RESUMO
This study proposes a new method to evaluate the effectiveness of orebody grade estimations, drawing upon the analysis of existing evaluation methods for grade estimation. This new approach addresses factors such as uneven sampling and asymmetric estimation range, which are challenging to overcome with existing evaluation techniques. The core principle of this method involves documenting how frequently individual samples are used during grade estimation and calculating the total distance weights for each sample. Subsequently, the usage frequency and total weight of the samples are standardized, and these standardized values are weighted based on the sample grades. A comparison is made between the weighted sample grades and the estimated grades, with the closeness between the two serving as a metric for assessing the effectiveness of the estimation. This study compares the new evaluation method to the direct comparison and cross-validation methods, examining the effectiveness of grade estimation using the inverse distance weighting (IDW) method. The findings revealed that: (1) The new evaluation method theoretically accounts for the systematic deviation between the statistical measures of estimated and sample grades resulting from uneven sample distribution, offering a fresh approach for enhancing the effectiveness of orebody grade estimation. (2) In the grade estimation of experimental Fe samples, the frequency of usage and the sum of distance weights were unequal. This inequality significantly contributes to the systematic deviation between the estimated and sample grades. (3) Comparing the new evaluation method to others confirms the stability and reliability of the new approach for evaluating the effectiveness of orebody grade estimation. This novel method demonstrates theoretical advantages and practical utility. (4) The deviation between the estimated grades and the statistical results of sample grades is influenced by the distribution pattern of sample grades, the spatial relationship between samples and estimation blocks, and the inherent systematic error associated with the IDW method. This systematic error cannot be overlooked.
RESUMO
Estimation of ore grade is very important for the value evaluation of ore deposits, and it directly affects the development of mineral resources. To improve the accuracy of the inverse distance weighting (IDW) method in ore grade estimation and reduce the smoothing effect of the IDW method in grade estimation, the weight calculation method involved in the IDW method was improved. The length parameter of the ore sample was used to calculate the weight of the IDW method. The length of the ore samples was used as a new factor of the weighting calculation. A new method of IDW integrated with sample length weighting (IDWW) was proposed. The grade estimation of Li, Al, and Fe in porcelain clay ore was used as a case study. A comparative protocol for grade estimation via the IDWW method was designed and implemented. The number of samples involved in the estimation, sample combination, sample grade distribution, and other factors affecting the grade estimation were considered in the experimental scheme. The grade estimation results of the IDWW and the IDW methods were used for comparative analysis of grades of the original and combined samples. The estimated results of the IDWW method were also compared with those of the IDW method. The deviation analysis of the estimated grade mainly included the minimum, maximum, mean, and coefficient of variation of the ore grade. The estimation effect of IDWW method was verified. The minimum deviations of the estimated grade of Li, Al, and Fe were between 9.129% and 59.554%. The maximum deviations were between 4.210 and 22.375%. The mean deviations were between - 1.068 and 7.187%. The deviations in the coefficient of variation were between 3.076 and 36.186%. The deviations in the maximum, minimum, mean, and coefficients of variation of the IDWW were consistent with those of the IDW, demonstrating the accuracy and stability of the IDWW method. The more the samples involved in the estimation, the greater the estimation deviations of IDW and IDWW methods. The estimated deviations of Li, Al, and Fe were affected by the shape of the grade distribution, when the same estimation parameters were used. The grade distribution pattern of the samples significantly influenced the grade estimation results. The IDWW method offers significant theoretical advantages and addresses the adverse effects of uneven sample lengths on the estimates. The IDWW method can effectively reduce the smoothing effect and improves the utilization efficiency of the original samples.
RESUMO
In order to study the influence of distance weight on ore-grade estimation, the inverse distance weighted (IDW) is used to estimate the Ni grade and MgO grade of serpentinite ore based on a three-dimensional ore body model and related block models. Manhattan distance, Euclidean distance, Chebyshev distance, and multiple forms of the Minkowski distance are used to calculate distance weight of IDW. Results show that using the Minkowski distance for the distance weight calculation is feasible. The law of the estimated results along with the distance weight is given. The study expands the distance weight calculation method in the IDW method, and a new method for improving estimation accuracy is given. Researchers can choose different weight calculation methods according to their needs. In this study, the estimated effect is best when the power of the Minkowski distance is 3 for a 10 m × 10 m × 10 m block model. For a 20 m × 20 m × 20 m block model, the estimated effect is best when the power of the Minkowski distance is 9.