# Prediction Model of Mining Subsidence Parameters Based on Fuzzy Clustering

Authors: Fei Cheng; Jun Yang; Ziwen Zhang; Jingliang Yu; Xuelian Wang; Yongdong Wu; Zhengyi Guo; Hui Li; Meng Xu
Journal: Journal of Mathematics
 (2022)

---

## Abstract

In view of the inaccuracy of rock movement observation data and the inaccuracy of mining subsidence prediction parameters, a prediction model of mining subsidence parameters based on fuzzy clustering is proposed. Through the analysis of the main geological and mineral characteristics of mining subsidence, the geological and mineral characteristics are simplified according to the third similar theorem. The feature equation is obtained by using the equation analysis method and dimension analysis method. The original fuzzy clustering method is improved, and the IWFCM_CCS algorithm based on competitive merger strategy is obtained. The data of rock movement observation are analyzed by fuzzy clustering. The membership matrix and clustering center of observation station data are obtained, and the regression model based on the weight of membership degree is established. The accuracy and feasibility of the parameter prediction model are verified by analyzing and comparing the actual measurement data and the predicted results of the model. The method reduces the error of the predicted parameters caused by the observation data and provides a method for the future calculation of the predicted parameters.


---

## Body

## 1. Introduction

Mining subsidence is expected to be developing in the direction of intelligence and visualization. Today, with the rapid development of technologies such as sensors, computers, Internet of Things, and data storage, enterprise information management systems have been continuously popularized. The advancement of modern surveying and mapping science and technology has resulted in more and more data generated from the observation of surface subsidence. If these data are analyzed and processed quickly, abnormal data can be eliminated, and useful data can be extracted; this will greatly improve the accuracy and efficiency of settlement predictions [1–6].Coal mining affects the production and life safety of people around, so the prediction of mining area deformation becomes very important. The accuracy of rock movement parameters affects the accuracy of the predicted results. Aiming at the problem of inaccurate calculation of rock movement parameters due to the large amount of data generated by rock movement observation, a mining subsidence parameter prediction model based on big data has been established [7–12]. Through the analysis and processing of rock movement observation data, the mining subsidence parameter prediction model is derived, which improves the accuracy and calculation efficiency of rock movement parameters, thereby improving the accuracy of mining subsidence prediction and the safety of the coal mining process.The following is a summary of the research. Section1 contains the introduction. Section 2 discusses the analysis of the main geological characteristics of mining subsidence. Section 3 discusses the preprocessing of rock movement observation data. Section 4 discusses the project example verification with tables, and finally, the conclusion is given in Section 5.


## 2. Analysis of the Main Geological Characteristics of Mining Subsidence

Mining subsidence happens when mining operations weaken or hollow out the Earth beneath or near a property’s foundations. The ground beneath a building moves downhill as a result of this. Types of mining subsidence are given below.


### 2.1. Simplified Geological Features

As the stress state around the mining area is constantly unbalanced and balanced during the mining process, mining subsidence is caused by complex physical and mechanical changes. Figure1 shows the main geological factors related to surface subsidence.Figure 1
Factors of mining subsidence.It can be seen from Figure1 that many complex factors are involved in the mining subsidence process. The mining subsidence method must be simplified in order to conduct additional research on it.From the similar third theorem [13], geological mining conditions can be obtained: mining conditions are the first mining, the coal mining method is longwall mining, and the roof management method is the full caving method.


