Qualitative Characterization of Granular Materials and Moisture Measurements - Broadband Reflectometry for Enhanced Diagnostics and Monitoring Applications - page 90

Measurements were carried out on the same samples through each instrument:
starting from measurements on well-referenced siliceous sand samples, the analysis
was extended to agrofood granular materials (i.e., bran and corn flour). The com-
parison of results and related uncertainty limitation led to a consistent assessment
of the method from a metrological point of view.
As already mentioned on several occasions, a metrological characterization must
involve the consideration of both systematic and random errors. To minimize and
to compensate for systematic error effects, a preliminary calibration of the experi-
mental setup is mandatory (as detailed in Sect. 3.6.1). Nevertheless, further residual
uncertainty contributions are mainly related to random effects. Therefore, to eval-
uate the final uncertainty, a statistical analysis on repeated TDR-measurements of
dielectric constant was approached. To carry out the analysis, the uncertainty prop-
agation theory and the evaluation of the expanded uncertainty associated to the t -
Student distribution were considered for the estimation of the final measurement
uncertainty.
Once the uncertainty, associated to the ε app evaluation, was quantified for each

measurement point, results deriving from two sets of measurements (repeated with
the same instrument in different times) were unified in a single

θ − ε app fitting curve.
Subsequently, a non-linear regression method was considered in order to obtain a
specific regression (calibration) curve and the related uncertainty range

corresponding to the confidence level of 95%. In this way, a robust method for the
evaluation of the uncertainty limitation was provided, along with some practical
hints for minimizing error contributions.

ε app − θ

5.3.1 Details on the Experimental Procedure

The three materials considered for the comparative analysis were sand, corn flour,
and bran; their mass densities were 1.53, 0.66 and 0.67 g cm − 3 , respectively.
Each material was placed inside a 'large box' (approximately 1 m

0.3 m)
and was moistened at pre-established levels, according to the volumetric method
reported in [47]. To achieve the pre-established moisture levels, an appropriate vol-
ume of water was weighed through an electronic balance (with an uncertainty of
0.1 g), and added to the MUT. Material and water were then mixed, so as to ensure
a homogeneous moisture level: this was verified through preliminary TDR mea-
surements of the dielectric constant in different points of the material contained in
the 'large box'. Successively, a sample was removed from the box, placed inside a
cylindrical sample holder (with a diameter of 7 cm, graduated up to 2000 ml) and
characterized. Preliminary measurements confirmed that boundary effects due to
the used holder were negligible. As a matter of fact, this is one of the advantages of
TDR method over other well-known moisture content measurement methods, such
as capacitive method or ultrasonic sensor. In fact, in the last two cases, the involved
low-frequency range requires the use of large boxes intended to prevent interfer-
ences caused by boundary effects.

× 1m ×