# An Online Detection Method for Coal Dry Screening Based on Image Processing and Fractal Analysis
## 4 Results and Discussion
### The Relation between Fractal Dimension and Screening Efficiency  
In the practical coal-screening process, the size fraction is dissimilar because of the divergent production and excavation situations. In this study, the coal particle size fraction shown in Table 1 is fabricated for representative purposes. In this paper, the screening efficiency is used to evaluate the screening performance and is given by Equation (17), correspondingly [22; 23]  
\[\eta=\frac{(\alpha-\theta)(\beta-\alpha)\times 100}{\alpha(\beta-\theta)(100- \alpha)}\times 100\% \tag{17}\]  
where \(\eta\) is the screening efficiency (%), \(\alpha\) is the content of fine particles in feed (%), \(\beta\) is the content of fine particles in the undersized product (%), and \(\theta\) is the content of fine particles in the oversized product (%). For the purpose of studying the possibility of the fractal method, the relationship between the image fractal dimension and screening efficiency is revealed. Multiple groups of images screened with differing efficiencies serve as proxies for more precise fractal dimensions. Figure 9 demonstrates images of coal under different screening efficiencies and edge images after image processing. As the screening efficiency increases, the proportion of fine particles in the sieve decreases, while the proportion of large particles increases dramatically. The form of the edge image is that the proportion of large-particle coal is increasing. Additionally, the complexity of the graphic outline is simplified. Because the fractal dimension is the same at different scales or different heights, the fractal dimension changes with the complexity of the edge image. Hence, the fractal dimension can be adopted as an indicator of coal particle size distribution and can be employed as a measure of \begin{table}
\begin{tabular}{c c c c c c} \hline Size (mm) & 1–3 & 3–6 & 6–13 & 13–25 & 25–50 \\ \hline Weight (kg) & 4 & 5 & 4 & 3 & 2 \\ \hline Wt (\%) & 22.2\% & 27.8\% & 22.2\% & 16.7\% & 11.1\% \\ \hline \end{tabular}
\end{table} 
Table 1: Coal particle size fraction before screening. Figure 8: Images of different coal particle sizes. screening efficiency on the side. Due to coal accumulation, varying light-source conditions, the uneven height of coal on the conveyor belt, and other factors, it is challenging to measure the precise particle size distribution of coal on site using the method described in the literature. In addition, in the field situation, the measurement of the particle size distribution is of little significance, but it is significant to detect the working status and efficiency of the vibrating screen in real time. Figure 9: _Cont._  
Figure 9: \(Cont.\)  
For the weighted mean of the fractal dimension, multiple groups of coal-edge images are produced. Figure 10 indicates that as the screening efficiency increases, the fractal dimension of coal gradually decreases in a similar linear manner, and the slope ratio at the beginning and the end of the curve is lower than the slope in the middle part. In general, the fractal dimension of a two-dimensional edge image is between 2 and 3, so when it approaches 2 or 3, the curve will become smooth. When the fractal dimension is closer to the median of 2 and 3, it will be simpler to distinguish. Different fractal dimensions of the edge image are caused by the presence of small particles on the sieve following sieving. To a certain extent, the fractal dimension can show the proportion of small particles on the sieve. The larger the fractal dimension is, the smaller the particles are on the sieve. When the screening efficiency reaches 100%, the fractal dimension becomes 2.5454. With the decrease in the screening efficiency, the nearly linear change in the fractal dimension reaches 2.6223. Due to the fact that the fractal dimension decreases monotonically with the screening efficiency, which is indicative of good discrimination, it is possible to predict the screening efficiency based on the coal-edge fractal dimension.