Estimation of Fe grade at an ore deposit using extreme gradient boosting trees (XGBoost)

Estimating the spatial distribution of ore grade is one of the most critical steps to proceed with an investment decision on a deposit. Kriging is the most widely used method to estimate the ore grade, but alternative techniques are being developed. Machine learning algorithms can be used as alternative methods to classical kriging. In this paper, the iron (Fe) grade of a deposit is estimated with the XGBoost algorithm, and the results are compared with kriging estimation results. For the estimations, samples collected from drillholes were used. Due to the different natures of the estimation methods, different steps were taken to perform the estimations. The results show that XGBoost produced higher-range estimates, which is a desired result in ore grade estimation, and the minimum and maximum of the estimates were lower and higher than the kriging estimates, respectively. However, like kriging, the estimation results were smoother than composites, and the variance of the XGBoost estimates was lower than the variance of composites. This means that even though estimation with XGBoost mitigates the smoothing effect, the estimation results suffer from smoothing like kriging. Background Due to limited time and financial resources, ore grade estimation generally depends on limited data, generally from drillings. The limited data should be used with care to make reliable estimations of the spatial distribution of the target ore grade. Some alternative techniques like machine learning algorithms are being developed that provide a rich spectrum of approaches to classical geostatistical methods. Machine learning algorithms directly learn from available data to perform mainly regression and classification tasks while generally not making any assumption about available data. In this study, Fe grade estimation of an iron deposit (located in Türkiye) is performed using the XGBoost algorithm, and the results are compared with traditional ordinary kriging. Due to the different natures of these estimation methods, different steps must be taken to perform estimations. In the stimation with the XGBoost algorithm, hyperparameter optimization is performed using grid search. In estimations with both methods, composites of Fe grades are considered as input data. Finally, estimations are compared with these composite values and each other by means of summary statistics and residual values when kriging estimate results are considered as base. The results show that estimations with the XGBoost algorithm produced estimates with higher ranges than kriging. But the method still suffers from smoothing like kriging, and the minimum and maximum values of estimates were higher and lower than composite values, respectively. Methodology XGBoost is a member of the ensemble learning family, which is a supervised, parallel, scalable tree boosting system that can be used to solve both regression and classification problems. An ensemble can be defined as the fusion of two or more trained models to improve performance of underlying individual models, while the fusion of the models increases the generalization, local and specific information are also captured. These properties make ensemble techniques one of the most powerful methods among the machine learning alternatives. The aim of gradient boosting is to approximate the function F(x), which maps x onto corresponding outputs y while data set D = {xi, yi}1N is given. This approximation is reached by minimization of the loss function L(y, F(x)). Additive approximation of the F(x) function is reached by weighted sum of functions:(1) where pm is the weight associated with the mth function hm(x). The approximation is first reached by constant approximation of F*(x) as:(2) and following models are minimized as:(3) F* is optimized greedily by using gradient descent optimization. As kriging is well known in the mining industry, methodological details are not given here. Results and discussion In the spatial estimation of the ore grade, the statistics of the estimation results are expected to be as close as possible to the statistics of the composites. However, the statistics of the estimations are generally smoother, and this phenomenon is well known in geostatistical estimation.Results of the estimations can be assessed by using summary statistics and cross-plots. Summary statistics of the composites, kriging and XGBoost are given in Table 1. As expected, a well-known smoothing effect is observed at both estimation results. Both methods produced smoother estimation results while variances of the estimations are notably lower than the variance of the composites. XGBoost produced estimation results with higher variation than acceptable due to the higher estimation range. Comparison of the estimates are followed by cross-plotting kriging estimates against XGBoost estimates (Fig. 1). As seen from Fig. 1, the estimation results show moderately positive association in linear characteristics with 0.63 Pearson correlation coefficient. In grade estimation, the XGBoost algorithm can be a good candidate as an alternative to the industry standard kriging while estimations can only be performed with input-output data pairs, which consist of X, Y and Z coordinates and grade measurements at those locations, respectively. In XGBoost estimation, grade continuity is implicitly captured by the algorithm, which is mainly dependent on hyperparameters specific to the algorithm. However, the results of the estimations are dependent on estimation of these parameters which are appropriate to a given data set. Conclusion In this paper, the XGBoost algorithm was used to estimate the Fe grade of a deposit. This study is the first in literature in which the spatial estimation of Fe grade is made using the XGBoost algorithm. For comparison, the kriging method is used. The estimation results show that XGBoost can be used in grade estimation as an alternative to kriging. The XGBoost produced a higher estimation range than kriging, which is desired in grade estimation at an ore deposit. In correlation with the higher estimation range of XGBoost, the standard deviation of the estimation results with XGBoost was higher than kriging. Estimates were moderately correlated with kriging estimates. Like kriging, XGBoost suffers from smoothing, and the standard deviation of the estimation method was significantly lower than the composites. XGBoost requires hyperparameter tuning to reach an acceptable level of estimation, and default parameters are not the best option to estimate the grade distribution. In hyperparameter tuning, grid search can be used, which can sometimes require high computing power. References A list of all references is available in the full paper.

Estimation of Fe grade at an ore deposit using extreme gradient boosting trees (XGBoost)

Authored by: Fırat Atalay

To view this article you must be a member of SME/UCA.

Gold retains key reserve status despite surging bond yields, central bankers say

China demands copper supply commitments for Anglo Teck merger approval, sources say

Leaders in mining excellence honored by NMA, federal agencies

Gold retains key reserve status despite surging bond yields, central bankers say

China demands copper supply commitments for Anglo Teck merger approval, sources say

Leaders in mining excellence honored by NMA, federal agencies

To view this article you must be a member of SME/UCA.

A sustainable complexation leaching of critical metals from spent lithium-ion batteries by glycine in a neutral solution

Analysis of raise boring with grouting as an optimal method for ore pass construction in incompetent rock mass — A case study

Related Articles

Rare earth elements in the global economy: Usage, recovery and the quest for supply security — A review

A systematic evaluation of localization signals in the advancing openpit mine Aitik

From foundation to future: Revisiting AI integration in mining engineering education through current perspectives of students, educators and industry

Iron ore tailings reprocessing by electrostatic separation plus two-stage froth flotation

Gold retains key reserve status despite surging bond yields, central bankers say

China demands copper supply commitments for Anglo Teck merger approval, sources say

Leaders in mining excellence honored by NMA, federal agencies

Gold retains key reserve status despite surging bond yields, central bankers say

China demands copper supply commitments for Anglo Teck merger approval, sources say

Leaders in mining excellence honored by NMA, federal agencies

Use Single Sign On