A method for constructing a comprehensive prediction model for rock drillability classification
By introducing rock engineering system theory and artificial neural network coding method, the overall interaction matrix GRSE is constructed, which solves the problem of deviation in rock drillability prediction in the existing technology, and achieves more accurate and efficient rock drillability regional grading and Improved rock drilling efficiency.
Patent Information
- Application Number
- CN202111375841.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-11-19
- Publication Date
- 2025-02-18
- Estimated Expiration
- 2041-11-19
AI Technical Summary
The prior art is difficult to comprehensively and objectively reflect the drillability of rocks, resulting in deviations in the prediction of rock drillability level values.
Using the theory of rock engineering system RES, rock drilling engineering is regarded as a complete system, and the overall interaction matrix GRSE is constructed through artificial neural network coding method, the interaction mechanism path between various factors is analyzed, and the main factors and influence weights are comprehensively analyzed. Predict the rank value of the drillability of rocks.
It improves the accuracy and operability of rock drillability area classification, adapts to the specific situations of different regions, improves the drilling efficiency, and improves the perforation efficiency of shifts by 15% to 20%.
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Figure CN114298369B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of mineral resource mining, and in particular relates to a method for constructing a rock drillability classification comprehensive prediction model. Background Art
[0002] In the process of mining mineral resources, rock drilling is an important part of the tunneling and mining process, and is also one of the most important parameters in mine economics. Generally speaking, the rock drillability grade represents the relative resistance of the ore rock to the damage of the drill tool, and the average drilling speed is usually selected as an indicator for evaluation.
[0003] The research methods of rock drillability can be roughly divided into two categories: various rock physical and mechanical parameters and various statistical analysis methods. The former analyzes the correlation between various indicators and drillability values by testing various physical and mechanical properties of rocks, such as Shore hardness, compressive strength, tensile strength, abrasiveness, rock structure parameters, etc. The latter uses the chipping energy method, rock cuttings fractal method, acoustic wave analysis method, chemical component analysis method and fuzzy mathematics theory to establish a data model to evaluate the drillability value of rocks. Due to the differences in rock structure, mineral composition and rock drill working parameters, the prediction of rock drillability values may be biased, resulting in a single research method that cannot comprehensively and objectively reflect the drillability of rocks.
[0004] Domestic and foreign scholars have successfully solved many rock system engineering problems by using RES (Rock Engineer System) theory research, and analyzed the mechanism and path of each parameter by constructing a core interaction matrix. Hudson first used the binary interaction matrix BIM, which only considered the influence between a pair of variables; Y. Jiao and Hudson improved BIM by considering the interaction of each variable, and further constructed a fully coupled matrix FCM; T. N. Singh used the neural network coding method to study the abrasiveness and drillability of different materials to select suitable drill bits for rock drills. Domestic scholars Yang Yingjie, Zhang Qing and others used artificial neural network tools to first propose the global interaction strength GRSE (Global Relative Strength of Effect) matrix to reveal the relative size and direction of each influencing factor; Yu Weijian and others used the comprehensive interaction matrix GIM to analyze the stability of underground tunnels; Huang Qisong and others introduced the relative action strength RSE matrix to construct a coal seam spontaneous combustion hazard prediction model. At present, RES theory is widely used to solve fuzzy and complex rock system engineering problems, providing a new way to predict the state of underground rocks under construction disturbance conditions.
[0005] The drillability of rock is affected by a combination of factors such as natural conditions and construction parameters, and the mechanism of each factor is also complex and changeable. The rock structure and composition in different regions are different, and the selection of rock drilling parameters is greatly affected by the experience of workers, resulting in many restrictions on the drilling speed. Summary of the invention
[0006] The purpose of the present invention is to solve the shortcomings of the above-mentioned background technology, provide a method for constructing a rock drillability classification comprehensive prediction model, introduce the rock engineering system theory RES, regard the rock drilling engineering as a complete system, and list as many influencing factors in the system as possible; construct the overall interaction matrix GRSE by artificial neural network coding method to analyze the interaction mechanism path between the factors of the whole system; comprehensively analyze its main factors and influencing weights to predict the grade value of rock drillability and divide the drillability area.
