Hybrid machine learning approach for accurate prediction of the drilling rock index | Scientific Reports

Oct 17, 2024

Scientific Reports volume 14, Article number: 24080 (2024) Cite this article

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The drilling rate index (DRI) of rocks is important for optimizing drilling operations, as it informs the choice of appropriate methods and equipment, ultimately improving the efficiency of rock excavation projects. This study presents a hybrid machine learning approach to predict the DRI of rocks accurately. By integrating grey wolf optimization with support vector machine (GWO-SVM), random forest (GWO-RF), and extreme gradient boosting (GWO-XGBoost) models, the aim was to enhance predictive accuracy. Among these, the GWO-XGBoost model exhibited superior predictive performance, achieving a coefficient of determination (R²) of 0.999, mean absolute error (MAE) of 0.00043, root mean square error (RMSE) of 1.98017, and severity index (SI) of 0.0350 during training. Testing results confirmed its accuracy with R² of 0.999, MAE of 0.00038, RMSE of 1.80790, and SI of 0.0312. Furthermore, the GWO-XGBoost model outperformed the other models in terms of precision, recall, f1-score, and multi-class confusion matrix results for each DRI class. The GWO-RF model also demonstrated high accuracy, ranking second, while the GWO-SVM model showed comparatively lower performance. This research aims to advance rock excavation practices by providing a highly accurate and reliable tool for DRI prediction. The results highlight the significant potential of the GWO-XGBoost model in improving DRI predictions, offering valuable intuitions and practical applications in the field.

Drillability refers to a rock’s ability to be drilled or penetrated, considering factors such as intact rock properties, abrasiveness, instability, and the implications of drilling into hard rock1. Effective drilling practices can increase productivity and provide a safe working environment, particularly in mining operations2. The drilling rate index (DRI) is influenced by two categories of factors, including controllable and uncontrollable3. According to existing research, factors such as “speed of bit rotation, borehole imaging, weight on bit (WOB), rate of pumping, pressure of standpipe, and torque” are considered controllable. In contrast, the type and size of the drill bit, fluid properties, density, and physical and chemical characteristics are identified as uncontrollable factors4,5,6,7,8. In-depth drillability investigations help to accurately describe the in-situ rock properties at the site9. Various rock samples are collected from important layers to analyze reservoir properties and fluid parameters, aiming to optimize drilling performance10. DRI significantly influences the budget of the mining sector and the design of mining construction projects11. The examination of rock drillability has diverse applications in rotating machinery and engine protection, as evidenced by thermal imaging analysis of electric impact drilling through discontinuity recognition12. Additionally, researchers have endeavored to assess the suitability of rock DRI13,14,15,16.

To achieve high precision in mining operations, hybrid machine learning (ML) techniques, such as the grey wolf optimization (GWO) method, are increasingly being used to assess rock drillability of rocks and analyze related data17. predicted the DRI for 32 different rock types using two models, including a GWO model, demonstrating robust accuracy18. evaluated drilling element parameters using a hybrid GWO-SVM (support vector machine) approach, and obtained highly accurate predictive results. Similarly19, predicted the rate of penetration (ROP) using various hybrid models, including a GWO model, and obtained an R² of 0.996. In addition20, developed a robust ROP prediction model for the Xinjiang oilfield using stacking ensemble learning. Integrating K-nearest neighbor (KNN) and SVM via stacking, optimized with genetic algorithm (GA), and achieved 92.5% accurate ROP prediction. This approach enhances drilling parameter optimization and efficiency. DRI as a predictor of drillability in tunneling and quarry projects using Pearson’s correlations and various linear and non-linear regression models, highlighting density and abrasivity as significant factors in DRI prediction2122. developed artificial neural network (ANN) and regression analysis to estimate the DRI of rocks, achieved effective outcomes23. analyzed the ROP of rocks using various input parameters, including uniaxial compressive strength (UCS), viscosity (µ), and weight on bit (WOB). The study applied linear regression analysis (LRA), ridge regression (RR), and lasso regression (LR) models. Among these, ridge regression demonstrated the highest accuracy in performance. The study by24 focuses on the real-time prediction of rock porosity during complex lithology drilling using ML techniques. The study developed and validated random forest (RF) and decision tree (DT) models using carbonate, sandstone, and shale lithological datasets. Results show strong prediction capability, with RF outperforming DT. Adam suggested the feature extraction technique that employs neural networks and SVM to determine the drill angles of various faults. This technique, named BCAoMID-F (maximum image difference fusion binarization of common areas), is based on maximizing image difference fusion for binarization in common areas2526. employed a combination of ANN models to predict the DRI, a critical factor in drilling prediction models. Their study aimed to estimate the DRI indirectly by incorporating strength properties and indices. The findings demonstrated that the SAA-ANN hybrid model outperformed other models. A novel ANN approach has significantly improved performance in predicting DRI27,2829. demonstrated that ANNs can effectively predict DRI by utilizing inputs such as UCS, Brazilian tensile strength (BTS), and rock brittleness. The selection of drill bits has become simpler due to advancements in predictive intelligence techniques. Various ML techniques have been evaluated to determine possible reasons for the inconsistency in drilling data30. Barbosa et al.31 investigated applying ML techniques to predict and optimize drilling rates. Xu et al.32 explored PR prediction using supervised ML techniques, namely KNN, chi-squared automatic interaction detection (CHAID), SVM, CART, and neural network (NN). Field and lab data were used, with inputs including rock properties. KNN emerged as the best model, highlighting significant factors for PR prediction. A notable technological advancement is the estimation of ROP, which can significantly enhance drilling performance. Sabah et al.33 compared various ML algorithms to evaluate the accuracy and efficiency of data mining techniques in predicting ROP. The performance of the multi-layer perceptron-particle swarm optimization (MLP-PSO) model was found to be comparable to that of SVR. Khandelwal et al.27 aimed to develop an effective DRI prediction model based on rock properties. Initial regression analyses highlighted statistical significance but insufficient practical accuracy. Subsequent hybrid GA-ANN method demonstrated superior DRI prediction due to bias and weight updates during training. The study34 proposed the development of an adaptive neuro-fuzzy inference system (ANFIS) and multiple regression (MR) to forecast the ROP of diamond drilling, considering its significant impact. Additionally, the Monte Carlo simulation (MCS) is considered a suitable method for estimating and identifying anomalies in rock penetration features35. Zhou et al.36 predicted mud pit volume (MPV) and ROP using SVR and long-short-term memory (LSTM) techniques. Mehrad et al.37 focused on optimizing drilling parameters through ROP prediction, emphasizing data-driven methods. Outliers were handled using Tukey’s method. Optimal feature selection, utilizing the NSGA-II algorithm with an MLP, resulted in a six-parameter least square support vector machine-cuckoo optimization algorithm (LSSVM-COA) hybrid algorithm. LSSVM-COA demonstrated superior accuracy in ROP prediction, outperforming other models including SVR-COA, MLP-COA, and Motahhari’s approach. While reliable ROP prediction across wells was achieved, larger datasets are needed for further model development. In comparison to models based on recurrent neural networks (RNNs) and autoregressive integrated moving averages with exogenous variables (ARIMAX), Gao et al.38 demonstrated that the LSTM achieved the highest performance and accuracy in predicting the PR. To forecast drilling and blasting-induced outbreaks in tunnels39, proposed the use of ANN and GA-ANN models. Additionally, the DRI of different types of intact rock has been predicted using various techniques. RF was employed in40, while “Bayesian lithology classification and an optimized back propagation neural network (BPNN)” was used in41. Other models include ANN in42, ANN and XGBoost in43, ensemble machine learning in44, and PSO-RF techniques in45.

