Exploration
Marco Antonio Cotrina-Teatino; Jairo Jhonatan Marquina-Araujo; Jose Nestor Mamani-Quispe; Solio Marino Arango-Retamozo; Joe Alexis Gonzalez-Vasquez
Abstract
Traditional geostatistical methods such as kriging exhibit limitations by assuming linear and symmetric dependencies, which can lead to smoothed estimates and the loss of local variability. To address these issues, this study applies Archimedean copulas (Clayton, Gumbel, and Frank) for the estimation ...
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Traditional geostatistical methods such as kriging exhibit limitations by assuming linear and symmetric dependencies, which can lead to smoothed estimates and the loss of local variability. To address these issues, this study applies Archimedean copulas (Clayton, Gumbel, and Frank) for the estimation of copper ore grades in a deposit located in Peru. A total of 5,654 composites, each 15 meters in length, were obtained from 185 diamond drill holes. The data were transformed to a uniform scale to allow for copula fitting. Dependence structures were modeled by lag distance, with the dependence parameter fitted using fifth-degree polynomials, and three-dimensional conditional estimation was implemented. Results indicate that ordinary kriging yielded RMSE = 0.161, MAE = 0.104, R2 = 0.692, and a correlation of 0.861. The Clayton copula slightly improved these metrics (RMSE = 0.154, MAE = 0.101, R2 = 0.717, R = 0.871), while the Gumbel copula captured higher local variability (RMSE = 0.161, MAE = 0.116, R2 = 0.692, R = 0.855). The Frank copula achieved the best performance with RMSE = 0.137, MAE = 0.090, R2 = 0.778, and R = 0.905. In conclusion, Archimedean copulas significantly enhance geostatistical estimation by better capturing spatial dependence, offering a robust alternative to classical geostatistical methods.
Exploration
Marco Antonio Cotrina Teatino; Jairo Jhonatan Marquina-Araujo; Jose Nestor Mamani-Quispe; Solio Marino Arango-Retamozo; Joe Alexis Gonzalez-Vasquez
Abstract
The geochemical and spatial characterization of legacy mine tailings is essential for identifying reprocessing opportunities and informing environmental management. However, the high compositional complexity of polymetallic tailings requires robust multivariate approaches. This study evaluates and compares ...
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The geochemical and spatial characterization of legacy mine tailings is essential for identifying reprocessing opportunities and informing environmental management. However, the high compositional complexity of polymetallic tailings requires robust multivariate approaches. This study evaluates and compares the performance of four unsupervised clustering algorithms Euclidean K-Means, Riemannian K-Means, Gaussian Mixture Model (GMM), and Agglomerative Clustering applied to 927 samples from the Quiulacocha tailings deposit in Peru, using six major elements (Zn, Pb, Cu, Fe, Ag, Au) and spatial coordinates. All methods consistently identified three main geochemical domains. Cluster 1 was enriched in Cu and Au, Cluster 2 in Pb and Fe, and Cluster 3 in Zn, Ag, and Fe. Covariance-based methods (Riemannian K-Means and Agglomerative Clustering) outperformed others in internal validation (Silhouette scores up to 0.58) and consistency (Adjusted Rand Index = 1.00), offering more interpretable and geologically coherent partitions. CLR transformation reduced clustering performance, highlighting the importance of preserving raw geochemical variance for spatial segmentation. These findings demonstrate the effectiveness of multivariate clustering for unraveling compositional heterogeneity in tailings and delineating domains of potential economic value. The approach provides a quantitative framework for supporting reprocessing decisions, reducing risk, and guiding future research on mine waste valorization.
Exploration
Marco Antonio Cotrina Teatino; Jairo Jhonatan Marquina-Araujo; Jose Nestor Mamani-Quispe; Solio Marino Arango-Retamozo; Joe Alexis Gonzalez-Vasquez; Kevin Daniel Rondo-Jalca
Abstract
The classification of mineral resources significantly impacts mine planning, economic feasibility, and regulatory compliance. Despite its importance, such classification frequently depends on the subjective judgment of the Qualified Person (QP), owing to the absence of internationally standardized technical ...
