Dynamic Sensitivity Evaluation for Force Transducers by Using a Gray-Bootstrap Method

The sensitivity of force transducers can be calibrated by traceable measurement of dynamic force. It is usually considered as a static parameter in industrial measurement. However, the force transducer will generate inaccurate outputs when the static sensitivity (SS) is used for dynamic measurement with changed frequencies. To overcome this problem, the dynamic sensitivity (DS) is investigated by evaluating its calibration error based on a gray bootstrap model (GBM). First, the force transducer is dynamic calibrated by periodic force to build an error model. Second, the calibration errors are rolling predicted by gray model to generate a sequence matrix. Third, the confidence intervals are solved for the calibrated force in time history by bootstrap sampling from the rolling sequence matrix. Fourth, the optimal sensitivities at different frequencies are evaluated by probability density function and fit by the least square method. The experimental result shows that relative errors (REs) are quite small as 0.2% at 160 Hz, −0.1% at 315 Hz, and −0.3% at 1000 Hz. The degree of reliability (DR) is great enough and approximately equal, which reveals that the DS of force transducers is superior to SS when it comes to dynamic measurement of force.