Monte Carlo Method for the Measurement Uncertainty Evaluation Considering Non-positive Definite Correlation
JU Yan-fei1,2, WANG Jun-biao2,CHANG Chong-yi2,ZHAO Ze-ping2
1. Postgraduate Department, China Academy of Railway Sciences, Beijing 100081, China
2. Railway Science & Technology Research & Development Center, China Academy of Railway Sciences Corporation Limited, Beijing 100081, China
Abstract：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.
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2022, Vol. 43 
