Application of Neural Network Algorithms for Central Wavelength Determination of Fiber Optic Sensors

Round 1

Reviewer 1 Report

The main question addressed by the research is whether neural network algorithms can be practically used to determine the central wavelength of a single Fiber Bragg grating (FBG) sensor. The research aims to demonstrate that the proposed method of using neural networks can achieve a much higher resolution in determining the central wavelength compared to the resolution with which the input data were sampled.

 The manuscript would benefit from enhancements in certain logical aspects. A number of specific areas where improvements could be made are listed below.

 1.     The introduction section would benefit from a more comprehensive discussion of the existing literature on the use of machine learning methods to enhance FBG sensors

2.     It is important to clearly articulate the novelty of the proposed approach towards the end of the introduction section, as this can help contextualize the research within the broader field.

 3.     The selection of the neural network type and architecture should be meticulously outlined in the methodology section, with a clear justification of the decision-making process.

 4.     The results section should provide a rigorous comparison of the proposed method with other state-of-the-art approaches for enhancing FBG sensors using machine learning. For example

 a.      B. Li et al., "Robust Convolutional Neural Network Model for Wavelength Detection in Overlapping Fiber Bragg Grating Sensor Network," 2020 Optical Fiber Communications Conference and Exhibition (OFC), San Diego, CA, USA, 2020, pp. 1-3.

b.      An, Yang, Xiaocen Wang, Zhigang Qu, Tao Liao, and Zhongliang Nan. "Fiber Bragg grating temperature calibration based on BP neural network." Optik 172 (2018): 753-759.

c.      A. C. Zimmermann, C. L. N. Veiga and L. S. Encinas, "Unambiguous Signal Processing and Measuring Range Extension for Fiber Bragg Gratings Sensors Using Artificial Neural Networks— A Temperature Case," in IEEE Sensors Journal, vol. 8, no. 7, pp. 1229-1235, July 2008, doi: 10.1109/JSEN.2008.926523.

d.      Negri, Lucas, Ademir Nied, Hypolito Kalinowski, and Aleksander Paterno. 2011. "Benchmark for Peak Detection Algorithms in Fiber Bragg Grating Interrogation and a New Neural Network for its Performance Improvement" Sensors 11, no. 4: 3466-3482. https://doi.org/10.3390/s110403466

 There exists a considerable body of relevant literature on this topic.

 5.     There is scope for improvement in the quality of English writing in the manuscript, which could be addressed through additional proofreading and editing.

6.     To enhance the completeness of the study, it would be beneficial for the conclusion section to incorporate a discussion of the limitations of the proposed method as well as suggestions for future research directions.

 

 

 

Author Response

The authors thank the Reviwer for the valuable remarks and suggestions. Please, find our replies below.

The main question addressed by the research is whether neural network algorithms can be practically used to determine the central wavelength of a single Fiber Bragg grating (FBG) sensor. The research aims to demonstrate that the proposed method of using neural networks can achieve a much higher resolution in determining the central wavelength compared to the resolution with which the input data were sampled.

 The manuscript would benefit from enhancements in certain logical aspects. A number of specific areas where improvements could be made are listed below.

1. The introduction section would benefit from a more comprehensive discussion of the existing literature on the use of machine learning methods to enhance FBG sensors

Thanks for the remark, we have added a paragraph in lines 68-87.

 

2. It is important to clearly articulate the novelty of the proposed approach towards the end of the introduction section, as this can help contextualize the research within the broader field.

The difference between our approach and the previously proposed approaches is indicated in lines 89-95.

 

3. The selection of the neural network type and architecture should be meticulously outlined in the methodology section, with a clear justification of the decision-making process.

We chose a simple backpropagation neural network (BPNN) with a three-layer perceptron architecture, which has low computational complexity, allowing the trained neural network to be used at high speed even on the simplest microcontrollers, which is important for determining a rapidly changing physical quantity. This was mentioned in lines 175-180.

