Longwall Face Automation: Coal Seam Floor Cutting Path Planning Based on Multiple Hierarchical Clustering

Abstract

Space adaptability between mining equipment and coal-rock mass, to ensure the machines cut in a coal seam, is an importance technique in longwall mining automation. In order to guide the mining equipment cutting in the coal seam, a cutting path planning method based on multiple hierarchical clustering was proposed. Morphology similarity and the coplanarity measurement method were defined to evaluate the similarity of clusters. The coal seam floor series in the face-advancing direction were clustered according to the morphology similarity and coplanarity, respectively. Taking the morphology-based and coplanarity-based cluster centers as generating lines and stretching angle, respectively, the coal seam floor was reconstructed. The reconstructed floor can be regarded as the cutting path. The coal seam geological model of the 18,201 longwall face was analyzed with the proposed cutting path planning method. Comparing the reconstructed floor and original floor, the amounts of coal left and cut gangue were 1999 m³ and 1856 m³, respectively, for the segmental floor. For the case of whole floor, the amounts of coal left and cut gangue were 5642 m³ and 5463 m³, respectively. The coal loss rates only were 0.57% and 0.87% for the segmental and whole coal seam, respectively.

1. Introduction

Longwall mining, as the most efficient extracting method for underground coal mines, will remain the principal extraction method in the world in the foreseeable future [1,2]. Usually, the equipment used for working in a longwall mining face include a longwall shearer, an armored face conveyor (AFC), and more than 100 hydraulic supports, as shown in Figure 1. The shearer cuts the coal seam while traveling across the longwall face along rails attached to the AFC. The cut coal is transported by the AFC. The hydraulic supports provide temporary support of the roof material above the extracted coal seam. As the shearer moves across the coal seam, large hydraulic push rams attached to the supports advance the AFC progressively in the face-advancing direction, and thereby the longwall mining moves in a programmed sequence. Longwall mining is a coupling process between the mining equipment and coal-rock mass. In addition to the mechanical adaptability between the mining equipment and coal-rock mass (such as coal fracture mechanics induced by the shearer drum and pick cutter [3,4,5,6]), the space adaptability between them, which means that the mining equipment cuts in the coal seam, is a key issue that must be addressed in longwall mining automation.

Longwall mining automation, which can improve productivity and safety for mining personnel, is the focus of the world coal industry. Two key problems facing longwall mining automation are that of machine and face guidance to ensure the machines cut in the seam, and the face is kept straight [7,8]. Face alignment [9,10,11], produced from the shearer positioning with an inertial navigation system (INS), has been researched and applied widely in many coal mines [12,13]. It can keep the face straight for consistent production and minimal wear of the conveyor system. Ensuring the machines cut in the seam needs two technologies: horizon control and extraction control. Horizon control guides the machine to follow the seam undulations in the direction of the longwall face’s advance. Extraction control allows the machine to follow defined floor and roof profiles along the face, better following any given coal seam undulations for optimal extraction and production [14].

Enhanced horizon control (EHC), an outcome of the ARCAP landmark project, which is based on a cut model and some other information (manual input, coal interface input, and other seam information), can make a prediction of what the next floor and roof horizon should be [15]. The EHC is a memory-cut-based method [16], and will absolutely degenerate into a memory cut if the other information (manual input, coal interface input, and other seam information) becomes unavailable. Memory cutting is incapable of working for uneven coal seams [17]. Shield-data-based horizon control (SDHC) [18], based on the fact that the coal seam trend is given by the inclination of the support’s canopy, automatically adjusts the cutting drum height according to data from the roof support so that the longwall face follows the seam trend in the face-advancing direction. In fact, EHC and SDHC are not completely the same as horizon control, described in reference [14]. They include some functions of extraction control, described in reference [14]. The intrinsic and principal problem is to maintain the alignment of the shearer’s exploitation gradient with the coal seam gradient in the face-advancing direction, regardless of EHC, SDHC, and horizon control, described in reference [14]. The coal seam gradient in the face-advancing direction is the control target of horizon control.

