考虑非正定相关性的测量不确定度蒙特卡洛评定方法

当采用蒙特卡洛法评定测量不确定度考虑输入量相关性时,需基于Nataf逆变换产生服从任意边缘概率分布的相关多维随机变量。为了解决Nataf逆变换过程中输入量相关系数矩阵非正定时,无法产生线性变换矩阵的问题,提出了基于Barzilai-Borwein梯度法的迭代修正算法。进而探讨了输入量服从非正态分布且相关的蒙特卡洛法实施步骤。最后,采用提出的迭代修正算法并基于Nataf逆变换的蒙特卡洛方法,对高速轮轨试验台轮轨纵向蠕滑率不确定度进行了评定,验证了该算法的可行性及有效性。

Monte Carlo Method for the Measurement Uncertainty Evaluation Considering Non-positive Definite Correlation

When the Monte Carlo method is used to evaluate the measurement uncertainty and the input quantities correlation is considered, it is necessary to generate relevant multi-dimensional random variables that obey any marginal probability distribution based on the Nataf inverse transformation. In order to solve the problem that the linear transformation matrix cannot be generated when the input correlation coefficient matrix is not positive definite in the Nataf inverse transformation process, an iterative correction algorithm based on the Barzilai-Borwein gradient method is proposed. Furthermore, it discusses the implementation steps of Monte Carlo method that the input quantities obey non-normal distribution. Finally, the iterative correction algorithm proposed and the Monte Carlo method based on Nataf inverse transformation are used to evaluate the uncertainty of the wheel-rail longitudinal creep rate of the high-speed wheel-rail system, which verifies the feasibility and effectiveness of the algorithm.