[0007] The technical solution adopted by the present invention is: a method for constructing a rock drillability classification comprehensive prediction model, characterized in that it includes the following steps:
[0008] S1, obtain the influencing factors of rock drillability based on rock mechanical properties and rock drilling construction parameters;
[0009] S2, obtaining variable parameter values of various influencing factors based on historical construction data, and combining them to form a first sample set;
[0010] S3, training a first neural network model using a first sample set; the input of the first neural network model is the variable parameter value of each influencing factor, and the output is the variable parameter value of each influencing factor;
[0011] S4, constructing the overall interaction intensity matrix of each influencing factor by the trained first neural network model, which is used to quantitatively describe the magnitude and direction of the interaction intensity between each influencing factor;
[0012] S5, calculate the weight of each influencing factor on rock drillability according to the overall interaction intensity matrix;
[0013] S6, based on the historical construction data, obtaining the variable parameter values of each influencing factor and the corresponding average perforation speed, and combining them to form a second sample set; training the second neural network model through the second sample set; the input of the second neural network model is the variable parameter values of each influencing factor, and the output is the average perforation speed;
[0014] Calculate the classification index value of the drillability of the ore rock based on the second sample set data and the weight of the rock drillability of each influencing factor;
[0015] S7, defining the difficulty of rock drillability corresponding to the numerical range of the rock drillability classification index value, and the rock drillability difficulty is used as the output of the rock drillability classification comprehensive prediction model.
[0016] In the above technical solution, in step S1, the influencing factors include: rock physical and mechanical property parameters: compressive strength, tensile strength, rock quality indicators; rock drill working parameters: thrust pressure, impact pressure, rotation speed; main mineral component content: gypsum content, equivalent quartz content, iron ore grade.
[0017] In the above technical solution, in step S4, the trained first neural network model obtains network weights, encodes the GRSE matrix based on the network weights, and generates an overall interaction intensity matrix of each influencing factor.
[0018] In the above technical solution, in step S6, a second sample set L is defined, where L = {l1, l2, l3 ... l r}, where l r ={X r , Y r}; l r is the parameter variable of the influencing factor of the rth sample; X r Y represents the variable parameter value of each influencing factor of the rth sample; r represents the average piercing speed of the rth sample.
[0019] In the above technical solution, in step S4, for the trained first neural network model, the overall interaction strength GRSE of a certain input node i to a certain output node k is ki The calculation formula is as follows:
[0020]
[0021] Where C is the GRSE of the output ki The maximum value of the normalized coefficient is 1; subscripts j1, j2, ..., j n They refer to the corresponding nodes on the hidden layer respectively; W is the weight between the nodes in the hidden layer; n is an integer;
[0022] Through the overall action strength GRSE ki Establish the corresponding overall interaction intensity matrix:
[0023]
[0024] In the above technical solution, in step S5, the comprehensive influence value S of each influencing factor is calculated. i ,
[0025]
[0026] GRSE ki is the comprehensive interaction strength value of input node i on output node k; the value of n is the number of influencing factors.
[0027] According to the comprehensive impact value S of each influencing factor i Calculate the weight of each influencing factor on rock drillability as U i :
[0028]
[0029] In the above technical solution, in step S6, the ore rock drillability classification index value K p The calculation formula is as follows:
[0030] K p = l r ·U i
[0031] Among them, l r is the parameter variable X of each influencing factor of the rth sample i ; U i is the weight of each influencing factor variable on rock drillability.
[0032] In the above technical solution, in step S7, the ore rock is statistically summarized and analyzed according to the actual average drilling speed of the ore rock, and is divided into four ore rock drillability difficulty states: easy, medium, difficult and extremely difficult; the ore rock drillability difficulty corresponding to the numerical range of the ore rock drillability classification index value is determined according to the corresponding relationship between the average drilling speed in the sample set and the ore rock drillability classification index value.
[0033] The beneficial effects of the present invention are as follows: the steps adopted by the present invention are relatively simple and easy to use. Introducing the rock engineering system theory RES, regarding the rock drilling project as a complete system, and using the artificial neural network coding method to construct the overall interaction matrix GRSE to analyze the interaction mechanism path between the factors of the entire system is an innovative approach. The method has good operability in the classification and application of rock drillability areas and has good economic value. The rock drilling construction parameters are adjusted on site according to different partitions to adapt to the specific conditions of different areas, so that the rock drilling efficiency has been generally improved, and the perforation efficiency of the shift has been increased by 15% to 20%.