 

4. The results section should provide a rigorous comparison of the proposed method with other state-of-the-art approaches for enhancing FBG sensors using machine learning. For example
   1. B. Li et al., "Robust Convolutional Neural Network Model for Wavelength Detection in Overlapping Fiber Bragg Grating Sensor Network," 2020 Optical Fiber Communications Conference and Exhibition (OFC), San Diego, CA, USA, 2020, pp. 1-3.
   2. An, Yang, Xiaocen Wang, Zhigang Qu, Tao Liao, and Zhongliang Nan. "Fiber Bragg grating temperature calibration based on BP neural network." Optik 172 (2018): 753-759.
   3. A. C. Zimmermann, C. L. N. Veiga and L. S. Encinas, "Unambiguous Signal Processing and Measuring Range Extension for Fiber Bragg Gratings Sensors Using Artificial Neural Networks— A Temperature Case," in IEEE Sensors Journal, vol. 8, no. 7, pp. 1229-1235, July 2008, doi: 10.1109/JSEN.2008.926523.
   4. Negri, Lucas, Ademir Nied, Hypolito Kalinowski, and Aleksander Paterno. 2011. "Benchmark for Peak Detection Algorithms in Fiber Bragg Grating Interrogation and a New Neural Network for its Performance Improvement" Sensors 11, no. 4: 3466-3482. https://doi.org/10.3390/s110403466

 There exists a considerable body of relevant literature on this topic.

We thank the Reviewer for the list of works proposed for comparison, their review is given in lines 68-87.

 

5. There is scope for improvement in the quality of English writing in the manuscript, which could be addressed through additional proofreading and editing.

Thank you for the remark. The text has been edited.

 

6. To enhance the completeness of the study, it would be beneficial for the conclusion section to incorporate a discussion of the limitations of the proposed method as well as suggestions for future research directions.

The authors thank the Reviewer for a fair remark. Indeed, we omitted to describe the limitations of the method in the manuscript. To cover this point, the following paragraph has been added in lines 375-390:

“The main limitation of the proposed method is the impossibility of the central wavelength determination of the FBG with FWHM of less than 200 pm (~1.5 larger than the spectrum resolution). This limitation is due to the fact that when FWHM is less than the specified value, the FBG reflection spectrum obtained by the I-MON-512-based interrogator has 1–2 significant values, which do not allow to determine the value of the central wavelength with a given (required) accuracy. At the same time, there is a limitation in the impossibility of determining the central wavelength of the FBG with FWHM greater than the specified interval for finding the FBG (Δ = 3 nm). The third limitation is the impossibility of determining the central wavelengths of two or more FBGs in the wavelength section under consideration (Δ = 3 nm).

It must be noted that the second constraint is not a fundamental limitation of the proposed method, and in order to mitigate it, it is enough to retrain the neural network for a wider interval. The first limitation, however, can be removed only by increasing the physical resolution of the spectrum analyzer. Further research will be dedicated to the development of approaches for the central wavelength determination of two or more FBGs with overlapping spectra.”

Reviewer 2 Report

Authors introduced a novel method related to neural network algorithm to find out the central wavelength of FBG fiber sensor. The proposed method has been demonstrated as an efficient way to select the central wavelength. It could be accepted once the following issues have been addressed.

 

1.      In the introduction, the author is suggested to introduce the current methods used to determine the resonance wavelength rather than one sentence ‘Diverse methods have been proposed to improve the precision of determining the position of the spectra of sensor sensing elements.‘

2.      In equation 1, what is the R meaning? Additionally, what is the parameter meaning is equation 2?

3.      It is better to compare this proposed method compared with current methods.

Author Response

The authors thank the Reviewer for the comments and concerns. Please, find our replies below.

Authors introduced a novel method related to neural network algorithm to find out the central wavelength of FBG fiber sensor. The proposed method has been demonstrated as an efficient way to select the central wavelength. It could be accepted once the following issues have been addressed.

1. In the introduction, the author is suggested to introduce the current methods used to determine the resonance wavelength rather than one sentence ‘Diverse methods have been proposed to improve the precision of determining the position of the spectra of sensor sensing elements‘

Thank you for your comment. The reviewer is right, a lot of subpixel processing methods have been proposed, including clarification of the wavelength center by several upper points, approximation of the spectrum by various curves (Gauss, Lorentz, parabolic), the center of mass method and their modifications. A full review of these methods could take a multi-page report, and we do not want to divert the reader from the main goal of the work. However, references to the main works are given in lines 47-53.

 

2. In equation 1, what is the R meaning? Additionally, what is the parameter meaning is equation 2?

After equation 1, in lines 150-151, the following was added: “In equation (1), the set R denotes the set of reflection coefficients R_i, i = 0..509, belonging to the wavelength range λ ∈ [1510, 1595] nm.”