### 2.2. Feature Extraction

#### 2.2.1. Equation Analysis Method

Based on the linear elastic model of inclined coal seams, the following equations are listed:(1)∂σy∂y+∂τyz∂z+λρg=0∂τyz∂y+∂σz∂z+ρg=0εy=∂u∂yεz=∂w∂zγyz=∂u∂z+∂w∂yγyz=21+μEτyzεy=1+μE1−μσy−μσzεz=1+μE1−μσz−μσy.In the formula,σy and σy, respectively, represent the normal stress in two directions; τyz represents the shear stress; εy and εz represent the normal strain, respectively; γyz represents the shear strain; and W and U represent the sinking value and horizontal movement, respectively.When the two mining subsidence phenomena conform to the similar third theorem, we can get(2)y″=y0y′z″=z0z′u″=u0u′w″=w0w′εy″=εy0εy′εz″=εz0εz′γyz″=γyz0γyz′σy″=σy0σy′σz″=σz0σz′τyz″=τyz0τyz′E″=E0E′μ=μ0μ′λ″=λ0λ′ρ″=ρ0ρ′g″=g0g′.TakingZ0=H, W0=mcosα, E0=Emid, g0=g and combining the boundary conditions that when z=H, then σy=σz=τyz=0, the similarity criterion can be obtained.(3)Π1′=yHΠ2′=zHΠ3′=wmcosαΠ4′=umcosαΠ5′=HεymcosαΠ6′=EEmidΠ7′=ρgH2EmidmcosαΠ8′=λΠ9′=μ.Becausey,z,w,u, and εy are external features, Π1′∼Π5′ is a dependent variable feature. Therefore, four geological and mineral features Π6′∼Π9′ are extracted by the equation analysis method.


#### 2.2.2. Dimensional Analysis

For mining subsidence, on the basis of formula (3), the loose layer thickness h, strike length l, and inclined width m are added. The mass system is adopted, and the basic physical quantities are M, L, and T. Therefore, the mining subsidence equation is(4)fy,z,w,u,H,h,L1,L3,m,α,εy,E,ρ,g,λ,μ,M,L,T=0.Because of the homogeneity of the dimensions of equation (4), an exponential equation can be obtainedh.(5)a11+a12+a17=0a1+a2+a3+a4+a6+a7+a8+a9+a10−a11−3a12+a13+a18=0−2a11−2a13+a19=0.According to the similarity transformation of the matrix, 16 similarity criteria can be obtained:(6)π1=yLπ2=zLπ3=wLπ4=uLπ5=εyπ6=HLπ7=hLπ8=L3Lπ9=L1Lπ10=mLπ11=ELT2Mπ12=ρL3Mπ13=gT2Lπ14=απ15=λπ16=μ.Among them,π1∼π4,π6∼π13 have no actual physical meaning, and 13 similar criteria can be obtained.(7)Π1″=yHΠ2″=zHΠ3″=wmΠ4″=umΠ5″=εyΠ6″=HmΠ7″=hHΠ8″=L3HΠ9″=L1HΠ10″=ρgHEΠ11″=αΠ12″=λΠ13″=μ.In the same way,Π1″∼Π5″ belong to the dependent variable characteristics, and the geological and mineral characteristics are Π6″∼Π13″.


#### 2.2.3. Comprehensive Selection of Geological and Mineral Features

According to formulae (3) and (7), the following analysis and processing can be made:① Because of the similarity ofy,z,w,u, Π1=Π1″,Π1=Π2″,Π1=Π3″,Π1=Π4″,Π1=Π5″.② SinceΠ6″×Π″=Π7′×cosα, which corresponds to the coal seam depth ratio, Π10=Π7″.③ Due to the influence of loose layers,Π6=h/H−h.④ Due to the influence of the working surface dimensions,Π7=L3/H,Π8=L1/H.⑤ Due to the effects of modulus of elasticity, inclination angle, lateral stress coefficient, and Poisson’s ratio, letΠ9=E/Emid,Π11=α,Π12=λ,Π13=μ.Similar criteria are selected from this:(8)Π1=yHΠ2=zHΠ3=wmcosαΠ4=umcosαΠ5=HεymcosαΠ6=hH−hΠ7=L3HΠ8=L1HΠ9=EEmidΠ10=ρgH2EmidmcosαΠ11=αΠ12=λΠ13=μ.In the same way,Π1∼Π5 belong to the characteristics of the dependent variable, and the geological and mineral characteristics are Π6∼Π13.


