Intelligent Height Adjustment Method of Shearer Drum Based on Rough Set Significance Reduction and Fuzzy Rough Radial Basis Function Neural Network

Abstract

The intelligent adjustment method of the shearer drum is the key technology to improve the intelligent level and safety degree of fully mechanized mining face. This paper proposes a shearer drum intelligent height adjustment model based on rough set significance attribute reduction (AR) and fuzzy rough radial basis function neural network (FRRBFNN) optimized by adaptive immune genetic algorithm (AIGA). The model first selects the parameters of shearer process monitoring based on the importance attribute reduction algorithm of rough set, and establishes the attribute reduction set of shearer operation characteristic parameters and the drum height decision rule base. Next, a fuzzy rough radial basis function neural network determined by the decision rule space is proposed. By introducing the fuzzy rough membership function as the connection weight, the network can accurately describe the complex nonlinear relationship between the working characteristic parameters of the attribute shearer and the drum height, and measure the uncertainty of the coal seam distribution. Finally, to further optimize the performance of FRRBFNN, the adaptive immune genetic algorithm is introduced to optimize its parameters, to build a high-precision shearer drum height prediction system. For the evaluation method of the model, we use three indicators: mean absolute error, mean absolute percentage error, and root mean square error. Based on the measured data in Yujialiang area, Shaanxi Province, the experimental results show that—compared with the FRRBFNN and support vector regression (SVR) models, a gated current neural network (GRU), a radial basis function neural network (RBF), the memory strengthen long short-term memory (MSLSTM) model, and the adaptive fuzzy reasoning Petri net (AFRPN)—the MAE of the AR-AIGA-FRBFNN model for predicting the height of the left and right rollers are 18.3 mm and 17.2 mm, respectively; the MAPE is 0.96% and 0.93%, respectively; and the RMSE is 21.2 mm and 22.4 mm, respectively. The AR-AIGA-FRBFNN model is therefore more effective than the other considered methods.

1. Introduction

As the depth of underground coal mining increases, the disasters such as gas explosion, rock collapse and water inrush occur more frequently in the process of mechanized coalface mining, all of which seriously threaten the lives of the human miners [1]. To improve this situation, unmanned fully mechanized coal mining is considered to be an effective method, notably in view of its high recovery ratio and extremely low mortality rate in recent years [2,3]. The intelligent shearer, one of the main pieces of equipment at a fully mechanized coalface, is key when using this method. However, it has always been difficult to regulate the shearer drum height to fully realize the intelligence ability of the shearer, since the natural occurrence boundary of coal seams is very irregular due to frequent sinking of roof rocks and rising of floor rocks.

To solve the problem of intelligent height adjustment of coal mining machinery, the early methods adopted by researchers were simple sensing adjustment methods based on coal-rock interface recognition, such as $\gamma$ ray detection [4], radar detection [5], image recognition [6], infrared temperature detection [7], etc. However, due to the complex geological conditions of coal mines, the coal seam state and coal rock properties are so variable that the above methods are not universally applicable, and these techniques have not been applied in engineering due to the harsh working face environment and the difficulty of real-time identification [8].

To overcome these issues, the researchers proposed the memory cutting technology of indirect perception of the coal-rock interface. By contrast with the coal-rock interface identification method, memory cutting technology is the next cutting path predicted by historical cutting parameters, and does not use the coal-rock interface as the basis for the height adjustment of the shearer drum, which is more convenient for actual operation [9].

Although the traditional memory cutting technology can reduce the number of underground workers to a certain extent and improve the degree of automation of the shearer, due to the complex environment of the comprehensive mining face and the drastic changes in the coal-rock interface, the memory path fails; thus, the traditional memory cutting technology relies on human intervention, and its cutting accuracy [10] is low. To solve this problem, Li et al. proposed a memory cutting method of adjacent coal seams based on hidden Markov model and using the correlation of adjacent coal seam data [11]. Chen et al. built a depth LSTM model by inputting the truncation trajectory data of the previous moment, and introduced the scale factor to compensate the response attenuation, which optimized the prediction accuracy of the model for the drum cutting track [12]. However, because it is difficult to describe the complex coal seam state only depending on the coal seam cutting track information, Chen and Li did not achieve the expected results.

To further improve the adjustment and precision, Wang et al. analyzed the coal and rock state through multiple data, and optimized the cutting path of the shearer drum based on a genetic algorithm [13]. Xie et al. used the virtual memory cutting method based on a virtual cutting process to predict the AFC shape, and used SVM and ELM network to conduct multi-input information analysis and roll height prediction [14]. Zhou et al. established a fuzzy cut-off rule set by analyzing multiple cut-off data attribute parameters, and optimized the cut-off path of the shearer drum by using fuzzy cut-off rule decision [15]. Wang, Xie, Zhou and others adopted multi-sensor data fusion methods to reveal the complex mapping relationship between the input parameters and the cut-off track of the shearer drum, and improved the cut-off accuracy of the shearer drum. However, these methods still cannot fully describe the uncertainty of the coal seam change, which inevitably leads to the redundancy of the characteristic parameters, affecting the drum tuning accuracy.

In the latest research on the problem of shearer drum height adjustment, Wang et al. proposed the adaptive fuzzy reasoning Petri net model to adapt to the complex nonlinear problem of the shearer drum cutting trajectory [16]. Zhao et al. built the shearer adaptive cutting control model through the multi-objective grey wolf optimizer algorithm [17]. Wang and Zhao’s research further analyzed the difficult problem of drum cutting, but they did not consider the redundancy and correlation between the data attributes of multiple input sensors, which reduced the prediction accuracy of the model.

Considering the redundancy and correlation between the data attributes of the multi-input sensors, it is necessary to reduce the working characteristic parameters of the shearer to remove the redundant attributes. For attribute reduction, researchers have carried out much research. Among this, the attribute reduction algorithm based on rough set theory has great advantages. It does not need prior knowledge and can objectively evaluate uncertain factors [18,19]. Chen et al. used the rough set conditional information entropy method to measure the collapse risk of mountain tunnels [20]. Li et al. used the attribute significance method to objectively weight the various condition attributes that affect the operation to cold air [21].

Therefore, we designed an attribute reduction algorithm based on the significance of rough set theory to reduce the attributes of shearer operating parameters.

There is uncertainty in coal seam changes, and there is a complex nonlinear relationship between the cutting track of the shearer drum and the operating characteristic parameters. Artificial neural networks and artificial intelligence algorithms have strong nonlinear fitting and generalization ability [22,23]. Roohollah et al. established an accurate estimation model of the impact of blasting operations on the environment by combining genetic programming algorithm (GP) and gene expression programming algorithm (GEP) [24]. Li et al. built a coal seam permeability prediction model based on multiple linear regression and a GEP algorithm, and effectively predicted the coal seam permeability [25].

The radial basis function neural network is widely used in the field of intelligent control because of its excellent nonlinear approximation [26]. However, when the RBF neural network processes uncertain information, the generalization performance of the trained model is degraded due to the lack of a mechanism to measure the uncertain features [27].

To solve this problem, researchers combined fuzzy theory with a radial basis function neural network, and proposed the fuzzy radial basis function neural network. Bao et al. introduced the Takagi–Sugeno (T-S) fuzzy rule inference system into a radial basis function neural network, and thus constructed the T-S fuzzy radial basis function neural network [28]. Wang et al. defined its basis function to be scalar, and combined this with T-S fuzzy rules to model unsteady aerodynamics, thereby proposing a fuzzy scalar radial basis function neural network [29]. The fuzzy RBF neural network can avoid the shortcomings of slow convergence speed and poor generalization ability of traditional neural network models. However, the fuzzy Radial Basis Function neural network constructed in combination with T-S fuzzy inference system makes the network structure unusually large due to the input of multi-dimensional variables, thus reducing the convergence speed and affecting the model accuracy [30]. Therefore, it is necessary to improve the fuzzy radial basis function neural network to guide the intelligent drum height adjustment in the fully mechanized mining face and realize high-precision coal mining under complex and changeable geological conditions.

