【作者】 康志茹；

【导师】 傅广生；

【作者基本信息】 河北大学 ， 光学工程， 2006， 博士

【摘要】 温度测量不可避免的带有不确定度。测量不确定度表示测量结果的可靠程度,是与测量结果不可分割的重要组成部分。温度测量依据温标,温标不确定度传播方程是计算和分析温度测量不确定度的重要工具,该方程表达是否正确,将对整个温度测量领域产生影响。本文从三个方面对90国际温标和辐射内插温标不确定传播方程进行了系统研究。一是利用隐函数微分法,给出了一般模型——多元非线性隐函数内插测量模的不确定度传播系数的表达式。这是一个普遍结果,任何一个物理内插测量模型的不确定度传播系数都可以从这个结果中直接导出,为物理量测量不确定度研究提供了理论依据。以此为基础,本文给出了13.8033K～933.473K温区90国际温标不确定度传播方程和辐射内插温标不确定度传播方程。使用直接微分法给出了0.01℃(273.16K)～961.78℃(1234.93K)分温区的不确定度传播方程。本研究结果与90国际温标给出的不确定度传播曲线进行了比较,结果一致。二是对90国际温标不确定度分量,温标的非一致性进行了研究。给出了0℃(273.158K)以上温区非一致性函数及其极值。通过87支标准铂电阻温度计试验,其中80支标准铂电阻温度计为正常工艺制造,其非一致性小于1mK,属于同一分布。其余7支标准铂电阻温度计为非正常工艺制造,其非一致性大于1mK,属于另一分布。对前者进行了χ2检验,非一致性符合正态分布N ( 0.061,0.3052),其扩展不确定度为1mK,包含因子为3。合理地将非一致性引入了不确定度传播方程,使90国际温标不确定度传播方程更加真实的反映了测量结果的质量。三是以非一致性研究结果为基础,给出了0℃～660.323℃温区标准铂电阻温度计的两个二次偏差函数,一个由水三相点、锡凝固点和铝凝固点的测量值来确定;另一个由水三相点、锌凝固点和铝凝固点的测量值来确定;比同温区90国际温标定义的三次内插函数少了一个固定点,它是90温标很好的近似,经27支标准铂电阻温度计检验,其误差不超过4.7mK,可作为次级温标使用。使用这两个偏差函数可以节省固定点投资和检测时间。更多还原

【Abstract】 An equation of propagation of uncertainty on the ITS-90 is an important tool for the uncertainty evaluation in temperature measurement. The result presented by the equation is conclusive. In this paper, a study of equations of propagation of uncertainty on interpolation scales is made.Firstly, based on implicit differentiation, a set of the sensitive coefficients of a multivariate non-linear interpolation has been achieved in terms of implicit function for a general case. Those of all interpolation in physical measurement, including temperature measurement, can be deduced from the result. .In particular, the sensitivity coefficients of the interpolation which is linear for their coefficients are still linear combinations of the basis functions comprising the interpolation, only with different constants that can be presented in the determinant form. This solves the question to express the equation of propagation of uncertainty of a complex interpolation comprised of many different basic functions. From the results; this paper gives the equations of propagation of uncertainty on ITS-90 in the range 13.8033K to 933.473K and on radiation interpolation scale. By direct differentiation to the ITS-90 interpolation in the sub-range 0.01℃(273.16K) to 961.78℃(1234.93K), a special sectional function, this paper gives the equation of propagation of uncertainty on ITS-90 in the range, of which the sensitivity coefficients are also linear combinations of basic functions comprising the interpolation only with different constant, and sectional functions. Comparing the curves of the sensitivity coefficients of the equations with those published by Supplementary Information for the International Temperature Scale of 1990, they are consistency.Secondly, the ITS-90 inconsistency, as an uncertainty resource, is considered in the paper. Eighty seven SPRTs in the range 0°C to 660.323°C were investigated. The results show seventy–nine SPRTs with inconsistencies less than 1.0mK in one distribution and the remaining eight SPRTs with inconsistencies much greater than 1.0mK in a separate distribution. The design of the later differs from that of the former to a certain extent. A chi-squared test for the former showed that the inconsistency had a normal distribution N ( 0.061,0.3052). As an uncertainty component, its expanded uncertainty is 1mK, coverage factor is 3. An inconsistency function with respect to temperature above 0℃is obtained and is introduced into the equation of propagation of uncertainty of ITS-90.Thirdly, based on the result of inconsistency, two quadratic deviation functions in the range 0℃to 660.323℃are given, one can be determined from the calibration values at the triple point of water and the freezing points of sin and Aluminum, and another can be determined from the calibration values at the triple point of water and the freezing points of zinc and Aluminum. The two functions are very closing approximate to the ITS-90 deviation function in the range 0℃to 660.323℃. Fifty SPRTs have been used to check the functions and the error are not more than 4.7mK. Using them, we can reduce one of the freezing points of sin and zinc from four fixed points defined by ITS-90 in the range 0℃to 660.323℃and save the cost of calibration. The precision of the deviation functions is sufficient for secondary measurement.更多还原