### 2.3. Characteristic Expressions of Expected Parameters

Based on the observation data, the multiple correlation coefficient method is used to analyze the primary and secondary characteristics of geology and minerals, and the expression can be obtained as [14](9)fyH,zH,wmcosα,umcosα,Hmcosαεy,hH−h,EEmid,ρgH2Emidmcosα,α=0.Therefore, the characteristic expressions of ground subsidence and horizontal movement are(10)w=f1yH,zH,hH−h,EEmid,ρgH2Emidmcosα,αu=f2yH,zH,hH−h,EEmid,ρgH2Emidmcosα,α.The characteristic expression of the sinking coefficient is(11)q=f1y/H,z/H,h/H−h,E/Emid,ρgH2/Emidmcosα,αmcosα.According to the boundary conditions of the mining area,z=H, and z has nothing to do with Y; then,(12)q=g1hH−h,EEmid,ρgH2Emidmcosα,α.The characteristic expression of the horizontal movement coefficient is(13)b=g2hH−h,EEmid,ρgH2Emidmcosα,α.The characteristic expression that mainly affects the angle tangent is(14)tanβ=g3hH−h,EEmid,ρgH2Emidmcosα,α.The characteristic expression of the inflection point offset is(15)sH=g4hH−h,EEmid,ρgH2Emidmcosα,α.


## 2.1. Simplified Geological Features

As the stress state around the mining area is constantly unbalanced and balanced during the mining process, mining subsidence is caused by complex physical and mechanical changes. Figure1 shows the main geological factors related to surface subsidence.Figure 1
Factors of mining subsidence.It can be seen from Figure1 that many complex factors are involved in the mining subsidence process. The mining subsidence method must be simplified in order to conduct additional research on it.From the similar third theorem [13], geological mining conditions can be obtained: mining conditions are the first mining, the coal mining method is longwall mining, and the roof management method is the full caving method.


## 2.2. Feature Extraction

### 2.2.1. Equation Analysis Method

Based on the linear elastic model of inclined coal seams, the following equations are listed:(1)∂σy∂y+∂τyz∂z+λρg=0∂τyz∂y+∂σz∂z+ρg=0εy=∂u∂yεz=∂w∂zγyz=∂u∂z+∂w∂yγyz=21+μEτyzεy=1+μE1−μσy−μσzεz=1+μE1−μσz−μσy.In the formula,σy and σy, respectively, represent the normal stress in two directions; τyz represents the shear stress; εy and εz represent the normal strain, respectively; γyz represents the shear strain; and W and U represent the sinking value and horizontal movement, respectively.When the two mining subsidence phenomena conform to the similar third theorem, we can get(2)y″=y0y′z″=z0z′u″=u0u′w″=w0w′εy″=εy0εy′εz″=εz0εz′γyz″=γyz0γyz′σy″=σy0σy′σz″=σz0σz′τyz″=τyz0τyz′E″=E0E′μ=μ0μ′λ″=λ0λ′ρ″=ρ0ρ′g″=g0g′.TakingZ0=H, W0=mcosα, E0=Emid, g0=g and combining the boundary conditions that when z=H, then σy=σz=τyz=0, the similarity criterion can be obtained.(3)Π1′=yHΠ2′=zHΠ3′=wmcosαΠ4′=umcosαΠ5′=HεymcosαΠ6′=EEmidΠ7′=ρgH2EmidmcosαΠ8′=λΠ9′=μ.Becausey,z,w,u, and εy are external features, Π1′∼Π5′ is a dependent variable feature. Therefore, four geological and mineral features Π6′∼Π9′ are extracted by the equation analysis method.


