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A Coaxial Line Fixture Based on a Hybrid PSO-NLR Model for in Situ Dielectric Permittivity Determination of Carasau Bread Dough

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Food quality is crucial in today's processing industry. The organoleptic properties of most foods materials are known to depend on their water content. The monitoring of food quality and moisture content calls for engineering solutions. To this aim, given their non-destructive nature and cost-effective features, microwave sensors are a valuable tool. However, for some peculiar food processing industries, suitable engineered microwave devices must be designed. Therein, we will focus on the case of Carasau bread industry. Carasau bread is a typical food product from Sardinia (IT). In this work, we will present the design, realization and characterization of a coaxial fixture, working between 0.5 and 3 GHz, for the determination of the complex dielectric permittivity of Carasau bread dough. Through a non-linear regression model based on particle swarm optimization routine, the scattering parameters are used to retrieve the electromagnetic properties of bread doughs. By making a comparison with the complex dielectric permittivity measured with an open-ended coaxial probe, an average error of 3% for the real part and 6% for the imaginary part have been found. The proposed device is driven by a Raspberry Pi that controls the acquisition of a Pocket-VNA, thus representing a cost-effective electronic system for industrial applications.
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IEEE TRANSACTIONS ON AGRIFOOD ELECTRONICS, VOL. 00, 2024 1
A Coaxial Line Fixture Based on a Hybrid PSO-NLR
Model for in Situ Dielectric Permittivity
Determination of Carasau Bread Dough
Giacomo Muntoni , Member, IEEE, Nicola Curreli , Member, IEEE, Davide Toro, Andrea Melis ,
Matteo Bruno Lodi , Member, IEEE, Antonio Loddo, Giuseppe Mazzarella , Senior Member, IEEE,
and Alessandro Fanti , Senior Member, IEEE
Abstract—Food quality is crucial in today’s processing industry.
The organoleptic properties of most food materials are known to
depend on their water content. The monitoring of food quality and
moisture content calls for engineering solutions. To this aim, given
their nondestructive nature and cost-effective features, microwave
sensors are a valuable tool. However, for some peculiar food pro-
cessing industries, suitable engineered microwave devices must be
designed. Therein, we will focus on the case of the Carasau bread
industry. Carasau bread is a typical food product from Sardinia
(IT). In this work, we will present the design, realization, and
characterization of a coaxial fixture, working between 0.5 and
3 GHz, for the determination of the complex dielectric permittivity
of Carasau bread dough. Through a nonlinear regression model
based on a particle swarm optimization routine, the scattering
parameters are used to retrieve the electromagnetic properties of
bread doughs. By making a comparison with the complex dielectric
permittivity measured with an open-ended coaxial probe, an aver-
age error of 3% for the real part and 6% for the imaginary part has
been found. The proposed device is driven by a Raspberry Pi that
controls the acquisition of a pocket-vector network analyzer (VNA),
thus representing a cost-effective electronic system for industrial
applications.
Index Terms—Coaxial fixture, dielectric constant determination,
food processing, food properties, nonlinear regression (NLR),
particle swarm optimization (PSO).
Manuscript received 18 September 2023; revised 5 February 2024; accepted
23 March 2024. This work was supported in part by the Ministero dello Sviluppo
Economico, AGRIFOOD Programma Operativo Nazionale (PON) Imprese e
Competitività (I&C) 2014–2020, through the Project “Ingegnerizzazione e Au-
tomazione del Processo di Produzione Tradizionale del Pane Carasau Mediante
L’utilizzo di Tecnologie IoT (IAPC), under Grant CUP: B21B19000640008
COR: 1406652 and in part by the Italian Ministry of Enterprises and Made in
Italy (MIMIT), “ACCORDI PER L’INNOVAZIONE” (2021–2026), through the
Project “Tecnologie ICT e Dell’industria 4.0 per L’analisi e L’ingegnerizzazione
di Sistemi Alimentari Complessi per la Produzione di Pani Artigianali Locali ad
Alto Valore Aggiunto (AISAC), under Grant CUP: CUP: B29J23001120005.
This article was recommended by Associate Editor C. Josephson. (Correspond-
ing author: Alessandro Fanti.)
Giacomo Muntoni, Davide Toro, Andrea Melis, Matteo Bruno Lodi, Giuseppe
Mazzarella, and Alessandro Fanti are with the Department of Electrical and
Electronic Engineering, University of Cagliari, 09123 Cagliari, Italy (e-mail: gia
como.muntoni@unica.it; davidetoro18@gmail.com; andrea.melis89@unica.it;
matteob.lodi@unica.it; mazzarella@unica.it; alessandro.fanti@unica.it).
Nicola Curreli is with the Italian Institute of Technology, 16163 Genoa, Italy
(e-mail: nicola.curreli@iit.it).
Antonio Loddo is with the Vecchio Forno SUNALLE, 08023 Fonni, Italy
(e-mail: antonio.loddo@sunalle.it).