[0034] In the modern mining process of mineral resources, domestic and foreign scholars have successfully solved many rock system engineering problems by using RES theory research, and analyzed the action mechanism and path between various parameters by constructing a core interaction matrix. This invention uses the comprehensive prediction model of rock drillability based on RES theory to conduct a comprehensive prediction and analysis of the physical and mechanical properties of the ore and rock, the rock drilling parameters and the content of the main mineral components. Based on the prediction results, the prediction area of the ore and rock drillability is obtained, and on-site rock drilling construction is guided. Because the rock drilling process adapts to the specific conditions of different regions, the rock drilling efficiency has been generally improved. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] Figure 1 A three-layer BP network diagram that reflects the impact of input parameters on output parameters.
[0036] Figure 2 are the normalized internal parameter values of each factor variable and the average piercing speed.
[0037] Figure 3 It is the comprehensive interaction matrix GRSE of each influencing factor.
[0038] Figure 4 A three-dimensional display of the comprehensive interaction matrix GRSE.
[0039] Figure 5 It is the combined effect of various factors on the system.
[0040] Figure 6 The influence of various factors on the drillability of ore.
[0041] Figure 7 This is the Kp indicator point value chart for the engineering sample.
[0042] Figure 8 Kp values and descriptions of various types of mineral rocks, where the engineering sample values on the horizontal axis are the corresponding sample numbers.
[0043] Fig. 9 This is a drillability zoning map of a certain mineral rock.
[0044] Fig.10 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION
[0045] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments to facilitate a clear understanding of the present invention, but they do not constitute a limitation on the present invention.
[0046] The principle and spirit of the present invention will be described below with reference to several exemplary embodiments shown in the accompanying drawings. It should be understood that these embodiments are described only to enable those skilled in the art to better understand and implement the present invention, and are not intended to limit the scope of the present invention in any way.
[0047] The patent of this invention provides a comprehensive prediction model for rock drillability classification; the prediction model is based on the rock engineering system (RES) theory, comprehensively considers various rock mechanical properties and rock drilling construction parameters as a complete system, and uses a neural network coding method to construct a global interaction intensity (GRSE) matrix, and establishes a comprehensive prediction model for rock drillability classification, revealing the complex relationship between various influencing factors and the degree of influence on rock drillability.
[0048] In order to invent such a prediction model, the inventors have put in a lot of creative work in studying the technical principles. Although the research process of the principles is not equivalent to the technical solution of the embodiment of the present invention itself, it is also an important part of reflecting the creativity of the present invention.
[0049] Rock drillability is affected by a variety of natural conditions, construction parameters and other factors, and the mechanism of each factor is also complex and changeable. The rock structure and composition of different regions are different, and the selection of rock drilling parameters is greatly affected by the experience of workers, resulting in many restrictions on the drilling speed. Therefore, the rock engineering system theory RES is introduced to regard the rock drilling project as a complete system, and as many influencing factors as possible are listed in the system; the overall interaction matrix GRSE is constructed by artificial neural network coding method to analyze the interaction mechanism path between the factors of the whole system; the main factors and influence weights are comprehensively analyzed to predict the grade of rock drillability and divide the drillability area.
[0050] 1. Construction and coding of comprehensive interaction matrix;
[0051] In order to quantitatively describe the magnitude and direction of the interaction between various variables in the rock engineering system, it is necessary to encode the GRSE matrix. At present, the main encoding methods for characterizing the importance of non-diagonal units include binary method (0-1), expert semi-quantitative (ESQ), curve slope method (x i -y i ), partial differential solution (PDE), complete numerical analysis and artificial neural network (ANN). The most mature and widely used BP artificial neural network can specifically reflect the complex relationship between each input variable and each output variable, such as Figure 1 .
[0052] For the first trained neural network model, the overall interaction strength GRSE of a certain input node i on a certain output node k ki The calculation formula is as follows. Through the overall action strength GRSE ki The corresponding overall interaction intensity matrix can be established.