In various geotechnical engineering fields, the prediction and rating criteria for the DRI differ. Despite extensive analyses of DRI surveys yielding various results, there remains ambiguity in the probabilistic prediction of DRI. Currently, there is no established systematic approach for accurately predicting DRI.

This study introduces a hybrid ML approach, including GWO-SVM, GWO-RF, and GWO-XGBoost, for accurately predicting the DRI of rocks. This approach aims to address the imprecision in discrete models that may arise with other methods. To the best of the author’s knowledge and based on the literature review, this study is the first to utilize a hybrid ML approach for predicting DRI, incorporating nine distinct input parameters.

The key objective of this study is to predict the DRI using an advanced hybrid ML approach. To achieve this, the study employs a systematic approach. Initially, a diverse set of rock samples representing sedimentary, metamorphic, and igneous types, with strengths ranging from weak to extremely strong, was collected for laboratory analysis. Subsequently, several ML models, including GWO-SVM, GWO-RF, and GWO-XGBoost, were applied. The performance of these models in predicting DRI across different rock types is evaluated and compared to identify the most accurate model.

This study involved compiling various rock types, including sedimentary, metamorphic, and magmatic rocks, with strength ranging from weak to very strong. To predict the DRI of these rocks, 57 datasets from the prior literature were collected46,47. These datasets contained specific input attributes, such as “the uniaxial compressive strength (UCS), Brazilian tensile strength (BTS), Brittleness test (S20), and Sievers’ J-miniature drill value (Sj). The modulus ratio (MR), shore hardness (SH), porosity (n) in %, shimazeks F abrasitivity (SFA) in N/mm, and equivalent quartz content (EQ C) in % were estimated using equations provided in Table 1, developed by different investigators (Eq. 148, Eq. 2 and Eq. 349, and Eq. 4 and Eq. 550).”

The dataset used in this study was chosen for its comprehensive detailing of rock properties relevant to DRI analysis. It includes crucial parameters essential for predicting drilling performance and aligns with the study’s objective of examining the influence of rock properties on DRI, ensuring accurate and robust results. Previously, Shahani et al.51 applied LSTM, simple RNN, and RF models on the same dataset for DRI prediction. However, to further validate the data, this study developed a hybrid ML approach, including SVM, XGBoost, and RF, using the GWO algorithm to estimate DRI through Python programming language.

Correlation matrix of parameters in the original dataset.

The diagonal correlation analysis presented in Fig. 1 provides insights into the relationships among the variables that impact DRI. To depict these relationships, this study utilized the RStudio software to create a heatmap, which illustrates the correlation coefficients among various significant DRI parameters. It is important to highlight that there appears to be a limited correlation between these influential factors and DRI on the whole. Consequently, all attributes have been incorporated to enhance the accuracy of the ultimate DRI prediction model.

Based on the analysis evaluating the relationship between the input parameters and the output variable, the selection of input parameters for the model was guided by their correlation with the target variable (DRI). Parameters showing stronger correlations were prioritized for their direct impact on model performance, while those with weaker correlations were included to account for potential non-linear interactions. This approach ensures that the model maintains a balance between predictive accuracy and generalizability by integrating both statistically significant and practically relevant factors. The robustness of the model is significantly enhanced through this careful parameter selection process.

Systematic hybrid-optimized machine learning approach.

This study employs a hybrid ML approach that integrates GWO with SVM18, RF52, and XGBoost53 models. The selection of SVM, RF, and XGBoost models was driven by their proven effectiveness in managing complex data sets. SVM is particularly adept at working with smaller datasets featuring high-dimensional attributes, offering reliable generalization54. RF is known for its robust handling of high-dimensional data and its ability to mitigate overfitting through ensemble techniques55. XGBoost is included for its gradient-boosting framework, which delivers superior accuracy and computational efficiency, essential for the intricacies of the data56. Together, the approach ensures a comprehensive assessment of model performance while effectively addressing the dataset’s specific challenges. Following rigorous data cleaning and preprocessing procedures to ensure accuracy and reliability, the dataset used in this study was confirmed as appropriate for this hybrid ML approach. Figure 2 illustrates a detailed methodology and systematic hybrid ML approach. This section primarily introduces SVM, RF, XGBoost, and the proposed GWO approach used in this study.

In 1997, Vapnik et al. introduced SVMs, which are a form of supervised learning57. SVMs find applications in regression analysis and classification tasks by employing hyperplane classifiers. The optimal hyperplane effectively separates the two classes, with support vectors playing a crucial role in its determination58. SVMs utilize a feature space of high dimensionality, incorporating kernel functions and Vapnik’s 𝜀-insensitive loss function to build the prediction function. The selection of the kernel function plays a crucial role in achieving successful support vector regression (SVR). SVM has been applied in various studies using a diverse set of kernel functions, such as “radial basis, exponential, polynomial, sigmoid, Gaussian, and linear” functions59.