After equation 2, in lines 216-221, the following was added: “In equation (2), the parameter α is responsible for the slope of the linear section near the ordinate 0. At α = 0, the sigmoid function turns into a line y = 0.5; for α = + ∞, into a threshold function. The choice of the parameter α = 0.5, or another value close to 0, leads to an increase in the length of the "linear" section of the function, as a result of which the sigmoid function behaves like a linear function (in the working section), while maintaining its nonlinearity.”

 

3. It is better to compare this proposed method compared with current methods.

In lines 68-87, we have included an overview of neural network methods for determination of the central wavelengths of sensors based on fiber Bragg gratings.

Reviewer 3 Report

This paper used the neural network algorithms to determine the central wavelength of FBG. The configuration of the neural network and the algorithm for producing the training and control datasets are specified. However, considering the data (noise and central wavelengths) are mainly generated by simulation, the reliability of the algorithm is of concern if it is used in the real spectral demodulation.

 

Major concerns:

 

1.      The wavelength range is quite small, and whether it can be used to demodulate central wavelengths in real spectra is questionable. In addition, as there are multiple peaks, such as the side-lobes, in the spectrum, it is difficult to determine the central wavelengths using this algorithm.

2.      Page 2, Line 85-87, “Because of the impossibility of reliable control of the true FBG central wavelength via hardware and software, given the problem requirements, real spectra obtained from the I-MON-512 spectrum analyzer cannot be used as input data for a neural network model.” The fluctuation of the true FBG center wavelength under the same conditions should be taken into account at all times, instead of being excluded by numerical simulation.

3.      Page 3, Line 115-117, “The amplitude of the noise component aN is assumed to be less than 0.2 % of the maximum amplitude, and the minimum value in the FBG spectrum is assumed to be less than 20 % of the maximum amplitude.” In real application, there are large fluctuations in noise, and how to realize the noise reduction is necessary.

4.      Page 3-4, Line 129-131, “As a neural network, we use one of the most commonly used architectures in data approximation, linear and nonlinear regression problems — a three-layer Rosenblatt's perceptron with variable S-A connections [37].” A simple three-layer neural network model may be difficult to demodulate correctly in terms of a large amount of full spectrum data, multiple collection points, and multiple peaks.

5.      The real experiment data (a set of unknown spectral center wavelengths) should be added in the test to compare the accuracy of demodulation .

Author Response

We thank the Reviewer for the valuable remarks and suggestions. Please, find our replies below.

This paper used the neural network algorithms to determine the central wavelength of FBG. The configuration of the neural network and the algorithm for producing the training and control datasets are specified. However, considering the data (noise and central wavelengths) are mainly generated by simulation, the reliability of the algorithm is of concern if it is used in the real spectral demodulation.

Major concerns:

1. The wavelength range is quite small, and whether it can be used to demodulate central wavelengths in real spectra is questionable. In addition, as there are multiple peaks, such as the side-lobes, in the spectrum, it is difficult to determine the central wavelengths using this algorithm.

Thanks for the comment, it is really important for practical application. We have added the information about the limitations of the proposed method in lines 367-390.

 

2. Page 2, Line 85-87, “Because of the impossibility of reliable control of the true FBG central wavelength via hardware and software, given the problem requirements, real spectra obtained from the I-MON-512 spectrum analyzer cannot be used as input data for a neural network model.” The fluctuation of the true FBG center wavelength under the same conditions should be taken into account at all times, instead of being excluded by numerical simulation.

Fluctuations of the FBG center wavelength in the sensor can be caused by either temperature fluctuation or strain fluctuation (vibration). The measurement rate, as a rule, is several orders of magnitude higher than the frequency of temperature and strain fluctuations. The noises taken into account in our work (lines 144-145) correspond to the own noises of the measuring equipment. To accurately determine the central wavelength by means of a neural network during its training, the true central wavelength of the FBG is needed. It is not possible to obtain this value using the equipment with a resolution of 167 pm, therefore, it was decided to use model data that best matches the real characteristics of the I-MON-512 spectrum analyzer, and the noise characteristics of the spectra were obtained from the technical specifications of the spectrum analyzer.

