• Study Resource
• Explore

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Transcript
```12
11
10
9
8
7
Y-axis (mm)
12
11
10
9
8
7
P0 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10
6
5
4
Y1
3
2
1 Y10
Y2
Y3
Y4
Y5
Measured distance (mm)
Y9
Y8
Y7
Y6
Y5
6
5
4
Y6
Y7
3
2
1
Y8
Y9
X-axis (mm)
1 2 3 4 5 6 7 8 9 10 11 12
Y10
Y = Î²Ì0 + Î²Ì1 X
Y4
Y3
Y2
Y1
Reference distance (mm)
1 2 3 4 5 6 7 8 9 10 11 12
(a) 10 repeated COP measurements at each
point P were obtained, averaged and the relative position, Y , with respect to the point
P0 was computed. In total, for each of the
points, four average values (distances) were
computed, two in the P0 â P10 direction and
two in the P10 â P0 one.
(b) The averaged measured values of the
force platform system (Y ) are plotted against
the quantity values (X ) that have been taken
by the millimetric grid. Then, a linear regression analysis has been used to maintain
the calibrated system in a state of statistical
control.
Figure B.5 The static performance characteristics of the force measurement system was studied
by plotting the output signal (Y ) obtained by the force platform (Fig. B.5a) system against the
known input signal (X ) in order to generate a scatter plot, wherein a straight-line was fitted with
the method of least squares, as it is assumed that the output signal is linearly proportional to the
input signal (Fig. B.5b).
It is assumed that biases are corrected by the manufactureâs calibration procedure, therefore,
only the uncertainties of the correction are presented. In order to estimate the intercept and the
slope of the fitted line, the method of least square error is used which minimizes the sum of the
squared residuals by taking into consideration that nominal values have no uncertainties and the
uncertainty in the measured values is constant over the range of the curve fit. Once the coefficients
of the linear model are found, the estimated regression lines for the measured signals can be read.
The residuals of the fitted model (Fig. B.6) were analyzed to test the goodness of the fitted linear
regression models and to identify possible outliers using the getOutliers() function of the package
extremevalues (Loo, 2010) in R environment (R Core Team, 2013).
B.3.4.
Error Model and Sources
The error model for "COP is the sum of the errors encountered during the measurement process
"COP = "res + "ran + "reg + "lnr + "hys
where
"res is the error associated with the digital resolution of the system display
"ran is the error associated with repeated measurements
151
```