基于0-1测试法的混沌识别及其在地质中的应用

发布时间：2018-06-16 17:25

本文选题：混沌识别 + 0-1测试法　；参考：《广州大学》2017年硕士论文

【摘要】：0-1测试法是通过输出值K(c)是否趋近于1或0来判断离散序列是否具有混沌性的一种新方法。首先以Verhulst种群模型生成的离散序列为研究对象,验证了 0-1测试法的有效性;其次,分析了 0-1测试算法中不同数据长度N和振幅α及添加正态白噪声后对混沌测试效果的影响;最后,将0-1测试法和传统的最大Lyapunov指数法应用于山东上庄金矿成矿元素序列的混沌识别中,识别了多成矿化学元素序列的混沌特征。本文的主要研究结果如下:(1) 0-1测试法有效性检验。以Verhulst种群模型生成的离散序列为研究对象,通过得到对应的分岔图、λ-K(c)图和0-1测试图检验了方法的有效性。结果显示:分岔图和λ-K(c)图所反映系统的状态相一致,周期、弱混沌和强混沌序列的p-q轨迹图、n-Mc(n)和c-K(c)散点图存在明显的差异性,其中周期序列K(c)值趋于0,完全混沌序列的K(c)值趋于1,而弱混沌序列K(c)值介于0与1之间,说明0-1测试法能有效识别序列的混沌状态。(2)数据长度对0-1测试法的影响分析。选取Verhulst种群模型生成的五组不同状态的离散序列为研究对象,分析了不同数据长度N对0-1测试法的影响。研究发现:随着数据长度N的不断增加,周期序列K(c)值基本保持在0附近;弱混沌序列K(c)值缓慢增加,而强混沌序列的K(c)值迅速趋近于1。因此,可通过改变数据长度获得K(c)值的变化趋势及速率来区分序列混沌程度。(3)噪声对0-1测试法的影响分析。对三组不同性质的Verhulst序列(周期、弱混沌、强混沌)添加含噪水平为5%的正态白噪声后,对应的K(c)值和0-1测试图变化不大,表明0-1测试法具有一定的抗噪性。(4)振幅α对0-1测试法的影响分析。选取三种不同性质的Verhulst序列,探究了 0-1测试算法中振幅α对混沌识别的影响。随着振幅α从0不断增加到6,弱混沌序列K(c)值对振幅α最敏感,K(c)值下降最快,其次分别是强混沌序列和周期序列,当振幅α在区间[0,6]上时,序列的α-K(c)图可以很好的区分序列的混沌程度。(5) 0-1测试法和最大Lyapunov指数法在地质中的应用分析。以山东上庄金矿成矿元素序列为例,运用0-1测试法,分析成矿元素含量序列的混沌特征,并与最大Lyapunov指数法比较。结果显示:成矿元素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,且两种方法混沌识别的结果基本一致,其中Au元素序列具有强混沌性,有利于其成矿。
[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 伪 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 伪 on the 0-1 test method is analyzed. Three kinds of Verhulst sequences with different properties are selected to investigate the effect of amplitude 伪 on chaos recognition in 0-1 test algorithm. With the increase of amplitude 伪 from 0 to 6, the value of weak chaotic sequence K _ (C) is the most sensitive to amplitude 伪, followed by strong chaotic sequence and periodic sequence, respectively, when amplitude 伪 is in the interval [0 ~ 6]. The 伪 -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.
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P611;O415.5

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