### 2.2.2. Dimensional Analysis

For mining subsidence, on the basis of formula (3), the loose layer thickness h, strike length l, and inclined width m are added. The mass system is adopted, and the basic physical quantities are M, L, and T. Therefore, the mining subsidence equation is(4)fy,z,w,u,H,h,L1,L3,m,α,εy,E,ρ,g,λ,μ,M,L,T=0.Because of the homogeneity of the dimensions of equation (4), an exponential equation can be obtainedh.(5)a11+a12+a17=0a1+a2+a3+a4+a6+a7+a8+a9+a10−a11−3a12+a13+a18=0−2a11−2a13+a19=0.According to the similarity transformation of the matrix, 16 similarity criteria can be obtained:(6)π1=yLπ2=zLπ3=wLπ4=uLπ5=εyπ6=HLπ7=hLπ8=L3Lπ9=L1Lπ10=mLπ11=ELT2Mπ12=ρL3Mπ13=gT2Lπ14=απ15=λπ16=μ.Among them,π1∼π4,π6∼π13 have no actual physical meaning, and 13 similar criteria can be obtained.(7)Π1″=yHΠ2″=zHΠ3″=wmΠ4″=umΠ5″=εyΠ6″=HmΠ7″=hHΠ8″=L3HΠ9″=L1HΠ10″=ρgHEΠ11″=αΠ12″=λΠ13″=μ.In the same way,Π1″∼Π5″ belong to the dependent variable characteristics, and the geological and mineral characteristics are Π6″∼Π13″.


### 2.2.3. Comprehensive Selection of Geological and Mineral Features

According to formulae (3) and (7), the following analysis and processing can be made:① Because of the similarity ofy,z,w,u, Π1=Π1″,Π1=Π2″,Π1=Π3″,Π1=Π4″,Π1=Π5″.② SinceΠ6″×Π″=Π7′×cosα, which corresponds to the coal seam depth ratio, Π10=Π7″.③ Due to the influence of loose layers,Π6=h/H−h.④ Due to the influence of the working surface dimensions,Π7=L3/H,Π8=L1/H.⑤ Due to the effects of modulus of elasticity, inclination angle, lateral stress coefficient, and Poisson’s ratio, letΠ9=E/Emid,Π11=α,Π12=λ,Π13=μ.Similar criteria are selected from this:(8)Π1=yHΠ2=zHΠ3=wmcosαΠ4=umcosαΠ5=HεymcosαΠ6=hH−hΠ7=L3HΠ8=L1HΠ9=EEmidΠ10=ρgH2EmidmcosαΠ11=αΠ12=λΠ13=μ.In the same way,Π1∼Π5 belong to the characteristics of the dependent variable, and the geological and mineral characteristics are Π6∼Π13.


## 2.2.1. Equation Analysis Method

Based on the linear elastic model of inclined coal seams, the following equations are listed:(1)∂σy∂y+∂τyz∂z+λρg=0∂τyz∂y+∂σz∂z+ρg=0εy=∂u∂yεz=∂w∂zγyz=∂u∂z+∂w∂yγyz=21+μEτyzεy=1+μE1−μσy−μσzεz=1+μE1−μσz−μσy.In the formula,σy and σy, respectively, represent the normal stress in two directions; τyz represents the shear stress; εy and εz represent the normal strain, respectively; γyz represents the shear strain; and W and U represent the sinking value and horizontal movement, respectively.When the two mining subsidence phenomena conform to the similar third theorem, we can get(2)y″=y0y′z″=z0z′u″=u0u′w″=w0w′εy″=εy0εy′εz″=εz0εz′γyz″=γyz0γyz′σy″=σy0σy′σz″=σz0σz′τyz″=τyz0τyz′E″=E0E′μ=μ0μ′λ″=λ0λ′ρ″=ρ0ρ′g″=g0g′.TakingZ0=H, W0=mcosα, E0=Emid, g0=g and combining the boundary conditions that when z=H, then σy=σz=τyz=0, the similarity criterion can be obtained.(3)Π1′=yHΠ2′=zHΠ3′=wmcosαΠ4′=umcosαΠ5′=HεymcosαΠ6′=EEmidΠ7′=ρgH2EmidmcosαΠ8′=λΠ9′=μ.Becausey,z,w,u, and εy are external features, Π1′∼Π5′ is a dependent variable feature. Therefore, four geological and mineral features Π6′∼Π9′ are extracted by the equation analysis method.