The random forest (RF) ensemble ML technique was introduced by Breiman in 200160. RF is beneficial for both regression analysis and classification tasks, employing a cutting-edge approach known as bagging or bootstrap aggregating. RF establishes a distinctive connection between model representation and predictive accuracy across various recognized AI computing methods61.

In this study, the model’s performance was evaluated using RF with 100 trees and default parameter settings.

XGBoost is an ensemble learning algorithm62 composed of multiple CART regression trees, where the final prediction is the cumulative result of the predictions from these trees. It employs gradient tree boosting (GTB) for ensemble learning, combining multiple trees to construct the final model. Moreover, XGBoost is optimized using GTB, ensuring both high accuracy and efficiency in model construction63. The objective function formula is as follows:

where \(\:Obj\) is the objective function, \(\:L\left(y\right)\) is the loss function, \(\:\varOmega\:\left({f}_{k}\right)\) is the regularization term. The loss function is denoted as \(\:L\left(y\right)\), measures the disparity between the predicted value (\(\:{\widehat{y}}_{i}\)) and the actual target label (\(\:{y}_{i}\)) for a given training sample. \(\:N\) represents the number of leaves in a decision tree, while γ and λ are uniformity characteristics employed to maintain model structure consistency and mitigate overfitting. Additionally, \(\:w\) signifies the weight assigned to each leaf.

The use of XGBoost for DRI prediction offers several advantages. Unlike conventional methods, such as chart-based methods and multiple regression analysis, XGBoost can incorporate multiple logging information, resulting in more reasonable predictions of rock DRI. This capacity minimizes the influence of subjective factors, thereby enhancing the scientific validity of the predictions. Compared to algorithms, such as ANN, SVM, and RF, XGBoost is better equipped to handle outliers or missing values, superior ability to prevent overfitting, and has greater adaptability to new samples, thus improving the model’s generalization capability. Furthermore, XGBoost surpasses traditional algorithms in both model accuracy and computational efficiency.

The grey wolf optimization (GWO) algorithm is a swarm intelligence-based optimization technique developed in 2014 by Mirjalili et al.64. This algorithm draws inspiration from the hunting behavior of grey wolves, characterized by their social hierarchy, which is categorized into four roles: Alpha (α), Beta (β), Delta (δ), and Omega (ω). The Alpha represents the top members of the pack, while the other classes support the hunting strategy. The GWO utilizes a mathematical framework that mimics the wolves’ strategies, such as tracking prey, encircling, and attacking. Notable for its strong convergence capabilities, minimal parameters, and ease of implementation, GWO has gained considerable attention from research scholars and has been effectively utilized in areas such as parameter optimization, etc.

SVM, RF, and XGBoost are widely used algorithms in data prediction. These algorithms offer improved predictive capabilities when integrated with the GWO technique18,65,66. The GWO algorithm improves the prediction accuracy of SVM, RF, and XGBoost by optimizing their parameters. To determine ideal parameter values, GWO dynamically adjusts the locations of alpha, beta, delta, and omega wolves. For SVM, GWO optimizes parameters like the kernel function and regularization, improving its predicting performance. Similarly, GWO fine-tunes RF parameters, such as the number of trees and maximum depth, leveraging the social behavior of grey wolves for improved accuracy. In the case of XGBoost, GWO optimizes hyperparameters including learning rate, tree depth, and subsampling ratio to maximize predicting effectiveness. Through its iterative optimization process, GWO discovers the optimal parameter combination for XGBoost, resulting in enhanced predictive capabilities. The combination of SVM, RF, and XGBoost with GWO enhances the predictive efficiency of the developed models for DRI by leveraging the strengths of these algorithms along with the optimization capabilities of GWO. This hybrid approach provides a robust and efficient solution for accurate data prediction in various domains. Figure 3 presents the procedure of the GWO-optimized prediction models used in this study. Table 2; Fig. 4 depict the parameter optimization process using GWO on the training data, highlighting the best values for C and gamma obtained through the optimization. After optimization, the models are evaluated on test data to assess their performance and generalizability. Negative accuracy values represent a minimized loss function.

Models hybridized by GWO.

Parameters optimization curves of the SVM, RF, and XGBoost models optimized by GWO.

Cross-validation (CV) is a crucial technique used to ensure that a developed ML model remains independent of how the dataset is split into train and test sets. Generally, the training dataset is partitioned into k subsets, or ‘folds.’ The ML model is trained on k − 1 of these folds, while the remaining one is used for validation. This process is iterated k times, effectively reducing variance and improving model robustness. The term ‘k-Fold’ in k-Fold CV refers to this repeated process. The results from each k-fold iteration are averaged to yield a single performance metric for the ML model. This study employed the repeated k-fold cross-validation method, utilizing 10 splits and 3 repeats. This approach partitions the dataset into 10 folds, with each fold serving as a test set once per iteration, and the entire process repeats three times, yielding 30 unique train and test splits. By averaging the results across multiple iterations, the repeated k-Fold method minimizes variance and provides a more stable performance estimate. We utilized negative mean squared error (MSE) as the scoring metric, converting it into a format that is maximizable. This thorough evaluation process ensures that our model’s performance is not dependent on any single split, thus enhancing the robustness and accuracy of the results.

The performance metrics are used to evaluate the accuracy of a model. The performance of each hybrid ML model in DRI prediction is evaluated using the performance metrics, including coefficient of determination (R2)67,68,69, mean absolute error (MAE)70, root mean square error (RMSE)71,72, and severity index (SI). These metrics suggest that lower values of MAE, RMSE, and SI indicate better performance, while a higher R² score reflects a more effective model in capturing the variance of the target variable.

where, \(\:\stackrel{-}{{D}_{o}}\) and \(\:\stackrel{-}{{D}_{p}}\) represents are the mean values of the original and predicted DRI, \(\:{D}_{o}\) and \(\:{D}_{p}\) are the original and predicted values of DRI, respectively.

