空间点元位置不确定性对空间距离与面积度量的影响

Influence of Three-Dimensional Point Position Uncertainty on Three- Dimensional Distance and Area Measurement

采用置信域模型研究了空间点元的位置不确定性;基于误差传播定理,估算了由于空间点元位置不确定性而引起的空间距离不确定性及空间三角形面积不确定性;采用蒙特卡罗法在CAD平台上模拟点元概率密度分布的基础上,统计并验证了空间两点间距离不确定性及空间三角形的面积不确定性的正确性。相关研究为空间点元应用过程中产生的不确定性评估提供了理论依据,为工程质量验收提供定量化标准。

In the paper, three-dimensional point position uncertainty is firstly studied using the confidence region model. Secondly the three-dimensional distance uncertainty and area uncertainty are estimated by the three-dimensional point position uncertainty, according to the error propagation techniques. Then, it is appropriate to use the Monte Carlo approach on a CAD platform, to simulate the point probability density distribution and to verify the correctness of the three-dimensional distance uncertainty and the three-dimensional triangle area uncertainty. The purpose of this paper is to provide the theoretical basis of the uncertainty assessment that it is caused by three-dimensional point application. And it is significant for the quality of the project acceptance to provide quantitative standards.