## 2.2.2. Dimensional Analysis

For mining subsidence, on the basis of formula (3), the loose layer thickness h, strike length l, and inclined width m are added. The mass system is adopted, and the basic physical quantities are M, L, and T. Therefore, the mining subsidence equation is(4)fy,z,w,u,H,h,L1,L3,m,α,εy,E,ρ,g,λ,μ,M,L,T=0.Because of the homogeneity of the dimensions of equation (4), an exponential equation can be obtainedh.(5)a11+a12+a17=0a1+a2+a3+a4+a6+a7+a8+a9+a10−a11−3a12+a13+a18=0−2a11−2a13+a19=0.According to the similarity transformation of the matrix, 16 similarity criteria can be obtained:(6)π1=yLπ2=zLπ3=wLπ4=uLπ5=εyπ6=HLπ7=hLπ8=L3Lπ9=L1Lπ10=mLπ11=ELT2Mπ12=ρL3Mπ13=gT2Lπ14=απ15=λπ16=μ.Among them,π1∼π4,π6∼π13 have no actual physical meaning, and 13 similar criteria can be obtained.(7)Π1″=yHΠ2″=zHΠ3″=wmΠ4″=umΠ5″=εyΠ6″=HmΠ7″=hHΠ8″=L3HΠ9″=L1HΠ10″=ρgHEΠ11″=αΠ12″=λΠ13″=μ.In the same way,Π1″∼Π5″ belong to the dependent variable characteristics, and the geological and mineral characteristics are Π6″∼Π13″.


## 2.2.3. Comprehensive Selection of Geological and Mineral Features

According to formulae (3) and (7), the following analysis and processing can be made:① Because of the similarity ofy,z,w,u, Π1=Π1″,Π1=Π2″,Π1=Π3″,Π1=Π4″,Π1=Π5″.② SinceΠ6″×Π″=Π7′×cosα, which corresponds to the coal seam depth ratio, Π10=Π7″.③ Due to the influence of loose layers,Π6=h/H−h.④ Due to the influence of the working surface dimensions,Π7=L3/H,Π8=L1/H.⑤ Due to the effects of modulus of elasticity, inclination angle, lateral stress coefficient, and Poisson’s ratio, letΠ9=E/Emid,Π11=α,Π12=λ,Π13=μ.Similar criteria are selected from this:(8)Π1=yHΠ2=zHΠ3=wmcosαΠ4=umcosαΠ5=HεymcosαΠ6=hH−hΠ7=L3HΠ8=L1HΠ9=EEmidΠ10=ρgH2EmidmcosαΠ11=αΠ12=λΠ13=μ.In the same way,Π1∼Π5 belong to the characteristics of the dependent variable, and the geological and mineral characteristics are Π6∼Π13.


## 2.3. Characteristic Expressions of Expected Parameters

Based on the observation data, the multiple correlation coefficient method is used to analyze the primary and secondary characteristics of geology and minerals, and the expression can be obtained as [14](9)fyH,zH,wmcosα,umcosα,Hmcosαεy,hH−h,EEmid,ρgH2Emidmcosα,α=0.Therefore, the characteristic expressions of ground subsidence and horizontal movement are(10)w=f1yH,zH,hH−h,EEmid,ρgH2Emidmcosα,αu=f2yH,zH,hH−h,EEmid,ρgH2Emidmcosα,α.The characteristic expression of the sinking coefficient is(11)q=f1y/H,z/H,h/H−h,E/Emid,ρgH2/Emidmcosα,αmcosα.According to the boundary conditions of the mining area,z=H, and z has nothing to do with Y; then,(12)q=g1hH−h,EEmid,ρgH2Emidmcosα,α.The characteristic expression of the horizontal movement coefficient is(13)b=g2hH−h,EEmid,ρgH2Emidmcosα,α.The characteristic expression that mainly affects the angle tangent is(14)tanβ=g3hH−h,EEmid,ρgH2Emidmcosα,α.The characteristic expression of the inflection point offset is(15)sH=g4hH−h,EEmid,ρgH2Emidmcosα,α.


