A Novel Wide Range Machine Learning Polynomial Regression Formulation for Enhanced Load Cell Calibration Accuracy

Calibration of measuring instruments is of utmost importance in the field of metrology. It is a mandatory pre-requisite for establishing the fidelity of the measurements as well as to lend confidence. Even more critical is the requirement for the master equipment deployed to calibrate the devices in use. This entails that high accuracy needs to be guaranteed in the calibration process, and that the uncertainty be quantified precisely. The widely used conventional least squares polynomial regression formulation for load cell calibration is based on the non-normalized residual, which is the difference between the measured and master values. The nature of this formulation is such that it imparts more weightage on measured values at higher ranges resulting in good accuracy. However, there is a limitation of this same formulation that results in lesser accurate fit at lower values especially if the instrument is to be used in operation over a wide range including lower ranges of the measurand. To address this challenge, the smart concept of the normalized residual is hereby deployed, which normalizes the difference between the measurand and master values by the measurand values themselves. The nature of this formulation is such that it imparts appropriate weightage on measured values at lower ranges resulting in good accuracy of fit, thus overcoming the limitation of the non-normalized residual formulation at lower ranges. Further, the author indigenously superposes both the formulations into a unified machine learning polynomial regression formulation that encompasses use of normalized residual formulation at lower range of operation, as well as retaining the non-normalized residual formulation at higher range of operation, thus ensuring good accuracy of fit over the entire wide range of measurement, which is desirable for wide operating range application of an instrument. A case study for load cell device under calibration is illustrated to espouse the novel formulation leading to enhanced accuracy of prediction compared to the conventional approach.