Drillability classification and identification for rock mass based on machine learning

In order to better apply the drilling method to underground mines, rock drillability classification and identification in situ by drilling process monitoring technology is a convenient and effective method to achieve the rock mass drillability. In this study, a database was established based on 188 groups of drilling parameters, drillability parameters and rock mechanics parameters. By analyzing the correlation between mechanical parameters and drillability parameters, rock drillability was classified using the TOPSIS-RMR method. Then, drilling force (F), torque (T), rotation speed (N), rate of penetration (V), specific energy (SE) and drillability index (Id) were used as machine learning input variables to predict drillability grades. Finally, the machine learning classification models include SVM, ELM, BPNN, RBF, RF and LSTM are compared to select the optimal model. The efforts and results can be used to evaluate the rock mass drillability and provide support for the design optimization of drilling and blasting method. It can effectively protect the safety and improve efficiency of underground mining.


Background
China possesses significant deposits of lead and zinc minerals, making it the second-largest producer globally, surpassed only by Australia.Given the rapid pace of industrialization, modernization, and urbanization, it becomes imperative to exploit vast quantities of lead and zinc ore to sustain these developments.The rapid development of lead and zinc industry has caused an impact on the ecological environment, so it is necessary to make strict requirements from the mining process to achieve sustainable development.In addition, Deep mine development will become the new norm, and deep rocks are in a complex environment of high situ stress, high temperature, high water pressure and strong excavation disturbance [1].In order to improve resource utilization and reduce the risk of disaster, drilling and blasting methods must be improved.Therefore, rock drillability classification and identification in situ by drilling process monitoring technology is proposed.
The performance of drilling is intrinsically dependent on the rock mass drillability, which is a parameter that reflects the interaction between the drill bit and the rock, and is influenced by a combination of various factors.These factors can be categorized into two groups: controllable and uncontrollable [2].Controllable factors include machine and drilling parameters such as drill bit type and diameter, drilling force and rotation speed, while uncontrollable factors include rock characteristics that cannot be directly controlled, such as rock composition, texture, and brittleness [3].In short, there are many factors affecting drillability classification, complex classification system, single drilling performance evaluation index and other deficiencies, which make mine drilling and blasting construction explosive consumption and overall construction risk factor large.
At present, neural networks are often introduced to predict or classify traditional rock mechanical properties.For example, Sarkar et al. [4] uses feedforward and backpropagation neural network technology to predict the compressive strength of surrounding rock by using wave velocity, point load and density of rock mass.Ocak et al. [5] used multi-layer perceptron neural networks (MLPNN) to predict the elastic modulus of intact rocks.
In order to understand the distribution of drillability among different rock strata, researchers have established numerous empirical relationships through laboratory tests and field engineering experiments.Including schmidt hammer number, point load index, shore hardness, taber abrasion, rock brittleness, equivalent quartz content (EQC), drilling rate index (DRI), bit wear index (BWI), coefficient of rock strength (CRS), impact strength index (ISI), cerchar abrasion index (CAI), cerchar hardness index (CHI), specific energy (SE), texture coefficient (TC), among others [6].Therefore, based on the aforementioned indices, a novel method for classifying the drillability grades of the rock mass has been proposed.In this method, mechanical parameters of rock mass are used to classify different grades, and machine learning method is used to evaluate the drillability grade of rock mass in real time during drilling.

Method
In order to realize the rock mass drillability classification and identification, TOPSIS-RMR method and machine learning classification model were selected in this study, and the optimal model of identification was determined by comparing different models.The research route of this study is shown in Figure 1.The classification method and machine learning model are introduced below.