## 3. Fuzzy Clustering of Observation Data

### 3.1. Preprocessing Rock Movement Observation Data

Observation data are used as a classification sample, and clustering features are set ash/H−h, E/Emid, ρgH2/Emidmcosα, and α, and feature matrix Xn×4 is established.


#### 3.1.1. Calculation of the Average and Standard Deviations of Each Feature

(16)x¯j=1n∑i=1nxij,sj=1n∑i=1nxij−x¯jj=1,2,3,4.


#### 3.1.2. Calculation of the Standardized Value of the Feature

(17)yij=xij−x¯jsji=1,2,…n;j=1,2,3,4.


#### 3.1.3. Calculation of the Normalized Value of the Feature

(18)zij=yij−yminymax−ymini=1,2,…,n;j=1,2,3,4.


### 3.2. Fuzzy Clustering

Aiming at the problem that the point density search method may have outliers and inability to initial clustering, the density of the cluster centers is restricted to more than half of the average density, and the clustering validity function is used to determine the optimal number of clusters [15].(19)VCSC=1/n∑i=1c∑j=1nuijmxj−vi22/cc−1∑i,t=1;i≠tcvi−vt2.Due to multiple re-initial clustering, multiple cluster centers with large differences appear. In order to solve this problem, here the sample set is determined first, and then the sample set is arithmetically averaged, so that a more reasonable clustering center can be obtained.(20)Vnew′=niVi+njVjni+nj=1ni+nj∑k=1nixk+1ni+nj∑k=1njyk.The basic process of fuzzy clustering of the IWFCM_CCS algorithm based on competitive merger strategy is shown in Figure2 [16–24].Figure 2
The flow of the IWFCM_CCS algorithm based on competitive merger strategy.It is calculated thatC=4, which is the optimal value, and the cluster center is(21)Vmat=0.030490.393750.041950.234470.023540.450120.035710.089750.095030.239750.044270.095240.022470.439200.040740.46751.Analyze the membership degree matrix and suppose that theith station belongs to categories 1, 2, 3, and 4 as U1i, U2i, U3i, and U4i; then, U1i,U2i,U3i,U4i are weights for linear regression calculation. In order to determine the relationship between the dependent variable Π5 and the independent variables Π1, Π2, Π3, and Π4, a corresponding weighted linear regression model can be established:(22)Qj=∑i=1nUjia+bΠ1i+cΠ2i+dΠ3i+eΠ4i+fΠ5i2j=1,2,3,4.Through regression analysis, a linear model of expected parameters is obtained:(23)q=0.88575+0.03425hH0−h−0.10526EEmid−3.60475×10−5ρgH02Emidmcosα−2.75187×10−3αb=0.24819−0.00316hH0−h−0.00727EEmid+1.0402×10−5ρgH02Emidmcosα+2.6088×10−3αtanβ0=1.72130+0.01821hH0−h+0.19523EEmid−1.30872×10−5ρgH02Emidmcosα+2.93701×10−3αtanβ1=1.86926−0.02731hH1−h−0.05642EEmid−1.07727×10−5ρgH12Emidmcosα+4.38102×10−4αtanβ2=1.94122−0.18620hH2−h+0.16602EEmid−3.05790×10−5ρgH22Emidmcosα+5.03640×10−3αs0H0=0.14202−0.03801hH0−h−0.01558EEmid−4.10583×10−5ρgH02Emidmcosα−1.15100×10−4αs1H1=0.04025−0.00281hH1−h+0.01443EEmid−1.67628×10−5ρgH12Emidmcosα+2.54414×10−3αs2H2=0.07102−0.02515hH2−h+0.00402EEmid−1.32990×10−6ρgH22Emidmcosα−8.32504×10−5.


