Study of Atmospheric Particulates’ Fractal Feature Based on Fractal Combined with Bior 3.7 Wavelet

Abstract

A method based on fractal combined with Bior 3.7 wavelet is proposed to analyze atmospheric particulates’ fractal feature. By the use of microscope, atmospheric particulate samples were taken into digital images. After a series of image processing including Bior 3.7 wavelet decomposition and reconstruction, and fractal-dimension calculation. Results indicate that: There is a inverse relation between particulates’ fractal dimension and grain size. Larger the fractal dimension of particulate is, the higher content of fine particulate matter it will have; Smaller the particulate’s fractal dimension is, greater its degree of sphericility is and smaller its specific surface area is; To a higher level’s detail signal of atmospheric particulates, the fractal dimension of this detail signal turns small. What’s more, the H signal, V signal and D signal are the same as atmospheric particulates’ detail signal. So, higher level’s detail signal of atmospheric particulates includes more large diameter particles Introduction Fractal has five basic characteristics: self-similarity, the tractability of structure, the irregularity of form, the iteration of generation, and the non-integer of dimension. Because of the shape of environmental system is irregular and has the characteristic of random variation, the fractal theory is applied in the study on the particulate matters in recent years. YANG Jing .etc analyzed and studied the fractal characteristics of coal dust, and determined the relationship between the fractal dimension and the average grain size based on the laser grain size tester With MIP mercury intrusion test, HAN Ping .etc calculated and compared the fractal dimensions of cement-based materials in different shapes under different stress. XIE Xianjian .etc studied the fractal dimension variation characteristics of waterstable aqqreqate under different eucalyptus grandis plantations, and analyzed the relationship between fractal dimension and soil properties. The above researches discussed fractal characteristics for single particle, and seldom further analyzed image information. There is a profound intrinsic relationship between fractal geometry and wavelet transform, so the microscopic image’ fractal feature of atmospheric particulates collected from mainly related areas of Huangdao district is analyzed with the use of Bior 3.7 wavelet. The Experimental Results and Discussion Based on Matlab 7.0 environment, firstly the particulate matter digital image collected through a microscope was read into a tow-dimensional array; Secondly the image was grayed, and was decomposed into three levels by the use of Bior 3.7, then its detail signals were collected; Finally the detail signal’s fractal dimension was calculated. 9 particulate samples are kitchen dust, road dust, biological incineration particulates, sea salt, coal dust, automobile exhaust, lime, cement, and soil. Their feature dimension and three levels’ feature dimension are shown in Table 1. 9 samples’ physical information (grain size, degree of sphericility, and specific surface area) is shown in Table 2. The detail signals’ fractal dimensions are International Conference on Intelligent Systems Research and Mechatronics Engineering (ISRME 2015) © 2015. The authors Published by Atlantis Press 2107 shown in Table 3. In Table 3, H1: the first-level horizontal detail signal, V1: the first-level vertical detail signal, D1: the first-level diagonal detail signal; H2: the second-level horizontal detail signal, V2: the second-level vertical detail signal, D2: the second-level diagonal detail signal; H3: the third-level horizontal detail signal, V3: the third-level vertical detail signal, D3: the third-level diagonal detail signal. Table 1 fractal dimension of particulate matter Fractal dimension Fractal dimension of detail signal First level Second level Third level Coal dust 2.1271 2.0967 2.0935 2.0809 Kitchen dust 2.1574 2.1330 2.1193 2.1043 Sea salt 2.3026 2.2193 2.2051 2.1846 Automobile exhaust 2.1959 2.1532 2.1275 2.1154 Biological incineration particulates 2.1400 2.1249 2.0839 2.0721 Lime 2.2004 2.1492 2.1328 2.1185 Cement 2.1210 2.1064 2.0665 2.0550 Soil 2.0935 2.0784 2.0716 2.0427 Road dust 2.0523 2.0605 2.0477 2.0390 Table 2 physical information of particulate matter Grain size (μm) Degree of sphericility Specific surface area ( 2 / cm g) Coal dust 8.5 0.850 267.119 Kitchen dust 6.9 0.829 275.907 Sea salt 3.8 0.803 883.541 Automobile exhaust 4.6 0.820 431.060 Biological incineration particulates 7.7 0.849 275.868 Lime 4.0 0.819 521.030 Cement 9.6 0.851 251.497 Soil 10.1 0.886 238.094 Road dust 36.2 0.925 64.850 Table 3 fractal dimension of particulate matte’s detail signal Fractal dimension H1 V1 D1 H2 V2 D2 H3 V3 D3 Coal dust 2.0905 2.0996 2. 1001 2.0873 2.0940 2. 0991 2.0881 2.0849 2.0697 Kitchen dust 2.1320 2.1306 2.1364 2.1013 2.1291 2.1276 2.1006 2.1211 2.0904 Sea salt 2.2122 2.2443 2.2015 2. 2068 2.2110 2.1976 2. 1734 2.2022 2.1447 Automobile exhaust 2.1445 2.1778 2.1373 2.1243 2.1283 2.1300 2.1177 2.1242 2.1001 Biological incineration particulates 2.1304 2.1476 2.0968 2. 0800 2.0956 2.0762 2. 0656 2.0744 2.0717 Lime 2.1375 2.1814 2.1286 2.1311 2.1476 2.1198 2.1282 2.1356 2. 0887 Cement 2.1127 2.1259 2.0805 2.0681 2.0654 2.0660 2.0541 2.0499 2.0609 Soil 2.0722 2.0831 2.0800 2.0700 2.0747 2.0702 2.0355 2.0545 2.0381 Road dust 2.0646 2.0638 2.0532 2.0420 2.0486 2.0524 2.0330 2.0454 2.0385