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The classification of mineral resources significantly impacts mine planning, economic feasibility, and regulatory compliance. Despite its importance, such classification frequently depends on the subjective judgment of the Qualified Person (QP), owing to the absence of internationally standardized technical criteria for delineating resource categories. To mitigate this limitation, an innovative methodology integrating clustering based on Riemannian geometry with machine learning techniques was developed for mineral resource classification. A database of 5,654 composited samples from 185 diamond drill holes in a copper deposit in central Peru was utilized to classify 318,443 blocks. Copper grades were estimated through Ordinary Kriging (RMSE = 0.102; MAE = 0.069), generating geostatistical variables kriging variance, average distance to samples, and number of samples that served as input features for the classification. Clustering was performed using both classical KMeans and Riemannian KMeans, followed by spatial smoothing via XGBoost and Random Forest algorithms. Absolute coordinates were incorporated to address spatial discontinuities in classification outputs. The combination of the Riemannian model with Random Forest produced the highest classification performance, with a Silhouette index of 0.26 and a Davies-Bouldin index of 0.72. The resulting metal content was estimated at 4.24 Mt of copper at 0.44% grade (measured), 6.49 Mt at 0.34% Cu (indicated), and 7.68 Mt at 0.32% Cu (inferred), demonstrating close alignment with QP estimates while exhibiting improved spatial coherence. In summary, the Riemannian-based approach outperformed classical KMeans and conventional classification methods, providing a more robust, objective, and globally consistent alternative.
Exploration
Marco Antonio Cotrina-Teatino; Jairo Jhonatan Marquina-Araujo; Jose Nestor Mamani-Quispe; Jorge Chira-Fernandez; Cesar De la cruz-Poma; Solio Marino Arango-Retamozo
Abstract
The sustained increase in mining waste, particularly in the form of tailings, poses a significant environmental and economic challenge, especially in contexts where these deposits retain residual metal content. This study assessed the gold potential of Tailings Deposit I at La Cienega (Peru) by integrating ...
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The sustained increase in mining waste, particularly in the form of tailings, poses a significant environmental and economic challenge, especially in contexts where these deposits retain residual metal content. This study assessed the gold potential of Tailings Deposit I at La Cienega (Peru) by integrating geostatistical estimation and machine learning models optimized through metaheuristic algorithms. The methodology involved geochemical characterization, three-dimensional estimation using Ordinary Kriging (OK) as a geostatistical method, and prediction of gold grades through three models: XGBoost optimized with Particle Swarm Optimization (XGB+PSO), Support Vector Regression with Genetic Algorithm (SVR+GA), and Random Forest optimized using Ant Colony Optimization (RF+ACO). Estimates were validated using Leave-One-Out cross-validation and performance metrics including RMSE, MAE, Bias, and correlation coefficient (R). The RF+ACO model achieved an RMSE of 0.32 ppm, MAE of 0.24 ppm, Bias of 0.006, and an R value of 0.56. Average predicted grades ranged from 1.14 to 1.33 ppm, with estimated gold contents between 981.00 and 1,147.12 ounces, while OK yielded 1,028.77 ounces at an average grade of 1.19 ppm. These findings suggest that properly optimized machine learning models can provide reasonable estimates of metal content in tailings, particularly in settings characterized by high spatial heterogeneity and limited geological continuity.
Environment
Marco Antonio Cotrina Teatino; Jairo Jhonatan Marquina-Araujo; Jose Nestor Mamani-Quispe; Juan Antonio Vega-Gonzalez; Moises Bartolome Guia-Pianto
Abstract
The Quiulacocha tailings deposit in central Peru, containing 70 Mt of historical mine waste, presents both environmental risks and opportunities for secondary metal recovery. This study applies data-driven machine learning techniques to estimate the remaining silver resources using 927 one-meter composites ...
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The Quiulacocha tailings deposit in central Peru, containing 70 Mt of historical mine waste, presents both environmental risks and opportunities for secondary metal recovery. This study applies data-driven machine learning techniques to estimate the remaining silver resources using 927 one-meter composites from 40 vertical drillholes. Three supervised learning models—Random Forest (RF), k-Nearest Neighbors (KNN), and Extreme Gradient Boosting (XGBoost)—were trained using spatial coordinates (X, Y, Z) as the sole input features. Model validation was performed using leave-one-out cross-validation (LOOCV), and results were benchmarked against ordinary kriging (OK). Among the models, RF delivered the highest predictive performance (mean error = 0.53 g/t, RMSE = 7.21 g/t, R = 0.82), outperforming OK (R = 0.63, RMSE = 10.47 g/t). Block model predictions indicated higher silver content from machine learning models: 1,532.86 t (RF), 1,542.16 t (XGBoost), and 1,492.09 t (KNN), compared to 1,463.73 t from OK. Additionally, XGBoost maintained superior grade-tonnage relationships under elevated cutoff thresholds, highlighting its potential to delineate high-grade subdomains within the deposit. These findings confirm the value of machine learning in resource estimation under conditions of low spatial continuity, such as tailings, where material mixing and irregular deposition patterns limit correlation across space.
