Enhancing Microwave Photonic Interrogation Accuracy for Fiber-Optic Temperature Sensors via Artificial Neural Network Integration

Round 1

Reviewer 1 Report

The physical and mathematical part of the thesis looks good. Some doubts are raised by the construction part, which was treated as if it did not exist at all - supplementation is necessary here. On the other hand, there are deficiencies in  the ANN implementations. The data pattern for training and testing has not been given explicitly, the network topology has not been provided, comparative studies of various numerical methods have not been given.

“ It is demonstrated that the neural network model can accurately predict temperature variations, showcasing the feasibility of combining microwave photonic methods with machine learning for high-precision fiber-optic sensing.” -> It is demonstrated that the artificial neural network implementation can predict temperature variations with accuracy equal ..... (how accurately, give a number ); (the other part of sentence is propaganda).

Please give a scheme of examined set-up including ANN topology.

Please make an investigation of number of required neurons, as number as big as 200 in hidden layers looks much too big.

Please see that NN is biological by standard. You write about ANN – artificial neural network.  (title of paper also need correction)

some minor corrections:

 “to create a training sample neural network” -> In my opinion: -> to create a sample for artificial neural network training

Author Response

Comments and Suggestions for Authors

The physical and mathematical part of the thesis looks good. Some doubts are raised by the construction part, which was treated as if it did not exist at all - supplementation is necessary here. On the other hand, there are deficiencies in  the ANN implementations. The data pattern for training and testing has not been given explicitly, the network topology has not been provided, comparative studies of various numerical methods have not been given.

We thank the Reviewer for the valuable remarks and suggestions that helped us to increase the quality of the manuscript. Please find our point-by-point replies below. We would like to note that the comparison of various numerical methods for the FPI spectrum interrogation was out of the scope of the current manuscript, as it focuses on the ANN implementation in the specific application. Instead, we have added a comparison between various configurations of the ANN in Section 5. A comparative study of various numerical methods applied to the microwave photonic interrogation of the FPI will be conducted in further works.

“ It is demonstrated that the neural network model can accurately predict temperature variations, showcasing the feasibility of combining microwave photonic methods with machine learning for high-precision fiber-optic sensing.” -> It is demonstrated that the artificial neural network implementation can predict temperature variations with accuracy equal ..... (how accurately, give a number ); (the other part of sentence is propaganda).

Thank you for the remark. The sentence was revised as follows: “It is demonstrated that the artificial neural network implementation can predict temperature variations with accuracy equal to 0.018 °С in the range from −10 to ‎ +10 °С, and 0.147 in the range from −15 to ‎ +15 °С.”

Please give a scheme of examined set-up including ANN topology.

Thank you for the suggestion. The scheme of the microwave photonic interrogation approach considered in the manuscript has been added in Section 2, along with the following description:

“The optical frequency comb can be formed using a wideband optical source (denoted as 1 if Figure 1), the radiation from which is reflected from the superstructured fiber Bragg grating 3 (described in details in Paragraph 3.3) and directed to the Fabry–Perot interferometer through the circulators 2 and 4.

The signal reflected from the FPI is directed to the photodetector through the circulator 4. On the photodetector, as on the element with a quadratic transfer characteristic, the cross beating of all frequency components forming the optical frequency comb will be formed, and the frequency of beating components will be a multiple of the frequency spacing of the optical comb. The amplitude of the beating components is a multiple of the product of the amplitudes of the probing components of the optical frequency comb and the Fabry–Perot reflection spectrum. The flat shift of the comb spectrum leads to a change in the resulting amplitudes of the probing radiation and, as a consequence, in the amplitudes of the beating signal at the photodetector’s output. The beating signal is filtered using bandpass filters 7, the number of which corresponds to the number of the considered beating components, and is processed by the analog-to-digital converter 8. The obtained data is processed in the ANN-based unit 9 defining the measured value of temperature.”

The ANN topology is described in Section 5 as flows (lines 349-353): “… a fully connected ANN corresponding to probing with an optical frequency comb containing five frequency components, the input layer of which consisted of 4 neurons, followed sequentially by hidden layers containing 700, 500, 300, and 200 neurons, respectively. The output layer consisted of one neuron.” The authors believe that the inclusion of the scheme in the manuscript depicting all the layers of neurons would be cumbersome.