[0053]
[0054] Where C is the GRSE of the output ki The maximum value of the normalized coefficient is 1; j1, j2, …, j n They refer to the corresponding nodes on the hidden layer respectively; W is the weight between the nodes in the connecting layers.
[0055] From the above formula, we can see that the GRSE of the trained first neural network model is ki The size of the value is only related to the value of W, which is a static invariant.
[0056]
[0057] 2. Comprehensive analysis of factors affecting rock drillability;
[0058] After investigating and analyzing the geological conditions of Chengchao Iron Mine and the working data of the deep hole trolley hydraulic rock drill in the tunnel, it was found that the factors affecting the drillability of the ore rock are very complex, mainly including the engineering geological conditions of the rock mass itself and the rock drilling construction working parameters, etc. The former is the engineering geological basis or material basis, and the latter provides external factors or disturbance factors. Hard minerals (such as quartz and magnetite) and higher rock quality index (RQD) can significantly reduce the rock drilling and perforation speed. The selection of rock drilling construction parameters (such as thrust pressure, impact pressure, rotation speed, etc.) directly affects the rock drilling efficiency. In addition, the content of other hard mineral components such as feldspar, plagioclase and minerals with equivalent hardness can be converted into quartz content, that is, the equivalent quartz content EQC is used to reflect the total content of quartz and other hard minerals.
[0059] The above factors are refined into the following 9 influencing factors: rock physical and mechanical properties parameters: compressive strength UCS / MPa (X1), tensile strength T / MPa (X2), rock quality index RQD / % (X3); rock drill working parameters: thrust pressure F / bar (X4), impact pressure P / bar (X5), rotation speed R / rpm (X6); main mineral component content: gypsum content CS / % (X7), equivalent quartz content EQC / % (X8), iron ore grade TFe / % (X9). In the process of rock drilling and perforation, these influencing factors together constitute the entire rock drilling system. The changes of all factors in the system have direct and indirect effects on the changes of the average drilling speed m / min (Y). Figure 2 The normalized internal values of each influencing factor variable and the average piercing speed are listed.
[0060] 3. Establishment of interaction matrix based on BP network;
[0061] Using the artificial neural network toolbox provided by MATLAB, the BP network inter-layer node activation function uses the logarithmic S-type function Log-Sigmod; the weight adjustment learning algorithm uses trainlm. The first neural network model uses a three-layer network structure. The input nodes (X1~X9) and output nodes (X1~X9) composed of influencing factors are both 9, and the number of hidden layer nodes is 12, that is, a 9-12-9 network structure. When the number of learning steps reaches 400, the detection error reaches 10 -2 , indicating that the first neural network model has achieved a good effect. The remaining 5 samples were used for testing, and the error did not exceed 20%. The trained network weight W was substituted into formula (1) and formula (2) to obtain the overall interaction intensity matrix of each influencing factor, as shown in Figure 3 .
[0062] Figure 3 The left column is the input parameter number, the top row is the output parameter number, and the diagonal items are GRSE ik (k=i) is the self-compounding effect of the corresponding parameter, that is, the value is 1. The corresponding item on the off-diagonal line is the effect intensity of the corresponding input parameter on the output parameter GRSE ki (k≠i) size, and the sign of the corresponding term indicates its composite interaction. For example, GRSE 19 GRSE 29 It is the positive sign term of rock compressive strength (X1) and tensile strength (X2) corresponding to the iron ore grade (X9), indicating the degree of driving effect of the former on the latter. Figure 3 Most of the terms in are not zero, which shows that the interactions between the parameters are very complex.
[0063] The data in the above figure can be more vividly illustrated with graphics, such as Figure 4 .
[0064] 4. Comprehensive factor analysis of rock drilling system;
[0065] In order to analyze the main factors affecting the rock drilling system, the comprehensive influence value S of each influencing factor on the entire system is defined. i And make a comprehensive analysis of the impact of various factors on the system Figure 5 .
[0066]
[0067] Where S i is the comprehensive impact value; GRSE ki is the comprehensive interaction strength value of input node i on output node k; n = 1, 2, ..., 9; i = 1, 2, ..., 9.