Digital Object Identifier 10.1109/TAFE.2024.3385185
I. INTRODUCTION
FOOD quality inspection is one of the most discussed topics
within the scientific community devoted to the techno-
logical development of the agrifood industry. Transition to a
digital control, sustainability, traceability, and high quality are
the milestones of the path toward the future of the industry [1],
[2],[3].
Microwave (MW) devices for the estimation of the dielectric
properties of food and food-related products are increasing in
popularity for the unmatched advantage of offering accuracy in
the measurement process while maintaining a nondestructive
approach [4],[5],[6],[7],[8]. The utility is not limited to
human food but also to cattle and poultry processed feed [9],
[10], covering a large portion of the food processing, and finds
application also in adulteration and contamination detection
[11],[12],[13], and traceability [14],[15].
The MW measurements of food materials aim to retrieve
primarily the moisture content of the product, which is one
of the most important indices of the food quality [5],[7],[8].
From an MW engineering point of view, the water presence
strongly affects the dielectric signature of the material, thus
implying that electromagnetic devices are suitable platforms
to characterize food materials. In order to estimate the water
content but also the different peculiar characteristics of the food,
an MW device’s primary goal is the dielectric characterization
of the material through the measurement of the complex per-
mittivity defined as ε=ε, wherein εis the real part
of the dielectric permittivity and ε is the imaginary part of the
dielectric permittivity, i.e., the so-called loss factor, accounting
for the energy losses inside the material, which are proven to
be relevant in food products [4]. The dielectric characteriza-
tion, aimed to retrieve the product moisture, is of significant
importance, particularly for baked products, wherein water is
one of the main ingredients of the dough. Thus, a reliable and
repeatable dielectric estimation of the product is pivotal for both
large- and small-scale baked food industries. The latter includes
also traditional products, i.e., products that are made following
certain technical specifications, or following a traditional recipe,
or are regulated by national and/or regional certifications, as in
the case of the Carasau bread, a typical Italian flat and crunchy
bread made in Sardinia [16]. Carasau bread’s raw ingredients
© 2024 The Authors. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see
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2IEEE TRANSACTIONS ON AGRIFOOD ELECTRONICS, VOL. 00, 2024
include remilled semolina of durum wheat, sea salt, natural
yeast, and dechlorinated drinking water [3],[17],[18],[19].
The production process of the Carasau is exhaustively explained
in [3],[17],[18], and [21], wherein the necessity of having the
accurate estimation of the water content inside the dough is high-
lighted. Briefly, Carasau bread doughs, obtained by kneading
the raw ingredients, undergo a first leavening. Then, the doughs
are sheeted, go through a second leavening step and finally go
through two different baking phases [3],[17],[18],[19],[20],
[21]. The dough’s water content, therefore, is an information that
is pivotal to avoid defected batches due to a suboptimal amount
of water. Thus, the accurate dielectric characterization of the
Carasau doughs is mandatory to guarantee a waste-free produc-
tion line. The dielectric characterization of the doughs should be
performed in situ on several samples of the same batch during the
kneading process [17], using a dedicated measurement system.
This preventive measurement would allow for an adjustment
in the recipe, based on the optimal moisture, by adding more
semolina or more water depending on the case. One possible
solution is the employment of commercial open-ended coaxial
probes (OECPs) that are widely used to trace the dielectric
profile of solids and liquids [22]. However, commercial coaxial
probes are very expensive and they might struggle to work safely
within the operating conditions of the bakery, with high tem-
perature and high humidity, as well as the prominent presence
of flour dust. Additionally, the measurement process using an
OECP demands for a precise calibration protocol. Furthermore,
the reliability of the measurement calls for a recalibration after
each measurement, or, at least, the assessment of drift effects.
All these aspects hamper the adoption of OECP in an industrial
scenario [3].
Other approaches can be used to derive the dielectric permit-
tivity of food materials. For instance, inverse scattering proce-
dures, guided-wave approaches, or transmission/reflection (T/R)
techniques have been implemented [23],[24],[25],[26],[27],
[28],[29],[30],[31],[32],[33],[34],[35],[36],[37],[38],[39],
[40],[41],[42],[43]. Even though several devices and method-
ologies are available, none of them can be immediately applied
to the challenging goal of estimating the dielectric permittivity
of the Carasau bread doughs during their industrial production.
Given the lack of technological solutions, a low cost, solid,
rapid, although accurate alternative, should be employed to
empower the small-scale food industry, such as the bakery
considered in this work. Preferably, these solutions for industrial
applications have to be cost effective. In this framework, they
must be interfaced with a miniaturized version of a network
analyzer (such as a pocket-vector network analyzer (VNA)) [44].
Pocket-VNA is a performing electronic platform that achieves
stable and accurate measurements up to 6 GHz with a very
small cost [44]. Furthermore, the use of pocket-VNA would
allow to provide protection against the production line’s harsh
environment, using a suitable case or some sort of coverage, thus
ensuring to perform the MW measurements at the production
site. In this perspective, it is worth noting that several scientific
studies tend to avoid excessively large measurement systems in
order to achieve a certain degree of portability, thus making the
choice of a pocket-VNA even more appealing [7],[8].