Please make an investigation of number of required neurons, as number as big as 200 in hidden layers looks much too big.

Thank you for the comment. As we have mentioned in Section 5, various configurations of ANN have been tested in this work. We have listed several of them in newly added Table 1. Please, see the description below:

1) 1 hidden layer of 50 neurons. In this configuration, the minimum value of the loss function during the training process was 0.03. When testing the model, the average deviation of the predicted and true temperatures (mean absolute error) reached 4 °C, which is an unsatisfactory result. Increasing the number of neurons in one hidden layer to 200 did not provide a significant improvement. The value of the loss function during the training process was 0.02. The average deviation of the predicted and true temperatures reached 3.5 °C, which is also unsatisfactory.

2) 2 hidden layers: layer 1 of 50 neurons, layer 2 of 20 neurons. In this ANN configuration, the value of the loss function during the training process was 0.005. But when checking the operation of the model, the average deviation of the predicted and true temperatures reached 1.5 °C, which is also insufficient. But in this case, it can be assumed that increasing the depth of the neural network leads to the increased accuracy.

3) 2 hidden layers: layer 1 of 100 neurons, layer 2 of 50 neurons. In this configuration of the neural network, the value of the loss function during the training process was 0.001. The average deviation of the predicted and true temperatures reached 1 °C.

4) 3 hidden layers: layer 1 of 50 neurons, layer 2 of 20 neurons, layer 3 of 20 neurons. In this configuration of the ANN, the value of the loss function during the training process was 0.0008. But when checking the operation of the model, the average deviation of the predicted and true temperatures reached 0.5 °C, which we also consider insufficient. Increasing the number of neurons in the hidden layers to 150, 100, 50, respectively, did not lead to a significant improvement in the performance of the ANN. The average deviation between the predicted and true temperatures was 0.48 °C.

5) 4 hidden layers consisting of 100, 100, 50 and 50 neurons, respectively. In this configuration of the artificial neural network, the value of the loss function during the training process was 0.0002. When checking the operation of the model, the average deviation of the predicted and true temperatures decreased to 0.39 °C.

6) The configuration used in this study included 4 hidden layers of 700, 500, 300 and 200 neurons, respectively. In this configuration, the value of the loss function during the training process was 0.00005. When checking the operation of the model, the average deviation of the predicted and true temperatures reached 0.147 °C.

7) 4 hidden layers of 1500, 1000, 500 and 400 neurons, respectively. The average deviation of the predicted and true temperatures decreased insignificantly to 0.12 °C. Addition of 1 or 2 layers with various number of neurons did not lead to the improvement of the result.

Therefore, the configuration including 4 hidden layers of 700, 500, 300 and 200 neurons, respectively, was chosen for this study.

Comments on the Quality of English Language

Please see that NN is biological by standard. You write about ANN – artificial neural network.  (title of paper also need correction)

Thank you for the remark. The title and text have been corrected accordingly.

some minor corrections:

 “to create a training sample neural network” -> In my opinion: -> to create a sample for artificial neural network training

Thank you for the suggestion. The sentence was corrected.

Reviewer 2 Report

The manuscript “Enhancing Microwave Photonic Interrogation Accuracy for Fiber Optic Temperature Sensors via Neural Network Integration” proposed a method to enhance the accuracy of temperature measurement using a fiber-optic sensor based on Fabry-Perot interferometer, by combining an optical comb generator in microwave frequency and a neural network to link the signal of the Fabry-Perot interferometer with the electrical signal of the photodetector. The manuscript modelled the signal from each component of the fiber optical temperature sensor, and obtained an accurate temperature detection at 0.08°C after neural network training. Although this work is mainly on theoretical calculation and neural network integration with no experimental results, the researchers did a good work on building the fiber-optical detection model. I would recommend its publication on Optics with the following revisions:

1.       In line 67, “when processing and small number” should be “when processing a small number”.

2.       In line 95, “step of 5-10 GHz (40-80 pm) and full width at half height up to 30-35 GHz (40-80 pm)”, please revise the pm values in the brackets, because different frequency ranges are indicated with the same pm values. Please also indicate what is the optical wavelength used in the modelling of the Fabry-Perot interferometer.

3.       In Section 2, please explain why the microwave applied can further improve the temperature sensor's accuracy. Draw a figure to show the sensor structure and the principle of the work.