In this study, the rough set decision rule extraction system replaces the rule determination method of the fuzzy radial basis function neural network, determines the network model structure according to the decision rules, reduces the complexity of the model structure, and introduces the fuzzy rough membership value as the connection weight value between the hidden layer and the fuzzy rough membership layer to enhance the adaptability of the model to uncertain information and improve the prediction accuracy. Finally, an adaptive immune genetic algorithm is designed to optimize the network parameters and realize the intelligent adjustment of the shearer drum height.

In summary, the research proposes the AR-AIGA-FRRBFNN shearer drum intelligent height adjustment model. The main contributions of the article are as follows:

First, an intelligent height adjustment method of shearer drum height based on AR-AIGA-FRRBFNN is proposed, which: accurately describes the complex relationship between coal seam state and shearer drum; predicts the change trajectory of shearer drum height with high accuracy.

Second, to remove the redundant feature parameters in the characteristic parameters of shearer operation, we: design a rough set-based significance algorithm for attribute simplification; selectively remove the partial simplification of redundant attributes; construct the optimal attribute simplification set; and improve the prediction accuracy of drum height.

Third, in order to adapt to the irregular changes of coal-rock interface and accurately describe the complex coupling relationship between coal-rock state and shearer drum: a fuzzy rough radial basis network model based on decision rule inference is proposed; a deep neural network model is constructed through the decision rule inference system; and the fuzzy rough affiliation $\eta$ is used as the weight between the hidden layer and the fuzzy rough affiliation layer, so that the network has the ability to measure uncertainty information and achieve high accuracy in predicting the height of shearer drum.

Finally, to further improve the prediction accuracy of FRRBFNN on shearer drum height, we: designed an adaptive immune genetic algorithm to optimize the parameters of the FRRBF network; determined the AIGA fitness function according to the direction of population evolution; and calculated the optimal crossover rate and mutation rate according to the adaptive algorithm, significantly improving the algorithm performance and effectively optimizing FRRBFNN parameters.

The rest of this study is as follows: the first section introduces the overall framework of this study; the second section introduces the theory of rough set, the definition of the fuzzy rough membership function and the theoretical model of Radial Basis Function neural network; the third section introduces the AR-AIGA-FRRBFNN shearer drum height prediction model proposed in this study; the fourth section is the experimental section: through the collected Yujialiang historical cutting data, the initial decision table is established, the attribute reduction based on the significance algorithm is carried out for the initial decision table, the attribute reduction set and decision rule set are constructed, the AR-AIGA-FRRBFNN shearer drum height prediction model is constructed through the decision rule set, and the attribute reduction set is used for model training—describing the whole process of shearer drum height prediction and height adjustment control—and the model algorithm is compared and verified; the fifth section is the conclusion.

2. Model Framework

The shearer drum height adjustment control model proposed in this study is shown in Figure 1. Although there is uncertain data in the original dataset, the model can extract useful information from it and build the shearer drum height adjustment decision rule set, to build the best network prediction model. Prediction values that meet accuracy requirements can also be generated for a shearer drum raising decision dataset with multiple input features and non-uniform types of feature values. The main process of the proposed shearer drum height adjustment control model is as follows.

First, the initial characteristic parameters are determined through the field data collected by the Yujialiang automatic data acquisition system. Secondly, the significance attribute simplification algorithm of rough set theory is used to simplify the attributes of the initial feature parameter table, which eliminates the redundant parameters in the initial feature parameters, to establish the attribute simplification set and the decision rule set. Then, the structural parameters of the FRRBFNN are determined by the decision rule set, the fuzzy rough membership degree $\eta$ is introduced, the cluster center $\omega$ output by each neuron in the fuzzy rough membership layer is used as the connection weight, and the FRRBFNN model is constructed. Finally, the adaptive immune genetic algorithm is designed to optimize the parameters of FRRBFNN, and the AIGA-FRRBFNN is trained by taking the attribute approximate set as its input data, and the trained model predicts the height of the shearer drum during the actual operation, to realize the intelligent height control of the drum.

3. Theoretical Method

3.1. Rough Set Theory

Rough set theory was proposed by Polish professor Pawlak [31] in 1982. It can effectively analyze all kinds of incomplete information, discover the implicit knowledge behind a large amount of data, reveal the significance of conditional attributes to decision-making attributes, and remove redundant or irrelevant properties.

In rough set theory, an information system is defined as being four-tuple $\left(U,A,V,f\right)$, where $U$ is a non-empty finite object set, representing the domain; A is a set of non-empty finite attributes; $V$ is the range of attribute set; and f is an information function. For $x\in U$ and $a\in A$, there is $f\left(x,a\right)\in V$. If there is $A\in C\cup D$ and $C\cup D\ne \varnothing$, the information system is called a decision system, where C is the set of conditional attributes and $D$ is the set of decision attributes.

Definition 1. 

Given a decision system $S=\left(U,C\cup D,V,f\right)$, let $ind\left(p\right)$ denote the indiscernibility relation on attribute set $p\subseteq A$, then:

$$ind(p)=\left\{(x,y)\in U\times U|\forall a\in P,a(x)=a(y)\right\}$$

(1)

where $a\left(x\right)$ represents the value of attribute a of object x.  $ind\left(p\right)$ means that object $x$ and object $y$ in the information system cannot be distinguished according to the attribute values on attribute set $P$. Symbol $U/ind\left(p\right)$ denotes the partition based on indiscernibility relation $ind\left(p\right)$ on domain $U$.

Definition 2. 

Given a decision system $S=\left(U,C\cup D,V,f\right)$, the lower and upper approximations of set $X\subseteq U$ with respect to its indiscernibility relation $ind\left(p\right)$ are:

$$\underset{¯}{P}(X)=\cup \left\{Y_i|Y_i\in U/P,Y_i\subseteq X\right\}$$

(2)

$$\overline{P}(X)=\cup \left\{Y_i|Y_i\in U/P,Y_i\cap X\ne \varnothing \right\}$$

(3)

Definition 3. 

Given a decision system $S=\left(U,C\cup D,V,f\right)$, let P denote a conditional attribute set in a decision system and $D$ denote a decision attribute set, then the $PO{S}_P\left(D\right)$ of P relative to $D$ is:

$$PO{S}_P(D)=\underset{X\in U/Q}{\cup }\underset{¯}{P}(X)$$

(4)

If there is $PO{S}_{C-c_i}(D)=PO{S}_C(D)$ for $\forall c\in C$, attribute $C$ is a redundant attribute in the decision table. If $PO{S}_C\left(D\right)\ne PO{S}_{C-c_i}\left(D\right)$, then $c_i$ is said to be important about $D$ in $C$, and the set of all important knowledge about $D$ in $C$ is called the core of $C$ relative to $D$, denoted as $COR{E}_D\left(C\right)$.

3.2. Fuzzy Rough Membership Function

In actual classification learning, the relationship between the features describing the sample may be fuzzy, therefore, fuzzy rough sets are born as an extended model of Pawlak’s rough sets [32]. The fuzzy rough affiliation function reflects the fuzzy partition of the argument domain about the equivalence relation under the premise that the latter is fuzzy.

In the rough set, for any $A\in U$, the rough membership function x of element $r_A\left(x\right)$ is:

$$r_A\left(x\right)=\frac{\left|{\left[x\right]}_R\cap A\right|}{\left|{\left[x\right]}_R\right|}$$

(5)

where ${\left[x\right]}_R$ denotes the equivalence class of element $x$ with respect to the equivalence relation $R$.

