用1-范數(shù)、2-范數(shù)、∞-范數(shù)處理多維時間序列,檢測結(jié)果較為低劣。在第四章,論文選取了三組不同的初始值、相同的積分區(qū)間、相同的積分步長下Lorenz方程的數(shù)值解與參考向量(1,0,0)作內(nèi)積,得到三組不同的單點(diǎn)時間序列,用滑動T-檢驗法對其進(jìn)行檢測,并將檢測到的突變時間與相應(yīng)的真實突變時間節(jié)點(diǎn)作對比,得知,總體而言,檢測結(jié)果較為良好。
[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，

本文編號：1523589