非精确输入下地质统计制图的区间值Kriging模型
Interval-Valued Kriging Models for Geostatistical Mapping with Imprecise Inputs
摘要：
由于测量过程中的各种限制和不确定性，许多地球科学数据是不精确的。在地统计制图框架中保持这种不精确性的一种方法是将测量值表征为区间而不是单个值。为了有效地分析区间数据，本文提出并发展了基于随机集理论和广义L2度量的区间克立格模型。这些模型克服了先前开发的数学困难，并且在计算上更可行。数值实现我们的区间值克里金法提供了一个基于惩罚的约束优化算法。在美国犹他州的设计地面雪荷载预测的应用程序，展示了所提出的模型的优势，在保留关键来源的不确定性，以更有效的基于风险的设计方案。
英文摘要：
Many geosciences data are imprecise due to various limitations and uncertainties in the measuring process. One way to preserve this imprecision in a geostatistical mapping framework is to characterize the measurements as intervals rather than single values. To effectively analyze the interval-valued data, this paper proposes and develops interval-valued kriging models based on the theory of random sets and a generalized L2 metric. These models overcome the mathematical difficulties of a previous development and are computationally more feasible. Numerical implementation of our interval-valued kriging is provided using a penalty-based constrained optimization algorithm. An application to the prediction of design ground snow loads in Utah, USA, is presented that demonstrates the advantages of the proposed models in preserving crucial sources of uncertainty towards a more efficient risk-based designing scheme.
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