In this work, the electromagnetic device employed for the
estimation of the complex permittivity of the Carasau bread
dough is a coaxial fixture, made of leaded brass for the metal
parts and polylactic acid (PLA) for the sample holder and the
alignment gaskets (which are hollow structures). The presented
structure has been inspired by the work shown in [38].In
comparison, the coaxial device herein proposed is equipped
for solids and liquids dielectric measurements, thanks to the
3-D-printed sample holder that prevents leakage, opening up
its employment to a wider range of materials. The device is a
part of an ad hoc system, connected to a suitable pocket-VNA,
whose outputs are read by a Raspberry Pi 4. In order to achieve
the accurate dielectric properties of dielectric materials, a hybrid
particle swarm optimization (PSO)–nonlinear regression (NLR)
model is presented in this work. The algorithm solves, frequency
by frequency, the scattering equations with a regression algo-
rithm that finds a perfect match using a nonlinear least-square
solution. The absolute minimum was then found using a PSO
algorithm.
The hybrid PSO-NLR inversion algorithm is implemented
within the board and provides the estimated value of the complex
permittivity of the dough in the range of 0.5–3 GHz. The latter
frequency range has been chosen considering the entire mea-
surement system, not only the MW device. A low-frequency
bandwidth grants good performance, low overall cost of the
equipment, and less variability of the complex dielectric permit-
tivity. The estimated values have been compared with the ones
obtained, within the same frequency range, using a commercial
coaxial probe, showing roughly the same accuracy.
II. LITERATURE REVIEW
Several numerical strategies for the determination of MW
dielectric properties are available in the open literature. Most
of the work in this area is based on the determination of the
scattering parameters, for each frequency in a given range,
in order to determine the permittivity parameters, through the
explicit or implicit solution of a system of nonlinear scattering
equations at each particular frequency [23],[24],[25]. Among
guided-wave techniques for the nondestructive determination of
the dielectric properties of materials, several open-ended rectan-
gular waveguides [26],[27],[28],[29], rectangular waveguide
[30],[31],[32],[33],[34], and coaxial lines’ [35],[36],[37],
[38],[39] techniques have been developed.
Out of the different techniques, the T/R method is well known
for its high accuracy, wide frequency range, and simplicity [38].
For instance, in [39], a method is presented for determining
the humidity of granular materials using a two-port MW sensor.
From the measurement of the scattering parameters, the complex
dielectric constant is derived and, accordingly, the desired prop-
erties. The authors in [40] and [41] reported a method to measure
the dielectric constant of a liquid material under test based on the
measurement of the return loss (S11). In [42], a two-port coaxial
sensor is used to calculate the scattering parameters, which were
converted to electrical parameters using the Nicolson, Weir, and
Ross method, and then a least-square problem is imposed for the
extraction of the dielectric constant. A similar method has been
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MUNTONI et al.: COAXIAL LINE FIXTURE BASED ON A HYBRID PSO-NLR MODEL 3
presented in [43] for the extraction of the dielectric constant of
the ice.
Considering that past works presenting algorithms for the
inverse problem of dielectric permittivity measurements have
a variable tradeoff between accuracy and computational time,
a different approach for the considered peculiar food industry
application has to be sought. In this work, a hybrid solution
has been chosen, combining an NLR model that points to an
initial guess of the result within the entire operating bandwidth,
thus producing an early estimation of the complex dielectric
permittivity, with a PSO algorithm that finds the optimal solution
using an iterative process. A detailed explanation of the inversion
algorithm is reported in Section IV.
III. COAXIAL FIXTURE SENSOR
A. Geometry and Theoretical Foundations
The sensor is modeled as a coaxial fixture with seven different
sections, four of which are independent.
1) Sections Iand VII: The initial and final sections of the
fixture consist of two standard 50 Ωcoaxial lines employed
as an interface between the device and the VNA. The
dielectric used in the coaxial cable is Teflon (εr=2.1,
tan =0.0002). In the fabricated prototype (see Fig. 4),
these sections are represented by the commercial Sub-
Miniature version A (SMA) connectors.
2) Sections II and VI:The conical sections are tapered trans-
mission lines that match the input coaxial line to the
central line. These conical sections have a length equal
to 54.5 mm. For a perfect alignment of the device and
to sustain the structure, four 3.75-mm-thick PLA (εr=
2.54,tanδ=0.015) gaskets, two per conical section, are
located in the initial and final part (see Fig. 1).
3) Sections III and V:They are employed to separate the
central section from the conical ones and to effectively
create a socket for the sample holder. As in the conical
sections, they host two hollow PLA gaskets (one per
section) for alignment and support. The length of each
section is equal to 30 mm.
4) Section IV:The central section has a length of 60 mm
(bringing the total length of the central section to 120 mm).
It hosts the sample holder, a hollow donut-like structure
with PLA walls to be fabricated with 3-D printing.
A dimensional drawing of the device is reported in Fig. 1.
The coaxial fixture is entirely enclosed in a metallic shell.
The metal chosen for the shell and the inner core is leaded brass,
whereas, for the outermost coaxial section, copper has been used.