Exploitation
Marco Antonio Cotrina-Teatino; Jairo Jhonatan Marquina-Araujo; Solio Marino Arango-Retamozo; Luis Alex Rios-LLaure; Jose Nestor Mamani-Quispe; Salomon Ortiz-Quintanilla
Abstract
This work aimed to optimize fuel consumption and CO2 emissions in mining haul trucks through a sustainability focused machine learning approach in a gold mine in La Libertad, Peru. The methodology comprised three stages. First, operational data from 26 m3 haul trucks (10,103 records over 12 months) were ...
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This work aimed to optimize fuel consumption and CO2 emissions in mining haul trucks through a sustainability focused machine learning approach in a gold mine in La Libertad, Peru. The methodology comprised three stages. First, operational data from 26 m3 haul trucks (10,103 records over 12 months) were normalized using Z-score scaling. Second, a Ridge regression model was trained to predict fuel consumption based on variables such as truck utilization, trips, road gradient, material type, haul distance, and operating hours. Finally, three operational strategies were simulated: Controlled Reduction (CRS), Balanced Efficiency (BES), and Maximum Utilization (MUS), to evaluate environmental, economic, and social impacts. The results indicated that the Ridge model achieved strong predictive performance in estimating fuel consumption (R2 = 0.83; MSE = 38.16). According to the simulated scenarios, environmentally, CRS reduced fuel consumption by 30% and CO2 emissions by 1,481.3 tons; BES achieved 7.99% savings and 394.9 tons less CO2. Economically, CRS saved USD 664,924.6 in fuel costs and BES USD 177,276.3. Socially, the carbon cost decreased by USD 11,406.1 (CRS) and USD 3,041.0 (BES). MUS increased emissions by 864.3 tons and fuel costs by USD 387,966.4. This research proposes a novel integration of machine learning and sustainability analysis applied to haul trucks in open-pit mining material transport. It also offers a replicable, data-driven framework for mining companies to reduce emissions, optimize costs, and align their operations with sustainability goals.
Exploitation
Marco Antonio Cotrina Teatino; Jairo Jhonatan Marquina Araujo; Jose Nestor Mamani Quispe; Solio Marino Arango-Retamozo; Johnny Henrry Ccatamayo-Barrios; Joe Alexis Gonzalez-Vasquez; Teofilo Donaires-Flores; Maxgabriel Alexis Calla-Huayapa
Abstract
Mining plays a crucial role in the economy of many countries, contributing significantly to GDP, employment, and industrial development. However, optimizing drilling and blasting operations remains a key challenge in open-pit mining due to its direct impact on operational costs and rock fragmentation ...
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Mining plays a crucial role in the economy of many countries, contributing significantly to GDP, employment, and industrial development. However, optimizing drilling and blasting operations remains a key challenge in open-pit mining due to its direct impact on operational costs and rock fragmentation efficiency. This work aims to optimize fragmentation (X50) and drilling and blasting costs using hybrid machine learning models, an innovative approach that improves predictive accuracy and economic feasibility. Six models were developed: Artificial Neural Networks (ANNs), Decision Trees (DT), Extreme Gradient Boosting (XGBoost), Random Forest (RF), and Support Vector Regression (SVR), optimized using Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The dataset, comprising 100 blasts, was split into 70% for training and 30% for testing. The SVR+PSO model achieved the highest accuracy for fragmentation prediction, with an RMSE of 0.27, MAE of 0.21, and R2 of 0.92. The RF+GA model was most effective for cost prediction, with an RMSE of 414.58, MAE of 354.14, and R2 of 0.99. Optimization scenarios were implemented by reducing burden (4.3 m to 3.8 m) and spacing (5.0 m to 4.5 m), achieving a 5.7% reduction in X50 (17.6 cm to 16.6 cm) and a 9.5% cost decrease (63,000 USD to 57,000 USD per blast). Predictions for 30 future blasts using the RF + GA model estimated a total cost of 1.7 MUSD, averaging 55,180 USD per blast. These findings confirm the effectiveness of machine learning in cost optimization and improving blasting efficiency, presenting a robust data-driven approach to optimizing mining operations.
