基于去滑動(dòng)均值趨勢(shì)的多重分形方法及其應(yīng)用研究
發(fā)布時(shí)間：2018-10-22 12:34
【摘要】：多重分形是定義在分形結(jié)構(gòu)上的有無(wú)窮多個(gè)標(biāo)度指數(shù)所組成的一個(gè)集合,是描述不同的局域條件、或在演化過程中不同層次所導(dǎo)致的特殊的結(jié)構(gòu)行為與特征。由于地質(zhì)作用過程的長(zhǎng)期性和多期性,礦化過程往往呈多期次重復(fù)性成礦,這種多次礦化疊加使得元素空間分布的結(jié)構(gòu)具有嵌套結(jié)構(gòu),導(dǎo)致各種地球化學(xué)元素在地質(zhì)體中逐步富集或貧化,反映出地球化學(xué)元素在巖石等介質(zhì)中的分布具有非均質(zhì)性和奇異性,因此,適合用多重分形方法研究。去滑動(dòng)均值趨勢(shì)多重分形方法(MFDMA)是運(yùn)用滑動(dòng)窗技術(shù)研究分形序列多重分形特征的一種有效方法,已在生物醫(yī)學(xué)、經(jīng)濟(jì)學(xué)、計(jì)算機(jī)科學(xué)等領(lǐng)域中應(yīng)用廣泛。本文首先通過典型二項(xiàng)重分形模型研究數(shù)據(jù)容量、位置參數(shù)對(duì)去滑動(dòng)均值趨勢(shì)多重分形方法(MFDMA)的影響;其次,對(duì)比分析了去滑動(dòng)均值趨勢(shì)多重分形方法與去趨勢(shì)波動(dòng)多重分形方法(MFDFA)在不同噪聲情況下的分形特征,并對(duì)得到的Hurst指數(shù)進(jìn)行敏感性分析;最后,運(yùn)用去滑動(dòng)均值趨勢(shì)多重分形方法(MFDMA)研究上莊次生暈成礦元素的奇異性特征。主要結(jié)果如下:(1)分析位置參數(shù)對(duì)MFDMA算法結(jié)果的影響。選取MFDMA算法位置分別參數(shù)為0、0.5、1,分析Hurst指數(shù)與理論值的差異程度。結(jié)果顯示:在位置參數(shù)為0時(shí),MFDMA算法計(jì)算的Hurst指數(shù)曲線趨于理論值的效果最好,均方根誤差最小。(2)分析數(shù)據(jù)容量對(duì)MFDMA算法結(jié)果的影響。分別選取二項(xiàng)重分形序列中數(shù)據(jù)容量N為256、512、1024的三組數(shù)據(jù),分析數(shù)據(jù)容量N對(duì)MFDMA方法的影響。結(jié)果顯示:隨著數(shù)據(jù)容量的增大,運(yùn)用MFDMA計(jì)算的Hurst指數(shù)曲線快速逼近至理論值曲線,均方根誤差逐漸減小,表明數(shù)據(jù)容量越大計(jì)算結(jié)果的精度越高。(3)分析噪聲對(duì)MFDMA算法結(jié)果的影響。通過二項(xiàng)重分形模型添加高斯噪聲、白噪聲和尖峰噪聲,分析噪聲及強(qiáng)度對(duì)MFDMA計(jì)算Hurst估計(jì)值的影響,并與MFDFA進(jìn)行對(duì)比。結(jié)果顯示:高斯噪聲、白噪聲強(qiáng)度的增強(qiáng)對(duì)MFDMA有干擾作用,其中隨著二項(xiàng)重分形模型參數(shù)增大,噪聲的影響減少,抗噪能力增強(qiáng);而MFDFA分辨噪聲數(shù)據(jù)的能力較弱,容易受到噪聲及其強(qiáng)度的影響;此外,尖峰噪聲容易干擾MFDMA與MFDFA方法的分析結(jié)果,利用小波降噪法分析消除尖峰噪聲后發(fā)現(xiàn),降噪后的MFDMA方法Hurst指數(shù)估計(jì)值均方根誤差普遍低于降噪前的均方根誤差,因此,MFDMA相較于MFDFA具有更強(qiáng)的穩(wěn)健性。(4)運(yùn)用MFDMA算法分析山東上莊金礦成礦元素含量序列的多重分形特征。結(jié)果顯示:Cu和Au的多重分形特征最明顯,元素Hg、Zn、Pb次之,元素Ag、As、Sb最弱,其多重分形譜的形態(tài)差異可為礦化強(qiáng)度的識(shí)別提供依據(jù)。
[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.
【學(xué)位授予單位】：廣州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O189
本文編號(hào)：2287172
[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.
【學(xué)位授予單位】：廣州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O189
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