Each section has been designed to have a 50 Ωimpedance.
For the central line and the outermost sections, this condition is
easily achievable following the well-known formula [45]:
Z=ζ
2πεr
ln b
a(1)
wherein ζis the free-space impedance (377 Ω), εris the per-
mittivity of the dielectric, ais the radius of the core, and b
is the radius of the dielectric. For the central line, we have
a=10mm and b=25mm. The most critical sections are
Fig. 1. Dimensional drawing of the coaxial fixture, highlighting the sections
and the materials.
the conical ones. In fact, due to the presence of different modes
of propagation, the conical section could have different mode
impedances, especially at high frequencies. For low frequencies,
the fundamental mode impedance formula is defined as follows
[46]:
Z=ζ
2πεr
ln cot (ϑ/2)
cot (ϕ/2) (2)
wherein ϑis the angle between the coaxial central axis and the
inner conductor perimeter and ϕis the angle between the coaxial
central axis and the outer dielectric perimeter (see Fig. 1for
reference). The first one is given by the difference in diameter
between the inner conductor of the central line and the inner
conductor of the external line, and by the length of the conical
section. Given these values, we have ϑ=0.1745 rad =10°. The
second one is given by the following formula:
ϕ=2tan
12πe(Zcone)2 tan ϑ/
2
=0.3973 rad =22.8.(3)
B. Numerical Study
Once the theoretical foundation has been established, and
a presizing of the system has been done, the coaxial fixture
has been numerically designed within the CST Studio Suite
2019 (3-Ds, Simulia, DE) simulation environment. In Fig. 2,the
scattering parameters of the empty coaxial fixture are shown, dis-
playing a fairly good matching and reasonable losses throughout
the entire operating bandwidth (0.5–3 GHz).
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4IEEE TRANSACTIONS ON AGRIFOOD ELECTRONICS, VOL. 00, 2024
Fig. 2. Simulated scattering parameters of the empty coaxial fixture.
(a) Reflection parameters (S11,S22 ). (b) Transmission parameters (S12,S21).
Fig. 3. Simulated scattering parameters of the coaxial fixture with a sample
of Carasau bread dough.
Given that the coaxial fixture is supposed to provide informa-
tion about the complex dielectric permittivity of the Carasau
bread dough, we performed numerical simulations to assess
in silico how the scattering parameters of the structure would
behave when the medium inside the sample holder is the bread
Fig. 4. Photos of the realized device. (a) Unassembled coaxial fixture.
(b) Assembled coaxial fixture.
dough obtained following the original Carasau recipe (see raw
ingredients and dielectric profile shown in [19]).
In Fig. 3, such simulation results are shown. From a direct
comparison with Fig. 2, the difference in the frequency response
can be observed. The presence of the bread sample is highlighted
by the poor impedance matching and the high losses w.r.t. the
empty fixture case. From these features of the scattering param-
eters, it is possible to derive, through a suitable methodology,
the dielectric permittivity of the food sample under test placed
in Section IV of the device, as shown in Fig. 1.
C. Realization
The coaxial fixture has been realized by the company IFI s.r.l.
located in Cagliari (Sardinia), Italy. Photos of the realized pro-
totype are reported in Fig. 4. The metallic components are made
of leaded brass (CuZn39Pb2). Since the entire coaxial fixture
employs air as a dielectric (with the exception of the external
lines where Teflon is used), in order to support the structure
integrity, several hollow PLA gaskets are scattered along the
body of the coaxial fixture. Their presence can be neglected
from an electromagnetic point of view. Other than supporting
the structure, these gaskets allow a perfect alignment, which
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MUNTONI et al.: COAXIAL LINE FIXTURE BASED ON A HYBRID PSO-NLR MODEL 5
is essential for the subminiature version a (SMA) connectors
soldering.
The coaxial device is enclosed in a cylindrical case, made of
leaded brass, and sealed using four long screws and nuts (see
Fig. 4). The core of the central section is divided into three
parts with conical interlocking. It allows for a fairly convenient
insertion of the donut-like sample holder.
It is worth noting that the fabricated prototype has the sole
purpose of demonstrating the capability of the presented mea-
surement system. In order to perform the measurement, the
fixture has to be disassembled and reassembled, a procedure that
is time-consuming and would not be suitable for a commercial
scenario. A possible solution could be to separate the coaxial
fixture into two main parts, with a threading on the metallic
shell, and attach the two main parts to rotating automated arms.
This would allow to screw/unscrew the entire coaxial fixture in
a matter of seconds. In this case, the dielectric gaskets should be
permanently attached to the body of the coaxial fixture, whereas
the inner conductor should be divided into two parts, each one
permanently connected to a main part of the coaxial fixture,
keeping the conical interlocking as in the prototype described in
this article. The main concern in this case would be to guarantee
the electrical contact of the metallic parts. The sample holder
would be the only extractable part of the automated fixture,
very much similar to the one described in this article, equipped
with a removable lid. This solution would allow a prompt
loading/unloading procedure of the coaxial system, suitable for
commercial purposes.