In the rough set, if the equivalence relation $R$ is fuzzy, then $U/R$ is a fuzzy weak division, forming a fuzzy clustering $\left\{F_1,F_2,\dots ,F_H\right\}$ as a fuzzy set, and the upper and lower approximations of its output class set $C_c$ also constitute a fuzzy set, whose affiliation function is defined as:

$${\mu }_{\underset{¯}{C_c}}\left(F_j\right)=\underset{x\in C_c}{{\displaystyle \inf }}\max \left\{1-{\mu }_{F_j}\left(x\right),{\mu }_{C_c}\left(x\right)\right\}\forall x$$

(6)

$${\mu }_{\overline{C_c}}\left(F_j\right)=\underset{x\in C_c}{{\displaystyle \sup }}\min \left\{{\mu }_{F_j},{\mu }_{C_c}\left(x\right)\right\}\forall x$$

(7)

where ${\mu }_{F_j}\left(x\right)\ne 0$ indicates whether $x$ belongs to $C_c$. The fuzzy rough affiliation function is defined as:

$${\tau }_{C_c}\left(x\right)=\left\{\begin{array}{c}\frac{1}{H}{\displaystyle \sum _{j=1}^H{\mu }_{F_j}\left(x\right)t_{C_c}^j, \exists j,{\mu }_{F_j}\left(x\right)>0}\\ 0, \mathrm{else}\end{array}\right.$$

(8)

where $t_{C_c}^j\left(x\right)=\frac{\left|F_j\cap C_c\right|}{\left|F_j\right|}$, and $H$ is the number of clusters of ${\mu }_{F_j}\left(x\right)\ne 0$.

3.3. Radial Basis Function Neural Network

A radial basis neural network is a typical three-layer feedforward neural network, the advantages of which include a strong nonlinear approximation ability and fast convergence speed [33]. It includes an input layer, a hidden layer and an output layer. The network input is $X=\left(x_1,x_2,\dots ,x_n\right)$ and the network output is $Y=\left(y_1,y_2,\dots ,y_n\right)$. The output of the $kth$ neuron of the RBFNN output layer can be defined as:

$${\widehat{y}}_k={\displaystyle \sum _{i=1}^h{\omega }_{ik}{\phi }_j\left(x\right)}, k=1,2,\dots ,n$$

(9)

where $h$ denotes the number of neurons in the hidden layer, $n$ denotes the number of neurons in the output layer, ${\omega }_{ik}$ denotes the connection weight between the $k$ output layer and the $i$ hidden layer neuron, and the Gauss function is generally used as the hidden layer activation function, as shown in Equation (10).

$${\phi }_i\left(x\right)=\exp \left(-\frac{\left|x-{\mu }_i\right|}{2{\sigma }_i^2}\right), i=1,2,\dots ,h$$

(10)

In the formula, $x$ is the m dimensional input sample, ${\mu }_i$ is the center of the $i$ Gaussian function, ${\sigma }_i$ is the width of the $i$ function, and $h$ is the number of neurons in the hidden layer.

4. Intelligent Height Adjustment Model of Shearer Drum Based on AR-AIGA-FRRBFNN

To predict the running track of the shearer drum height with high accuracy, this study proposes a shearer drum height prediction model based on AR-AIGA-FRRNFNN. This section mainly introduces the relevant theories of the proposed model, including the theory attribute reduction algorithm based on rough set significance, the theory of fuzzy rough radial basis function neural networks, and the parameter optimization of the fuzzy rough radial basis function neural network based on an adaptive immune genetic algorithm.

4.1. Significance Based Attribute Reduction Algorithm for Initial Feature Parameters of Coal Mining Machine

Based on the significance of attributes, the minimum attribute reduction set is directly selected as the shearer drum height decision rule set, and the dependency and significance of each conditional attribute are calculated in turn to provide important parameters for subsequent decision-making. When constructing the shearer drum intelligent height adjustment model, it is necessary to perform attribute reduction before training the model. The process of realizing the shearer drum height decision attribute reduction is as follows:

Step 1: The state attribute domain $U$ of the shearer and drum is divided into equivalence classes. In this study, the attribute reduction algorithm based on significance is used to divide the attribute set $C$ and the drum height decision $D$, the equivalence class $ind\left(C\right)=\left\{c_1,c_2,\dots ,c_n\right\}$, $ind\left(D\right)=\left\{D_1,D_2,\dots ,D_n\right\}$ is obtained.

Step 2: The dependence of the drum height decision $D$ on the condition attribute set $C$ is calculated.

$$r\left(C,D\right)=\frac{\left|PO{S}_C\left(D\right)\right|}{\left|U\right|}$$

(11)

Step 3: The significance of the conditional attribute $C$ that removes a certain attribute $c_i$ to the decision height $D$ of the drum is calculated.

$$r\left(C-c_i,D\right)=\frac{\left|PO{S}_{C-\left\{c_i\right\}}\left(D\right)\right|}{\left|U\right|}$$

(12)

Step 4: The significance of the conditional attribute $c_i$ for the decision attribute $D$ is calculated.

$$si𝘨\left(c_i,C,D\right)=r\left(C,D\right)-r\left(C-c_i,D\right)$$

(13)

Equation (13) represents the degree to which a single factor $c_i$ affects the coal miner drum height decision after removing the conditional attribute $c_i$, i.e., the significance of $c_i$ to the decision attribute $D$. The kernel $COR{E}_D\left(C\right)$ of the conditional attribute set $C$ relative to the decision attribute $D$ is calculated, such that $B=COR{E}_D\left(C\right)$.

Step 5: The influence of the condition $c_i$ on the classification ability of $B$ on the decision attribute $D$ is calculated.

$$si𝘨\left(c_i,B,D\right)=r\left(B,D\right)-r\left(B-c_i,D\right)$$

(14)

If $si𝘨\left(c_i,B,D\right)=0$, this means that removing the conditional attribute $c_i$ does not affect the classification ability of the conditional attribute set $B$ to the decision attribute $D$, that is, the conditional attribute $c_i$ is a redundant attribute. The larger the value of $si𝘨\left(c_i,B,D\right)$, the more important the conditional attribute $c_i$ is, and the greater the influence of $c_i$ on the classification effect of $B$ on $D$. The specific process of attribute reduction is shown in Figure 2.

4.2. Shearer Drum Height Prediction Model Based on FRRBFNN

The attribute reduction set obtained in the previous section is used for the input data of the network model in this section. Through the ability of decision-making rules to analyze and reason information, the fuzzy rough membership function is introduced into the radial basis neural network to form a fuzzy rough radial basis neural network, which can not only reflect the complex value of the shearer height adjustment characteristic parameter and the shearer drum non-linear cutting relationship, but also has the ability to measure the uncertainty of the coal seam distribution. The topology of the multi-input-single-output FRRBFNN model is shown in Figure 3.

The input layer is to import external data into the network, that is, each neuron in this layer represents an input variable $x_i$. Each neuron in this layer represents the corresponding shearer drum characteristic parameter $c_i$ after attribute reduction.

The second layer is a hidden layer which calculates the membership degree of the input variable; the membership function is a Gauss membership function:

$${\lambda }_{ij}\left(x_i\right)=\exp \left(-\frac{{‖x_i-{\mu }_{ij}‖}^2}{2{\sigma }_{ij}^2}\right), j=1,2,\dots ,n_i$$

(15)

$${\phi }_k\left(x_t\right)={\displaystyle \prod _{i=1}^n{\lambda }_{ij}\left(x_i\right)}=\exp \left(-{\displaystyle \sum _{i=1}^n\frac{{‖x_{ti}-{\mu }_{ij}‖}^2}{2{\sigma }_{ij}^2}}\right)$$

(16)

where ${\mu }_{ij}$ and ${\sigma }_{ij}$ represent the center and width of the membership function, respectively; $k\in \left[1,H\right]$, $H={\displaystyle \prod _{i=1}^n{n}_i}$ represents the maximum number of rules; $x_t$ represents all inputs of the kth neuron; $x_{ti}$ represents the $i$ component of the input in the k neuron; and ${\phi }_k\left(x_t\right)$ represents the fitness of the k decision rule.