## 3.1. Preprocessing Rock Movement Observation Data

Observation data are used as a classification sample, and clustering features are set ash/H−h, E/Emid, ρgH2/Emidmcosα, and α, and feature matrix Xn×4 is established.


### 3.1.1. Calculation of the Average and Standard Deviations of Each Feature

(16)x¯j=1n∑i=1nxij,sj=1n∑i=1nxij−x¯jj=1,2,3,4.


### 3.1.2. Calculation of the Standardized Value of the Feature

(17)yij=xij−x¯jsji=1,2,…n;j=1,2,3,4.


### 3.1.3. Calculation of the Normalized Value of the Feature

(18)zij=yij−yminymax−ymini=1,2,…,n;j=1,2,3,4.


## 3.1.1. Calculation of the Average and Standard Deviations of Each Feature

(16)x¯j=1n∑i=1nxij,sj=1n∑i=1nxij−x¯jj=1,2,3,4.


## 3.1.2. Calculation of the Standardized Value of the Feature

(17)yij=xij−x¯jsji=1,2,…n;j=1,2,3,4.


## 3.1.3. Calculation of the Normalized Value of the Feature

(18)zij=yij−yminymax−ymini=1,2,…,n;j=1,2,3,4.


## 3.2. Fuzzy Clustering

Aiming at the problem that the point density search method may have outliers and inability to initial clustering, the density of the cluster centers is restricted to more than half of the average density, and the clustering validity function is used to determine the optimal number of clusters [15].(19)VCSC=1/n∑i=1c∑j=1nuijmxj−vi22/cc−1∑i,t=1;i≠tcvi−vt2.Due to multiple re-initial clustering, multiple cluster centers with large differences appear. In order to solve this problem, here the sample set is determined first, and then the sample set is arithmetically averaged, so that a more reasonable clustering center can be obtained.(20)Vnew′=niVi+njVjni+nj=1ni+nj∑k=1nixk+1ni+nj∑k=1njyk.The basic process of fuzzy clustering of the IWFCM_CCS algorithm based on competitive merger strategy is shown in Figure2 [16–24].Figure 2
The flow of the IWFCM_CCS algorithm based on competitive merger strategy.It is calculated thatC=4, which is the optimal value, and the cluster center is(21)Vmat=0.030490.393750.041950.234470.023540.450120.035710.089750.095030.239750.044270.095240.022470.439200.040740.46751.Analyze the membership degree matrix and suppose that theith station belongs to categories 1, 2, 3, and 4 as U1i, U2i, U3i, and U4i; then, U1i,U2i,U3i,U4i are weights for linear regression calculation. In order to determine the relationship between the dependent variable Π5 and the independent variables Π1, Π2, Π3, and Π4, a corresponding weighted linear regression model can be established:(22)Qj=∑i=1nUjia+bΠ1i+cΠ2i+dΠ3i+eΠ4i+fΠ5i2j=1,2,3,4.Through regression analysis, a linear model of expected parameters is obtained:(23)q=0.88575+0.03425hH0−h−0.10526EEmid−3.60475×10−5ρgH02Emidmcosα−2.75187×10−3αb=0.24819−0.00316hH0−h−0.00727EEmid+1.0402×10−5ρgH02Emidmcosα+2.6088×10−3αtanβ0=1.72130+0.01821hH0−h+0.19523EEmid−1.30872×10−5ρgH02Emidmcosα+2.93701×10−3αtanβ1=1.86926−0.02731hH1−h−0.05642EEmid−1.07727×10−5ρgH12Emidmcosα+4.38102×10−4αtanβ2=1.94122−0.18620hH2−h+0.16602EEmid−3.05790×10−5ρgH22Emidmcosα+5.03640×10−3αs0H0=0.14202−0.03801hH0−h−0.01558EEmid−4.10583×10−5ρgH02Emidmcosα−1.15100×10−4αs1H1=0.04025−0.00281hH1−h+0.01443EEmid−1.67628×10−5ρgH12Emidmcosα+2.54414×10−3αs2H2=0.07102−0.02515hH2−h+0.00402EEmid−1.32990×10−6ρgH22Emidmcosα−8.32504×10−5.