TOPSIS-RMR method
The TOPSIS method is typically utilized for multi-objective decision making.It involves cotrend processing and normalization matrix to identify the optimal and worst targets among multiple targets.The Euclidean distance is then calculated and the proximity between each index value and the ideal solution is obtained and sorted as the basis for evaluating the quality of the target.The Rank-sum ratio method (RSR) is a well-known comprehensive evaluation technique.It involves obtaining dimensionless RSR values by sorting indexes in the original data matrix, which can be used to directly rank or grade evaluation targets.
The combination of TOPSIS and RSR methods can overcome the limitations of using a single method and obtain more accurate and comprehensive results.These two methods provide different perspectives for analyzing and evaluating the targets.The RSR method focuses on sorting while the TOPSIS method provides a grading perspective.This combined approach can identify and alleviate issues related to data dispersion and information loss [7].The specific steps are as follows: (1) Construct a standardized decision matrix Assuming that the drillability grade of m rock samples with n characteristic variables is to be divided, the original data matrix is: The original data are treated with the cotrend processing and normalization.The data in this study are normalized by . The calculated standard matrix is： (2) Calculate relative proximity Di The optimal vector Y + and the worst vector Y -are obtained according to the standard matrix.
where，   12 max , , , Build the weight index W=[W1, W2, …, Wn] based on the correlation between rock machnical parameters and rock drillability parameters.And W is considered in the calculation of the distance Bi + and Bi -between each evaluation object and the optimal vector and the worst vector.
Based on the correlation between rock machnical parameters and drillability parameters, a weight index W=[W1, W2, …, Wn] is constructed, and W is taken into account when calculating Bi + and Bi -by equation ( 5) and equation ( 6). The where Bi + and Bi -respectively represent the distance between the ith rock sample and the optimal vector and the worst vector, and ij y represent the value of the j th index of the i th rock sample.
The relative proximity Di between each index and the optimal value is calculated comprehensively： (3) Determine Di distribution Di value is used as RMR value to sort its size; At the same time, the frequency (f) and the cumulative frequency (∑) of each rock sample are listed; Determine the rank (R) and the average rank (R * ); Calculate the ranking cumulative frequency p=R * /n×100% (the last item is modified with (1-1/4n)×100% ); Query 'Percentage and probability unit conversion Table' according to the ranking cumulative frequency to get the value of Probit.
(4) Calculate regression equation As shown in equation ( 8), Probit was taken as the independent variable and Di value as the dependent variable to calculate the regression equation.

Machine classification model
This study adopts the following machine learning classification models: Support Vector Machines (SVM), Extreme Learning Machines (ELM), Backpropagation Neural Networks (BPNN), Radial Basis Neural Network (RBNN), Random Forests (RF), and Long Short-Term Memory Networks (LSTM).Here's a brief introduction to each of the machine learning classification model: The SVM is a powerful algorithm that is effective in handling high-dimensional data.It works by mapping the data to a higher dimensional space where a hyperplane is used to separate the data into different classes [8].The ELM is a fast and efficient algorithm that uses a randomly generated input layer and a single hidden layer to establish a nonlinear mapping between inputs and outputs.The output layer weights can be easily calculated through a linear regression [9].The BPNN is capable of learning complex relationships between inputs and outputs, and can adapt well to new data.BP algorithms use a supervised learning approach to adjust the weights between the neurons in each layer during training [10].The RBNN is capable of capturing non-linear patterns in data.The hidden layer in RBNN networks uses radial basis functions to model the data and the output layer weights are calculated through a linear regression [11].The RF is a robust algorithm that is capable of handling noise and outliers in data.RF uses an ensemble learning approach by constructing multiple decision trees and combining them to reduce the risk of overfitting [12].The LSTM is a type of recurrent neural network that can be used for sequential data.LSTM networks use a memory cell to remember longterm dependencies in the data and process input sequences in a sequential manner [13].
Overall, the machine learning classification model includes a wide range of algorithms that can handle various types of data and achieve high accuracy and efficiency in classification tasks.

Rock mass drillability classification and identification
Through data collection, a total of 188 sets of diamond coring bit data consisting of drilling parameters, drillability parameters, and mechanical parameters were gathered [14].The drilling parameters include drilling force (F), torque (T), rotation speed (N), rate of penetration (V), The drillability parameters include specific energy (SE) and drillability index (Id) and drilling rate index (DRI), and the mechanical parameters include uniaxial compressive strength (UCS), tensile strength (TS), Cerchar abrasion index (CAI) and Leeb hardness (HL).These parameters are closely linked to the interaction between rock mass and drill bit, which can well reflect rock mass drillability [15].The specific data distribution is shown in Table 1.