The third layer is the fuzzy rough membership layer, whose output is the membership degree of the current input to the corresponding rule; the number of neurons in this layer is the number of decisions corresponding to the decision conclusion. Its input and output are expressed as:

$$I{N}_c={\displaystyle \sum _{h=1}^H{\phi }_h}\left(x_t\right){\eta }_{hc}, h=1,2,\dots ,H$$

(17)

$${\Phi }_c\left(x_t\right)=\frac{I{N}_c}{{\displaystyle \sum _{i=1}^{C}I{N}_i}}=\frac{{\displaystyle \sum _{h=1}^H{\eta }_{hc}{\phi }_h\left(x_t\right)}}{{\displaystyle \sum _{i=1}^C{\displaystyle \sum _{h=1}^H{\eta }_{hc}{\phi }_h\left(x_t\right)}}}, i=1,2,\dots ,C$$

(18)

where $H$ is the number of neurons in the third layer; $C$ is the number of neurons in the fourth layer, which is the same as the number of clusters of decision attributes in the decision rule; and ${\eta }_{hc}=\frac{1}{H}{t}_c^h$ is the fuzzy rough membership degree.

The fourth layer is the output layer, which is used for defuzzification to obtain the exact value of the output:

$$y\left(x_t\right)={\displaystyle \sum _{i=1}^C{\omega }_c{\Phi }_c}\left(x_t\right)$$

(19)

where ${\omega }_c$ is the fuzzy set center of the decision attribute.

4.3. Parameter Optimization of FRRBFNN Based on Adaptive Immune Genetic Algorithm

The parameters in FRRBFNN have the center ${\mu }_{ij}$ and width ${\sigma }_{ij}$ of the membership function corresponding to the hidden layer membership function, the connection weight ${\eta }_{hc}$ between the hidden layer and the fuzzy rough membership layer, and the connection weight ${\omega }_c$ between the fuzzy rough membership layer and the output layer. These parameters directly determine the accuracy of the entire network model, so the network determines the value of the most suitable parameters ${\mu }_{ij}$,${\sigma }_{ij}$, ${\eta }_{hc}$ and ${\omega }_c$ through the appropriate algorithm, which is the key to the optimization of network parameters. The center ${\mu }_{ij}$ and width ${\sigma }_{ij}$ of the Gaussian membership function are usually calculated by unsupervised clustering algorithms, such as K-means method, etc. However, the number of categories of clustering methods must be preset, and the selection of the number of categories will directly affect the performance of clustering, thus affecting the network performance.

The immune genetic algorithm is an improved genetic algorithm based on the organism’s own immune regulation mechanism. The algorithm has significant advantages such as an immune memory function, an antibody diversity preservation function and a self-regulation function [34]. However, due to the preset crossover rate and mutation rate in the evolutionary iteration process, the local optimal solution will inevitably occur, which will affect the prediction accuracy of the shearer drum height. To solve this problem, adaptive crossover rate and mutation rate are designed, and adaptive immune genetic algorithm is constructed. The specific steps of FRRBFNN parameter optimization based on AIGA algorithm are as follows:

Step 1: The variables ${\mu }_{ij}$, ${\sigma }_{ij}$, ${\eta }_{hc}$ and ${\omega }_c$ are optimized as antibodies, and encoded.

Step 2: The operation parameters of AIGA are determined, including the population size $Q$, the maximum number of iterations $T$, the original number of iterations $𝘨=0$ and the fitness objective function $F_{𝘨oal}$.

Step 3: The fitness of each antibody is calculated. According to the actual situation of the height adjustment of the shearer drum, this study selects the FRRBFNN fitness function as the appropriate fitness function.

$$F=\frac{1}{1+E}, E=\frac{1}{n}{{\displaystyle \sum _{i=1}^n\left(\widehat{y}-y\right)}}^2$$

(20)

where $E$ is the prediction error of the FRRBFNN, $n$ is the number of test samples, $\widehat{y}$ and y are the predictions of the $i$ test sample point value and true value, respectively. When $E$ is the minimum value, the parameter value of FRRBFNN is the best.

Step 4: For the current population $p_t$, according to the fitness of the antibodies, to prevent the optimal antibody of the current population from being lost in the next generation, the “elite retention” strategy is adopted [35]. The one with the highest fitness is selected and stored in a dedicated variable as the elite antibody. The specific operation is as follows: when the genetic algorithm evolves to the t generation, $x_1\left(t\right)$ in the population is the optimal antibody. Let $A\left(t+1\right)$ be a new generation group: if $A\left(t+1\right)$ does not exist $x_1\left(t\right)$, then add $A\left(t+1\right)$ as an antibody of $A\left(t+1\right)$, and $A\left(t+1\right)$ eliminates an antibody with the lowest fitness.

Step 5: Antibody selection operation: When the concentration is constant, the greater the fitness is, the greater the probability of the antibody being selected. When the fitness is constant, the higher the antibody concentration is, the smaller the probability of the antibody being selected. Antibody similarity and concentration are defined as follows: there is an antibody population of size m, where each antibody can be represented as a one-dimensional vector with m elements.

Take any two antibodies $x=\left\{x_1,x_2\dots ,x_n\right\}$, $y=\left\{y_1,y_2\dots ,y_n\right\}$, let the fitness of antibodies $x$ and $y$ be $f\left(x\right)$ and $f\left(y\right)$, assuming that $\epsilon$ is a suitably small positive constant $\left(\epsilon >0\right)$. If $1-\epsilon \le Q_S\left(x,y\right)=\frac{f\left(x\right)}{f\left(y\right)}\le 1+\epsilon$ is established, then the antibodies $x$ and $y$ are said to be similar. In the formula, $Q$ is an index reflecting the quality similarity of antibodies $x$ and $y$, and $\epsilon$ is called the antibody similarity threshold. In an antibody population of size m, the number of antibodies antibody $k\left(k=1,2,\dots ,m\right)$ is called the concentration of antibody $k$, and is recorded as $C^k$ [36].

Step 6: Calculation of adaptive optimal crossover rate $C$ and mutation rate $V$: the crossover and mutation operations are performed according to the calculated optimal crossover rate $C$ and mutation rate $V$. The calculation formula of crossover rate $C$ and mutation rate $V$ is [37]:

$$C=\left\{\begin{array}{ll}{C}_1-\frac{\left(C_1-C_2\right)\left(F^{\prime }-F_{av𝘨}\right)}{F_{\max }-F_{av𝘨}}& , F^{\prime }\ge F_{av𝘨}\\ C_1& , F^{\prime }<F_{av𝘨}\end{array}\right.$$

(21)

$$V=\left\{\begin{array}{ll}{V}_1-\frac{\left(V_1-V_2\right)\left(F_{\max }-F\right)}{F_{\max }-F_{av𝘨}}& , F\ge F_{av𝘨}\\ V_1& , F<F_{av𝘨}\end{array}\right.$$

(22)

In the formula, $F_{\max }$ represents the maximum individual fitness value of the current population, $F_{av𝘨}$ represents the average fitness value in the current population, $F^{\prime }$ represents the hybrid fitness value of two individuals, and $F$ represents the fitness of mutant individuals. $C_1>C_2$, $V_1>V_2$.

Step 7: The population is updated, by looping the above operation for the new generation population, continuously updating the fitness value and average fitness value of the population optimal antibody until the maximum fitness satisfies $F_{\max }>F_{𝘨oal}$, or the number of iterations satisfies $𝘨>T$, when the algorithm ends. Otherwise, $𝘨=𝘨+1$ and the the process returns to step 3.