This study aims to assess the efficiency of the developed hybrid ML models, including GWO-SVR, GWO-RF, and GWO-XGBoost in achieving significant DRI. The original and predicted output values were then organized for ease of analysis and performance evaluation of these models. The final results were analyzed by comparing the predicted models using various performance indices, including R2, MAE, RMSE, and SI, to determine the most successful model in data prediction. 30% of the dataset’s 57 patterns were used for model testing, while the remaining 70% were utilized for training.

The scattered plots comparing the actual DRI values with the predicted DRI outputs estimated by the GWO-SVR, GWO-RF, and GWO-XGBoost models on the test datasets are illustrated in Fig. 5. In Fig. 5, the R2 values of GWO-SVM, GWO-RF, and GWO-XGBoost are 0.952, 0.991, and 0.999, respectively.

Table 3 shows the performance indices of the developed GWO-SVM, GWO-RF, and GWO-XGBoost models calculated by Eq. (8) to (11). In this study, based on the developed GWO-SVM, GWO-RF, and GWO-XGBoost models, GWO-XGBoost outpaced other models at the training dataset R2 = 0.999, MAE = 0.00043, RMSE = 1.98017 and SI = 0.0350 and test dataset with R2 = 0.999, MAE = 0.00038, RMSE = 1.80790 and SI = 0.0312. Therefore, GWO-XGBoost is an applicable hybrid ML model that can be applied to accurately predict the DRI, as shown in Fig. 6.

Scatter plots of original DRI versus predicted DRI at the test data.

Radar graphs of the performance indices of the developed novel hybrid-optimized ML models.

The Taylor diagram provides a concise qualitative representation of how well the model aligns with standard deviations and correlations, as expressed by73. Figure 7 illustrates the correlation between the predicted DRI and the actual DRI for developed hybrid ML models, including GWO-SVR, GWO-RF, and GWO-XGBoost from Fig. 7. This comparison is based on standard deviation (STD), RMSE, and R2. According to the results, the GWO-XGBoost model demonstrated a notably stronger correlation with the original DRI compared to the other models developed in this study for predicting DRI.

Taylor diagram representation of the models.

In assessing the predictive accuracy of the GWO model for determining the DRI within the context of regression analysis, focus was given to GWO optimization for SVM, RF, and XGBoost models. when predicting DRI by classification models. Table 4 displays the classification of rock DRI based on its strength. The classification of the original DRI dataset for each rock is shown in Table 5.

Figure 9 illustrates the division of the original DRI dataset into distinct classes based on the drilling strength of the rocks. As demonstrated in Fig. 8, the DRI classes include 2 datasets for extremely low and low, 20 datasets for medium, 27 datasets for high, and 3 datasets for very high and extremely, respectively.

Table 6 shows the best C and best gamma of the developed hybrid classification models from Fig. 9. Figure 9 shows the parameters optimization curves of the SVM, RF, and XGBoost models optimized by GWO for predicting DRI on the training data. Negative accuracy values could represent a minimized loss function.

DRI class of the original dataset.

Parameters optimization curves of the SVM, RF, and XGBoost models optimized by GWO.

To evaluate the effectiveness of the developed hybrid models for DRI classification, three statistical metrics, such as precision, recall, and f1-score are introduced. Precision measures the ability to correctly predict the datasets, recall indicates the capacity to accurately predict the original features to the maximum extent, and the f1-score provides a comprehensive metric that reflects both recall and precision. Correspondingly, these performance indicators are used in this study to evaluate the performance of the model. The confusion matrix is defined by Eq. (12). A confusion matrix serves as a benchmark that is commonly used to illustrating the performance of a classification model on a testing dataset for which the true values are known.

where, u represents the number of DRI classes, \(\:{D}_{11}\:\) is the number of features accurately predicted for class a, and \(\:{D}_{ab}\) denotes the number of features of class that are categorized to class b.

Based on the confusion matrix, the precision, recall, and f1-score measures for each DRI class are respectively determined by Eq. (13) to Eq. (15).

Tables 7 and 8, respectively, contain the findings of these metrics for the training dataset and test dataset. Additionally, as the findings are presented as percentages, a value near 100 denotes a strong correlation between the actual and predicted classes.

In summary, precision is a measure of the classifier’s confidence in predicting a specific class. It represents the ratio of true positives (TP) to the sum of true positives and false positives (FP). FP, which contributes to the overall cost of the model, is considered a component of precision. The final model selection is based on the highest precision value obtained among the evaluated models. On the other hand, recall is the proportion of accurate positive (TP) and negative (TN) predictions out of all actual positives and negatives. The f1-score combines precision and recall scores. It is used to effectively assess the accuracy of a model. It is essential to understand when and how to apply the f1-score to conduct thorough model testing and ensure its correctness.

As shown in Table 7, all the developed hybrid models demonstrate the highest precision for all DRI classes, achieving 100% accuracy, except for class 2, which shows 93% precision for both GWO-SVM and GWO-XGBoost. Additionally, class 3 exhibits 94% precision with GWO-RF. All the predictive models successfully predict DRI classes with positive results. Similarly, for Recall, all DRI classes reach 100% except for class 2, which attains 95% recall with GWO-SVM and 94% recall with GWO-XGBoost, while class 3 achieves 93% recall with GWO-RF. Regarding the f1-score, GWO-SVM achieves 96% for both class 2 and class 3, whereas GWO-RF and GWO-XGBoost achieve 97% for these classes. Thus, the DRI classes were accurately assessed at the highest level, as indicated by the correctly assessed True Positive (TP) values for each model.

The statistical metrics, including precision, recall, and f1-score, were calculated for each model using the test dataset. The resulting values are presented in Table 8. The DRI class dataset comprises only classes 1, 2, 3, and 4. An analysis of the results in Table 8 shows that all models, such as GWO-SVM, GWO-RF, and GWO-XGBoost, exhibit exceptional precision with a remarkable accuracy of 100%, except for classes 2 and 3. For these classes, precision rates are 80%, 83%, and 83%, and 73%, 80%, and 89%, respectively. In terms of recall, class 1 and class 4 achieve a perfect score of 100%, whereas classes 2 and 3 attain recall rates of 67%, 83%, and 83%, and 89%, 80%, and 80%, respectively. Regarding the f1-score, class 1 achieves a perfect score of 100%, while the other classes do not reach this level of performance. Therefore, the assessment reveals that the DRI classes were evaluated accurately at the highest level, as supported by the correctly assessed TP values for each model.