 

3. Page 3, Line 115-117, “The amplitude of the noise component aN is assumed to be less than 0.2 % of the maximum amplitude, and the minimum value in the FBG spectrum is assumed to be less than 20 % of the maximum amplitude.” In real application, there are large fluctuations in noise, and how to realize the noise reduction is necessary.

Thank you for your comment. We also performed studies at a noise of 1% of the maximum amplitude value, which does not affect the accuracy of the method. However, the 0.2% parameter was taken from the I-MON-512 spectrum analyzer data sheet and this value corresponds to the actual noise components of the spectrum analyzer.

 

4. Page 3-4, Line 129-131, “As a neural network, we use one of the most commonly used architectures in data approximation, linear and nonlinear regression problems — a three-layer Rosenblatt's perceptron with variable S-A connections [37].” A simple three-layer neural network model may be difficult to demodulate correctly in terms of a large amount of full spectrum data, multiple collection points, and multiple peaks.

The reviewer is absolutely right. In this work, the determination of the central wavelengths of a large number of sensors is possible only with spectral separation of channels, in which all sensors are located in separate ranges with a width of Δ = 3 nm and have non-overlapping spectra. Determination of the central wavelengths of overlapping spectra is the goal of further research, as we mentioned in lines 389-390.

 

5. The real experiment data (a set of unknown spectral center wavelengths) should be added in the test to compare the accuracy of demodulation.

The method presented in this paper was implemented on a prototype interrogator based on the I-MON-512, which is used in our laboratory [Anfinogentov, V.; Karimov, K.; Kuznetsov, A.; Morozov, O. G.; Nureev, I.; Sakhabutdinov, A.; Lipatnikov, K.; Hussein, S.M.R.H.; Ali, M.H. Algorithm of FBG Spectrum Distortion Correction for Optical Spectra Analyzers with CCD Elements. Sensors 2021, 21, 2817. https://doi.org/10.3390/s21082817]. At the same time, we cannot present the results of a direct assessment of the wavelength center with greater accuracy than the spectrum analyzer used, because we do not have a device of the required accuracy class. However, we performed indirect estimates of measurement accuracy by varying the temperature similarly to the above work and determining the shift of the central wavelength according to the method. The error in the obtained results was within the expected range.

Reviewer 4 Report

Introduction 1

• Line 29 Fiber optic sensor system design of the

point and/or quasi-distributed type is impossible

without solving the key problem for this type of

system, which is finding the central wavelength

in the reflection spectrum with the most

accuracy. Thus, the frequency shift of the central

wavelength of a fiber optic sensor

• Most Fiber optic sensor interrogation system is

based on measuring the central wavelength shift

of a fiber optic sensor, like a Bragg grating (FBG)

[1-3]

Introduction 2

• Line 38 The primary factor limiting the

estimation accuracy of the physical impact

magnitude in fiber optic sensor systems is the

inadequate resolution of the devices used to

measure the spectral properties of such

sensors. Increasing the resolution of a device's

built-in spectrum analyzer can improve its

technical capabilities, but this usually comes

at a cost that rises almost exponentially

 

"Problem Elaboration" 1

• Line 72 Consider the problem as it appears

when determining the FBG central wavelength

shift using the KNRTU-KAI-built laboratory

interrogator based on

• Change to In our situation, we were using an

I-MON-512 Interrogation unit [24]

• Line 74 replace Let with "Assuming"

 

Problem Elaboration 2

• Line 85 Because of the impossibility of reliable

control of the true FBG central wavelength via 85

hardware and software, given the problem

requirements, real spectra obtained from the 86

I-MON-512 spectrum analyzer cannot be used as

input data for a neural network model.

• Change to "Without knowing the true FBG

central wavelength, the data collected from the I-

MON-512 cannot be used as input data for the

neural network model.

 

Problem Elaboration 3

• Line 88 Therefore, it was determined that neural network training should be carried out optimally using model data...

• Change to "So instead, we used a

mathematical model based in homogeneous layers method [36]and transfer matrices [35]

Problem Elaboration 4

Line 150 The problem is determining the position of FBG central wavelength with an error not exceeding ~Δl·10–3, having only spectrum data {λi, Ri} (i = 0, M − 1)

Change to "The problem is simplified to calculating the true FBG center wavelength with an error less than ~Δl·10-3, having only spectrum data {λi, Ri} (i = 0, M − 1)

 

Choice of words

Line 313 physical quantity, please use "discrete" instead

Line 321 allows to increase, please change to "increased"

Line 327 replace the word laser with the broad band light source

 

Summary of the review

• The only difficulty I found is that Authors use a very long winded style

• From time to time the author will explain the

same thing over and over again

 

• The I-MON-512 does not use a laser, it is based on a broad band light source

Author Response

Thank you for the remarks and suggestions. Please, find our replies below.