Exploration
Marco Antonio Cotrina-Teatino; Jairo Jhonatan Marquina-Araujo; Jose Nestor Mamani-Quispe; Solio Marino Arango-Retamozo; Johnny Henrry Ccatamayo-Barrios; Joe Alexis Gonzalez-Vasquez; Teofilo Donaires-Flores; Maxgabriel Alexis Calla-Huayapa
Abstract
This work aimed to categorize mineral resources in a copper deposit in Peru, using a machine learning model, integrating the K-prototypes clustering algorithm for initial classification and Random Forest (RF) as a spatial smoother. A total of 318,443 blocks were classified using geostatistical and geometric ...
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This work aimed to categorize mineral resources in a copper deposit in Peru, using a machine learning model, integrating the K-prototypes clustering algorithm for initial classification and Random Forest (RF) as a spatial smoother. A total of 318,443 blocks were classified using geostatistical and geometric variables derived from Ordinary Kriging (OK) such as kriging variance, sample distance, number of drillholes, and geological confidence. The model was trained and validated using precision, recall, and F1-score metrics. The results indicated an overall accuracy of 97%, with the measured category achieving 98% precision and an F1-score of 0.98. The total estimated tonnage was 5,859.36 Mt, distributed as follows: 1,446.13 Mt (measured), 2,249.22 Mt (Indicated), and 2,164.01 Mt (Inferred), with average copper grades of 0.43%, 0.33%, and 0.31% Cu, respectively. Compared to the traditional geostatistical methods, this hybrid approach improves classification objectivity, spatial continuity, and reproducibility, minimizing abrupt transitions between categories. The RF model proved to be a robust tool, reducing classification inconsistencies and better capturing geological uncertainty. Future studies should explore hybrid models (K-means with RF, ANN with K-Prototypes, gradient boosting, and deep learning) and incorporate economic variables to optimize decision-making in resource estimation.
Exploration
Jairo Jhonatan Marquina Araujo; Marco Antonio Cotrina Teatino; José Nestor Mamani Quispe; Eduardo Manuel Noriega Vidal; Juan Antonio Vega Gonzalez; Juan Vega-Gonzalez; Juan Cruz-Galvez
Abstract
The objective of this research work to employ machine learning techniques including Multilayer Perceptron Artificial Neural Networks (ANN-MLP), Random Forests (RFs), Extreme Gradient Boosting (XGBoost), and Support Vector Regression (SVR) to predict copper ore grades in a copper deposit located in Peru. ...
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The objective of this research work to employ machine learning techniques including Multilayer Perceptron Artificial Neural Networks (ANN-MLP), Random Forests (RFs), Extreme Gradient Boosting (XGBoost), and Support Vector Regression (SVR) to predict copper ore grades in a copper deposit located in Peru. The models were developed using 5654 composites containing available geological information (rock type), as well as the locations of the samples (east, north, and altitude) and secondary ore grade (Mo) obtained from drilling wells. The data was divided into 10% (565 composites) for testing, 10% (565 composites) for validation, and 80% (4523 composites) for training. The evaluation metrics included SSE (Sum of Squared Errors), RMSE (Root Mean Squared Error), NMSE (Normalized Mean Squared Error), and R² (Coefficient of Determination). The XGBoost model could predict the ore grade with an SSE of 15.67, RMSE = 0.17, NMSE = 0.34, and R² = 0.66, the RFs model with an SSE of 16.40, RMSE = 0.17, NMSE = 0.36, and R² = 0.65, the SVR model with an SSE of 19.94, RMSE = 0.19, NMSE = 0.43, and R² = 0.57, and the ANN-MLP model with an SSE = 21.00, RMSE = 0.19, NMSE = 0.46, and R² = 0.55. In conclusion, the XGBoost model was the most effective in predicting copper ore grades.