The concept of the transparent longwall face [19,20] was proposed, which aims at autonomous cutting by the longwall shearer in the coal seam with the use of a high-precision transparent geological model [21,22,23]. But research about how to decide the cutting path of the longwall shearer according to the geological model is rarely reported. Based on the coal seam geological model, the authors of this paper proposed a coal seam floor gradient identification method using piecewise linear representation (PLR), as shown in Figure 2a [17]. This method synthesized the control resolution of the shearer range arm and the geometric characteristics of the coal seam, so that horizon control was achieved with the maximum exploitation rate within the shearer’s capacity. But this method can only analyze one cross section (such as 2–2′ in Figure 2a) in the face-advancing direction, so it is insufficient for coal seams with undulations in the face direction or different floor series in the face-advancing direction. As shown in Figure 2b,c, the floor series at different face positions have different morphologies, and the gradients in the face direction are different. The distribution of the whole coal seam gradient in the face-advancing direction is necessary for the horizon control of longwall mining.

According to the concept of the transparent longwall face, the objective of this work is to obtain a coal seam floor cutting path planning method based on the geological model. In this work, the distribution of the coal seam gradient in both the face-advancing direction and the face direction was obtained using a multiple hierarchical clustering algorithm, as shown in Figure 3. First, a morphology similarity and coplanarity measurement method was proposed to evaluate the similarity of clusters. The floor series (Fs) were clustered using a hierarchical clustering algorithm according to the morphology similarity. The cluster centers are the representative morphology of the zones covered by each cluster. By analyzing the morphology-based cluster centers using the PLR method in Ref. [17], the distribution of the coal seam gradient in the face-advancing direction can be obtained. The surfaces (M_k) composed of two neighbor floor series are clustered according to the coplanarity. The gradient of the coplanarity-based cluster center is the representative gradient of the zones covered by each cluster, so the distribution of the coal seam gradient in the face direction can be obtained. Meanwhile, taking the morphology-based and coplanarity-based cluster centers as the generating lines and stretching angle, respectively, the coal seam floor is reconstructed. And the reconstructed floor is the planned cutting path.

The rest of this paper is structured as follows. Section 2 introduces the hierarchical clustering algorithm. Section 3 describes the morphology and gradient similarity measurement method. Section 4 introduces the validity measure method of clustering in order to determine the optimal number of clusters. The cutting path planning method and its limitations are described in Section 5. Section 6 presents the results and discussion. Finally, Section 7 concludes the paper and discusses future avenues for research.

2. Hierarchical Clustering Algorithm

Clustering is the most well-known and frequently utilized unsupervised learning technique in data mining, pattern recognition, image segmentation, and so on [24,25,26,27]. The cluster algorithm is a set of methodologies for automatic classification of samples into a number of groups using a measure of similarity, so that the samples in one group are similar to each other and samples belonging to different groups are not similar to each other. Usually, there are seven categories of clustering algorithms, in particular (i) graph-based algorithms, (ii) hierarchical clustering algorithms, (iii) partitioning clustering algorithms, (iv) density-based clustering algorithms, (v) grid-based algorithms, (vi) combinational clustering algorithms, and (vii) model-based clustering algorithms [28].

Hierarchical clustering algorithms create a hierarchical decomposition of the given set of data objects. On the basis of how the hierarchical decomposition is formed, hierarchical methods can be classified into two categories: agglomerative and divisive hierarchical clustering algorithms. The agglomerative hierarchical clustering algorithm is known as a bottom-up approach. It starts with each object forming a separate group. It keeps on merging the objects or groups that are close to one another. It keeps on doing so until all of the groups are merged into one or until the termination condition holds [29]. The divisive hierarchical clustering algorithm is commonly known as the top-down approach. All objects initially belong to a single root group. Then the group is iteratively split up into sub-groups until each object is in one cluster or the termination condition takes holds [29,30]. In the paper, the agglomerative hierarchical clustering algorithm is selected because that it is usually more accurate than the divisive hierarchical clustering algorithm [30].

For both agglomerative and divisive hierarchical clustering algorithms, the termination condition usually is the number of groups or the similarity threshold value. In engineering applications, the number of clusters are not always known a priori. Different similarity measures lead to different types of clusters, and the effectiveness of the clustering algorithm depends intensively on the definition of the similarity. In the next two sections, the similarity measurement and the decision of the cluster number are discussed.

