基于最小二乘法拟合的流量计不确定度分析方法

Uncertainty analysis method offlowmeter based on least square fitting

为确定标准表法流量标准装置中非固定流量点使用的标准流量计的不确定度,使用最小二乘法对其流量和仪表系数测量数据进行拟合,计算拟合曲线的标准偏差,分析流量计的不确定度。最小二乘法拟合分别采用不同次数的多项式和分式进行,并对拟合曲线进行比较。结果表明线性拟合操作简单,但拟合效果随测量数据的线性关系程度区别较大;曲线拟合随着模型次数增加拟合效果越好,不确定度越小,但高次多项式存在效果不佳的情况;分式拟合能较好地实现低次高精度的曲线拟合,在非线性关系数据的应用效果优于多项式拟合,能够满足流量计的不确定度要求。

In order to determine the uncertainty of the standard flowmeter used at the non fixed flow point in the flow standard device of the standard meter method,the least square method is used to fit the measured data of its flow and instrument coefficient,calculate the standard deviation of the fitting curve,and analyze the uncertainty of the flowmeter.The least square method is fitted by polynomials and fractions of different degrees,and the fitting curves are compared.The results show that the linear fitting operation is simple,but the fitting effect varies greatly with the linear relationship of the measured data.With the increase of the number of models,the better the fitting effect and the smaller the uncertainty,but the practical application effect of high-order polynomials is poor.Fractional fitting can better achieve low-order and high-precision curve fitting,and its application effect in nonlinear relationship data is better than polynomial fitting,which can meet the uncertainty requirements of flowmeter.