4.       In Section 3.2, will the temperature change vary the dielectric constant of the optical fiber? If so, will the ignorance of this optical fiber’s temperature change affect the accuracy of the temperature sensor?

5.       In Figures 1, 3, 4 and 5, the Y-axis should be amplitude of the optical signal, or intensity (which is the square of the amplitude) of the optical signal. If it is a “refractive index”, is it a combined reflective index of the whole system? How is this reflective index calculated?

6.       In line 255, “…ω_k = 2π·с/λ_k is the frequency, Δω = 2π·с/Δλ is the frequency discretization step”, Δω should be calculated by Δω = 2π·с·Δλ /(λ²).

7.       In Figures 6 and 7, the Y-axis should be intensity, not amplitude, because a photodetector’s output is the square of the amplitude.

8.       In Section 5, please indicate the software suite and the neural network algorithm (for example, Convolutional neural network (CNN), Recurrent neural network (RNN), etc.) for training and validation of the temperature sets.

The quality of the English language is fine, which meets the criteria for scientific publication. 

Author Response

The manuscript “Enhancing Microwave Photonic Interrogation Accuracy for Fiber Optic Temperature Sensors via Neural Network Integration” proposed a method to enhance the accuracy of temperature measurement using a fiber-optic sensor based on Fabry-Perot interferometer, by combining an optical comb generator in microwave frequency and a neural network to link the signal of the Fabry-Perot interferometer with the electrical signal of the photodetector. The manuscript modelled the signal from each component of the fiber optical temperature sensor, and obtained an accurate temperature detection at 0.08°C after neural network training. Although this work is mainly on theoretical calculation and neural network integration with no experimental results, the researchers did a good work on building the fiber-optical detection model. I would recommend its publication on Optics with the following revisions:

The authors thank the Reviewer for the valuable comments and suggestions that helped us to improve the quality of the manuscript.

1. In line 67, “when processing and small number” should be “when processing a small number”.

Thank you for the remark. The sentence was corrected.

2. In line 95, “step of 5-10 GHz (40-80 pm) and full width at half height up to 30-35 GHz (40-80 pm)”, please revise the pm values in the brackets, because different frequency ranges are indicated with the same pm values. Please also indicate what is the optical wavelength used in the modelling of the Fabry-Perot interferometer.

Thank you for the careful review. We have corrected the values and indicated the range of the optical wavelength used in the modelling of the Fabry-Perot interferometer (from 1520 nm to 1595 nm).

3. In Section 2, please explain why the microwave applied can further improve the temperature sensor's accuracy. Draw a figure to show the sensor structure and the principle of the work.

Thank you for the suggestion. The scheme of the proposed microwave photonic interrogation approach is presented in Figure 1, along with the supplemented description in Section 2 (lines 95-123): “According to the proposed microwave photonic interrogation approach, the scheme of which is presented in Figure 1, the probing of the FPI the reflection spectrum is carried out by an optical frequency comb including 5-7 optical spectral components in the optical part of the spectrum with a step of 5-10 GHz (40-80 pm) and full width at half height up to 30-35 GHz (240-280 pm). The considered wavelength range of the FPI reflection spectrum is from 1520 nm to 1595 nm. The optical frequency comb can be formed using a wideband optical source (denoted as 1 in Figure 1), the radiation from which is reflected from the superstructured fiber Bragg grating 3 (described in details in Paragraph 3.3) and directed to the Fabry–Perot interferometer through the circulators 2 and 4. The signal reflected from the FPI is directed to the photodetector through the circulator 4. On the photodetector, as on the element with a quadratic transfer characteristic, the cross beating of all frequency components forming the optical frequency comb will be formed, and the frequency of beating components will be a multiple of the frequency spacing of the optical comb. The amplitude of the beating components is a multiple of the product of the amplitudes of the probing components of the optical frequency comb and the Fabry–Perot reflection spectrum. The flat shift of the comb spectrum leads to a change in the resulting amplitudes of the probing radiation and, as a consequence, in the amplitudes of the beating signal at the photodetector’s output. The beating signal is filtered using bandpass filters 7, the number of which corresponds to the number of the considered beating components, and is processed by the analog-to-digital converter 8. The obtained data is processed in the ANN-based unit 9 defining the measured value of temperature. Such microwave photonic interrogation approach does not rely on the spectrometer, the resolution of which is limited by the CCD array, thereby enhancing the maximum achievable measurement resolution.”