3. Morphology Similarity and Coplanarity Measurement

3.1. Morphology Similarity Measurement

Usually, the distance between two series, such as the Manhattan distance [31], Euclidean distance [32], and dynamic time warping (DTW) distance [33], is used to evaluate the similarity. The smaller the distance is, the greater the similarity is. Both the Manhattan distance and Euclidean distance are incapable of morphology recognition because these two distances are calculated from the absolute differences of vectors. In Figure 2b, The Z-axis coordinates of the coal seam floor series vary largely from 0 to about 70 m. Both the Manhattan and Euclidean distance will be very large even if the floor series have similar morphologies. DTW is usually used to calculate the shape similarity between two series with different lengths. DTW distance is computed by first finding the best warped path to align the two series. It is only because of the warped path that the position information of the floor series is eliminated. It is obvious that DTW distance is not an appropriate evaluation index for the morphology similarity of the floor series.

The gradient of the coal seam floor series is not only the key parameter describing the morphology, but also the target of horizon control. The PLR of the floor series including gradient information can be used to calculate the morphology similarity distance. Figure 4 shows the schematic of the morphology similarity measurement according to the PLR of the floor series. PLR_i and PLR_j are the PLR series of two floor series, Fs_i and Fs_j, at different positions on the longwall face. The subscripts i and j represent different X-axis values. The solid circles on each PLR series represent turning points, while the hollow circles represent alignment points that are projected from corresponding turning points on the other PLR series. The distance between Fs_i and Fs_j, D(Fs_i, Fs_j), is calculated according to the follow formula,

$$D({\mathrm{Fs}}_i,{\mathrm{Fs}}_j)=D({\mathrm{PLR}}_i,{\mathrm{PLR}}_j)=\sqrt{{\displaystyle \sum _{k=1}^{n-1}\{(ra{d}_{ik}-ra{d}_{jk}}{)}^2+{(\Delta z_{ik}-\Delta z_{jk})}^2\}}$$

(1)

where n is the length of the alignment PLR of the floor series. The smaller the distance is, the greater the morphology similarity is. If the distance equal zero, the two series are the same or similar.

3.2. Coplanarity Measurement

The coal seam floor is composed of k surfaces, which are formed by orderly connecting the k + 1 floor series, as shown in Figure 3. Clustering based on coplanarity automatically classifies the k surfaces into a number of clusters. Each cluster center is used to represent a floor zone of the coal seam that is covered by the cluster. In each zone, the gradient in the face direction of each cluster center is take as the extension direction of the cluster centers obtained with clustering based on morphology similarity.

Each surface sample, composed of two neighboring floor series, Fs_i and Fs_{i + 1}, is defined as

$$M_i{=\mathrm{Fs}}_i\cup {\mathrm{Fs}}_{i+1}=\left\{(x_i,y_{i1},z_{i1}),\cdots (x_i,y_{in},z_{in}),(x_{i+1},y_{(i+1)1},z_{(i+1)1}),\cdots , (x_{i+1},y_{(i+1)n},z_{(i+1)n})\right\}$$

(2)

Figure 5 shows the schematic of the coplanarity measure between surfaces M_i and M_j. A(x_iv, z_iv) and B(x_{(i + 1)v}, z_{(i + 1)v}), with a same coordinate in the face-advancing direction y_v, are the points belonged to Fs_i and Fs_{i + 1}, respectively. Line AB is the intersecting line of surface M_i and the X–Z plane at y_v. The slope of M_i at y_v is defined as ${\theta }_v^{<i,i+1>}$. Analogously, the slope of M_j at y_v is defined as ${\theta }_v^{<j,j+1>}$. Points C’ and D’ are determined with the slope ${\theta }_v^{<i,i+1>}$ and the X-axis coordinates of points C and D. The collinearity between lines AB and CD, $co{l}_v^{i,j}$, is calculated as follows,

$$\left\{\begin{array}{l}co{l}_v^{i,j}=| {\epsilon }_{jv} |+| {\epsilon }_{(j+1)v} |+|{\epsilon }_{jv}-{\epsilon }_{jv}|\\ {\epsilon }_{jv}=\frac{z_{(i+1)v}-z_{iv}}{x_{(i+1)v}-x_{iv}}(x_{jv}-x_{iv})\\ {\epsilon }_{(j+1)v}=\frac{z_{(i+1)v}-z_{iv}}{x_{(i+1)v}-x_{iv}}(x_{(j+1)v}-x_{iv})\end{array}\right.$$

