**1. Introduction**

Macerals of coking coal closely relate to its characteristics, such as coke ability, caking ability, and thermal crushing performance, which directly influence the optical texture component distribution and quality of the coke [1–3]. Automatic classification and identification of different macerals in coal are of great significance for the effective evaluation of coal process properties [4]. Inertinite is one of the main groups in coal, and the classification of its macerals is of theoretical significance and application value for the efficient cleaning utilization of coal.

In view of the computational complexity, and the heavy workload, along with the subjective factors of the conventional manual and semi-manual method for maceral analysis, the methods of image processing and pattern recognition have been employed to analyze the components in coal [5,6]. Besides, based on the advantages of data analysis and processing, the machine learning approach is widely used in various fields [7]. Edward Lester [8] developed an image analysis technique to separate the major maceral groups of liptinite, vitrinite, fusinite, and semi-fusinite from the background resin according to the gray scales of the surface images captured with suitable camera exposure times. Nonetheless, even though the foregoing technique can work in some situations, it has not been implemented for a deep identification of macerals. There exists a fact that the characteristics of shape, color, contour, and texture of the microscopic image are essential for information expression of macerals in coal. Some related references have been published. To name a few, the authors of [9] completed the

detection of approximately circular particles in the microscopic image of coal by the contour features, and the authors of [10] proposed a method to extract the outline of the maceral area by using structural elements. The texture features of local binary patterns (LBP) and the gray level co-occurrence matrix (GLCM) were combined to identify three major groups in coal macerals [11]. Grey scale, GLCM, Tamura, contourlet transform, and supervised locality preserving projections methods were employed by the authors in the previous work [12–15] to describe features of macerals. However, because the complex construction of macerals and similar morphological features among some different macerals exist, these techniques may not characterize them perfectly, especially for the features of texture.

In recent years, the fractal theory, first coined in [16], has been rapidly developed as a powerful analytical tool, which can reflect the heterogeneity and irregularities of a physical surface. There are several published techniques for characterizing the surface irregularity of coal with the mono-fractal method [17–21]. Nevertheless, it can not provide a comprehensive and accurate description of the details of image changes at different scales owing to the single scale of fractal dimensions. Coal's surface is known to be non-stationary and heterogeneous as a consequence of the long-term and multi-stage effects of geological processes. Some local trends in texture and dramatic changes in gray value are universal in microscopic images of macerals. Fortunately, a method named multifractal detrended fluctuation analysis (MF-DFA) can quickly eliminate local trends [22], making itself more suitable for describing the texture characteristics of the microscopic images of macerals. Given the superiority in solving non-stationary problems, the MF-DFA method has applications in quite a few fields [23–26]. Nevertheless, it was the first attempt that the approach was applied for the purpose of the classification of macerals in coal.

The major goal of our work was to find an artificial intelligence method to distinguish eight groups of inertinite macerals with few but stable and effective texture features. We analyzed and verified the multifractal properties of inertinite macerals by the method of MF-DFA. Additionally, multifractal descriptors of microscopic images were proposed based on the multifractal spectrum. In order to demonstrate the effectiveness of the multifractal descriptors, a comparison experiment of stability was implemented. Finally, we built an automatic classification model with support vector machine (SVM) to identify the inertinite macerals.

### **2. Materials**

According to International Commission for Coal Petrology (ICCP) standard, coal is classified across three main maceral groups; i.e. vitrinite, liptinite, and inertinite [27]. Macerals of inertinite mainly come from woody fiber of plant or fungus [28]. The plant cellular structure of fusinite is relatively complete, and some of them have clear intercellular space and cellular wall. The cells of the pyrofusinite are crushed and shattered to present the shape of "arc" or "star-like", while the oxyfusinite has an unbroken cellular structure that exhibits a sieve shape. Semifusinite, the transitional maceral between telinite and fusinite, is located in the form of irregular strips. Secretinite is generally a product of silk carbonization reaction of secretions (tannin, resin, etc.), and few of them are derived from gelation of humus coal. Besides, the microscopic images are irregularly elliptical. Funginite is mainly derived from the remains of fungi or the secretions of higher plants, and has a honeycomb-like or reticulated multicellular structure inside. Additionally, the outer shape is flattened circular or ring-shaped due to extrusion. The cellular structure of the macrinite has a high protrusion and is generally an irregular matrix. A fragment of the inertinite group of particles have a particle size of less than 30 μm, angular or irregular in shape, and has no generally cellular structure. Most of the micrinites are distributed in asphaltene or mineral asphaltene with minor particle size and often small, nearly circular particles. Note that for fusinite, the two sub-macerals named pyrofusinite and oxyfusinite will be analyzed together with other six types of macerals in our work, as the texture differences are significant and obvious.

From Figure 1, we can observe that there are some morphological differences among different macerals of inertinite in coal. However, their textures are fairly clear with singularity and conspicuous self-similarity. For such non-stationary structures, MF-DFA analysis can characterize them more effectively and show better processing power. In view of this, this paper performed the method of MF-DFA on each maceral image. For implementation, we used inertinite image data with 60 grayscale microscopic images of 227 × 227 pixels in size per group. The size was chosen to ensure that each image contained only one specific component, which is beneficial for subsequent feature extraction and classification experiments.

**Figure 1.** Typical microscopic images of inertinite in coal. (**a**) Pyrofusinite; (**b**) oxyfusinite; (**c**) semifusinit; (**d**) secretinite; (**e**) funginite; (**f**) macrinite; (**g**) inertodetrinite; (**h**) micirinite.