IV. INVERSION ALGORITHM
A flux diagram of the inversion algorithm is reported in Fig. 5.
After the calibration of the sensor, the first step is the acquisition
of the S-parameters using a VNA. The said parameters are then
converted into transmission parameters, obtaining the ABCD
matrix (i.e., transmission matrix), which is useful to simplify the
two-port network. Based on the description of the entire coaxial
transmission line provided in Section II, the total transmission
matrix can be seen as the product of the transmission matrices
of the single sections
[Ttot]=[Tcoax][Tcone ][Tair][Tx][Tair ][Tcone][Tcoax ]
(4)
wherein Tcoax is the transmission matrix of the outermost section
(a standard coaxial cable with the dielectric component made of
Teflon), Tcone is the transmission matrix of the conical section,
Tair is the transmission matrix of the section before the sample,
and Txis the transmission matrix of the section containing the
sample. All the transmission matrices are known except for Tx.
In order to derive the unknown complex permittivity, a least-
square problem has to be solved, in the following form:
Ax(εRe
Im)ATo t |2+
Bx(εRe
Im)BTo t |2
+|Cx(εRe
Im)CTo t |2min!(5)
wherein ATot ,BTo t , and CTot are the elements of the total trans-
mission matrix TTot , whereas Ax,Bx, and Cxare the elements
of the unknown transmission matrix Tx. The values εRe and εIm
Fig. 5. Flux diagram of the inversion algorithm.
that minimize the function are the real and imaginary parts of
the unknown complex permittivity of the sample.
The estimation of the complex permittivity can be intended
as a constrained optimization problem in which the global
minimum falls inside a given interval [47]. This range of values
is relative to a water-based dough, so it is reasonable to fix an
interval ε[1,100]for the real permittivity, and an interval
ε [0,100]for the imaginary permittivity.
The algorithm has been developed using a MATLAB (v.
R2019b, The MathWorks Inc., Cambridge, MA) script, relying
on the function fmincon and a PSO routine, which is widely
used to solve multivariable electromagnetic problems [48].The
employed PSO algorithm is divided into three parts: generation
of the particles’ position and velocity, updating of the particles’
velocity, and updating of the particles’ position. These three
steps are repeated for every iteration until convergence. The
initial position and velocity of the ith particle are randomly
determined within the domain at the instant k=0, through the
following formulae:
xi
0=xmin +rand (xmax xmin)(6)
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6IEEE TRANSACTIONS ON AGRIFOOD ELECTRONICS, VOL. 00, 2024
Fig. 6. Schematic representation of the measurement system employed for the
experimental validation.
Fig. 7. Measurement system.
vi
0=xi
0
Δt(7)
wherein rand is a uniformly distributed random variable. The
movement of each particle is influenced by its local best known
position and the swarm moves toward the best solution for every
given instant. The velocity is updated based on the formula
vi
k+1 =wvi
k+1 +c1rand pixi
k
Δt+c2rand pg
kxi
k
Δt.
(8)
The first term of this equation indicates the current direction
of the particles, the second term represents the influence of the
particles’ memory, i.e., how much the next direction will be
Fig. 8. Comparison between the complex permittivity of the Carasau bread
dough with 50% water content measured using the DUT (i.e., the coaxial fixture)
depicted as blue circles and using a commercial coaxial probe, depicted as a red
line. (a) Real part. (b) Imaginary part.
TAB L E I
MEASUREMENT ERROR
influenced by the previous position of the particle, and the last
term represents the influence that the other particles’ position
has on the ith particle. Finally, the last step is the update of the
position at the instant k+1using the formula
xi
k+1 =xi
k+xi
k+1Δt. (9)
The algorithm stops when one of the following conditions is
met.
1) The minimum tolerance is reached, i.e., the difference
between the minima of one iteration and the previous one
is lower than the value imposed as a tolerance.
2) The maximum number of iterations is reached, i.e., the
algorithm was not able to find the optimum value in a
fixed number of iterations.
3) The minimum value is found.
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MUNTONI et al.: COAXIAL LINE FIXTURE BASED ON A HYBRID PSO-NLR MODEL 7
Fig. 9. Percentage error variation of the DUT (coaxial fixture) when compared
with the commercial coaxial probe for the real and imaginary part of the complex
dielectric permittivity of the original recipe (50% water content) Carasau bread
dough.
Fig. 10. Comparison between the complex permittivity of the Carasau bread
dough with 46% water content measured using the DUT (i.e., the coaxial fixture)
depicted as blue circles and using a commercial coaxial probe, depicted as a red
line. (a) Real part. (b) Imaginary part.
Fig. 11. Comparison between the complex permittivity of the Carasau bread
dough with 54% water content measured using the DUT (i.e., the coaxial fixture)
depicted as blue circles and using a commercial coaxial probe, depicted as a red
line. (a) Real part. (b) Imaginary part.
Fig. 12. Percentage error variation of the DUT (coaxial fixture) when com-
pared with the commercial coaxial probe for the real and imaginary part of
the complex dielectric permittivity of the Carasau bread dough with 46% of
water.
