Parameter estimation method of multidimensional measurement model with small sample based on MCM

Zhihao Zhao; Zhiwen Chen; Zuyang Zhang; Qiangxian Huang; Hongli Li; Rongjun Cheng; Liansheng Zhang

doi:10.1117/12.3032736

13 September 2024 Parameter estimation method of multidimensional measurement model with small sample based on MCM

Zhihao Zhao, Zhiwen Chen, Zuyang Zhang, Qiangxian Huang, Hongli Li, Rongjun Cheng, Liansheng Zhang

Proceedings Volume 13178, Eleventh International Symposium on Precision Mechanical Measurements; 131781S (2024) https://doi.org/10.1117/12.3032736
Event: Eleventh International Symposium on Precision Mechanical Measurements, 2023, Guangzhou, China

Abstract

In response to the problem of solving multiple linear regression measurement model in the case of small sample calibration test data, a method of parameter estimation for regression coefficient of measurement model based on Monte Carlo sampling idea and uncertainty evaluation theory is presented. In detail, the general form of multidimensional linear regression measurement model is introduced, and the principle and evaluation process based on Monte Carlo method (MCM) of solving the estimates and their standard deviations of the regression coefficient in measurement model are put forward. The optimization scheme for Monte Carlo sampling is further given, which can be adopted to ensure the reliability of parameter estimation under small sample condition. Finally, the feasibility and practicability of the proposed method are verified by a simulation example. In the case of small sample test data, this method can not only estimate the estimated values of each parameter in the multidimensional measurement model, but also evaluate the corresponding standard deviation. It can obtain a more scientific, reasonable and accurate measurement model, which provides a reliable model guarantee for practical measurement and evaluation applications.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Zhihao Zhao, Zhiwen Chen, Zuyang Zhang, Qiangxian Huang, Hongli Li, Rongjun Cheng, and Liansheng Zhang "Parameter estimation method of multidimensional measurement model with small sample based on MCM", Proc. SPIE 13178, Eleventh International Symposium on Precision Mechanical Measurements, 131781S (13 September 2024); https://doi.org/10.1117/12.3032736

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