Rock mass drillability classification
TOPSIS-RMR method is used to classify the rock mass drillability.The drillability grade of rocks is determined by analyzing the correlation between rock mechanical parameters and drillability parameters.The drillability grades thus obtained served as the basis for training a machine learning classification model to identify the drillability grade in real time.To optimize the classification accuracy of the model, various models were trained and evaluated, and the most accurate model was selected.This comprehensive approach provides a reliable and efficient tool for assessing the drillability grade of a rock mass during drilling operations.
In order to avoid the randomness of a single drilling performance evaluation index, the correlation between UCS, TS, CAI, HL and V, SE, DRI was calculated, and the coefficient of determination R 2 was used as the evaluation index to evaluate the degree of the correlation.Then, the mean value of R 2 was calculated and normalized to obtain the weight index W. Table 2 shows the value of R 2 and weight index W.  3 shows the relative proximity Ci calculated after cotrend processing and normalization and the ranking situation.The frequency f, cumulative frequency ∑, rank R, average rank R * of each group and the corresponding Probit value are shown in Table 4.  4 was used as the dependent variable and the value of Probit as the independent variable to conduct linear regression.The regression equation was obtained as follows: 0.463 0.188 The Di critical value is calculated according to the fixed Probit critical value.The Probit critical value varies according to the number of levels.In this study, the drillability is divided into four levels, and the critical value of Probit is 3.5, 5 and 6.5 respectively.The calculated results of regression equation Di were 0.195, 0.477 and 0.759 respectively, and the drillability classification was carried out accordingly, as shown in the following Table 5.Among them, the higher the grade, the worse the drillability.

Drillability grades identification
In order to determine the most suitable machine learning classification model for drillability grade identification, SVM, ELM, BPNN, RBNN, RF and LSTM were selected for drillability grade identification.Take F, T, N, V, SE and Id from the database as input and the corresponding drillability grade as output.In a unified manner, 80% of the data is randomly selected to form training set, and the remaining 20% constitutes testing set.
The SVM model uses linear kernel function for classification, with penalty factor c=0.1.ELM sets the number of neurons in the hidden layer as 20, and uses sigmoid function to activate.BPNN sets the number of hidden layers as 15; The radial basis function expansion speed of RBNN model is set to 100.RF model sets the number of decision trees as 10 and the minimum number of leaves as 5. LSTM Sets the maximum number of iterations to 500.The confusion matrix and identification results for testing set of different machine learning classification models are shown in Figure 2 and Figure 3 respectively.The accuracy rates of SVM, ELM, BPNN, RBNN, RF and LSTM were 64.86%, 67.57%, 72.97%, 81.08%, 78.38% and 72.97% respectively.
According to the application results of classification model, RBNN model has the highest identification accuracy, and it can be considered that RBNN algorithm is the optimal algorithm for rock drillability classification perception and identification.

Discussion
The size of the dataset is a crucial factor in limiting performance of classification.Since the values of drilling force (F) and rotation speed (N) in the current database are fixed, the overall accuracy of identification is not an ideal level.Therefore, to enhance the reliability of classification, future research should focus on collecting a larger amount of data for the database.The existing rock mass mechanical parameters used for drillability classification are insufficient, as factors such as groundwater state, rock joint conditions, and RQD can also affect drillability.The current study only considers UCS, TS, CAI, and HL for drillability classification.Therefore, further research is necessary to incorporate various geological conditions into the classification process.
Although the aforementioned study indicates that TOPSIS-RMR method and RBNN model can achieve drillability classification and identification of rock mass.they can not provide a comprehensive assessment for different engineering projects.In future research, it is recommended to include practical engineering as the research subjects to verify the applicability of the classification method.

Conclusions
The drillability classification is based on the TOPSIS-RMR method to classify the drillability of each rock sample.Additionally, the drillability grade was identified by inputting the drilling force (F), torque (T), rotation speed (N), rate of penetration (V), specific energy (SE), and drillability index (Id) into the machine learning classification model.Finally, the optimal drillability grade classification model is determined by comparing identification accuracy of different models.The main achievements and conclusions of this study are as follows: (1) Based on TOPSIS-RMR method, the drillability of rock samples is successfully divided into four grades.The higher the grade, the worse the drillability.
(3) A rapid rock mass drillability classification method is established, and in-situ drillability recognition is realized based on monitoring while drilling technology and machine learning algorithm, which is helpful to improve the safety and efficiency of underground mining.

Figure 1 .
Figure 1.Schematic diagram of research methods in this study

5 )
Grading of rock drillabilityAccording to the estimated value of Di derived from regression equation, the drillability of rock samples is classified and sorted.

Table 2 .
The mean and weight of R 2

Table 3 .
TOPSIS evaluation resultsNumber Positive ideal solution Bi + Negative ideal solution Bi -Relative proximity

Table 4 .
Distribution of relative proximity(Di)

Table 5 .
Drillability grade of rock samples