本文選題：混沌識別 + 0-1測試法�。� 參考：《廣州大學》2017年碩士論文

【摘要】：0-1測試法是通過輸出值K(c)是否趨近于1或0來判斷離散序列是否具有混沌性的一種新方法。首先以Verhulst種群模型生成的離散序列為研究對象,驗證了 0-1測試法的有效性;其次,分析了 0-1測試算法中不同數(shù)據(jù)長度N和振幅α及添加正態(tài)白噪聲后對混沌測試效果的影響;最后,將0-1測試法和傳統(tǒng)的最大Lyapunov指數(shù)法應用于山東上莊金礦成礦元素序列的混沌識別中,識別了多成礦化學元素序列的混沌特征。本文的主要研究結果如下:(1) 0-1測試法有效性檢驗。以Verhulst種群模型生成的離散序列為研究對象,通過得到對應的分岔圖、λ-K(c)圖和0-1測試圖檢驗了方法的有效性。結果顯示:分岔圖和λ-K(c)圖所反映系統(tǒng)的狀態(tài)相一致,周期、弱混沌和強混沌序列的p-q軌跡圖、n-Mc(n)和c-K(c)散點圖存在明顯的差異性,其中周期序列K(c)值趨于0,完全混沌序列的K(c)值趨于1,而弱混沌序列K(c)值介于0與1之間,說明0-1測試法能有效識別序列的混沌狀態(tài)。(2)數(shù)據(jù)長度對0-1測試法的影響分析。選取Verhulst種群模型生成的五組不同狀態(tài)的離散序列為研究對象,分析了不同數(shù)據(jù)長度N對0-1測試法的影響。研究發(fā)現(xiàn):隨著數(shù)據(jù)長度N的不斷增加,周期序列K(c)值基本保持在0附近;弱混沌序列K(c)值緩慢增加,而強混沌序列的K(c)值迅速趨近于1。因此,可通過改變數(shù)據(jù)長度獲得K(c)值的變化趨勢及速率來區(qū)分序列混沌程度。(3)噪聲對0-1測試法的影響分析。對三組不同性質的Verhulst序列(周期、弱混沌、強混沌)添加含噪水平為5%的正態(tài)白噪聲后,對應的K(c)值和0-1測試圖變化不大,表明0-1測試法具有一定的抗噪性。(4)振幅α對0-1測試法的影響分析。選取三種不同性質的Verhulst序列,探究了 0-1測試算法中振幅α對混沌識別的影響。隨著振幅α從0不斷增加到6,弱混沌序列K(c)值對振幅α最敏感,K(c)值下降最快,其次分別是強混沌序列和周期序列,當振幅α在區(qū)間[0,6]上時,序列的α-K(c)圖可以很好的區(qū)分序列的混沌程度。(5) 0-1測試法和最大Lyapunov指數(shù)法在地質中的應用分析。以山東上莊金礦成礦元素序列為例,運用0-1測試法,分析成礦元素含量序列的混沌特征,并與最大Lyapunov指數(shù)法比較。結果顯示:成礦元素Au、Hg、Cu、Pb、Zn含量序列具有不同程度的的混沌特征,而As、Sb和Ag序列不具有混沌性,且兩種方法混沌識別的結果基本一致,其中Au元素序列具有強混沌性,有利于其成礦。
[Abstract]:The 0-1 test method is a new method to judge whether the discrete sequence is chaotic or not by whether the output value K _ (C) approaches 1 or 0. Firstly, the discrete sequence generated by Verhulst population model is taken as the research object to verify the validity of the 0-1 test method. The effects of different data lengths N and amplitude 偽 and normal white noise on the chaotic test results in 0-1 test algorithm are analyzed. The 0-1 test method and the traditional maximum Lyapunov exponent method are applied to the chaotic identification of ore-forming element sequences in Shangzhuang Gold Mine, Shandong Province, and the chaotic characteristics of multiple ore-forming chemical element sequences are identified. The main results of this paper are as follows: 1) validity test of 0-1 test method. The discrete sequence generated by Verhulst population model is taken as the object of study. The validity of the method is verified by obtaining the corresponding bifurcation diagram, 位 -Knc) graph and 0-1 test graph. The results show that the state of the system reflected by the bifurcation diagram and 位 -Knc) diagram is consistent, and there are obvious differences between the periodic, p-q locus diagrams of weak chaotic and strong chaotic sequences and c-Knc) scattered plot. The value of periodic sequence Knc) tends to 0, the value of complete chaotic sequence tends to 1, and the value of weak chaotic sequence Knc is between 0 and 1, which indicates that the 0-1 test method can effectively identify the chaotic state of the sequence. The effect of the data length on the 0-1 test method is analyzed. Five groups of discrete sequences of different states generated by Verhulst population model were selected as research objects, and the effects of different data lengths N on 0-1 test method were analyzed. It is found that with the increasing of data length N, the value of periodic sequence K _ (C) remains around zero, the value of weak chaotic sequence (K _ (C) increases slowly, and the value of strong chaotic sequence (K _ (C) rapidly approaches to (1). Therefore, the effect of noise on 0-1 test method can be distinguished by changing the change trend and rate of data length. For three groups of Verhulst sequences with different properties (periodic, weak chaos, strong chaos) with normal white noise with noise level of 5%, the corresponding values of Ku _ c and 0-1 test diagram have little change. It is shown that the 0-1 test method has a certain anti-noise-resistance. The effect of amplitude 偽 on the 0-1 test method is analyzed. Three kinds of Verhulst sequences with different properties are selected to investigate the effect of amplitude 偽 on chaos recognition in 0-1 test algorithm. With the increase of amplitude 偽 from 0 to 6, the value of weak chaotic sequence K _ (C) is the most sensitive to amplitude 偽, followed by strong chaotic sequence and periodic sequence, respectively, when amplitude 偽 is in the interval [0 ~ 6]. The 偽 -Knc) diagram of the sequence can well distinguish the chaotic degree of the sequence. The 0-1 test method and the maximum Lyapunov exponent method can be applied to the analysis of geology. Taking the metallogenic element sequence of Shangzhuang gold deposit in Shandong as an example, the chaotic characteristics of the metallogenic element content series are analyzed by using 0-1 test method, and compared with the maximum Lyapunov exponent method. The results show that the sequence of the content of au HgCU / Pb / Zn has different degree of chaos, while the sequences of As-Sb and Ag are not chaotic, and the results of the two methods are basically consistent, among which the sequence of au has strong chaos. In favor of its mineralization.
【學位授予單位】：廣州大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：P611;O415.5

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