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Fig. 13. Percentage error variation of the DUT (coaxial fixture) when com-
pared with the commercial coaxial probe for the real and imaginary part of the
complex dielectric permittivity of the Carasau bread dough with 54% of water.
Since the depicted method is statistical, there is no guarantee
that the solution found is the optimal value. However, it has
been preferred over other heuristic methods (e.g., genetic algo-
rithm) for its ability to operate in large domains and its reduced
computational load.
V. E XPERIMENTAL VALIDATION AND RESULTS
The schematic of the electronic measurement system em-
ployed for the experimental validation is reported in Fig. 6.The
two ports of the coaxial fixture are connected to the pocket-VNA.
The output of the VNA (S-parameter matrix) is read by the Rasp-
berry Pi 4. By using the pocket-VNA Saver tool, the Raspberry
can read the data of the network analyzer from the serial port,
extract it, and display it on a monitor. The VNA data can then
be saved into a file. Next, the board analyzes such file, runs the
algorithm described in Section IV, and provides the complex
permittivity of the sample in the operating frequency range. A
photograph of the described system is reported in Fig. 7.
For the experimental validation, a dough kneaded with the
Carasau bread traditional recipe [3] (50% of water w.r.t. the
semolina weight) has been characterized using the coaxial fix-
ture and the resulting complex permittivity has been compared
with the one obtained using the commercial DAK 3.5 Speag
OECP system [49]. The two samples used for the comparison
came from the same batch of Carasau dough. The probe takes
ten consecutive measurements of the same sample in a given fre-
quency range. These values are then averagedand they are shown
in Fig. 8as a red line. Considering our previous analyses [3],
[19],[21], we also included as a red shaded area the combined
standard deviations for the doughs variability and the dielectric
probe uncertainties and errors. The comparison is reported in
Fig. 8.
From the displayed results, it can be inferred that the coaxial
fixture is rather accurate when compared with the output of
the commercial measurement system. The information about
the measurement error made using the device under test (DUT)
(i.e., the coaxial fixture) w.r.t. the commercial coaxial probe is
reported in Table I, whereas Fig. 9shows the percentage error
variation within the operating frequency range. The measure-
ment made with the commercial probe in this case is taken
as a reference to calculate the error. The comparison is made
every 250 MHz within the frequency range 0.5–3 GHz. The
highest inaccuracy (15%) is found for the imaginary part of the
complex dielectric permittivity, as expected, since it is usually
the most challenging physical quantity to estimate. Nonetheless,
the calculated average error for the real and imaginary parts is
in the order of 3% and 6%, respectively.
For the sake of completeness and also to estimate the sen-
sitivity of the proposed methodology, the same measurement
comparisons have been performed for doughs with an incorrect
amount of water, i.e., 46% and 54% w.r.t. the semolina weight,
thus diverging from the original recipe. The results of these
measurements are reported in Fig. 10 and Fig. 11, respectively,
whereas the percentage error variation of the DUT compared
with the commercial coaxial probe is reported in Fig. 12 and
Fig. 13, respectively. Once again the highest inaccuracy is found
for the imaginary part, in both cases, having 10% for the dough
with less water and 11% for the dough with more water. The
calculated average error for the real and imaginary parts is in the
order of 2% and 4.5% for both cases. Considering these values,
it can be safely stated that the presented coaxial fixture, coupled
with the PSO-NLR algorithm and the ad hoc measurement
system, has sufficient accuracy to be considered a viable, more
rapid, and low-cost alternative to the commercial coaxial probe
for the dielectric characterization of the Carasau bread dough
within an industrial environment.
VI. CONCLUSION
Food dielectric characterization using MW devices is a viable,
low-cost, and nondestructive way to extrapolate some of the
most important features of agricultural products. By combining
a suitable coaxial fixture based on the mismatching of a coaxial
line section and a hybrid PSO-NLR algorithm, a cost-effective
and rather accurate MW device for the dielectric characteriza-
tion of the Carasau bread dough is presented in this article.
The coaxial fixture has been tested with a sample of bread
dough kneaded following the Carasau bread traditional recipe.
The results show that the presented coaxial device is able to
provide the accurate estimation of the complex permittivity of
the Carasau bread dough when compared with a commercial
coaxial probe, resulting in a cost effective, more rapid, and
more suitable alternative. The coaxial sensor works within the
operating frequency bandwidth of 0.5–3 GHz, taking advantage
of the benefits of the low-frequency spectrum, such as low-cost
measurement equipment while retaining good performance. The
presence of a 3-D-printed sample holder allows for the dielectric
estimation of solid and liquid materials, making the coaxial de-
vice an attractive solution also for other industrial applications.
ACKNOWLEDGMENT
The authors would like to thank M. Bauco and L. Lorusso from
the Rohde and Schwarz Italia for the VNA freely provided, and
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
MUNTONI et al.: COAXIAL LINE FIXTURE BASED ON A HYBRID PSO-NLR MODEL 9
F. Di Napoli from the M.F.M. of Urrai Salvatora and C.S.N.C
for providing the semolina wheat and for the useful information
about the industrial process.