Using the AIGA algorithm to optimize the parameters of FRRBFNN ${\mu }_{ij}$, ${\sigma }_{ij}$, ${\eta }_{hc}$ and ${\omega }_c$, these parameters are encoded as antibodies. The optimal antibody parameters are obtained through the AIGA algorithm until the network obtains the optimal parameter values. The flow of FRRBFNN parameter optimization algorithm based on AIGA is shown in Figure 4.

5. Experiments

5.1. Establishment of Dataset of Shearer Drum Height Prediction Model

5.1.1. Determine Initial Feature Parameters

The experimental data set comes from the 43101 fully mechanized mining face in Yujialiang Mine, Shaanxi, China. This fully mechanized mining face has a length of 351.4 m, an average coal seam thickness of 1.47 m, and an average height of 1.4 m. The degree is 3°–5°. The fully mechanized mining equipment is as follows: the hydraulic support adopts the ZY9200/09/18D double-column shield type, the shearer adopts the MG2 type, and the scraper conveyor adopts the SGZ800/1400 type. The collection time interval is from 7–23 April 2021, and the sampling period is 1.0 s. Figure 5 shows the cutting site of 43101 fully mechanized mining face, including shearer, scraper conveyor and hydraulic support.

There are various types of data for drum height adjustment, including sensing data such as current, temperature, and speed. At present, the monitoring system in the comprehensive collection can easily collect and record these data. The original dataset includes 15 conditional attributes and one set of decision attributes, and the total number of samples is 16,860. The condition attribute can be divided into two categories according to the operate mechanism of the shearer: the state attribute of the shearer, and the state attribute of the shearer drum, respectively. The condition attributes are shown in

Table 1. Initial feature parameters.

Status Attribute Object	Feature Coding	Feature Name	Feature Type	Unit
Shearer status attribute	$c_1$	Shearer location	Numerical	m
	$c_2$	Pitch angle	Numerical	°
	$c_3$	Right traction temperature	Numerical	°C
	$c_4$	Right traction current	Numerical	A
	$c_5$	Left traction temperature	Numerical	°C
	$c_6$	Left traction current	Numerical	A
	$c_7$	Traction direction	Boolean	Left/right
	$c_8$	Traction speed	Numerical	m/min
Drum status attribute	$c_9$	Right drum temperature	Numerical	°C
	$c_{10}$	Right drum current	Numerical	A
	$c_{11}$	Right drum height change	Numerical	m
	$c_{12}$	Left drum temperature	Numerical	°C
	$c_{13}$	Left drum current	Numerical	A
	$c_{14}$	Left drum height change	Numerical	m
	$c_{15}$	Roll angle	Numerical	°

, which lists the relevant operating characteristic parameters of shearer and drum, including current, voltage, temperature, relative position, angle and other sensing characteristic parameters.

In Table 1, two characteristic variables—the pitch angle $c_1$ of the shearer and the roll angle $c_{15}$ of the drum—reflect the fluctuation changes of the working face floor, and to a certain extent reflect the spatial position of the shearer. The height changes $c_{11}$ and $c_{14}$ of the shearer drum reflect the undulation of the working face roof. Therefore, Table 1 not only describes the operating conditions of the shearer, but also to a certain extent describes the environmental conditions of the working face.

The decision attribute is determined by subtracting the height of the left and right drums of the shearer at time t + 1 to the height of the left and right drums of the shearer at time t. When the drum height value at time t + 1 minus the drum height value at time t is equal to 0, the position of the drum of the shearer remains unchanged, and it is recorded as a decision attribute with a value of 0. When the drum height at time t + 1 minus the drum height at time t is greater than 0, the position of the drum of the shearer rises, and it is recorded as a decision attribute with a value of 1; When the drum height at time t + 1 minus the drum height at time t is less than 0, the position of the drum of the shearer drops, which is recorded as a decision attribute with a value of 2. The meaning of decision attributes is shown in

Table 2. Feature decision meaning table.

Right Roller Decision Attribute Classification		Left Roller Decision Attribute Classification
Decision Marker	Decision Implications	Decision Marker	Decision Implications
$d_r\left(0\right)$	drum unchanged	$d_l\left(0\right)$	drum unchanged
$d_r\left(1\right)$	drum rises	$d_l\left(1\right)$	drum rises
$d_r\left(2\right)$	drum lowers	$d_l\left(2\right)$	drum lowers

.

5.1.2. Data Preprocessing

The prediction of shearer drum adjustment is a complex problem based on data mining. The quality of the data determines the quality of the model extracted by the algorithm, and when the sample quality is poor, it is difficult to propose that the model achieves the desired effect. Therefore, in the data preprocessing stage, the original dataset is processed to remove missing values and outliers to build a high-quality dataset [38].

Some data in the original sample data are missing or abnormal. For samples with missing one-dimensional data, this paper uses Lagrangian interpolation to impute the missing values. For a sampling point with multiple attributes that are true or abnormal, the sample is deleted to ensure accuracy. It is inevitable to encounter some outliers due to electrical failure or sensor failure. According to the actual characteristics of these abnormal data, they are treated as missing values or corrected using the mean value, and some of them are deleted.

After the above processing, the missing and abnormal attribute values at the sampling points have been eliminated from the data samples. Among them, the data size of the left drum height adjustment dataset is 6935; the data size of the right drum height adjustment dataset is 6733. The dataset consisting of attribute set $\left\{c_1-c_{15},d_l\right\}$ is called dataset ${\rm I}$, and the dataset consisting of attribute set $\left\{c_1-c_{15},d_r\right\}$ is called dataset ${\rm I}{\rm I}$.

5.1.3. Attribute Reduction Based on Significance

Through K-means method discrete dataset ${\rm I}$ and dataset ${\rm I}{\rm I}$, using the feature reduction method introduced in Section 3 to reduce the dataset ${\rm I}$ and dataset ${\rm I}{\rm I}$. When the significance of an attribute c_i is 0, the influence degree of c_i relative to the decision attribute D is 0, that is, c_i is redundant and needs to be eliminated. The significance of each condition attribute is shown in

Table 3. The significance of each condition attribute of the left drum.

	$c_1$	$c_2$	$c_3$	$c_4$	$c_5$
$si𝘨\left(c_i,C,D\right)$	0.151	0.264	0	0.471	0.026
	$c_6$	$c_7$	$c_8$	$c_9$	$c_{10}$
$si𝘨\left(c_i,C,D\right)$	0.423	0	0.071	0	0
	$c_{11}$	$c_{12}$	$c_{13}$	$c_{14}$	$c_{15}$
$si𝘨\left(c_i,C,D\right)$	0	0.083	0.309	0.216	0.174

and

Table 4. The significance of each condition attribute of the right drum.

	$c_1$	$c_2$	$c_3$	$c_4$	$c_5$
$si𝘨\left(c_i,C,D\right)$	0.178	0.325	0.047	0.287	0
	$c_6$	$c_7$	$c_8$	$c_9$	$c_{10}$
$si𝘨\left(c_i,C,D\right)$	0.086	0	0.074	0.067	0.531
	$c_{11}$	$c_{12}$	$c_{13}$	$c_{14}$	$c_{15}$
$si𝘨\left(c_i,C,D\right)$	0.092	0	0	0	0.621

below.

It can be seen from Table 3 and Table 4 that the significance of the conditional attributes $c_3,c_7,c_9,c_{10},c_{11}$ of the left drum of the shearer to the decision attribute $D$ is 0, so the left drum condition attribute $C$ is relative to the core $B=\left\{c_1,c_2,c_4,c_5,c_6,c_8,c_{12},c_{13},c_{14},c_{15}\right\}$ of the decision attribute $D$; moreover, the significance of the condition attributes $c_5,c_7,c_{12},c_{13},c_{14}$ of the right drum of the coal machine to the decision attribute $D$ is 0, so the condition attribute $C$ of the right drum is relative to the core $B=\left\{c_1,c_2,c_3,c_4,c_6,c_8,c_9,c_{10},c_{11},c_{15}\right\}$ of the decision attribute $D$. Thence, according to Formula (14), the classification ability of conditional attribute $c_i$ for $B$ to $D$ is calculated, as shown in

Table 5. Classification ability of left drum condition attribute c for B to D.