4. In Section 3.2, will the temperature change vary the dielectric constant of the optical fiber? If so, will the ignorance of this optical fiber’s temperature change affect the accuracy of the temperature sensor?

As the Reviewer rightly noted, the temperature change does vary the dielectric permittivity of the optical fiber, and it was taken into account during modelling. To clarify this point, the following was added in Section 3.2 (lines 195-196): “The permittivity of the optical fiber ε₁ also has a linear temperature dependence similar to (7) with the temperature coefficient K_ε1.” We also indicated the temperature coefficient of fiber permittivity in line 199: K_ε1 = 8.6×10⁻⁶ T⁻¹.

5. In Figures 1, 3, 4 and 5, the Y-axis should be amplitude of the optical signal, or intensity (which is the square of the amplitude) of the optical signal. If it is a “refractive index”, is it a combined reflective index of the whole system? How is this reflective index calculated?

Thank you for the remark. We have corrected the designation of the Y-axis in Figures 1, 3, 4 and 5, as it characterizes the reflectivity of the considered optical components.

6. In line 255, “…ω_k= 2π·с/λ_k is the frequency, Δω = 2π·с/Δλ is the frequency discretization step”, Δω should be calculated by Δω = 2π·с·Δλ /(λ²).

We thank the Reviewer for the valuable remark. The misprint has been corrected.

7. In Figures 6 and 7, the Y-axis should be intensity, not amplitude, because a photodetector’s output is the square of the amplitude.

Thank you, the designations of the Y-axis in Figures 6 and 7 have been corrected.

8. In Section 5, please indicate the software suite and the neural network algorithm (for example, Convolutional neural network (CNN), Recurrent neural network (RNN), etc.) for training and validation of the temperature sets.

Thank you for the suggestion. We have specified the software in lines 355-356: “The ANN was implemented using Python 3.11 with the TensorFlow library.” The neural network algorithm is specified in lines 349-350: “…a fully connected ANN…”.

Reviewer 3 Report

This manuscript presents a system based on FPE/optical fiber temperature sensor combied with neural network.
The application is meritory but not novel. Nonetheless, it conteins a significant amonth of flaws that not allow to give recommendation for publication on these transactions.
First, the text reminds a final course report than a journal paper.
Second, there are not given enough information to allow the ocasional reader to reproduce the measurements and the NN algorithm.
The spelling of the abstract is poor, not allowed on a jjournal paper.
The major claim about the NN model it is not well described in section 5, lacking full details about the implementation, the availability of coude in Github, and so on.
The major amonth of material is provided describing the Bragg grating with n=4. Moreover, details about the implementation are not provided (OF manufactures/suppliers, references, optical details,....).
The red line in figure 5 is not symetrical around the central wavelenght (seeing at the naked eye) because the RESULTING spectrum is not equal to the product of FPE spectrum with the frequency COMB spectrum (is it what was intended? or what is it? this information os not given).
Looking in the naked eye, the the refarctuce indexes are simple shifts; where are the proofs of this?
Moreover, the measurement setup (for example, which photodetector was used, the OFs, the FBGs, the optical source, the optical circulator, the spectrometer to get the figures 3-6, and so on) and the used instrumentation and components were not provided to allow the ocasional reader to reproduce the experiments, and this is a complicator.

At last but not least, since this was used to measure the temperature, what was the effect of the environmental conditions (especially the environment temperature)? Does the environment temperature, moisture, dust were controlled? Does the environment temperature was the focus for measurements or the sensor is targeted to be applied on more specific application such as on high voltage poles for example? This issue must be clarified.

Extensive editing of English language required.

Author Response

This manuscript presents a system based on FPE/optical fiber temperature sensor combied with neural network.
The application is meritory but not novel. Nonetheless, it conteins a significant amonth of flaws that not allow to give recommendation for publication on these transactions.
First, the text reminds a final course report than a journal paper.

We thank the Reviewer for the valuable remarks and suggestions that helped us to improve the quality of the manuscript.

Second, there are not given enough information to allow the ocasional reader to reproduce the measurements and the NN algorithm.

