基于去滑动均值趋势的多重分形方法及其应用研究

发布时间：2018-10-22 12:34

【摘要】：多重分形是定义在分形结构上的有无穷多个标度指数所组成的一个集合,是描述不同的局域条件、或在演化过程中不同层次所导致的特殊的结构行为与特征。由于地质作用过程的长期性和多期性,矿化过程往往呈多期次重复性成矿,这种多次矿化叠加使得元素空间分布的结构具有嵌套结构,导致各种地球化学元素在地质体中逐步富集或贫化,反映出地球化学元素在岩石等介质中的分布具有非均质性和奇异性,因此,适合用多重分形方法研究。去滑动均值趋势多重分形方法(MFDMA)是运用滑动窗技术研究分形序列多重分形特征的一种有效方法,已在生物医学、经济学、计算机科学等领域中应用广泛。本文首先通过典型二项重分形模型研究数据容量、位置参数对去滑动均值趋势多重分形方法(MFDMA)的影响;其次,对比分析了去滑动均值趋势多重分形方法与去趋势波动多重分形方法(MFDFA)在不同噪声情况下的分形特征,并对得到的Hurst指数进行敏感性分析;最后,运用去滑动均值趋势多重分形方法(MFDMA)研究上庄次生晕成矿元素的奇异性特征。主要结果如下:(1)分析位置参数对MFDMA算法结果的影响。选取MFDMA算法位置分别参数为0、0.5、1,分析Hurst指数与理论值的差异程度。结果显示:在位置参数为0时,MFDMA算法计算的Hurst指数曲线趋于理论值的效果最好,均方根误差最小。(2)分析数据容量对MFDMA算法结果的影响。分别选取二项重分形序列中数据容量N为256、512、1024的三组数据,分析数据容量N对MFDMA方法的影响。结果显示:随着数据容量的增大,运用MFDMA计算的Hurst指数曲线快速逼近至理论值曲线,均方根误差逐渐减小,表明数据容量越大计算结果的精度越高。(3)分析噪声对MFDMA算法结果的影响。通过二项重分形模型添加高斯噪声、白噪声和尖峰噪声,分析噪声及强度对MFDMA计算Hurst估计值的影响,并与MFDFA进行对比。结果显示:高斯噪声、白噪声强度的增强对MFDMA有干扰作用,其中随着二项重分形模型参数增大,噪声的影响减少,抗噪能力增强;而MFDFA分辨噪声数据的能力较弱,容易受到噪声及其强度的影响;此外,尖峰噪声容易干扰MFDMA与MFDFA方法的分析结果,利用小波降噪法分析消除尖峰噪声后发现,降噪后的MFDMA方法Hurst指数估计值均方根误差普遍低于降噪前的均方根误差,因此,MFDMA相较于MFDFA具有更强的稳健性。(4)运用MFDMA算法分析山东上庄金矿成矿元素含量序列的多重分形特征。结果显示:Cu和Au的多重分形特征最明显,元素Hg、Zn、Pb次之,元素Ag、As、Sb最弱,其多重分形谱的形态差异可为矿化强度的识别提供依据。
[Abstract]:Multifractal is a set of infinitely many scale exponents defined on the fractal structure. It describes different local conditions or special structural behaviors and characteristics caused by different levels in the evolution process. Because of the long-term and multi-period characteristics of geological processes, the mineralization process often presents multiple repeated mineralization, which makes the structure of the spatial distribution of elements have nested structure. As a result of the gradual enrichment or dilution of various geochemical elements in geological bodies, the distribution of geochemical elements in rocks and other media is characterized by heterogeneity and singularity. Therefore, it is suitable to study by multifractal method. (MFDMA) is an effective method to study multifractal features of fractal sequences using sliding window technique. It has been widely used in biomedicine, economics, computer science and other fields. In this paper, we first study the effect of data capacity and position parameters on the multifractal method (MFDMA), which is based on the typical binomial multifractal model. The fractal characteristics of moving mean trend multifractal method (MFDFA) and de-trend fluctuation multifractal method (MFDFA) under different noise conditions are compared and analyzed. Finally, the sensitivity of the obtained Hurst exponents is analyzed. The singularity of ore-forming elements of secondary halo in Shangzhuang is studied by using the multifractal method of de-sliding mean trend (MFDMA). The main results are as follows: (1) the influence of location parameters on the results of MFDMA algorithm is analyzed. The position parameter of MFDMA algorithm is 0 / 0. 5 / 1, and the difference between Hurst exponent and theoretical value is analyzed. The results show that when the position parameter is 0, the Hurst exponent curve calculated by MFDMA algorithm is the best, and the root mean square error is the smallest. (2) the influence of data capacity on the result of MFDMA algorithm is analyzed. Three groups of data with data capacity N of 256 ~ 5121024 in binomial multifractal sequence were selected, and the influence of data capacity N on MFDMA method was analyzed. The results show that with the increase of data capacity, the Hurst exponent curve calculated by MFDMA is fast approaching to the theoretical value curve, and the root mean square error decreases gradually. It shows that the higher the data capacity, the higher the accuracy of the calculation results. (3) the influence of noise on the results of MFDMA algorithm is analyzed. By adding Gao Si noise, white noise and peak noise into binomial multifractal model, the influence of noise and intensity on Hurst estimation calculated by MFDMA is analyzed and compared with MFDFA. The results show that the enhancement of Gao Si noise and white noise intensity can interfere with MFDMA. With the increase of binomial multifractal model parameters, the effect of noise decreases and the anti-noise ability increases, while the ability of MFDFA to distinguish noise data is weak. In addition, the peak noise easily interferes with the analysis results of MFDMA and MFDFA methods, and the wavelet denoising method is used to eliminate the peak noise. The root mean square (RMS) error of Hurst exponent estimation of MFDMA method after denoising is generally lower than that of RMS before denoising. Therefore, MFDMA is more robust than MFDFA. (4) the multifractal characteristics of ore-forming element content series of Shangzhuang Gold Mine in Shandong Province are analyzed by MFDMA algorithm. The results show that the multifractal characteristics of Cu and Au are the most obvious, the element Hg,Zn,Pb is the second, and the element Ag,As,Sb is the weakest. The morphological difference of the multifractal spectrum can provide the basis for the recognition of mineralization intensity.
【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】：O189

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