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study demonstrated that this is dependent also on the magnitude of the vertical force. Moreover,
the quality of the COP signal was improved when Q ST decreased (Table 3.4) by increasing Fz
magnitude.
B.5.6.2.
Noise Curve
There is not a trend among the standard uncertainty of the Fz signal registered with the different
dead load weights (Figs. B.1 to B.4), although there are accuracy differences between the two
force platforms. Therefore, the highest standard uncertainty of both force platforms (u Fz = 2.1 N)
was chosen. Therefore, the u y in the COP measurements is modeled as an hyperbolic function
of the Fz magnitude as u Fz = c . According to Eq. (B.12) the minimum u y is obtained when the
dead load is placed at the geometrical centre of the top plate of the force platform as in this point
the same fraction of the Fz is registered by each load cell. Figure B.12 shows the experimental
obtained noise curve together with the minima curve of the model for different cases of statistically
correlated error sources, ρ = −0.9 to ρ = −0.1. The variance explained by the fitted regression
models (R2 ) are very high. For the Y-axis the experimental obtained COP uncertainty is better
modelled with statistically correlated error ρ = −0.8, while for the X-axis with ρ = −0.9.
B.5.6.3.
COP Denoise Procedures Comparison
The results showed that the MSE quintic splines following the proposed procedure with uncertainty
analysis provides more smoothed data in comparison with the others procedures.
B.5.6.4.
Spatiotemporal resolution criterion
The quality of the COP signal is improved when Q ST decreases (Table 3.4) either by increasing Fz
magnitude or by increasing sampling rate.
B.5.7.
Conclusion
The implementation of the Metrology “Guide to the Expression of Uncertainty of Measurement”
(GUM) approach (ISO-JCGM 100, 2010) to calculate standard uncertainties for specifying the
weighted factor for each coordinate of the noisy COP data was introduced. The obtained noise
curves can be used (the experimental or the theoretical) in order to obtained the weighted matrix
for smoothing purposes. The σCOP in the COP measurements is nonlinearly related to the Fz ,
with less magnitude when higher Fz is applied onto the plate of the force platform. According to
Eq. (B.12) the minimum σCOP is obtained when the dead load is placed at the geometrical centre
of the top plate of the force platform as in this point the same fraction of the Fz is registered by
each cell. The variance explained by the fitted fractional quadratic models (R2 ) is very high. The
obtained noise curves can be used (experimental or theoretical) in order to obtained the weighted
matrix (W) for the smoothing purposes.
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