IDW矿石品位估值结果的不确定性评价

Uncertainty Assessment for IDW Ore Grade Estimates

作为一种常用的矿石品位估值方法,距离幂次反比(inverse distance weighting,简称IDW)计算结果的可信度难以评估.对此,提出了一种基于统计学理论的解决途径.将参与IDW估值的样品品位视为指示化阈值,推导得出估值过程中其分配到的权重,即为待估点取这样品值的概率.基于这一结论构建出IDW估计值对应的条件累计分布函数(conditional cumulative distribution function,简称CCDF),从而完成待估位置矿石品位不确定性的建模.以一典型矿区的实际矿体勘探数据为基础进行了对比测试.针对每个估值点的CCDF进行了中位数、期望、方差等信息的提取,验证表明这一方法的计算结果与样品数据的实际情况之间存在较好的吻合度.在一定程度上说明了它在IDW品位估值结果不确定性评价方面的有效性.

As a typical ore grade estimation method,inverse distance weighting（IDW）has a long-time standing deficiency in reliability evaluation for its estimates,which has seriously limited its practicability.A statistical solution is presented in this paper to address the issue.A key character of IDW,that weight of each participation sample is the probability that the current un-sampled value is equal to the corresponding sample value,is proposed and proved by considering the participation samples as cutoff values during an indicating process.Based on this character,the conditional cumulative distribution function（CCDF）models related to the points to be estimated are constructed to fully characterize the uncertainty of IDW estimates.At last,a case study is carried out using cross validation and a test dataset from exploration engineering of a real ore-body.It is found that the real character of test dataset has been successfully revealed by the medium,expected and variance drawing from the constructed CCDFs,showing that the theoretical analysis and practical application can prove the validity and practicability of the proposed method to some extent.