(3)

The coplanarity measurement between surfaces M_i and M_j, $Col(M_i,M_j)$, is defined as the collinearity summation of all sub-samples in the two surfaces,

$$Cop({{\rm M}}_i,M_j)={\displaystyle \sum _{v=1}^{n}co{l}_v^{i,j}}$$

(4)

where n is the length of the floor series Fs_i.

4. Determining the Optimal Number of Clusters

In engineering applications, the termination condition of clustering usually is determined by the number of groups or the similarity threshold value. However, it is very difficult to determine the threshold value of morphology similarity and coplanarity, so the termination condition of clustering has to be determined by the number of groups. There are some cluster validity measures that are concerned with determining the optimal number of clusters and checking the quality of clustering results. In this paper, the Dunn index (DI), Davies–Bouldin index (DBI), and CS were used to determine the optimal number of clusters.

4.1. Dunn Index (DI)

The DI, a well-established cluster validity measure, was proposed by Dunn in the 1970s [34,35]. It is defined as

$$\mathrm{DI}=\underset{(C)}{\min }\left\{\frac{\underset{j\ne i}{\min }(d_{\min }(C_i,C_j))}{\underset{1\le l\le K}{\max }(diam(C_l))}\right\}$$

(5)

$$d_{\min }(C_i,C_j)=\underset{s_i\in C_k,s_j\in C_l}{\min }dist(s_i,s_j)$$

(6)

$$diam(C_l)=\underset{s_i,s_j\in C_l,i\ne j}{\max }dist(s_i,s_j)$$

(7)

where C and s represents cluster and samples, respectively. In Equation (5), the denominator represents the maximum distance between two samples belonging to the same cluster. The numerator represents the minimum distance between two samples belonging to different two clusters. The larger the DI is, the better the clustering is.

4.2. Davies–Bouldin Index (DBI)

The DBI, which can measure compact and separate clusters, was proposed by Davies and Bouldin [36]. It is defined as

$$\mathrm{DBI}=\frac{1}{K}{\displaystyle \sum _{i=1}^K\underset{i\ne j}{\max }}(\frac{\overline{C_i}+\overline{C_j}}{dist(C_i^0,C_j^0)})$$

(8)

$$\overline{C_i}=\frac{1}{\left|C_i\right|}{\displaystyle \sum _{l=1}^{\left|C_i\right|}dist(s_l,C_i^0)}$$

(9)

where K is the number of clusters, $\left|C_i\right|$ is the number of samples in C_i, and $\overline{C_i}$ is the average distance between all samples and the cluster center sample $C_i^0$ of cluster C_i. The lower value of $\overline{C_i}$ indicates the higher similarity and compact for all samples of cluster C_i. The denominator in Equation (8), $dist(C_i^0,C_j^0)$, is the distance between the cluster centers of cluster C_i and C_j. So this measure is a function of the ratio of the sum of within-cluster scatter to between-cluster separation, and it uses both the clusters and their sample means. The smallest DBI indicates a valid optimal partition.

4.3. CS

Chou [37] proposed the CS validity measure of clustering, which can deal with clusters with different densities and/or sizes. It is defined as

$$\mathrm{CS}=\frac{{\displaystyle \sum _{i=1}^K\left\{\frac{1}{\left|C_i\right|}{\displaystyle \sum _{s_j\in C_i}\underset{s_l\in C_i}{\max }\hspace{0.17em}dist(s_l,s_j)}\right\}}}{{\displaystyle \sum _{i=1}^K\underset{j\in K,j\ne i}{\min }dist(C_i^0,C_j^0)}}$$

(10)

The denominator in Equation (10) computes the average distance between cluster centers. The numerator measures the average largest distance between two data points lying in the same cluster. The denominator measures the sum of the minimum distance between the cluster centers. So, this measure is a function of the ratio of the sum of within-cluster scatter to between-cluster separation. The smallest CS indicates a valid optimal partition.