Overall, it was found that the GWO-XGBoost model demonstrated higher accuracy in predicting the DRI classes. GWO-RF also showed high accuracy, securing the second highest position after the GWO-XGBoost model. However, the GWO-SVM exhibited lower performance compared to the other developed models in this study.”

In the present study, precision and accuracy are crucial metrics for comparing the models. Precision refers to the proportion of correct predictions made by the model among all positive predictions, while accuracy measures the overall correctness of the model’s predictions. All the developed models exhibit the highest accuracy scores for all DRI classes except for a few classes observed in both the training and test datasets. These models prove to be superior choices for classification tasks related to DRI and other relevant fields of study.

Multiclass confusion matrix for DRI classification obtained from training dataset (a) to (c) and test dataset (d) to (f).

The multi-class confusion matrix, obtained through the implementation of the hybrid ML models, illustrates the classification of DRI for both the training and test datasets, as shown in Fig. 10. The statistical metrics reported for the models, detailed in Tables 7 and 8, were derived from the data in Fig. 10. Notably, the results displayed in Fig. 10 are consistent with those presented in Tables 7 and 8.

This study successfully developed hybrid ML models, including GWO-SVM, GWO-RF, and GWO-XGBoost, to predict the DRI of rocks with high accuracy. One main shortcoming is the limited discussion of relevant theoretical studies. Although some references are included, future research should incorporate a more comprehensive review of theoretical frameworks and earlier studies to strengthen the theoretical foundation and validate the results. Additionally, this study focused entirely on three hybrid ML models, which, although effective, may not cover the full spectrum of potential optimization techniques. Future research should explore other optimization algorithms and hybrid models to compare their effectiveness in predicting DRI. Expanding the range of models can provide deeper insights and potentially reveal more accurate or efficient methods. For future geomechanics projects, conducting thorough field investigations before making any decisions is crucial. For larger-scale studies, acquiring an extensive dataset is recommended to address limitations and improve the model’s robustness. The GWO-XGBoost model should serve as a foundational starting point for future projects. Further analysis, comprehensive reviews, and potential data refinement are necessary to ensure the model’s applicability to the specific context of each project.

This study effectively employed a hybrid machine learning approach to accurately predict the DRI of rocks, incorporating models such as GWO-SVM, GWO-RF, and GWO-XGBoost. Among these models, GWO-XGBoost demonstrated the highest performance, achieving superior predictive accuracy in both the training and test datasets. In addition, GWO-XGBoost outperformed the other models (GWO-SVM and GWO-RF) in terms of precision, recall, f1-score, and multi-class confusion matrix results for each DRI class. GWO-RF ranked second, while GWO-SVM exhibited comparatively lower performance.

The hybrid GWO-XGBoost model proved to be a highly accurate and reliable tool for predicting DRI, offering significant advancements for rock excavation practices. The results suggest that this model can be effectively used in mining, geology, and other related fields.

The data that support the findings of this study are available from the corresponding author on a reasonable request.

Artificial neural network

Autoregressive integrated moving average with explanation variable

Classification and regression trees

Chi-squared automatic interaction detection

Drilling rate index

Firefly algorithm

Field penetration index

Genetic algorithm

Grey wolf optimization

Invasive weed optimization algorithm

K-nearest neighbor

Long-short term memory

Machine learning

Multi-layer perceptron

Monte Carlo simulation

Multivariable regression

Penetration rate

Particle swarm optimization

Random forest

Recurrent neural network

Rate of penetration

Coefficient of determination

Severity index

Support vector machine

Weight on bit

Macias, F. J., Dahl, F., Bruland, A., Käsling, H. & Thuro, K. Drillability assessments in hard rock. InISRM Nordic Rock Mechanics Symposium-NRMS. Oct 11 (pp. ISRM-NRMS). ISRM. (2017).

Liu, C. et al. Recognition of interface and category of roadway roof strata based on drilling parameters. J. Petrol. Sci. Eng. 1, 204:108724 (2021).

Article Google Scholar

Hossain, M. E. & Al-Majed, A. A. Fundamentals of Sustainable Drilling Engineering (Wiley, 2015).

Book Google Scholar

Eren, T. & Ozbayoglu, M. E. Real time optimization of drilling parameters during drilling operations. InSPE Oil and Gas India Conference and Exhibition? 2010, SPE-129126. https://doi.org/10.2118/129126-MS

Liu, C. et al. Automatic identification of rock formation interface based on borehole imaging. Energy Sourc. Part A: Recov. Util. Environ. Effects 46(1):493–504. https://doi.org/10.1080/15567036.2021.1903121 (2024).

Payette, G. S. et al. A real-time well-site based surveillance and optimization platform for drilling: technology, basic workflows and field results. InSPE/IADC Drilling Conference and Exhibition. D011S002R001. https://doi.org/10.2118/184615-MS (2017).

Ettehadi Osgouei, R. Rate of penetration estimation model for directional and horizontal wells. Master’s thesis, Middle East Technical University, (2007).

Liu, C., Zheng, X., Muhammad Shahani, N. & Li, Z. Research on borehole forming characteristics of two-wing polycrystalline diamond compact bit in coal mines. Energy Sourc. Part A: Recov. Util. Environ. Effects 45(4):12329–12342. https://doi.org/10.1080/15567036.2020.1787562 (2023).

Hoseinie, S. H., Ataei, M. & Mikaeil, R. Effects of microfabric on drillability of rocks. Bull. Eng. Geol. Environ. 78, 1443–1449. https://doi.org/10.1007/s10064-017-1188-z (2019).

Article Google Scholar

Soleimani, M. Well performance optimization for gas lift operation in a heterogeneous reservoir by fine zonation and different well type integration. J. Nat. Gas Sci. Eng. 40, 277–287. https://doi.org/10.1016/j.jngse.2017.02.017 (2017).

Article Google Scholar

Shad, H. I., Sereshki, F., Ataei, M. & Karamoozian, M. Prediction of rotary drilling penetration rate in iron ore oxides using rock engineering system. Int. J. Min. Sci. Technol. 28(3), 407–413. https://doi.org/10.1016/j.ijmst.2018.04.004 (2018).