	$c_1$	$c_2$	$c_4$	$c_5$	$c_6$
$si𝘨\left(c_i,B,D\right)$	0.116	0.233	0.470	0	0.423
	$c_8$	$c_{12}$	$c_{13}$	$c_{14}$	$c_{15}$
$si𝘨\left(c_i,B,D\right)$	0.062	0	0.091	0.216	0.289

and

Table 6. Classification ability of right drum condition attribute c for B to D.

	$c_1$	$c_2$	$c_3$	$c_4$	$c_6$
$si𝘨\left(c_i,B,D\right)$	0.124	0.247	0	0.292	0.063
	$c_8$	$c_9$	$c_{10}$	$c_{11}$	$c_{15}$
$si𝘨\left(c_i,B,D\right)$	0.096	0	0.511	0.092	0.473

.

As can be seen from Table 5 and Table 6, for the left drum condition attribute set, deleting the condition attributes $c_5,c_{12}$ from the condition attribute set $B$ does not affect the classification ability of $B$ for $D$, so the final attribute reduction result of the left drum condition attribute set is $P_l=\left\{c_1,c_2,c_4,c_6,c_8,c_{13},c_{14},c_{15}\right\}$; and for the right drum condition attribute set, deleting the condition attributes $c_3,c_9$ from the condition attribute set B does not affect the classification ability of $B$ for $D$, so the final reduction result of the right drum condition attribute set is $P_r=\left\{c_1,c_2,c_4,c_6,c_8,c_{10},c_{11},c_{15}\right\}$.

5.2. Construction of Shearer Drum Height Prediction Model Based on AR-AIGA-FRRBFNN

Through the experiment in Section 5.1, we have established the experimental dataset. The main content of this section is to establish the shearer drum height prediction model based on AR-AIGA-FRRBFNN. The experimental dataset is used for the training and testing of the model, the model is compared with different algorithms to verify its performance, and the experimental results are discussed.

5.2.1. Establishment of Decision Rule Set for Shearer Drum Height

Select the characteristic parameter set P_l and P_r through the significance attribute reduction algorithm as the condition attribute of the shearer left and right drum height, and D_l and D_r as the decision attribute of the shearer left and right drum height, and combine the two to obtain the shearer left and right drum height decision data set. As shown in

Table 7. Left drum height decision table.

Left Drum Height Decision Rule
1	$c_1$$\left(6\right) \mathrm{AND} c_2$$\left(3\right) \mathrm{AND} c_4$$\left(7\right) \mathrm{AND}{c}_6$$\left(1\right) \mathrm{AND} c_8$$\left(1\right) \mathrm{AND} c_{13}$$\left(9\right) \mathrm{AND} c_{14}$$\left(1\right) \mathrm{AND} c_{15}$$\left(1\right)=d_l\left(0\right)$
2	$c_1$$\left(4\right) \mathrm{AND} c_2$$\left(5\right) \mathrm{AND} c_4$$\left(4\right) \mathrm{AND} c_6$$\left(7\right) \mathrm{AND} c_8$$\left(3\right) \mathrm{AND} c_{13}$$\left(9\right) \mathrm{AND} c_{14}$$\left(1\right) \mathrm{AND} c_{15}$$\left(3\right)=d_l\left(0\right)$
3	$c_1$$\left(1\right) \mathrm{AND} c_2$$\left(1\right) \mathrm{AND} c_4$$\left(9\right) \mathrm{AND} c_6$$\left(5\right) \mathrm{AND} c_8$$\left(1\right) \mathrm{AND} c_{13}$$\left(6\right) \mathrm{AND} c_{14}$$\left(1\right) \mathrm{AND} c_{15}$$\left(8\right)=d_l\left(0\right)$
4	$c_1$$\left(4\right) \mathrm{AND} c_2$$\left(1\right) \mathrm{AND} c_4$$\left(4\right) \mathrm{AND} c_6$$\left(7\right) \mathrm{AND} c_8$$\left(8\right) \mathrm{AND} c_{13}$$\left(3\right) \mathrm{AND} c_{14}$$\left(1\right) \mathrm{AND} c_{15}$$\left(10\right)=d_l\left(0\right)$
5	$c_1$$\left(6\right) \mathrm{AND} c_2$$\left(4\right) \mathrm{AND} c_4$$\left(2\right) \mathrm{AND} c_6$$\left(4\right) \mathrm{AND} c_8$$\left(9\right) \mathrm{AND} c_{13}$$\left(9\right) \mathrm{AND} c_{14}$$\left(4\right) \mathrm{AND} c_{15}$$\left(1\right)=d_l\left(0\right)$
6	$c_1$$\left(3\right) \mathrm{AND} c_2$$\left(1\right) \mathrm{AND} c_4$$\left(8\right) \mathrm{AND} c_6$$\left(4\right) \mathrm{AND} c_8$$\left(7\right) \mathrm{AND} c_{13}$$\left(1\right) \mathrm{AND} c_{14}$$\left(1\right) \mathrm{AND} c_{15}$$\left(1\right)=d_l\left(0\right)$
7	$c_1$$\left(6\right) \mathrm{AND} c_2$$\left(3\right) \mathrm{AND} c_4$$\left(7\right) \mathrm{AND} c_6$$\left(7\right) \mathrm{AND} c_8$$\left(8\right) \mathrm{AND} c_{13}$$\left(9\right) \mathrm{AND} c_{14}$$\left(4\right) \mathrm{AND} c_{15}$$\left(3\right)=d_l\left(0\right)$
8	$c_1$$\left(5\right) \mathrm{AND} c_2$$\left(5\right) \mathrm{AND} c_4$$\left(6\right) \mathrm{AND} c_6$$\left(3\right) \mathrm{AND} c_8$$\left(1\right) \mathrm{AND} c_{13}$$\left(9\right) \mathrm{AND} c_{14}$$\left(4\right) \mathrm{AND} c_{15}$$\left(7\right)=d_l\left(0\right)$
9	$c_1$$\left(3\right) \mathrm{AND} c_2$$\left(4\right) \mathrm{AND} c_4$$\left(2\right) \mathrm{AND} c_6$$\left(7\right) \mathrm{AND} c_8$$\left(7\right) \mathrm{AND} c_{13}$$\left(9\right) \mathrm{AND} c_{14}$$\left(1\right) \mathrm{AND} c_{15}$$\left(4\right)=d_l\left(0\right)$
…

and

Table 8. Right drum height decision table.

