Extraction of Coal and Gangue Geometric Features with Multifractal Detrending Fluctuation Analysis
Abstract
:1. Introduction
- Read digital image obtained from the camera by computers.
- Determine the identification characteristics of coal and gangue.
- Find gangue materials based on the identification algorithms.
- Determine the size and the location of gangue, and then convert these information to the control signals of high pressure air nozzle.
2. Preliminaries
2.1. Hurst Parameter, ACF, LRD, FD
2.2. fBm
3. MFDFA Algorithm
- Transform original data into mean-reduced cumulative sums,
- Divide time series into non-overlapping segments of equal length s, starting from the beginning. Since the length N of the series is often not a multiple of the considered time scale s, to not miss any data, another set of segments starting from the end of data is made. As a result, segments are obtained covering the whole dataset.
- Calculate the local trend for each of the segments by a least-square fit of the series.
- Calculate the mean square error for the estimate of each segment k of length s.
- Average all segments to obtain the qth order variance (or fluctuation) function for each size s:
- Repeat Steps (2)–(5) for different s evaluating new sets of variances .
- Plot for each q in log–log scale and estimate the linear fit with least squares. If slope varies with q, multifractality is suspected. Single slope shows monofractal scaling.
- Calculate multifractal exponent as
- Use Legendre transform to evaluate the q-order singularity–Hölder exponent and corresponding dimension :
4. Applying MFDFA to the Outline of Coal and Gangue
5. Pattern Recognition Methods and Discussions
5.1. Grayscale and Texture Features of the Image
5.2. Discussions
6. Conclusions
Author Contributions
Conflicts of Interest
References
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Liu, K.; Zhang, X.; Chen, Y. Extraction of Coal and Gangue Geometric Features with Multifractal Detrending Fluctuation Analysis. Appl. Sci. 2018, 8, 463. https://doi.org/10.3390/app8030463
Liu K, Zhang X, Chen Y. Extraction of Coal and Gangue Geometric Features with Multifractal Detrending Fluctuation Analysis. Applied Sciences. 2018; 8(3):463. https://doi.org/10.3390/app8030463
Chicago/Turabian StyleLiu, Kai, Xi Zhang, and YangQuan Chen. 2018. "Extraction of Coal and Gangue Geometric Features with Multifractal Detrending Fluctuation Analysis" Applied Sciences 8, no. 3: 463. https://doi.org/10.3390/app8030463