## 4. Project Example Verification

Due to the influence of factors such as the distribution of structures (buildings), it is prone to problems such as missing data in the observation station, which seriously affects the accuracy of mining subsidence prediction. Therefore, taking the observation station data of a mining area in northwestern Liaoning for the same period as an example, the actual predicted parameters and the predicted parameter values are compared to calculate the error between them. Average error and maximum error of predicted parameters are shown in Table1.Table 1
Average error and maximum error of predicted parameters.
Parametersqbtanβ0tanβ1tanβ2s0/H0s1/H1s2/H2Average error0.0930.0620.0210.1030.1100.0480.0470.049Maximum error0.130.0910.040.170.1400.0610.0540.067The following can be seen from Table1. ① The average error of the measured parameters and the predicted parameters is roughly equivalent to the tolerance, which meets the engineering accuracy requirements. ② The maximum error of the measured parameters and the predicted parameters is within the tolerance requirements, which shows that the error range of the predicted parameters is comparatively stable. Relative error probability distribution of expected parameters is shown in Figure 3. Error probability distribution of predicted parameters is shown in Figure 4.Figure 3
Relative error probability distribution of expected parameters.Figure 4
Error probability distribution of predicted parameters.It can be seen from Figure 3 that ①the number of stations with the relative error of the subsidence coefficient q less than 5% accounts for 72.64% of the total number of stations, the number of stations with a relative error less than 10% accounts for about 88.72% of the total number of stations, and the number of stations with a relative error less than 15% accounts for about 99.10% of the total number of stations. ② The percentage of the number of stations with relative errors of the main influence angle tangentstanβ0, and tanβ1, tanβ2less than 5% in the total number of stations is 70.42%, 68.20%, and 75.35%, respectively. The percentage of stations less than 10% to the total number of stations is 78.38%, 81.73%, and 83.68%, respectively. The percentages of stations less than 15% to the total number of stations were 97.87%, 98.53% and 99.29%, respectively.The following can be seen from Figure4. ① The number of stations with an error of less than 2% of the horizontal movement coefficient b accounts for about 62.10% of the total number of stations. The number of stations with an error less than 3% accounts for about 76.58% of the total number of stations. The number of stations with an error of less than 5% accounts for about 97.51% of the total number of stations. ② The percentage of the number of stations whose inflection point offset distances s0/H0, s1/H1, and s2/H2is less than 2% accounts for 54.74%, 45.12%, and 47.98% of the total number of stations, respectively. The percentage of the number of stations with an error less than 3% to the total number of stations is 62.35%, 70.21%, and 59.67%, respectively. The percentage of the number of stations with an error less than 5% to the total number of stations is 96.98%, 97.10%, and 98.43%, respectively.In summary, the subsidence coefficient, main influence angle tangent, horizontal movement coefficient, and inflection point offset calculated by this model meet the engineering accuracy requirements.


## 5. Conclusion

(1)
According to the similar third theorem, the geological and mineral characteristics are simplified, and the geological and mineral characteristics are comprehensively selected according to the actual situation, and the multiple correlation coefficient method is used to analyze the primary and secondary characteristics of the geological and mineral characteristics to obtain the characteristic expressions of the predicted parameters. Hardness, luster, color, streak, specific gravity, cleavage, fracture, and tenacity are all physical qualities that can be used to characterize and classify minerals.(2)
A fuzzy clustering approach of the IWFCM_CCS algorithm based on the competitive merger strategy is established to address the drawbacks of the point density search method, and the linear model of the predicted parameters is derived by regression analysis.(3)
The parameter prediction model is validated using data from observation stations in a specific mining area, and after comparison, it is determined that the model’s parameter prediction result meets engineering accuracy standards, providing a foundation for obtaining parameters in the future.



---

*Source: 7827104-2022-02-18.xml*