Right Drum Height Decision Rule
1	$c_1$$\left(5\right) \mathrm{AND} c_2$$\left(2\right) \mathrm{AND} c_4$$\left(2\right) \mathrm{AND} c_6$$\left(2\right) \mathrm{AND} c_8$$\left(1\right) \mathrm{AND} c_{10}$$\left(7\right) \mathrm{AND} c_{11}$$\left(3\right) \mathrm{AND} c_{15}$$\left(2\right)=d_r\left(0\right)$
2	$c_1$$\left(2\right) \mathrm{AND} c_2$$\left(4\right) \mathrm{AND} c_4$$\left(8\right) \mathrm{AND} c_6$$\left(6\right) \mathrm{AND} c_8$$\left(5\right) \mathrm{AND} c_{10}$$\left(10\right) \mathrm{AND} c_{11}$$\left(1\right) \mathrm{AND} c_{15}$$\left(5\right)=d_r\left(0\right)$
3	$c_1$$\left(6\right) \mathrm{AND} c_2$$\left(1\right) \mathrm{AND} c_4$$\left(3\right) \mathrm{AND} c_6$$\left(8\right) \mathrm{AND} c_8$$\left(5\right) \mathrm{AND} c_{10}$$\left(10\right) \mathrm{AND} c_{11}$$\left(1\right) \mathrm{AND} c_{15}$$\left(12\right)=d_r\left(0\right)$
4	$c_1$$\left(4\right) \mathrm{AND} c_2$$\left(1\right) \mathrm{AND} c_4$$\left(3\right) \mathrm{AND} c_6$$\left(8\right) \mathrm{AND} c_8$$\left(4\right) \mathrm{AND} c_{10}$$\left(9\right) \mathrm{AND} c_{11}$$\left(3\right) \mathrm{AND} c_{15}$$\left(3\right)=d_r\left(0\right)$
5	$c_1$$\left(4\right) \mathrm{AND} c_2$$\left(4\right) \mathrm{AND} c_4$$\left(8\right) \mathrm{AND} c_6$$\left(6\right) \mathrm{AND} c_8$$\left(4\right) \mathrm{AND} c_{10}$$\left(10\right) \mathrm{AND} c_{11}$$\left(3\right) \mathrm{AND} c_{15}$$\left(1\right)=d_r\left(0\right)$
6	$c_1$$\left(4\right) \mathrm{AND} c_2$$\left(1\right) \mathrm{AND} c_4$$\left(8\right) \mathrm{AND} c_6$$\left(6\right) \mathrm{AND} c_8$$\left(4\right) \mathrm{AND} c_{10}$$\left(6\right) \mathrm{AND} c_{11}$$\left(3\right) \mathrm{AND} c_{15}$$\left(9\right)=d_r\left(0\right)$
7	$c_1$$\left(5\right) \mathrm{AND} c_2$$\left(2\right) \mathrm{AND} c_4$$\left(1\right) \mathrm{AND} c_6$$\left(5\right) \mathrm{AND} c_8$$\left(3\right) \mathrm{AND} c_{10}$$\left(10\right) \mathrm{AND} c_{11}$$\left(3\right) \mathrm{AND} c_{15}$$\left(1\right)=d_r\left(0\right)$
8	$c_1$$\left(6\right) \mathrm{AND} c_2$$\left(4\right) \mathrm{AND} c_4$$\left(3\right) \mathrm{AND} c_6$$\left(6\right) \mathrm{AND} c_8$$\left(3\right) \mathrm{AND} c_{10}$$\left(8\right) \mathrm{AND} c_{11}$$\left(3\right) \mathrm{AND} c_{15}$$\left(8\right)=d_r\left(0\right)$
9	$c_1$$\left(1\right) \mathrm{AND} c_2$$\left(4\right) \mathrm{AND} c_4$$\left(2\right) \mathrm{AND} c_6$$\left(2\right) \mathrm{AND} c_8$$\left(6\right) \mathrm{AND} c_{10}$$\left(6\right) \mathrm{AND} c_{11}$$\left(2\right) \mathrm{AND} c_{15}$$\left(8\right)=d_r\left(0\right)$
…

, the characteristic attribute c represents the shearer operation characteristic parameters after attribute reduction, which corresponds to the attributes in Table 1, and the decision attribute d represents the change trend of the shearer drum.

The decision rule sets for the height adjustment of the left and right drums of the shearer in Table 7 and Table 8 contain 864 and 778 decision rules, respectively. Through the values of different condition attributes, such as the shearer position, pitch angle, traction current, etc.

5.2.2. AR-AIGA-FRRBFNN Model and Evaluation Method

According to the shearer drum height decision rules in Table 7 and Table 8, the network structure parameters of the shearer left and right drum height prediction model can be determined. The number of input layer neurons of the left drum height prediction network model is 8; the number of neurons in the hidden layer is 864, which represents the number of decision rules; the number of neurons in the fuzzy rough membership layer is 3, which represents the rule set with the same decision value; and the number of neurons in the output layer is 1, which represents the predicted shearer drum height. Similarly, the number of neurons in the input layer of the right drum height prediction network model is 8, the number of neurons in the hidden layer is 778, the number of neurons in the fuzzy rough membership layer is 3, and the number of neurons in the output layer is 1, representing the shearer drum height predicted by the network.

The parameters of the adaptive immune genetic algorithm include the population size $Q$, the initial crossover rate $C_1$ and $C_2$, and the initial mutation rate $V_1$ and $V_2$. In this study, AIGA operating parameters were determined by repeated experimental tests. We determined the population size to be $Q=100$, the maximum number of iterations to be $T=50$, the initial crossover rates to be $C_1=0.65$, $C_2=0.25$, the initial mutation rates to be $V_1=0.03$, $V_2=0.02$, the original number of iterations to be $𝘨=0$ and $e=0.01$, and the fitness objective function to be $F_{𝘨oal}=0.9901$.

The number of training sample sets was 90% of l and r, and the size of datasets were 6241 and 6059, respectively. The remaining 10% was used as test sets, and the size of datasets were 694 and 674, respectively.

In order to verify the reliability of the control model proposed in this study, the attribute reduction sets $p_l$ and $p_r$ were respectively input into the radial basis function neural network (RBF), support vector regression (SVR), gated recurrent unit neural network (GRU) three regression prediction models for training and prediction, and the attribute reduction set and the dataset without attribute reduction were input into the AIGA-FRRBFNN model for training and prediction comparison. Finally, these were compared with the roller height adjustment model, with the Memory Strengthen Long Short-term Memory (MSLSTM) [12], and with the adaptive fuzzy reasoning Petri net (AFRPN) [16] model proposed in the recent study.

Through repeated experiments, this study determined the best super parameters of the above prediction model and improved the prediction accuracy of the comparison model, as shown in

Table 9. Hyperparameters of different prediction models.

Model	Hyperparameters	Final Value
RBF	Primary function	Gaussian function
SVR	Kernel function type	Radial basis kernel function
	Kernel coefficient g	0.125
	penalty coefficientC	151
GRU	GRU helped layer	1
	Number of hidden layer neurons	250
MSLSTM [12]	MSLSTM layers	3
	Number of neurons in the first hidden layer	100
	Number of neurons in the second hidden layer	50
	Number of neurons in the third hidden layer	50
AFRPN [16]	Attenuation rate $\rho$	Self-adaption

.

In Table 9, the LIBSVM toolkit is used for SVR experiments. By calling newrbe function in matlab, the RBF neural network is established for the experiment. In order to evaluate the regression prediction effect of the model, this study compared six models, namely FRRBF, RBF, SVR, GRU, MSLSTM [12] and AFRPN [16], based on the mean absolute error (MAE), mean absolute percentage error (MAPE) and root mean square error (RMSE).

In this study, we used MATLAB R2018b for program development and performed our experiments on a hardware platform with an Intel(R) Core(TM) i5-6500 CPU @ 3.20 GHz, 16.0 GB RAM, and the Windows 7 64-bit operating system.

Based on AR-AIGA-FRRBF, AIGA-FRRBF, AR-GRU, AR-SVR, AR-RBF, MSLSTM, and AFRPN, the height prediction of the training samples of the left and right drums of the shearer is shown in

Table 10. Predicted height of the training sample of the left drum of the shearer.

