# An Online Detection Method for Coal Dry Screening Based on Image Processing and Fractal Analysis
## 1 Introduction  
Coal accounts for \(\sim\)30% of the world's energy resources [1]. In 2019, China produced 3.85 billion tons of raw coal, which increased by 4.0% year on year and accounted for 47.3% of global production [2]. Intelligent coal production is currently a major direction, and dry screening is the primary method in the field of coal screening. Therefore, the detection of coal dry screening in real-time has always been a significant challenge in its field. Currently, there is little research on real-time monitoring methods for coal dry screening. [PERSON] [3] developed a new online automatic optical inspection system (OAOIS) applying digital image processing to measure the coarse particle size distribution. [PERSON] [4] demonstrated the inconsistencies of length-based separation by mechanical sieving using standard sieves and developed a user-coded Java ImageJ plugin based on determining distinct lengths of all particles to analyse particle size distribution (PSD) and determine various PSD parameters. [PERSON] [5] determined the particle size distribution (PSD) of various coal particles (hard coal and lignite) produced by two mills (ball and Gy-Ro mill) using a novel size-analysis technique, namely 3D dynamic image analysis (DIA). [PERSON] [6] designed a machine vision system to predict the ash content of fine cleaned coal products based on image processing. [PERSON] [7] proposed a new effective and precise method for converting coarse aggregates' size-based distribution into a cumulative mass percentage. [PERSON] [8] established and enhanced the mass model of coarse coal particles, together with testing the results of adopting image analysis. Furthermore, [PERSON] [9] described a fast and reliable analysis of LiDAR point-cloud data containing surface scans of aggregate piles/masses using their algorithm. Moreover, [PERSON] [10] proposed a new method to evaluate the angularity of surface aggregates based on 3D point-cloud images. [PERSON] [11] proposed a digital image-processing-based online detection system for coarse aggregateparticle size and grain shape measurements (DIP). Additionally, [PERSON] [12] developed a full scan inspection system with optical line scan technology for particle size analysis using digital image processing. These approaches have made many efforts to develop image-processing methods for clear-boundary particles; in spite of that, these methods have high requirements, including light sources and particle spacing, which are not suitable for industrial production. In coal dry screening, it is arduous to use the previously mentioned methods because it is impossible to test the screening efficiency of a vibrating screen before the final product, because it is time-consuming and labour-consuming, and the above technology cannot measure the PSD of the coal heap. On the other hand, the fractal dimension can describe the granularity of the powder and aggregates. Besides, [PERSON] [13] developed BiVO4 microspheres with fractal granularity using a simple surfactant-assisted hydrothermal method and utilized them as promising anode materials for Li-ion batteries (LIBs). In addition, [PERSON] [14] investigated the size distribution and fractal characteristics of coal pores through nuclear magnetic resonance cryoporometry, which relates the fractal characteristics and size distribution of coal. Apart from that, [PERSON] [15] derived new analytical expressions for the fractal dimension, the cumulative probability of size, and the mass distributions for particles. [PERSON] [16] introduced the concept of fuzzy fractal dimension and demonstrated its role in analysing the granular properties of data. He also proposed a power law of information granularity in the context of fuzzy modelling. Furthermore, coal-screening efficiency is related to the fractal dimension. In this study, we developed a fractal method to indirectly describe coal-screening efficiency and coal particle size distribution on the basis of image processing.