Environmental Engineering Reference
In-Depth Information
t n 4 , 1 2 var
= B 0 +
app +
app
L up
B 1 ε
+
B 2 ε
+
B 3 ε
[ θ ]
(5.11)
app
where
α
is the significance level (5%) [34].
5.3.3
Measurement Results and Instrumental Performance
Comparison
Preliminarily, to validate the practical implementation of the proposed methodology,
repeatability tests were carried out on the considered material samples (sand, bran,
and corn flour), with both the HL1500 and the TDR80E04. For each instrument,
two series of measurements were performed, in different times, on each MUT: as
expected, both for the HL1500 and for the TDR80E04, a good agreement between
the first and the second series of measurements was observed.
The repeated measurements were grouped to extrapolate specific fitting curves
for each instrument. The resulting fitting curves were unified in a single 'global'
curve for each material and for each instrument (Fig. 5.1), and the corresponding
uncertainty values were calculated for each measured
ε app . Particularly, to verify the
adequacy of the normal function distribution in describing the uncertainty distribu-
tion, the t -Student distribution was considered for the whole series of measurement
data: the hypothesis was confirmed assuming a confidence level of 95% [34]. This
way, in Fig. 5.1, to each measured
ε app value the corresponding absolute uncertainty
bar ( U ε app ) is associated, exhibiting a maximum percentage relative standard uncer-
tainty lower than 10% for the HL1500, and lower than 5% for the TDR80E04. As
expected, the uncertainty affecting
ε app measured through the HL1500 is higher than
the uncertainty affecting the
ε app obtained through the TDR80E04. The metrological
characterization of the proposed method involves the analysis of regression curves
on each material sample and for both HL1500 and TDR80E04. The associated con-
fidence intervals are reported in Fig.s 5.2-5.4, in terms of lower and upper limits of
global calibration curves ( L low and L up ), as calculated from (5.10) and (5.11).
The graphs show the good agreement between measurements conducted through
the HL1500 and through the TDR80E04; the corresponding value of the confidence
band allows deducing the final uncertainty in moisture level evaluation. Results re-
lated with regression curves for lower and upper limits of confidence bands are
summarized in Table 5.1. It is worth pointing out that even though in some cases
Ta b l e 5 . 1 Absolute uncertainty range of regression curve for each considered material, asso-
ciated to a confidence level of 95%, calculated for the two TDR instruments
HL1500
TDR80E04
L up ( L low )
L up ( L low )
sand
0.056
0.024
bran
0.020
0.037
corn flour
0.031
0.022
 
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