ISO/TS 28038:2018 多项式校准函数的确定和使用

标准编号：ISO/TS 28038:2018

中文名称：多项式校准函数的确定和使用

英文名称：Determination and use of polynomial calibration functions

发布日期：2018-12

标准范围

1.1本文件涉及描述刺激变量和响应变量之间关系的多项式校准函数。这些函数包含由一组成对的刺激值和响应值组成的校准数据估计的参数。考虑了与数据相关的任何不确定性的性质有关的各种情况。1.2考虑到规定的不确定性信息，使用最小二乘法确定多项式函数参数的估计值。假设校准数据符合目的，因此不考虑异常值的处理。还假设校准数据误差来自正态分布。本文件的重点是选择适合任何特定情况下数据不确定性性质的最小二乘法。由于这些方法在技术文献中有很好的文档记录，并且实现它们的软件可以免费获得，因此本文档中没有对它们进行描述。1.3与校准数据相关的常见协方差矩阵类型被认为包括（a）响应数据不确定性，（b）响应数据不确定性和协方差，（c）刺激和响应数据不确定性，以及（d）刺激数据不确定性和协方差，以及响应数据不确定性和协方差。还处理了数据不确定性未知的情况。1.4给出了根据规定标准选择多项式校准函数阶数的方法。与所选多项式函数中的参数估计相关联的协方差矩阵可作为所用最小二乘法的副产品使用。1.5对于所选多项式函数，本文件描述了参数估计及其相关协方差矩阵的使用，以进行反向和直接评估。它还描述了如何使用ISO/IEC指南98-3:2008（GUM）的规定来提供相关的标准不确定度。1.6考虑到可能需要施加的某些约束（例如通过原点的多项式），以及可能使校准函数的行为更像多项式的变量变换的使用。还考虑了变量之间的角色互换。1.7测量科学几个领域的例子说明了本文件的使用。

1.1 This document is concerned with polynomial calibration functions that describe the relationship between a stimulus variable and a response variable. These functions contain parameters estimated from calibration data consisting of a set of pairs of stimulus value and response value. Various cases are considered relating to the nature of any uncertainties associated with the data.1.2 Estimates of the polynomial function parameters are determined using least‐squares methods, taking account of the specified uncertainty information. It is assumed that the calibration data are fit for purpose and thus the treatment of outliers is not considered. It is also assumed that the calibration data errors are regarded as drawn from normal distributions. An emphasis of this document is on choosing the least‐squares method appropriate for the nature of the data uncertainties in any particular case. Since these methods are well documented in the technical literature and software that implements them is freely available, they are not described in this document.1.3 Commonly occurring types of covariance matrix associated with the calibration data are considered covering (a) response data uncertainties, (b) response data uncertainties and covariances, (c) stimulus and response data uncertainties, and (d) stimulus data uncertainties and covariances, and response data uncertainties and covariances. The case where the data uncertainties are unknown is also treated.1.4 Methods for selecting the degree of the polynomial calibration function according to prescribed criteria are given. The covariance matrix associated with the estimates of the parameters in the selected polynomial function is available as a by‐product of the least‐squares methods used.1.5 For the chosen polynomial function this document describes the use of the parameter estimates and their associated covariance matrix for inverse and direct evaluation. It also describes how the provisions of ISO/IEC Guide 98‐3:2008 (GUM) can be used to provide the associated standard uncertainties.1.6 Consideration is given to accounting for certain constraints (such as the polynomial passing through the origin) that may need to be imposed and also to the use of transformations of the variables that may render the behaviour of the calibration function more polynomial‐like. Interchanging the roles of the variables is also considered.1.7 Examples from several areas of measurement science illustrate the use of this document.

标准预览图