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overview/
Giacomo Muntoni (Member, IEEE) received the
Bachelor’s degree in electronic engineering and the
Master’s degree in telecommunication engineering
from the University of Cagliari, Cagliari, Italy, in
2010 and 2015, respectively, and the Ph.D. degree
in electronic engineering and computer science from
the University of Cagliari, Cagliari, Italy, in 2019.
He is currently working as a Technologist in Ap-
plied Electromagnetics Group with the University of
Cagliari. His research activity involves the design
and characterization of antennas for biomedical and
aerospace applications, microwave-based dielectric characterization of mate-
rials, 3-D printing of RF components, and monitoring of the space debris
environment in low Earth orbit with Sardinia Radio Telescope, in collaboration
with Cagliari Astronomical Observatory.
Nicola Curreli (Member, IEEE) received the M.Sc.
degree in biomedical engineering from the Univer-
sity of Genoa, Genoa, Italy, in 2016, and the Ph.D.
degree in electronic engineering from the University
of Cagliari, Cagliari, Italy, and the Italian Institute of
Technology– IIT, Genoa, Italy, in 2020.
After completing the Ph.D. degree, he held a Fellow
position with Graphene Labs– IIT, where he con-
tributed to the Graphene Core 2 Project as a part
of the Graphene Flagship initiative. In 2019, he was
a Visiting Researcher with Physics and Mechanical
Engineering Departments, Columbia University, New York City, NY, USA, as a
part of the Marie Sklodowska-Curie RISE Action “SONAR H2020.” Between
2022 and 2023, he was a Visiting Researcher with the Molecular Foundry,
Lawrence Berkeley National Laboratory, Berkeley, CA, USA. He is currently
a Researcher with Functional Nanosystems– IIT, Genova, Italy. His research
interests include the study of low-dimensional materials, their characterization,
and their application in the field of photonics, and the design, implementation,
and analysis of linear and nonlinear integrated optical, microwave devices, and
antennas.
Dr. Curreli was a recipient of Marie Sklodowska-Curie Global Fellowship
“2DTWIST.” The fellowship is in collaboration with the Transport at Nanoscale
Interfaces Laboratory, Swiss Federal Laboratories for Materials Science and
Technology (EMPA), Switzerland. He was a recipient of the Young Scientists
Award at the General Assembly and Scientific Symposium of URSI in 2022. He
is also a member of the Topical Advisory Panel of Photonics and is an Academic
Editor for the Journal of Nanotechnologyand the International Journal of Optics.
He is a part of the Committee of the Young Professionals Affinity Group of IEEE
R8 Italy Section.
Davide Toro received the bachelor’s degree in elec-
tronic engineering from the University of Cagliari,
Cagliari, Italy, in 2018, and the master’s degree in
telecommunication engineering from the University
of Cagliari, Cagliari, Italy, in 2021.
He was an Assistant Researcher with Electromag-
netic Group, University of Cagliari, from 2018 to
2021. Since 2021, he has been a Technical Project
Manager with TIM. His research activity involves
the design and characterization of microwave com-
ponents for agrifood applications.
Andrea Melis received the bachelor’s degree in
biomedical engineering from the University of
Cagliari, Cagliari, Italy, in 2017.
He was an Assistant Researcher with the University
of Cagliari. His research interests include EM model-
ing and development of RF coils at low and high fre-
quencies, especially for MRI at high field, the design
and realization of WSN systems for the monitoring
of industrial processes, such as bread manufacturing,
and intelligent transportation systems.
Matteo Bruno Lodi (Member, IEEE) received the
bachelor’s degree in biomedical engineering from
the University of Cagliari, Cagliari, Italy, in 2016,
the master’s degree in biomedical engineering from
Politecnico di Torino, Turin, Italy, in 2018, and the
Ph.D.(Hons.) degree in electronic engineering and
computer science from the University of Cagliari,
Cagliari, Italy, in 2022.
From 2022 to June 2023, he was a Technologist
with Electromagnetic Group, University of Cagliari,
where he is currently an Assistant Professor. His
research interests include the modeling of bioelectromagnetic phenomena,
especially hyperthermia treatment, the study, manufacturing, and synthesis
of magnetic biomaterials for tissue engineering applications, and the use of
microwaves for biotechnology and environmental applications while working in
the design and characterization of antennas for space and wearable applications.
Dr. Lodi was the recipient of the Young Scientists Award at the General
Assembly and Scientific Symposium of URSI in 2020 and 2021, a Coauthor
of the “2021 IEEE IST Best Student Paper Award” at the IEEE International
Conference on Imaging Systems and Techniques, grant from the European
Microwave Association for the attendance of the ESoA course titled “Diagnostic
and Therapeutic Applications of Electromagnetics,”and COST Action CA17115
for the attendance of the IX International School of Bioelectromagnetism
Alessandro Chiabrera, where, in 2019, he was a recipient of the Best Poster
Award. He is a member of the WG2: “Better thermal-based EM therapeutics” of
the COST Action 17115 “MyWave.” In 2022, he was appointed as the Chair of
the IEEE Nanotechnology Council Young Professionals. He recently joined the
NTC technical committee (TC2) Nanobiomedicine, in the frame of the MENED
program. He is a member of the Editorial Board of the IEEE Future Directions
Technology Policy and Ethics Newsletter.
