计量测试中的函数逼近方法

Methods of function approximation in metrology testing

计量的性能有示值误差、直线性、稳定性和重复性等,在计量测试中一般要测量许多参考点数据,为了最大限度地减少测量误差,需要用适当的函数逼近方法对这些测量数据拟合其校准曲线。常见的函数逼近方法为一致逼近和平方逼近,重点介绍以多项式为基的线性最佳一致逼近和最小二乘法拟合,并结合图像解释该方法的几何意义。因通常的测量中遇到的问题不一定都是线性问题,以多项式函数为基的最小二乘拟合并不合适,此研究为在计量测试中开展以其他函数为基的最小二乘法研究提供了借鉴。

The performance of measurement has indication error,linearity, stability and repeatability.In the measurement testing,many reference point datas are generally measured.In order to minimize the measurement error,these measurement datas need to be fitted to their calibration curves using appropriate function approximation methods.The common function approximation methods are uniform approximation and square approximation.The linear optimal uniform approximation and least squares fitting based on polynomial are introduced,and the geometric meaning of the method is explained by combining the images.Since the problems encountered in the usual measurements are not always linear, the least squares fitting based on the polynomial function is not suitable. This study provides a reference for the study of least squares based on other functions in metrology testing.