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; 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; 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.
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.
Exploitation
Marco Antonio Cotrina Teatino; Jairo Jhonatan Marquina Araujo; Eduardo Manuel Noriega Vidal; Jose Nestor Mamani Quispe; Johnny Henrry Ccatamayo Barrios; Joe Alexis Gonzalez Vasquez; Solio Marino Arango Retamozo
Abstract
The primary objective of this research was to apply machine learning techniques to predict the production of an open pit mine in Peru. Four advanced techniques were employed: Random Forest (RF), Extreme Gradient Boosting (XGBoost), K-Nearest Neighbors (KNN), and Bayesian Regression (RB). The methodology ...
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The primary objective of this research was to apply machine learning techniques to predict the production of an open pit mine in Peru. Four advanced techniques were employed: Random Forest (RF), Extreme Gradient Boosting (XGBoost), K-Nearest Neighbors (KNN), and Bayesian Regression (RB). The methodology included the collection of 90 datasets over a three-month period, encompassing variables such as operational delays, operating hours, equipment utilization, the number of dump trucks used, and daily production. The data were allocated 70% for training and 30% for testing. The models were evaluated using metrics such as Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Variance Accounted For (VAF), and the Coefficient of Determination (R2). The results indicated that the Bayesian Regression model was the most effective in predicting production in the open pit mine. The RMSE, MAPE, VAF, and R2 for the models were 3686.60, 3581.82, 4576.61, and 3352.87; 12.65, 11.09, 15.31, and 11.90; 36.82, 40.72, 1.85, and 47.32; 0.37, 0.41, 0.41, and 0.47 for RF, XGBoost, KNN, and RB, respectively. This research highlights the efficacy of machine learning techniques in predicting mine production and recommends adjusting each model's parameters to further enhance outcomes, significantly contributing to strategic and operational management in the mining industry.