[0068] Depend on Figure 5It can be seen that compressive strength, tensile strength, RQD, impact pressure, EQC and iron ore grade have a positive effect on the rock drilling system, that is, they have a driving effect on other influencing factors; while the thrust pressure, rotation speed and gypsum content are the opposite, and have a weakening effect on other factors. The main factors affecting the system are: tensile strength, RQD, gypsum content, and iron ore grade. Among them, iron ore grade, quartz content and RQD are positively correlated with rock compressive strength and tensile strength; gypsum content is negatively correlated with rock compressive strength and tensile strength; impact pressure is strongly correlated with thrust pressure and rotation speed.
[0069] 5. Analysis of the main factors affecting rock drillability;
[0070] In order to further study the main factors affecting rock drillability, the above training method is also adopted. The variable parameter values of the above 9 influencing factors and the corresponding average perforation speed are combined into a whole sample set L, written as L = {l1, l2, l3…l r}, where l r ={X r , Y r}. The first 30 samples are used as learning samples, and the remaining 5 samples are used as test samples. The second neural network model is trained through the sample set; the input of the second neural network model is the variable parameter value of each influencing factor, and the output is the average punching speed. It is trained using the artificial neural network toolbox provided by MATLAB. At this time, the network model has 9 input nodes (X1~X9) and one output node Y (average punching speed), that is, a 9-12-1 network structure. 30 samples are also selected for pattern recognition research. When the number of iterations reaches 150, the error between the output parameter and the target parameter reaches 10 -2 , which shows that the network performance is good. The remaining 5 samples are used for testing, and the error does not exceed 15%.
[0071] The influence values of various factors on rock drillability can be obtained from the trained second neural network model. Figure 6 shown. Figure 6 It can be seen that the absolute values of the influence values of RQD, gypsum content, iron ore grade and impact pressure drillability are the largest. The influence of compressive strength, tensile strength, RQD, impact pressure and iron ore grade on ore drillability is positive, indicating that the greater the input of the parameter value, the greater the output value of the ore rock drillability, and the stronger the ability of the ore rock to resist drill tool breakage; while the influence of gypsum content, thrust pressure and rotation speed on ore rock drillability is negative, indicating that the greater the input value of the parameter, the smaller the output value of the ore rock drillability, and the weaker the ability of the ore rock to resist drill tool breakage.
[0072] The weight of each factor on rock drillability is defined as U i :
[0073]
[0074] Substituting the comprehensive influence of each factor into the formula, we can calculate the weight of each factor on rock drillability: i Among them, the weights of RQD, gypsum content, iron ore grade and impact pressure are i They are 0.18, -0.17, 0.13 and 0.14 respectively.
[0075] 6. Analyze the rock drillability grade;
[0076] In order to better classify the rock drillability area, the drillability level values of the collected sample set L are classified as K p Point value Figure 7 The figure shows the K corresponding to each input state. p value; according to the actual average drilling speed (Y) and K p The value is statistically summarized and analyzed into four states: easy, medium, difficult and extremely difficult (I, II, III and IV), and the K value under each input state is obtained from the actual sample. p Value range and specific description of the ore rock, such as Figure 8 ;
[0077] K p = l r ·U i
[0078] K p is the drillability classification index value of the ore rock; l r is the value X of each influencing factor of the rth sample i ; U i is the weight of each factor variable on rock drillability.
[0079] 7. Rock drillability zone classification and application;
[0080] Rock mechanical properties, mineral composition and rock drilling parameters have a comprehensive impact on rock drilling efficiency. The rock mechanical properties and chemical composition of different areas in the mining area continue to change, and the rock drilling parameters are also changing. Therefore, the regional classification of mine rock drillability has practical engineering significance.
[0081] The comprehensive index value K of the drillability of the mine rock is calculated by comprehensive analysis of the physical and mechanical properties of the mine rock, rock drilling parameters and the content of the main mineral components. p , according to the prediction results, the level is divided into four types of ore rock drillability prediction areas, such as Fig. 9Hard rock requires higher rock-breaking impact energy, which is suitable for the working parameters of the rock drilling rig with low thrust, high impact pressure and low rotation speed; while soft rock and medium-hard rock require lower rock-breaking impact energy, and the working parameters of the rock drilling rig need to be adjusted to high thrust, low impact pressure and high rotation speed.