Introduction 1

• Line 29 Fiber optic sensor system design of the point and/or quasi-distributed type is impossible without solving the key problem for this type of system, which is finding the central wavelength in the reflection spectrum with the most accuracy. Thus, the frequency shift of the central wavelength of a fiber optic sensor
• Most Fiber optic sensor interrogation system is based on measuring the central wavelength shift of a fiber optic sensor, like a Bragg grating (FBG) [1-3]

Thank you for the remark, the sentence was corrected to eliminate ambiguity (line 33).

 

Introduction 2

• Line 38 The primary factor limiting the estimation accuracy of the physical impact magnitude in fiber optic sensor systems is the inadequate resolution of the devices used to measure the spectral properties of such sensors. Increasing the resolution of a device's built-in spectrum analyzer can improve its technical capabilities, but this usually comes at a cost that rises almost exponentially

Thank you for the remark.

 

"Problem Elaboration" 1

• Line 72 Consider the problem as it appears when determining the FBG central wavelength shift using the KNRTU-KAI-built laboratory interrogator based on
• Change to In our situation, we were using an I-MON-512 Interrogation unit [24]
• Line 74 replace Let with "Assuming"

Thank you for the suggestions. The sentences were revised.

 

Problem Elaboration 2

• Line 85 Because of the impossibility of reliable control of the true FBG central wavelength via hardware and software, given the problem requirements, real spectra obtained from the I-MON-512 spectrum analyzer cannot be used as input data for a neural network model.
• Change to "Without knowing the true FBG central wavelength, the data collected from the I-MON-512 cannot be used as input data for the neural network model.

Thank you for the remark. The sentence was edited.

 

Problem Elaboration 3

• Line 88 Therefore, it was determined that neural network training should be carried out optimally using model data...
• Change to "So instead, we used a mathematical model based in homogeneous layers method [36]and transfer matrices [35]

Thank you for the concern. The sentence was changed accordingly.

 

Problem Elaboration 4

Line 150 The problem is determining the position of FBG central wavelength with an error not exceeding ~Δl·10–3, having only spectrum data {λi, Ri} (i = 0, M − 1)

Change to "The problem is simplified to calculating the true FBG center wavelength with an error less than ~Δl·10-3, having only spectrum data {λi, Ri} (i = 0, M − 1)

Thank you for the remark, the sentence was changed.

 

Choice of words

Line 313 physical quantity, please use "discrete" instead

Line 321 allows to increase, please change to "increased"

Line 327 replace the word laser with the broad band light source

Thank you for the remark, the words were changed.

 

Summary of the review

• The only difficulty I found is that Authors use a very long winded style
• From time to time the author will explain the same thing over and over again
• The I-MON-512 does not use a laser, it is based on a broad band light source

Thank you for the remarks and suggestions that helped us to increase the quality of the manuscript.

Round 2

Reviewer 1 Report

No further comments.

 

Author Response

Thank you for the comments and suggestions that helped us to improve the manuscript.

Reviewer 2 Report

The author have answered carefully all quesitons issued by reviewers

Author Response

Thank you for the appreciation of our work. 

Reviewer 3 Report

It is appreciated that the authors had made a significant improvement on the manuscript. The only thing of concern is the last question I had raised, that is, the real experiment. The frequently-used demodulation method using OSA can provide the  spectral resolution from 1 pm to 20 pm. In my opinion, the algorithm should be validated under those interogation system with higher spectral resolution (maybe in the next work).  

Author Response

Thank you for the appreciation of our manuscript. We are also grateful for the suggested validation procedure. We are planning to perform such experiments on our trained neural network in the near future, since at the moment we do not have the required OSA in our laboratory. We have arranged the experimental session, which will be conducted in a few months in another laboratory, where such OSA is available. The results will be reported in the next work.

Reviewer 4 Report

Comments for author File: Comments.pdf

Author Response

Dear Reviewer, 

Thank you for the additional comments and questions. Please, find our replies in the attached file.

Author Response File: Author Response.pdf