An Improved Weighted Least Squares Algorithm for the Analysis of Strain-Gage Balance Calibration Data

An improved version of an algorithm is presented that uses a weighted least squares fit of balance calibration data for the generation of the balance load prediction equations. The weighted least squares fit assigns a weighting factor between zero and one to each calibration data point that depends on a simple count of the number of intentionally loaded balance gages. The greater the number of the loaded gages is, the smaller a data point's weighting factor becomes. This strategy has two advantages. First, single-component loads become more influential during the regression analysis of the calibration data. In addition, the negative influence of load schedule asymmetries on the regression analysis results can more effectively be controlled. The original algorithm of 2017 was improved in 2020. Now, gage output differences relative to the natural zeros are exclusively used as input for the determination of the number of intentionally loaded gages. The improved weighted least squares fit can be applied with both the Non-Iterative Method and the Iterative Method that are used for the balance load prediction in the aerospace testing community. Machine calibration data of a force balance is used to illustrate benefits of the application of the improved weighted least squares fit of balance calibration data.