Improving accuracy in analog mass flow measurements 5th order polynomial curve fitting

Analog thermal mass flow instruments perform very accurate and repeatable measurements.

These instruments are calibrated to meet an accuracy/linearity specification such as +/- 1% Full-scale. In a typical calibration, ten or twenty representative data points are recorded and analyzed and uncertainties are calculated for each data point referenced to a precision measurement standard.

Careful examination of an analog mass flow instrument’s calibration data will reveal its output is not a purely linear expression. The sources of non-linearity include random and predictable errors. This presents an opportunity to improve the accuracy of the measurements.

A series of polynomial coefficients can be derived from the calibration data which, when applied to measurements, can reduce predictable uncertainties dramatically. This is the same methodology used by most digital mass flow instruments. It can be applied real-time to analog instruments interfaced with computers, or manually if post-processing is acceptable.

An instrument supplied with a 5th order polynomial fit is delivered with a standard calibration report and a supplemental polynomial analysis. The supplement contains two sets of five coefficients (standard and normalized) derived from an analysis of the calibration data. It includes a restated calibration report certifying the resultant uncertainites.

In order to realize the accuracies stated in the polynomial analysis, it is necessary to “plug-in” the output voltages and the coefficients to a 5th order polynomial calculation for each measurement.