Uncertainty Estimates

1. Uncertainty Estimates Application of an adapted definition for the description of the uncertainty of a strain-gauge balance

2. Contents • Introduction • Definition for Uncertainty Estimation • Application Recipe • Application on DNW balance stock • Conclusions

3. Introduction • At the 6th International Symposium on Stain-Gauge Balances a definition was postulated to describe the uncertainty for a stain-gauge balance. • DNW, AEDC and NASA volunteered to evaluate the proposed uncertainty definition. • A paper representing the DNW contribution to the evaluation has been published. (AIAA-2010-4546) • The proposed method is now used for several DNW balances with the intention to use it for all DNW balances.

4. Definition for Uncertainty Estimation • Uncertainty of the calibration • If K is set to 1 UCAL will represent an estimation of the sigma (standard deviation) • If K is set to 3 UCAL should represent “3*sigma”. Assuming a Gaussian distribution of the errors this should be close to the maximum error

5. Application Recipe • Confirm the residuals of each balance component are Gaussian • Verify maximum error is between 2 to 4 times the standard deviation • Take the absolute value of all residuals • Take uncertainty coefficient an to be the maximum of either • (maximum deviation)/3 out of a single load component calibration, or • standard deviation of the of a single load component calibration • Use equation with the coefficient bn set to zero to determine the initial uncertainty for each load components of the balance • Subtract 3 times the initial uncertainty from the residuals (per load component) and set values below zero to zero. • Divide the remainder (larger then zero) by for each load point individually • Take uncertainty coefficient bn to be the maximum value per component divided by 3

6. Application on DNW balance stock • B668 Errors of back calculation (incl. check points)

7. Application on DNW balance stock • Uncertainty coefficients and maximum errors for the balance load calibration • The uncertainty coefficients are rounded up to two digits. • The formulation reasonably well predicts the maximum error (K=3) over all loads. In the table the estimated maximum error is included. This is the value of UCAL when all forces and moments are simultaneously at their maximum (this is (ai+5bi) x 3/10). The maximum error during the calibration and the maximum error including the calibration check points is also included.

8. Application on DNW balance stock • Uncertainty as a function of the number of applied combined loads

9. Application on DNW balance stock • Better example

10. Application on DNW balance stock • Better example: Uncertainty as a function of the number of applied combined loads

11. Application on DNW balance stock • Uncertainty coefficients have been determined or all DNW-LLF balances and some DNW-LST and HST balances (in total 10 balances; 8 internal, 2 external so far) • Automated & dead weight calibrations • Moment & force balances • OFAT & MDOE calibrations • For those balances which are not calibrated or validated for multiple load combinations the bn coefficients can only be determined for , therefore also the maximum error can only be estimated for single load components(this is (an+1bn) x 3/10).

12. Conclusions • The postulated uncertainty definition is not perfect but applicable and has the feature that it can capture the common notion that the uncertainty increases with the number of applied combined loads to a balance. • Check points are essential to validate estimates of the uncertainty of a balance. • Uncertainty as a function of the number of applied combined loads can only be estimated if combined loads are applied during calibration. • The used uncertainty definition can be used for error propagation purposes