Antonio Loddo received the bachelor’s degree in
technologies, viticultural, oenological, and food from
the University of Sassari, Sassari, Italy, in 2019.
Since 2020, he has been working as a Researcher
with Agency M.F.M. S.R.L. His research activity
involves the food process engineering.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
MUNTONI et al.: COAXIAL LINE FIXTURE BASED ON A HYBRID PSO-NLR MODEL 11
Giuseppe Mazzarella (Senior Member, IEEE) re-
ceived the degree(summa cum laude) in electronic en-
gineering from the Università Federico II of Naples,
Naples, Italy, in 1984, and the Ph.D. degree in elec-
tronic engineering and computer science in 1989.
In 1990, he became an Assistant Professor with
the Dipartimento di Ingegneria Elettronica, Univer-
sità Federico II of Naples. Since 1992, he has been
with the Dipartimento di Ingegneria Elettrica ed Elet-
tronica, Università di Cagliari, Cagliari, Italy, first
as an Associate Professor and then, since 2000, as
a Full Professor, teaching courses in electromagnetics, microwave, antennas,
and remote sensing. He is the author (or coauthor) of more than 100 articles
in international journals and a reviewer for many EM journals. His research
interests include the efficient design of large arrays of slots, power synthesis
of array factor, with emphasis on the inclusion of constraints, microwave
holography techniques for the diagnosis of large reflector antennas, use of
evolutionary programming for the solution of inverse problems, in particular
problems of synthesis of antennas and periodic structures.
Alessandro Fanti (Senior Member, IEEE) received
the Laurea degree in electronic engineering and the
Ph.D. degree in electronic engineering and computer
science from the University of Cagliari, Cagliari,
Italy, in 2006 and 2012, respectively.
From 2013 to 2016, he was a Postdoctoral Fellow
with Electromagnetic Group, University of Cagliari,
where he is currently an Assistant Professor. He has
coauthored more than 100 scientific contributions
published in international journals, conference pro-
ceedings, and book chapters. His research interests
include the use of numerical techniques for modes computation of guiding
structures, optimization techniques, analysis, and design of waveguide slot
arrays, analysis, and design of patch antennas, radio propagation in urban envi-
ronment, modeling of bioelectromagnetic phenomena, and microwave exposure
systems for biotechnology and bioagriculture. He is a member of the IEEE
Antennas and Propagation Society, the Italian Society of Electromagnetism,
and the Interuniversity Center for the Interaction Between Electromagnetic
Fields and Biosystems. From 2020 to 2023, he had been acting as a Principal
Investigator of the IAPC Project, which was funded with five million euros
by the Italian Ministry of Economic Development (MISE), within the AGRI-
FOOD PON I&C (2014–2020). Since 2024, he has been acting as a Principal
Investigator of the AISAC Project, funded with 15 million euros by the Italian
Ministry of Enterprises and Made in Italy (MIMIT), within the “ACCORDI PER
L’INNOVAZIONE” (2021–2026). He is also an Associate Editor for the IEEE
Journal of Electromagnetics, and RF and Microwaves in Medicine and Biology.
Open Access funding provided by ‘Universit? degli Studi di Cagliari’ within the CRUI CARE Agreement
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
Carasau bread is a flat bread, typical of Sardinia (Italy). The market of this food product has a large growth potential, and its industry is experiencing a revolution, characterized by digitalization and automation. To monitor the quality of this food product at different manufacturing stages, microwave sensors and devices could be a cost-effective solution. In this framework, knowledge of the microwave response of Carasau dough is required. Thus far, the analysis of the microwave response of Carasau doughs through dielectric spectroscopy has been limited to the dynamics of fermentation. In this work, we aim to perform complex dielectric permittivity measurements up to 8.5 GHz, investigating and modeling the role of water amount, salt and yeast concentrations on the spectra of this food product. A third-order Cole–Cole model was used to interpret the microwave response of the different samples, resulting in a maximum error of 1.58% and 1.60% for the real and imaginary parts of permittivity, respectively. Thermogravimetric analysis was also performed to support the microwave spectroscopy investigation. We found that dielectric properties of Carasau bread doughs strongly depend on the water content. The analysis highlighted that an increase in water quantity tends to increase the bounded water fraction at the expense of the free water fraction. In particular, the free water amount in the dough is not related to the broadening parameter of the second pole, whereas the bound water weight fraction is more evident in the and parameters. An increase in electrical conductivity was observed for increasing water content. The microwave spectrum of the real part of the complex permittivity is slightly affected by composition, while large variation in the imaginary part of the complex dielectric permittivity can be identified, especially for frequencies below 4 GHz. The methodology and data proposed and reported in this work can be used to design a microwave sensor for retrieving the composition of Carasau bread doughs through their dielectric signature.
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