Article Google Scholar

Glowacz, A. Fault diagnosis of electric impact drills using thermal imaging. Measurement 171, 108815. https://doi.org/10.1016/j.measurement.2020.108815 (2021).

Article Google Scholar

Kahraman, S. A., Balcı, C., Yazıcı, S. & Bilgin, N. Prediction of the penetration rate of rotary blast hole drills using a new drillability index. Int. J. Rock Mech. Min. Sci. 37(5), 729–743. https://doi.org/10.1016/S1365-1609(00)00007-1 (2000).

Article Google Scholar

Altindag, R. The evaluation of rock brittleness concept on rotary blast hold drills. J. South Afr. Inst. Min. Metall. 102(1), 61–66 (2002).

Google Scholar

Bilgin, N. & Kahraman, S. Drillability prediction in rotary blast hole drilling. InProc. 18th Int. Mining Congress and Exhibition of Turkey, Antalya, Turkey. 177–182. (2003).

Kahraman, S. A., Bilgin, N. & Feridunoglu, C. Dominant rock properties affecting the penetration rate of percussive drills. Int. J. Rock Mech. Min. Sci. 40(5), 711–723. https://doi.org/10.1016/S1365-1609(03)00063-7 (2003).

Article Google Scholar

Fattahi, H., Ghaedi, H. & Malekmahmoodi, F. Prediction of rock drillability using gray wolf optimization and teaching–learning-based optimization techniques. Soft. Comput. 28(1), 461–476. https://doi.org/10.1007/s00500-023-08233-6 (2024).

Article Google Scholar

Liang, H., Yun, C., Kan, M. J. & Gao, J. Research and application of element logging intelligent identification model based on data mining. IEEE Access. 15, 7:94415–94423. https://doi.org/10.1109/ACCESS.2019.2928001 (2019).

Article Google Scholar

Ebrahimabadi, A. & Afradi, A. Prediction of rate of penetration (ROP) in petroleum drilling operations using optimization algorithms. Rudarsko-geološko-naftni Zbornik 39(3), 119–130. https://doi.org/10.17794/rgn.2024.3.9 (2024).

Article Google Scholar

Ren, Y. et al. Research on the rate of penetration prediction method based on stacking ensemble learning. Geofluids 2023(1), 6645604. https://doi.org/10.1155/2023/6645604 (2023).

Article Google Scholar

Karrari, S. S., Heidari, M., Hamidi, J. K. & Teshnizi, E. S. Estimation of drilling rate index values of granitic rocks with their mineralogical properties using different estimation models. Arab. J. Geosci. 15(9), 856. https://doi.org/10.1007/s12517-022-10120-7 (2022).

Article Google Scholar

Yetkin, M. E., Özfırat, M. K., Özfırat, P. M. & Elmacı, D. Estimation of Drilling Rate Index using Artificial neural networks and regression analysis. DOI: (2024). https://doi.org/10.21203/rs.3.rs-3930410/v1

Khosravimanesh, S., Esmaeilzadeh, A., Akhyani, M., Mikaeil, R. & Asl, M. M. Accurate prediction of drill bit penetration rate in rock using supervised machine learning techniques base on laboratory test data. Rudarsko-geološko-naftni zbornik. 1;39(1):115 – 30. https://orcid.org/0000-0001-6236-828X (2024).

Gamal, H., Elkatatny, S., Alsaihati, A. & Abdulraheem, A. Intelligent prediction for rock porosity while drilling complex lithology in real time. Comput. Intell. Neurosci. 2021(1), 9960478. https://doi.org/10.1155/2021/9960478 (2021).

Article PubMed PubMed Central Google Scholar

Glowacz, A. Ventilation diagnosis of angle grinder using thermal imaging. Sensors 21(8), 2853. https://doi.org/10.3390/s21082853 (2021).

Article ADS PubMed PubMed Central Google Scholar

Fattahi, H. & Bazdar, H. Applying improved artificial neural network models to evaluate drilling rate index. Tunn. Undergr. Space Technol. 70, 114–124. https://doi.org/10.1016/j.tust.2017.07.017 (2017).

Article Google Scholar

Khandelwal, M. & Armaghani, D. J. Prediction of drillability of rocks with strength properties using a hybrid GA-ANN technique. Geotech. Geol. Eng. 34(2), 605–620. https://doi.org/10.1007/s10706-015-9970-9 (2016).

Article Google Scholar

Gamal, H., Elkatatny, S. & Abdulraheem, A. Rock drillability intelligent prediction for a complex lithology using artificial neural network. InAbu Dhabi International Petroleum Exhibition and Conference. D021S030R003. https://doi.org/10.2118/202767-MS (2020).

Asadi, A., Abbasi, A. & Bagheri, A. Application of artificial neural networks in estimation of drilling rate index using data of rock brittleness and mechanical properties. InISRM Nordic Rock Mechanics Symposium-NRMS. ISRM-NRMS. (2017).

Tewari, S., Dwivedi, U. D. & Biswas, S. A novel application of ensemble methods with data resampling techniques for drill bit selection in the oil and gas industry. Energies 14(2), 432. https://doi.org/10.3390/en14020432 (2021).

Article Google Scholar

Barbosa, L. F., Nascimento, A., Mathias, M. H. & de Carvalho, J. A. Jr Machine learning methods applied to drilling rate of penetration prediction and optimization-A review. J. Petrol. Sci. Eng. 183, 106332. https://doi.org/10.1016/j.petrol.2019.106332 (2019).

Article Google Scholar

Xu, H., Zhou, J., Asteris, G., Jahed Armaghani, P. & Tahir, D. Supervised machine learning techniques to the prediction of tunnel boring machine penetration rate. Appl. Sci. 9(18), 3715. https://doi.org/10.3390/app9183715 (2019).

Article Google Scholar

Sabah, M. et al. A machine learning approach to predict drilling rate using petrophysical and mud logging data. Earth Sci. Inf. 12, 319–339. https://doi.org/10.1007/s12145-019-00381-4 (2019).

Article Google Scholar

Basarir, H., Tutluoglu, L. & Karpuz, C. Penetration rate prediction for diamond bit drilling by adaptive neuro-fuzzy inference system and multiple regressions. Eng. Geol. 173, 1–9. https://doi.org/10.1016/j.enggeo.2014.02.006 (2014).