Number of Sample	Predicted Drum Height/m							Real Drum Height/m
	AR-AIGA-FRRBF	AIGA-FRRBF	AR-GRU	AR-SVR	AR-RBF	MSLSTM [12]	AFRPN [16]
1	1.4637	1.4942	1.5320	1.5162	1.5691	1.5135	1.4898	1.44
2	1.4284	1.4750	1.5094	1.4893	1.5236	1.5091	1.4767	1.40
3	1.4477	1.4571	1.5476	1.4978	1.5721	1.4890	1.4635	1.43
4	1.4653	1.4835	1.5816	1.6060	1.6367	1.5243	1.4982	1.44
5	1.4816	1.4779	1.5273	1.4725	1.5565	1.5287	1.4673	1.45
6	1.5031	1.5283	1.5331	1.5126	1.5476	1.5397	1.5109	1.47
7	1.4907	1.4899	1.5662	1.5439	1.6101	1.5383	1.4976	1.44
8	1.5135	1.5362	1.5534	1.4819	1.5633	1.5546	1.5455	1.45
9	1.4762	1.5018	1.5125	1.4633	1.4875	1.5075	1.4894	1.43
…

and

Table 11. Predicted height of the training sample of the right drum of the shearer.

Number of Sample	Predicted Drum Height/m							Real Drum Height/m
	AR-AIGA-FRRBF	AIGA-FRRBF	AR-GRU	AR-SVR	AR-RBF	MSLSTM [12]	AFRPN [16]
1	1.4736	1.4876	1.5171	1.5315	1.6281	1.5128	1.4967	1.45
2	1.5165	1.5461	1.5875	1.5774	1.6472	1.4862	1.5458	1.49
3	1.5548	1.5567	1.5796	1.5643	1.5849	1.5076	1.5577	1.52
4	1.5951	1.6124	1.6647	1.6341	1.6762	1.6087	1.6021	1.57
5	1.6218	1.6185	1.6731	1.6681	1.6967	1.6363	1.6475	1.60
6	1.6335	1.6757	1.6970	1.6784	1.7313	1.6488	1.6324	1.62
7	1.6973	1.7234	1.7536	1.7747	1.8178	1.7336	1.7142	1.66
8	1.7741	1.7789	1.8437	1.8065	1.8567	1.7996	1.7869	1.73
9	1.7316	1.7573	1.8131	1.7898	1.8453	1.7861	1.7403	1.71
…

.

5.2.3. Prediction Results of Shearer Drum Height Based on AR-FRRBF

It can be seen from

Table 12. Comparison of prediction performance of left drum height of shearer with different models.

Model	MAE/mm	MAPE/%	RMSE/mm
AR-AIGA-FRRBF	18.3	0.96%	21.2
AIGA-FRRBF	32.1	1.70%	36.4
AR-GRU	56.0	2.93%	66.5
AR-SVR	49.7	2.62%	59.5
AR-RBF	63.6	3.35%	72.3
MSLSTM [12]	41.2	2.13%	47.2
AFRPN [16]	36.9	2.01%	43.3

and

Table 13. Comparison of prediction performance of right drum height of shearer with different models.

Model	MAE/mm	MAPE/%	RMSE/mm
AR-AIGA-FRRBF	17.2	0.93%	22.4
AIGA-FRRBF	24.4	1.31%	31.3
AR-GRU	45.2	2.41%	54.3
AR-SVR	36.1	1.94%	45.3
AR-RBF	59.6	3.22%	67.7
MSLSTM [12]	33.5	1.92%	39.3
AFRPN [16]	27.6	1.60%	33.8

that the AR-AIGA-FRRBF model can better extract the nonlinear variation features of the learning cut height, and obtain more accurate predictions. Through rough set significance attribute reduction, the prediction ability of the network can be effectively improved. Relative to the AIGA-FRRBF model, AR-GRU model, AR-SVR model, AR-RBF model, MSLSTM model and AFRPN model, the values of the shearer left drum height test set predicted by the AR-AIGA-FRRBF model were as follows: MAE decreased by 43.0%, 67.3%, 63.2%, 71.2%, 55.6%, and 50.4%, respectively; MAPE decreased by 43.5%, 67.2%, 63.4%, 71.3%, 54.9%, and 52.2%, respectively; and RMSE decreased by 41.8%, 68.1%, 64.4%, 70.7%, 55.1%, and 51.0%, respectively. Similarly, relative to the AIGA-FRRBF model, AR-GRU model, AR-SVR model, AR-RBF model, MSLSTM model and AFRPN model, the values of the shearer right drum height test set predicted by the AR-AIGA-FRRBF model were as follows: MAE decreased by 29.5%, 61.9%, 52.3%, 71.1%, 48.6%, and 37.7%, respectively; MAPE decreased by 29.0%, 61.4%, 52.0%, 71.1%, 51.5%, and 41.8%, respectively; and RMSE decreased by 28.4%, 58.8%, 50.6%, 66.9%, 43.0%, and 33.7%, respectively. The prediction accuracy has been improved.

5.3. Discussion

It can be seen from Figure 6 and Figure 7 that the predicted trajectory obtained by the AR-AIGA-FRRBFNN model is like the real trajectory, and the deviation from the real trajectory is small.

Compared with the AIGA-FRRBFNN model without significance attribute reduction, AR-AIGA-FRRBFNN has higher prediction accuracy and displays a smoother curve in most cases, which indicates that the method based on significance attribute reduction eliminates indicators that have less impact on shearer drum height decision-making, and improves the accuracy of drum height prediction. Compared with the AR-SVR model, AR-GRU and AR-RBF neural network models after significance attribute reduction, the AR-AIGA-FRBFNN has higher prediction accuracy. Compared with the MSLSTM neural network model and AFRPN model, the model proposed in this study has higher prediction accuracy, more stable prediction height fluctuation, and its prediction error is less than 0.075 m.

For the AR-SVR model, the poor performance may be due to the large dataset and large data dimensions, both of which would affect the prediction of the shearer drum height. For the AR-GRU and AR-RBF neural network models, the reason for the large prediction error may be that the fuzzy decision of shearer drum height affects the training of neurons. For the MSLSTM and AFRPN models, the prediction accuracy is not as high as the prediction model proposed in this study. The reason may be the redundancy of characteristic attributes in the parameter list.

To reduce the influence of prediction error on the actual application process at a fully mechanized mining face, some mechanisms should be added. A soft sensor is a model for industrial process monitoring, control, and optimization. It can evaluate some parameters that are difficult to measure, and integrate with other models to improve the performance of the model [39,40]. The soft sensor model can optimize the prediction performance to a certain extent. In addition, we can adjust the maximum number of training samples of AR-AIGA-FRRBFNN, or optimize the calculation method of discrete input data to further reduce the prediction error and adapt it to the needs of working conditions. This will be the focus of our future research.

It should be noted that the reliability of model is based on multiple data samples and multiple data dimensions. When the data sample is small or the data dimension is insufficient, it may be difficult to obtain enough decision rules to support the model. Therefore, the application problem of less data samples or data dimensions is not within the scope of application of the model.

In general, the AR-AIGA-FRRBF model can effectively predict the adjustment of the shearer drum height change, achieve a high accuracy, and can adapt to the change of the coal seam roof. The drum height adjustment method can be applied to production practice and has practical and research significance.

6. Conclusions

This paper proposes a fuzzy rough radial basis neural network model based on rough set attribute reduction and adaptive immune genetic algorithm optimization, which can adjust the height of the shearer drum according to real-time production data. Firstly, based on the significance attribute reduction algorithm of rough set, redundant attributes are eliminated, and a attribute reduction set and bulge decision rule dataset are established. Secondly, the challenges of intelligent cylinder adjustment for coal miners are analyzed, the fuzzy rough radial basis function neural network is proposed, and an adaptive immune genetic algorithm for parameter optimization of fuzzy rough radial basis function neural network is designed. Finally, the model is verified by the data collected in Yujialiang coal mine.

The experimental results show that the method has better performance than AIGA-FRRBF, AR-GRU, AR-SVR, AR-RBF, MSLSTM, AFRPN and other machine learning methods in the prediction of drum height value. Hereafter, to improve the accuracy and generalization of the model, we need to collect more fully mechanized mining face monitoring data and improve the optimization model to obtain more accurate prediction results.