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of (5) is trivial using numerical methods for the no-corrosion
model, given that we have only one parameter, λ0
. In the case
of this corrosion model, four parameters are available, and
the integral is most efficiently calculated using statistical integration,
namely Markov-Chain Monte Carlo. In this case, the
Metropolis-Hasting algorithm in a Python routine was implemented,
allowing integration with the Raspberry Pi system.
Given the data seen in Fig. 6, the evidence of corrosion can
be calculated using (5). To fully test this framework, an initial
flat region was appended in which the minimum wavelength
does not vary (except for noise, which was included). In this
region, the evidence should point clearly in favor of the noncorrosion
model. With this set of data, the calculation of the
evidence of corrosion at each time can be performed.
Fig. 7 plots the time evolution of the calculated corrosion
evidence, showing that once the corrosion process begins (at t
= 0, as seen in Fig. 6), the evidence quickly indicates the presence
of corrosion and allows for the user to be warned. This
points towards a correct implementation of the routine and its
validity as a process warning framework.
Final Remarks
Based on a low-cost platform for LPFG sensing, a spectral reconstruction
routine was developed and tested against OSA
data. This routine is based on the generalization of the logistic
distribution, which is used because of its good performance
against the variety of shapes the LPFG spectra can assume. A
Bayesian model comparison framework for physical processes
was also developed to be used in the low-cost system, and the
analysis of LPFG sensing of corrosion was tested. The results
clearly indicated the presence of corrosion when it was expected,
allowing the validation of both the curve fitting routine
and the model comparison framework, which could be used as
a warning system that could prove especially useful in extreme
environmental conditions.
Acknowledgment
Paulo Santos acknowledges the support from FCT grant
SFRH/BD/146784/2019, and Luis Coelho acknowledges
the support from FCT research contract grant CEECIND/
00471/2017.
References
[1] P. S. S. Santos, P. A. S. Jorge, J. M. M. M. de Almeida, and L.
Coelho, " Low-cost interrogation system for long-period fiber
gratings applied to remote sensing, " Sensors, vol. 19, pp. 15001513,
2019.
[2] H. Guo, G. Xiao, and J. Yao, " Interrogation of a long period
grating fiber sensor with an arrayed-waveguide-grating-based
demultiplexer through curve fitting, " IEEE Sensors J., vol. 8, no.
11, pp. 1771-1775, 2008.
[3] D. Tosi, " Review and analysis of peak tracking techniques for
fiber bragg grating sensors, " Sensors, vol. 17, p. 2368, 2017.
[4] G. Rego, P. V. S. Marques, J. L. Santos, and H. M. Salgado, " Arcinduced
long-period gratings, " Fiber Integrated Optic., vol. 24, pp.
245-259, 2005.
62
[5] T. Erdogan, " Cladding-mode resonances in short- and longperiod
fiber grating filters, " J. Opt. Soc. Am. A., vol. 14, no. 8, pp.
1760-1773, 1997.
[6] S. Khatibisepehr, B. Huang, and S. Khare, " Design of inferential
sensors in the process industry: a review of Bayesian methods, " J.
Process Contr., vol. 23, pp. 1575-1596, 2013.
[7] P. Gregory, Bayesian Logical Data Analysis for the Physical Sciences:
A Comparative Approach with Mathematica® Support, 1st
Cambridge, UK: Cambridge University Press, 2006.
Ed.
[8] L. C. C. Coelho, P. S. S. D. Santos, P. A. D. S. Jorge, J. L. Santos, and
J. M. M. M. de Almeida, " Real-time early warning strategies for
corrosion mitigation in harsh environments, " IEEE J. Lightwave
Technol., vol. 36, pp. 1152-1158, 2018.
Bernardo Santos Dias is a master's degree student at the
University of Porto, Porto, Portugal, where he is studying
experimental physics in the Faculty of Sciences. He is also a
Research Assistant at the Centre for Applied Photonics of the
Institute for Systems and Computer Engineering, Technology
and Science.
Paulo Sérgio Soares dos Santos (paulo.s.santos@inesctec.
pt) studied at the University of Porto, Porto, Portugal and received
the Graduate degree in technological physics in 2016,
and a M.Sc. degree in physical engineering in 2018 at the Faculty
of Sciences. He is currently performing research on the
detection of biochemical contaminants using optical fiber sensors
towards his Ph.D. degree.
Pedro Alberto da Silva Jorge is a Senior Researcher at Institute
for Systems and Computer Engineering, Technology and Science,
Porto, Portugal, where he leads the Biochemical Sensors
team exploring the potential of optical fiber and integrated
optics technologies in industrial, environmental, and medical
applications. He received his Ph.D. degree in 2006 at the
University of Porto, Porto, Portugal, in collaboration with the
University of North Carolina, Charlotte, North Carolina, USA.
José Manuel Marques Martins de Almeida is an Associate Professor
with the Department of Physics at the University of
Trás-os-Montes and Alto Douro, Vila Real, Portugal and a Senior
Researcher in the Centre for Applied Photonics of the Institute for
Systems and Computer Engineering, Technology and Science,
Porto, Portugal. His current research interests include optical
sensors, integrated optics, spectroscopy, and biophysics. He received
his Ph.D. degree in 1998 and Habilitation in 2006 from the
University from the University of Porto, Porto, Portugal.
Luis Carlos Costa Coelho (luis.c.coelho@inesctec.pt) is a
Researcher at the Institute for Systems and Computer Engineering,
Technology and Science, Porto, Portugal, and his
research interests include the study and development of bio
and chemical sensors based on coated optical fiber devices. He
received his Ph.D. in physics in 2016 at the University of Porto,
Portugal, with the focus on thin film coating technology applied
to fiber optic sensing.
IEEE Instrumentation & Measurement Magazine
August 2021
Instrumentation & Measurement Magazine 24-5

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