Article Google Scholar

Saeidi, O., Torabi, S. R., Ataei, M. & Rostami, J. A stochastic penetration rate model for rotary drilling in surface mines. Int. J. Rock Mech. Min. Sci. 68, 55–65. https://doi.org/10.1016/j.ijrmms.2014.02.007 (2014).

Article Google Scholar

Zhou, Y., Chen, X., Wu, M. & Cao, W. A comprehensive evaluation method for states adjustment priority of drilling process. IFAC-PapersOnLine 53(2), 11956–11961. https://doi.org/10.1016/j.ifacol.2020.12.720 (2020).

Article Google Scholar

Mehrad, M., Bajolvand, M., Ramezanzadeh, A. & Neycharan, J. G. Developing a new rigorous drilling rate prediction model using a machine learning technique. J. Petrol. Sci. Eng. 192, 107338. https://doi.org/10.1016/j.petrol.2020.107338 (2020).

Article Google Scholar

Gao, B. et al. TBM penetration rate prediction based on the long short-term memory neural network. Undergr. Space 6(6), 718–731. https://doi.org/10.1016/j.undsp.2020.01.003 (2021).

Article ADS Google Scholar

Koopialipoor, M., Jahed Armaghani, D., Haghighi, M. & Ghaleini, E. N. A neuro-genetic predictive model to approximate overbreak induced by drilling and blasting operation in tunnels. Bull. Eng. Geol. Environ. 78, 981–990. https://doi.org/10.1007/s10064-017-1116-2 (2019).

Article Google Scholar

Kamran, M. A probabilistic approach for prediction of drilling rate index using ensemble learning technique. J. Min. Environ. 12 (2), 327–337. https://doi.org/10.22044/jme.2021.10689.2030 (2021).

Article Google Scholar

Fang, X., Feng, H. & Wang, H. Study on intelligent prediction method of rock drillability based on bayesian lithology classification and optimized BP neural network. Pet. Sci. Technol. 12 (17), 2141–2162. https://doi.org/10.1080/10916466.2022.2036759 (2022).

Article Google Scholar

Singh, T. N., Gupta, A. R. & Sain, R. A comparative analysis of cognitive systems for the prediction of drillability of rocks and wear factor. Geotech. Geol. Eng. 24, 299–312. https://doi.org/10.1007/s10706-004-7547-0 (2006).

Article Google Scholar

Gamal, H., Omotunde, O., Duarte, M., Mohamed, O. & Elkatatny, S. How complex lithology schemes affect drilling rate prediction: machine learning study. InInternational Petroleum Technology Conference IPTC. (2024). (p. D011S010R002) https://doi.org/10.2523/IPTC-23898-MS

Gamal, H., Alsaihati, A., Ziadat, W., Abdulhamid Mahmoud, A. & Elkatatny, S. Ensemble machine learning model for predicting rock drillability rate for composite lithology. InAbu Dhabi International Petroleum Exhibition and Conference SPE. (2022). (p. D031S074R003) https://doi.org/10.2118/211779-MS

Wang, S. F., Wu, Y. M., Cai, X. & Zhou, Z. L. Strength prediction and drillability identification for rock based on measurement while drilling parameters. J. Cent. South. Univ. 30(12), 4036–4051. https://doi.org/10.1007/s11771-023-5492-4 (2023).

Article Google Scholar

Yenice, H. Determination of drilling rate index based on rock strength using regression analysis. An. Acad. Bras. Cienc. 91(03), e20181095. https://doi.org/10.1590/0001-3765201920181095 (2019).

Article PubMed Google Scholar

Yenice, H., Özdoğan, M. V. & Özfırat, M. K. A sampling study on rock properties affecting drilling rate index (DRI). J. Afr. Earth Sc. 141, 1–8. https://doi.org/10.1016/j.jafrearsci.2018.01.015 (2018).

Article ADS Google Scholar

Kahraman, S. A. Performance analysis of drilling machines using rock modulus ratio. J. South Afr. Inst. Min. Metall. 103(8), 515–522 (2003).

Google Scholar

Zhou, J., Chen, C., Armaghani, D. J. & Ma, S. Developing a hybrid model of information entropy and unascertained measurement theory for evaluation of the excavatability in rock mass. Eng. Comput. 1, 1–24. https://doi.org/10.1007/s00366-020-01053-4 (2022).

Article Google Scholar

Hosseini, S. H., Ataie, M. & Aghababaie, H. A laboratory study of rock properties affecting the penetration rate of pneumatic top hammer drills. J. Min. Environ. 5(1), 25–34. https://doi.org/10.22044/jme.2014.216 (2014).

Article Google Scholar

Shahani, N. M., Kamran, M., Zheng, X. & Liu, C. Predictive modeling of drilling rate index using machine learning approaches: LSTM, simple RNN, and RFA. Pet. Sci. Technol. 40(5), 534–555. https://doi.org/10.1080/10916466.2021.2003386 (2022).

Article Google Scholar

Zhang, Y. L., Qin, Y. G., Armaghsni, D. J., Monjezi, M. & Zhou, J. Enhancing rock fragmentation prediction in mining operations: a hybrid GWO-RF model with SHAP interpretability. J. Cent. South. Univ. 18, 1–4. https://doi.org/10.1007/s11771-024-5699-z (2024).

Article Google Scholar

Shahani, N. M., Zheng, X., Liu, C., Hassan, F. U. & Li, P. Developing an XGBoost regression model for predicting young’s modulus of intact sedimentary rocks for the stability of surface and subsurface structures. Front. Earth Sci. 26, 9:761990. https://doi.org/10.3389/feart.2021.761990 (2021).

Article Google Scholar

Andrew, A. M. An introduction to support vector machines and other kernel-based learning methods. Kybernetes 30(1), 103–115 (2001).

Article MathSciNet Google Scholar

Li, H. B., Wang, W., Ding, H. W. & Dong, J. Trees weighting random forest method for classifying high-dimensional noisy data. In2010 IEEE 7th international conference on e-business engineering 2010 Nov 10 (pp. 160–163). IEEE. https://doi.org/10.1109/ICEBE.2010.99

Chen, T., Guestrin, C. & Xgboost A scalable tree boosting system. InProceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining 2016, (pp. 785–794).

