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An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method

机译：最小二乘法对标准线性不确定度定量的改进

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Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a measure of the sensitivity needed to calculate the uncertainty percentage contribution (UPC) and uncertainty magnification factors (UMF) due to each independent variable in the measurement/process being examined. The derivative information is typically obtained by either taking the symbolic partial derivative of an analytical expression or the numerical derivative based on central difference techniques. This paper demonstrates that linear multivariable regression is better suited to obtain sensitivity coefficients that are representative of the behavior of the data reduction equations over the region of interest. A main advantage of the proposed approach is the possibility of extending the range, within a fixed tolerance level, for which the linear approximation technique is valid. Three practical examples are presented in this paper to demonstrate the effectiveness of the proposed least-squares method.
机译：基于一阶泰勒级数展开的线性不确定性分析（已在ASME PTC（性能测试代码）19.1“测试不确定度”和ISO指南“测量不确定度表示”中进行了描述）已成为业界使用最广泛的技术和学术界。线性不确定性分析中的一种常用方法是使用局部导数信息作为计算不确定性百分比贡献（UPC）和不确定性放大因子（UMF）所需的灵敏度的度量，该不确定性百分比贡献是由于要检查的测量/过程中的每个自变量而引起的。通常通过采用解析表达式的符号偏导数或基于中心差分技术的数值导数来获得导数信息。本文证明，线性多变量回归更适合于获得灵敏度系数，该系数代表感兴趣区域上数据约简方程的行为。所提出的方法的主要优点是可以在固定的公差范围内扩展范围，线性近似技术对此有效。本文提出了三个实际的例子，以证明所提出的最小二乘法的有效性。

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