Among the three validity measure parameters, the DI is an extremely large index. In order to compare and analyze the three parameters conveniently, DI is converted into an extremely small index by reciprocal transformation. Meanwhile, the inverse of the DI, DBI, and CS were normalized with Equation (11).

$${\mathrm{X}}^{\prime }=\frac{\mathrm{X}-{\mathrm{X}}_{\min }}{{\mathrm{X}}_{\max }-{\mathrm{X}}_{\min }}$$

(11)

where X, X_max, X_min are the index parameter, and the maximum and minimum value of the index, respectively. X’ is the normalized value of the index parameter.

5. Cutting Path Planning Based on Clustering Algorithm

Figure 6 shows the flowchart of the agglomerative hierarchical clustering algorithm. The original data of the clustering algorithm include the floor series and its number m, and the predefined cluster number p = m − 1. According to the piecewise linear representation method proposed in reference [17], the floor series are transformed into the PLR series, and then the PLR series are aligned with each other with linear interpolation. Take each individual PLR series as a cluster, calculate the distances between each of the clusters. The pair of clusters with the minimum distance is merged into one cluster, and then update the cluster center and cluster number. Repeat steps 2 to 4 until the cluster number, K, is equal to the predefined cluster number, p. Finally calculate the clustering validity index and cluster results. Steps 1 to 5 are recursively repeated until the predefined cluster number, p, is equal to 1. The clustering validity and dendrogram were recorded during the recursive process. It should be noted that the implementations of the agglomerative hierarchical clustering based on morphology similarity and coplanarity are the same, but the distances between clusters must be calculated by Equations (1) and (4), respectively.

According to the recorded clustering validity and dendrogram, the morphology-based and conplanarity-based cluster centers and their cover zones were determined. The coal seam floor cutting path can be obtained through reconstructing the floor with the morphology-based and conplanarity-based cluster centers and their cover zones. The floor reconstructing process includes: (1) aligning the morphology-based and conplanarity-based clusters, so that the cover zones of the morphology-based cluster and conplanarity-based cluster are coincident; (2) taking the morphology-based cluster center as a generating line; (3) taking the gradient in the face direction obtained from conplanarity-based clustering as the stretching angle; and (4) moving the generating line at the stretching angle along the face direction in a cover zone.

The proposed cutting path planning method based on multiple clustering algorithms aims to guide the longwall shearer cutting in the coal seam by considering the geometry of the coal seam. So it is inapplicable to a low-thickness coal seam, in which undercut rock is unavoidable because the extracting thickness of longwall mining machines is larger than the thickness of the coal seam [38,39].

6. Results and Discussion

The coal seam geological model of the 18,201 longwall face in Shanxi province of China, as shown in Figure 2a, was used to verify the proposed cutting path planning method. The details of this geological model were described in Ref. [17]. In Figure 2a, the X-axis represents the longwall face direction, the Y-axis represents the face-advancing direction, and the Z-axis represents the vertically upward direction. Within the coal seam of the 18,201 face, there is a fault structure, which is located between 2200 m and 2300 m in the face-advancing direction. The clustering analysis of the coal seam floor was respectively performed under two cases: the segmental floor (Figure 7), located between 0 and 2100 m in the face-advancing direction, which does not include the fault structure, and the whole floor (Figure 2a), including the fault structure.

6.1. Clustering of Segmental Floor

6.1.1. Clustering Based on Morphology Similarity

Figure 8 shows the variation of the dendrogram and validity measure index during clustering based on morphology similarity. With the evolution of the clustering process, the neighbor floor series were agglomerated gradually into the same cluster, as shown in Figure 8a. The DBI increased with the decreasing of number of clusters. When the clusters were agglomerated to 36, the DBI reached the maximum. After that, it began to decrease rapidly. The DI decreased slowly until the number of clusters decreased to about 100. And then it increased slowly until the number of clusters decreased to about 5. It increased sharply when the clusters further agglomerated. The CS increased slowly when the number of clusters decreased until the cluster number reached about 120. After that, the CS remained constant at about 0.35 until the cluster number reached 7, and then it increased sharply.

