基于蒙特卡罗法的平面度测量不确定度评定

Uncertainty Evaluation of Flatness Measurement Based on Monte Carlo Method

摘要:

形位误差的测量不确定度评定是目前测量领域研究的热点；但由于其测量的复杂性和测量结果评定的多样性,导致在实际测量结果中形位误差测量的不确定度评定成了难题；为此,根据形状误差评定准则,选取最小二乘法建立数学模型,确定形状误差数学模型中各参数值的传递系数和单点不确定度,并分析具体的测量方法和测量过程中的不确定度来源,根据传统的GUM法对其进行不确定度评定；然后采用蒙特卡罗伪随机数的方法来模拟实际测量数据,从而得到平面度误差的不确定度；通过设置实验对比,验证了蒙特卡罗法评定平面度不确定度的可靠性和准确性；该方法不需要求出数学模型中的传递系数,利用MATLAB软件很容易实现,为平面度误差测量结果不确定度评定提供了更加简便的方法,值得推广和应用。

Abstract:

Evaluation of measurement uncertainty of shape and position error is a hotspot in the field of measurement. However, due to the complexity of measurement and the diversity of measurement results, the uncertainty of the measurement of the shape and position error in the actual measurement results has become a difficult problem. Therefore, according to the evaluation criterion of shape error, establish mathematical model adopting least squares method, determining the transfer coefficient of each parameter value of the shape error mathematical model and single point uncertainty, and uncertainty analysis of measurement methods and the specific process of the source, according to the traditional GUM method for uncertainty evaluation. Then the Monte Carlo pseudo random number method is used to simulate the actual measurement data, thus the flatness error uncertainty is obtained. The reliability and accuracy of Monte Carlo method to evaluate flatness uncertainty are verified by setting experimental comparison. This method does not need to calculate the transfer coefficient of mathematical model, it is easy to realize by using Matlab software, and provides a more convenient method for the uncertainty evaluation of flatness error measurement results.