[0082] The present invention discloses a rock drillability classification comprehensive prediction model based on RES theory, which comprehensively considers rock mechanical properties and rock drilling parameters. The prediction model can adjust the rock drilling construction parameters according to different on-site partitions; because the rock drilling process adapts to the specific conditions of different regions, the rock drilling efficiency has been generally improved, and the perforation efficiency of each shift can be increased by 15% to 20%. The present invention adopts a neural network coding method to construct a global interaction intensity (GRSE) matrix to predict the rock drillability, which can only be achieved through this solution. Other technical solutions that have no obvious difference from the innovation points of this solution on the basis of the solution can all be within the scope of this solution.
[0083] The contents not described in detail in this specification belong to the prior art known to professional and technical personnel in this field.
Claims
1. A method for constructing a rock drillability classification comprehensive prediction model, characterized by: The following steps are involved: S1, obtain the influencing factors of rock drillability based on rock mechanical properties and rock drilling construction parameters; S2, obtaining variable parameter values of various influencing factors based on historical construction data, and combining them to form a first sample set; S3, training a first neural network model using a first sample set; the input of the first neural network model is the variable parameter value of each influencing factor, and the output is the variable parameter value of each influencing factor; S4, constructing the overall interaction intensity matrix of each influencing factor by the trained first neural network model, which is used to quantitatively describe the magnitude and direction of the interaction intensity between each influencing factor; S5, calculate the weight of each influencing factor on rock drillability according to the overall interaction intensity matrix; S6, based on the historical construction data, obtaining the variable parameter values of each influencing factor and the corresponding average perforation speed, and combining them to form a second sample set; training the second neural network model through the second sample set; the input of the second neural network model is the variable parameter values of each influencing factor, and the output is the average perforation speed; Calculate the classification index value of the ore rock drillability based on the second sample set data and the weight of the rock drillability of each influencing factor; S7, defining the difficulty of rock drillability corresponding to the numerical range of the rock drillability classification index value, and the rock drillability difficulty is used as the output of the rock drillability classification comprehensive prediction model; In step S6, define a second sample set L, where L = {l1, l2, l3 ... l r }, where l r ={X r , Y r }; l r is the influencing factor parameter variable of the rth sample; X r Y represents the variable parameter value of each influencing factor of the rth sample; r represents the average piercing speed of the rth sample; In step S4, for the trained first neural network model, the overall interaction strength GRSE of a certain input node i to a certain output node k is ki The calculation formula is as follows: Where C is the GRSE of the output ki The maximum value of the normalized coefficient is 1; the subscripts i, k, j1, j2, ..., j n They refer to the corresponding nodes on the hidden layer of the first neural network model respectively; the input node i is also used to represent different influencing factors i; W pq is the weight between the nodes p and q in the hidden layer; n is an integer; where p,q∈{i,k,j1,j2,…,j n }; Through the overall action strength GRSE ki Establish the corresponding overall interaction intensity matrix: In step S5, the comprehensive impact value S of each influencing factor is calculated. i , GRSE ki is the comprehensive interaction strength value of input node i on output node k; According to the comprehensive impact value S of each influencing factor i Calculate the weight of each influencing factor on rock drillability as U i : In step S6, the ore rock drillability classification index value K p The calculation formula is as follows: K p =l r *U i 。 2. The method for constructing a rock drillability classification comprehensive prediction model according to claim 1, characterized in that: In step S1, the influencing factors include: rock physical and mechanical property parameters: compressive strength, tensile strength, rock quality index; rock drill working parameters: thrust pressure, impact pressure, rotation speed; main mineral component content: gypsum content, equivalent quartz content, iron ore grade.
3. The method for constructing a rock drillability classification comprehensive prediction model according to claim 1, characterized in that: In step S4, the trained first neural network model obtains network weights, encodes the GRSE matrix based on the network weights, and generates an overall interaction intensity matrix of each influencing factor.
4. A method for constructing a rock drillability classification comprehensive prediction model according to claim 3, characterized in that: In step S7, the ore rocks are statistically summarized and analyzed according to the actual average drilling speed of the ore rocks, and are divided into four ore rock drillability states: easy, medium, difficult and extremely difficult; The difficulty of ore rock drillability corresponding to the numerical range of the ore rock drillability classification index value is determined according to the corresponding relationship between the average perforation speed and the ore rock drillability classification index value in the second sample set.
Citation Information
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