The authors hope that the amendments introduced after consideration of the comments below, as well as suggestions of other reviewers, provide sufficient information to allow the readers to reproduce the findings of the work.

The spelling of the abstract is poor, not allowed on a jjournal paper.

Thank you for the remark. The abstract has been revised.

The major claim about the NN model it is not well described in section 5, lacking full details about the implementation, the availability of coude in Github, and so on.

Thank you for the comment. The following information has been added in Section 5 (lines 353-356): “The activation function for all hidden layers was LeakyReLU with the negative slope coefficient of 0.3, while for the output layer tanh function was used. The ANN was implemented using Python 3.11 with the TensorFlow library.” The code can be found in Gitlab via the link: https://gitlab.com/MakarovRr/fpi-temperature-model

The major amonth of material is provided describing the Bragg grating with n=4. Moreover, details about the implementation are not provided (OF manufactures/suppliers, references, optical details,....).

Thank you for the suggestion. The spectrum of the described fiber Bragg grating shown in Figure 4 was obtained via numerical simulation. The details were added in lines 225 – 228: “The model was implemented under assumption of the structure implementation within a single-mode optical; fiber with the core refractive index of 1.4586, induced refractive index of 1×10^-4, n = 4, homogeneous segment length 5 mm, grating period of 5.3129×10^-7 m.”

The red line in figure 5 is not symetrical around the central wavelenght (seeing at the naked eye) because the RESULTING spectrum is not equal to the product of FPE spectrum with the frequency COMB spectrum (is it what was intended? or what is it? this information os not given).

Thank you for the remark. Please, note that the red line in Figure 5 (Figure 6 after revisions) is, in fact, part of the FPI spectrum presented in Figure 2 presented in a narrow wavelength range. The resulting spectrum (green line in Figure 6) is the product of the initial frequency comb spectrum (blue line) with the FPI spectrum (red line). Since the slope of the red line is very small, therefore the asymmetry of the amplitudes of the resulting spectrum may not be visible in the naked eye.

Looking in the naked eye, the the refarctuce indexes are simple shifts; where are the proofs of this?

As we mentioned in the previous reply, the amplitudes of the resulting spectrum in Figure 6 are decreased in comparison with the initial frequency comb spectrum in accordance with the Fabry-Perot interferometer spectral response acting as a filter.

Moreover, the measurement setup (for example, which photodetector was used, the OFs, the FBGs, the optical source, the optical circulator, the spectrometer to get the figures 3-6, and so on) and the used instrumentation and components were not provided to allow the ocasional reader to reproduce the experiments, and this is a complicator.

Thank you for the suggestion. We have added a more detailed description of the considered microwave photonic interrogation approach in Section 2. The authors deliberately did not specify the models of the components incorporated in the scheme, as it can be implemented using different components. Figures 3 – 6 (Figures 4 – 7 after revisions) were obtained via numerical simulations conducted in accordance with the mathematical modeling approaches described in the manuscript. It must be noted that the validation of the mathematical models used in this study (such as the transfer matrix method) have been repeatedly conducted by the authors of the manuscript and other research groups (for example, please, refer to http://dx.doi.org/10.3390/a16020101).

At last but not least, since this was used to measure the temperature, what was the effect of the environmental conditions (especially the environment temperature)? Does the environment temperature, moisture, dust were controlled? Does the environment temperature was the focus for measurements or the sensor is targeted to be applied on more specific application such as on high voltage poles for example? This issue must be clarified.

Thank you for the comment. Indeed, Fabry-Perot interferometers are, in general, sensitive to various environmental factors, including moisture, dust, etc. However, the cross-sensitivity of such sensitive elements can be eliminated using various technical solution in the sensor design, such as the materials used, the casing, sensor placement, etc. In this work, it is assumed that the FPI is isolated from all the external factors except temperature variation, and acts only as a temperature sensor. We have added a sentence in the text for clarification (lines 91-93): “In this work, it is assumed that the FPI is isolated from all the external factors, such as humidity, pressure, dust, etc., except for the temperature variation.”. The proposed sensor can be used in various applications, where high-accuracy temperature measurements are required.

Round 2

Reviewer 1 Report

The correction of the work was done correctly. The work is ready for publication.

Reviewer 3 Report

My remarks were addressed.