Taking into account the dendrogram and the validity measure index, the number of clusters is determined as 7, as shown in Figure 8a. The morphology of the determined cluster centers is exhibited in Figure 9. According to the intuitive overall morphology, the clusters can be classified into two categories. One category includes the clusters No.1–4, and another includes the clusters No.5–7. This means that these clusters would be agglomerated into two clusters if the clustering process took a step further. This coincides with the dendrogram (Figure 8a). For each category, some observable morphology differences between the clusters are shown in Figure 9.

Table 1. The position and cover zone of the cluster centers based on morphology similarity.

No. of Clusters	Position of Cluster Center (X/m)	Zone of Cluster (X/m)
1	24.8	0–45.6
2	65.6	46.4–80.8
3	101.6	81.6–119.2
4	136.8	120–153.6
5	197.6	154.4–223.2
6	238.4	224–247.2
7	267.2	248–290.4

lists the position of the cluster centers and cover zone of each cluster. Each cluster center is the representative morphology of the cluster zone, and can be regarded as the generating line (generatrix) of the cluster zone. The floor in this cover zone can be re-constructed by stretching the generating line with a predefined angle along X-axis. The predefined angle can be determined by the cluster centers based on coplanarity.

6.1.2. Clustering Based on Coplanarity

Figure 10 shows the variation of the dendrogram and validity measure index during clustering based on coplanarity. Similar to the morphology-based clustering, the neighbor floor series were agglomerated gradually into the same cluster with the evolution of the clustering process. During the agglomerative clustering process, the DBI increased to the maximum when the number of clusters decreased to 99. Then it began to decrease with the agglomerative clustering process. The DI decreased with the agglomerating of clusters until the number of clusters decreased to 5. Then it increased rapidly when the number of clusters further decreased. The CS remained almost constant until the number of clusters decreased to about 15. Then it increased sharply. Considering the dendrogram and validity measure index, the number of clusters was selected as 6, as shown in Figure 10a.

Figure 11 presents the gradient surface of cluster centers based on coplanarity for the segmental floor. The position, cover zone of each cluster center surface, and the gradient in the face direction determined by the center surfaces are listed in

Table 2. The position, cover zone, and gradient in the face direction of the cluster center based on coplanarity.

No. of Clusters	Position of Cluster Center Surface (X/m)	Gradient in Face Direction of Cluster Center	Zone of Cluster (X/m)
1	6.4~7.2	9.7516°	0–12.8
2	30.4~31.2	9.7694°	13.6–46.4
3	80~80.8	9.7251°	47.2–111.2
4	144.8~145.6	9.6532°	112–180
5	201.6~202.4	9.5967°	180.8–231.2
6	257.6~258.4	9.5149°	232–290.4

. The gradient in the face direction of the cluster center represents the floor gradient in the cover zone of the cluster. It can be regarded as the stretching angle of the generating line determined by clustering based on morphology similarity.

6.1.3. Floor Reconstructing

In order to reconstruct the floor, the cover zones of the morphology-based cluster and conplanarity-based cluster should be coincident. But, comparing Table 1 and Table 2, it is found that the cover zones of the two kinds of clusters are different. The alignment of the two kinds of clusters was performed, as shown in Figure 12, so that the morphology and face-direction gradient are the same in each alignment cluster. After aligning the two kinds of clusters, the floor was divided into 11 zones.

Table 3. The cover zone, position, and stretching angle of the alignment clusters.

No. of Clusters	Zone of Cluster (X/m)	Position of Generating Line (X/m)	Stretching Angle
1	0–12.8	24.8	9.7516°
2	13.6–46.4		9.7694°
3	47.2–80.8	65.6	9.7251°
4	81.6–111.2	101.6
5	112–119.2		9.6532°
6	120–153.6	136.8
7	154.4–180	197.6
8	180.8–223.2		9.5967°
9	224–231.2	238.4
10	232–247.2		9.5149°
11	248–290.4	267.2

lists the cover zone, position, and stretching angle of the alignment clusters.