Vapnik, V., Golowich, S. E. & Smola, A. Support vector method for function approximation, regression estimation, and signal processing. Adv. Neural. Inf. Process. Syst. 281–287. (1997).

Sun, J. et al. Prediction of permeability and unconfined compressive strength of pervious concrete using evolved support vector regression. Constr. Build. Mater. 207, 440–449 (2019).

Article Google Scholar

Negara, A., Ali, S., AlDhamen, A., Kesserwan, H. & Jin, G. Unconfined compressive strength prediction from petrophysical properties and elemental spectroscopy using support-vector regression. In SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition. OnePetro. (2017).

Yang, P., Hwa, Y. & Zhou, B. A review of ensemble methods in bioinformatics. Curr. Bioinform. 5(4), 296–308 (2010).

Article Google Scholar

Meng, Q. et al. Liu TY.A communication-efficient parallel algorithm for decision tree. Adv. Neural Inform. Process. Syst. 1271–1279. (2016).

Meng, Q. et al. A communication-efficient parallel algorithm for decision tree. Adv. Neural. Inf. Process. Syst. 29. (2016).

Mirjalili, S., Mirjalili, S. M. & Lewis, A. Grey wolf optimizer. Adv. Eng. Softw. 69, 46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007 (2014).

Article Google Scholar

Ranka, S. & Singh, V. CLOUDS: A decision tree classifier for large datasets. InProceedings of the 4th knowledge discovery and data mining conference 1998, 2(8): 2–8.

Zhou, J. et al. Predicting TBM penetration rate in hard rock condition: a comparative study among six XGB-based metaheuristic techniques. Geosci. Front. 12(3), 101091. https://doi.org/10.1016/j.gsf.2020.09.020 (2021).

Article Google Scholar

Zhou, J., Huang, S., Zhou, T., Armaghani, D. J. & Qiu, Y. Employing a genetic algorithm and grey wolf optimizer for optimizing RF models to evaluate soil liquefaction potential. Artif. Intell. Rev. 55(7), 5673–5705. https://doi.org/10.1007/s10462-022-10140-5 (2022).

Article Google Scholar

Ding, X., Amiri, M. & Hasanipanah, M. Enhancing shear strength predictions of rocks using a hierarchical ensemble model. Sci. Rep. 14(1), 20268. https://doi.org/10.1038/s41598-024-71367-6 (2024).

Article PubMed PubMed Central Google Scholar

Fattahi, H. & Hasanipanah, M. An indirect measurement of rock tensile strength through optimized relevance vector regression models, a case study. Environ. Earth Sci. 80, 1–2. https://doi.org/10.1007/s12665-021-10049-2 (2021).

Article Google Scholar

Hasanipanah, M., Meng, D., Keshtegar, B., Trung, N. T. & Thai, D. K. Nonlinear models based on enhanced kriging interpolation for prediction of rock joint shear strength. Neural Comput. Appl. 33, 4205–4215. https://doi.org/10.1007/s00521-020-05252-4 (2021).

Article Google Scholar

Wang, Y., Hasanipanah, M., Rashid, A. S., Le, B. N. & Ulrikh, D. V. Advanced tree-based techniques for predicting unconfined compressive strength of rock material employing non-destructive and petrographic tests. Materials 16(10), 3731. https://doi.org/10.3390/ma16103731 (2023).

Article ADS PubMed PubMed Central Google Scholar

Wang, Y., Rezaei, M., Abdullah, R. A. & Hasanipanah, M. Developing two hybrid algorithms for predicting the elastic modulus of intact rocks. Sustainability 15(5), 4230. https://doi.org/10.3390/su15054230 (2023).

Article Google Scholar

Hasanipanah, M. et al. Intelligent prediction of rock mass deformation modulus through three optimized cascaded forward neural network models. Earth Sci. Inf. 15(3), 1659–1669. https://doi.org/10.1007/s12145-022-00823-6 (2022).

Article ADS Google Scholar

Taylor, K. E. Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Research: Atmos. 106 (D7), 7183–7192. https://doi.org/10.1029/2000JD900719 (2001).

Article ADS Google Scholar

Dahl, F., DRI, BWI, C. L. I., Standards, N. T. N. U. & Angleggsdrift, T. (2003). https://www.sintef.no/globalassets/sintef-byggforsk/berg-og-geo/dri-bwi-cli_standard-2011.pdf

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The authors are grateful to the esteemed editors and anonymous reviewers for their valuable suggestions to improve the quality of this study.

This research was supported by the Guizhou Provincial Education Department’s “Hundred Schools Thousands of Enterprises Science and Technology Research List” Project ([2024]013) and the Qiankehezhongyindi[2024]039.

School of Mines, China University of Mining and Technology, Xuzhou, 221116, China

Niaz Muhammad Shahani, Xigui Zheng, Xin Wei & Jiang Hongwei

The State Key Laboratory for Geo Mechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou, 221116, China

Xigui Zheng

School of Mines and Civil Engineering, Liupanshui Normal University, Liupanshui, China

Xigui Zheng

Guizhou Guineng Investment Co., Ltd, Guiyang, China

Xigui Zheng

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Conceptualization, Niaz Muhammad Shahani; Data curation, Xin Wei; Formal analysis, Xin Wei; Funding acquisition, Xigui Zheng; Investigation, Niaz Muhammad Shahani; Methodology, Niaz Muhammad Shahani; Supervision, Xigui Zheng; Validation, Xin Wei; Visualization, Jiang hongwei; Writing – original draft, Niaz Muhammad Shahani; Writing – review & editing, Xigui Zheng and Jiang Hongwei.

Correspondence to Xigui Zheng or Xin Wei.

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Shahani, N.M., Zheng, X., Wei, X. et al. Hybrid machine learning approach for accurate prediction of the drilling rock index. Sci Rep 14, 24080 (2024). https://doi.org/10.1038/s41598-024-75639-z

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Received: 25 July 2024

Accepted: 07 October 2024

Published: 15 October 2024

DOI: https://doi.org/10.1038/s41598-024-75639-z

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