Instrumentation & Measurement Magazine 24-5 - 60

Consider the two possible models to compare, given the
available set of data (in this case, the LPFG spectra). The two
models are defined in the following manner:
◗ Model M1
: " The data indicates the presence of a physical
process A. "
◗ Model M2: " The data does not indicate the presence of a
physical process A. "
In the example given, A could be any process measurable
with an LPFG sensor, if the expected behavior of the LPG spectra
in the presence of said process is known. In the context of
Bayesian statistics, the comparison of the models involves the
calculation of the odds ratio O12
, defined as:
O12  11p M I pD M I
p M I pD M I
22


,
,
|I) the
( )( )
( )( )
prior odds for the model
Mi
and p(D|Mi
hood of the model Mi
,I) the likeligiven
the
data. Generally, given
that no evidence is available
to assign higher prior
probability to each model,
p(M1
|I)/ p(M2
|I) = 1 is obtained,
and the odds ratio
reduces to the likelihood ratio.
Notice that in the case
O12
(2)
In (2), I represents the prior information available, D the
data available, p(Mi
Case Study: Detection of Corrosion
Using LPFG Sensing with a Low-cost
Platform
Given the framework developed in the previous sections, it
can be applied to the study of corrosion monitoring using data
from LPFG corrosion sensing [8]. To perform the tests to the
spectral reconstruction routine, the data regarding the time
evolution of a 40 nm thick Fe coated LPFG immersed in 3.5%
w/w solution of NaCl at 40 °C was taken. Although in the
original work a bare LPFG was also used for environmental
could be warned of the presence of corrosion in a specific structure
which is being monitored. This feature could be of high
importance in applications of this technology to extreme environmental
conditions, where the system could automatically
warn the user about the presence of a detrimental process.
> 1, the evidence indicates
a higher likelihood of
model M1
, with the opposite
in the case O12 < 1; alternatively,
if O12
more likely.
< 1, model M2
is
The calculation of each
likelihood involves the
marginalization over all
parameters of the model,
which can mean integration
over many variables,
thus requiring statistical
integration methods
such as Monte Carlo methods.
Such routines were
integrated wi thin the
framework of the low-cost
platform, allowing the user
to specify the model and set
up automatic alarms, such
as receiving a notification
(both in the user interface
and via email, for example)
when a physical or chemical
process is detected. An
example is given in the next
section, in which the user
60
Fig. 5. Transmission spectra of the LP1,6 cladding mode of a 40 nm thick Fe coated LPFG immersed in 3.5% w/w solution
of NaCl at 40 °C, up to 22 h. Data from [8] used with permission, © 2018, IEEE.
Fig. 6. Time evolution of the minimum value of the wavelength of the attenuation band of a 40 nm thick Fe coated LPFG
immersed in 3.5% w/w solution of NaCl at 40 °C. The minimum wavelength determined with the curve fitting routine and
the model for LPFG corrosion detection are also represented.
IEEE Instrumentation & Measurement Magazine
August 2021

Instrumentation & Measurement Magazine 24-5

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