According to the generating line and stretching angle listed in Table 3, the reconstructed floor is shown in Figure 13a, which can be regarded as the planned cutting path. The coal recovery is influenced by the difference between the reconstructed floor and original floor. The amount of cut gangue is a total volume of the reconstructed floor below the original floor. The amount of coal left is the total volume of the reconstructed floor overtop the original floor. By comparing the reconstructed and original floor, the amount of coal left is 1999.52 m³, and the amount of cut gangue is 1856.47 m³. The coal loss rate, loss_coal, is calculated according to Equation (12), as below

$$los{s}_{coal}=\frac{V_{coal\text{-}left}}{V_{coal\text{-}seam}}\times 100\%$$

(12)

where V_coal-left is the amount of coal left, and V_coal-seam is the volume of the coal seam, which is the volume between the roof and floor of the coal seam model. The volume of the segmental coal seam located between 0 and 2100 m in the face-advancing direction is 351,190.58 m³. Therefore, the coal loss rate only is 0.57% when exploiting the coal seam according to the planned cutting path. The planned floor cutting path can be used as the extraction control target of the longwall shearer, so that the longwall shearer can cut along these defined floor profiles for optimal extraction and production.

The distribution of the gradient in the face-advancing direction is shown in Figure 13b, which is obtained by analyzing the morphology-based cluster centers using the PLR method of Ref. [15]. This gradient information can be used as the horizon control target of the longwall shearer, so that the path of the longwall shearer can follow the coal seam undulations in the direction of the longwall face’s advance.

6.2. Clustering of Whole Floor

The variation of the dendrogram and validity measure index during whole floor clustering based on morphology similarity and coplanarity are presented in Figure 14 and Figure 15, respectively. According to the validity measure index, the optimized morphology-based and coplanarity-based cluster numbers are selected as 29 and 10, respectively. The alignment cluster number of the two kinds of clusters is 53. The reconstructed floor produced with the 53 alignment clusters is exhibited in Figure 16. By comparing the reconstructed floor and original floor, the amount of coal left is 5642.35 m³, and the amount of cut gangue is 5463.76 m³. The volume of the whole coal seam is 648,330.77 m³. The coal loss rate of the whole coal seam is 0.87%. Comparing Figure 8a and Figure 14a, the morphology-based clustering dendrograms of the segmental and whole floor are different. In the case of the whole floor, the agglomeration level is very low, in the zone of 0–80 m, in the face direction. The number of clusters is 22 in the zone. In the case of the segmental floor, the number of clusters is 2 in the same zone. The reason for the difference is that there is a deflective fault at the location of 2200 m in the face-advancing direction. The deflective fault fades away in the zone of 0–80 m in the face direction. The deflective and fading characteristics of the fault cause the dissimilar morphology of each floor series samples.

7. Conclusions

Space adaptability between mining equipment and the coal-rock mass, to ensure the machines cut in the seam, is an important technology in longwall automation. In this study, a cutting path planning method based on hierarchical clustering was proposed according to the concept of the transparent longwall face, so that the mining machines were guided in the coal seam.

(1)

Two distance functions including morphology similarity and the coplanarity measurement method were defined to evaluate the similarity of clusters. The coal seam floor series in the face-advancing direction were clustered according to the morphology similarity. The surfaces composed of two neighboring floor series were clustered according to the coplanarity. The planned cutting path was obtained by reconstructing the coal seam floor, taking the morphology-based and coplanarity-based cluster centers as generating lines and stretching angle, respectively. Meanwhile, the distribution of the coal seam gradient in both the face-advancing direction and face direction was withdrawn, which can be used as the horizon control target of the longwall shearer.

(2)

The coal seam geological model of the 18,201 longwall face was analysed using the proposed clustering method. Comparing the planned cutting floor and original floor, the amount of coal left and cut gangue was 1999 m³ and 1856 m³, respectively, for the segmental floor. For the case of the whole floor, the amount of coal left and cut gangue was 5642 m³ and 5463 m³, respectively.

(3)

The proposed cutting path planning method aims to guide the longwall shearer cutting in the coal seam by considering the geometry of the coal seam. So, it is inapplicable to the low-thickness coal seam, in which undercut rock is unavoidable because the extracting thickness of longwall mining machines is larger than the thickness of the coal seam. A cutting path planning method for low-thickness coal seams can be selected for future work.