CEEMDAN-MRAL Transformer Vibration Signal Fault Diagnosis Method Based on FBG
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper proposes a CEEMDAN-MRAL fault diagnosis method for transformer vibration signals using FBG sensing, combining CEEMDAN-based denoising, MTF image conversion, and a hybrid CNN-LSTM model. While the approach demonstrates high accuracy (97.94%) and efficiency (training time: 1705s), several concerns and questions require clarification to ensure the validity, novelty, and generalizability of the results. I recommend major revision to address the concerns below before acceptance.
- The CEEMDAN-wavelet threshold denoising and MTF-based image conversion are presented as key contributions. However, similar denoising strategies (e.g., CEEMDAN with wavelet thresholding) and time-series-to-image transformations (e.g., Gramian Angular Field, STFT spectrograms) have been widely explored in prior literature. What specific improvements or adaptations distinguish this work from existing methods?
- The paper states that signals were collected from a 110kV transformer. Are the results generalizable to other voltage levels or transformer types? Cross-validation across diverse datasets is missing.
- The MRAL-Net uses a fixed learning rate (0.0001) and batch size (32). Was hyperparameter tuning (e.g., learning rate schedules, batch size optimization) performed? How were overfitting risks mitigated (e.g., dropout, regularization)?
- Equation (6)–(8): The derivation of acceleration from FBG wavelength shift lacks clarity. How were parameters like Young’s modulus (E) and cantilever dimensions determined?
Author Response
Comments 1:The CEEMDAN-wavelet threshold denoising and MTF-based image conversion are presented as key contributions. However, similar denoising strategies (e.g., CEEMDAN with wavelet thresholding) and time-series-to-image transformations (e.g., Gramian Angular Field, STFT spectrograms) have been widely explored in prior literature. What specific improvements or adaptations distinguish this work from existing methods?
Response 1:Thank you for pointing this out. We agree this comments.We have made explanations according to the comments. The explanation for this question is as follows:
The traditional CEEMDAN-wavelet threshold method mostly uses a single index (such as correlation coefficient or permutation entropy) to screen IMF components, but this work introduces the joint criterion of sample entropy, variance contribution rate and correlation coefficient threshold to improve the accuracy of component classification.
Different from the Gramian Angle Field (GAF) or STFT spectrograms, MTF captures the state transition probability and dynamic evolution characteristics of time series by constructing a Markov state transition matrix. Benefits include:
1.The core idea of the Markov Transfer Field (MTF) is to convert time series data into images by constructing a state transition probability matrix for time series. Its key advantage is that it can simultaneously capture both the short-term dynamics and the long-term evolution of the sequence.
2.The Gramian Angular Field (GAF) maps time series into angles through polar coordinate transformations to generate Gramian Angular Fields. Its essence is static geometric relation encoding.
Comments 2:The paper states that signals were collected from a 110kV transformer. Are the results generalizable to other voltage levels or transformer types? Cross-validation across diverse datasets is missing.
Response 2:Thank you for pointing this out. We agree this comments.We have made explanations according to the comments. The explanation for this question is as follows:
The core frequency components of the transformer vibration signal are dominated by the magnetostriction of the iron core (the fundamental frequency is 100Hz, which is derived from the frequency doubling of the 50Hz system frequency) and the electromagnetic force of the winding (the fundamental frequency is 50Hz), and its frequency characteristics are strictly bound to the system frequency. The transformers of different voltage levels are all running at the system frequency of 50Hz, and the fundamental frequency of the vibration signal is consistent with the harmonic distribution mode.The CEEMDAN-wavelet threshold denoising method and MFT image conversion method can effectively alleviate this problem for the following reasons:
1.Denoising algorithms (e.g., CEEMDAN-wavelet threshold) rely on frequency separation characteristics and are insensitive to linear scaling of amplitude (difference in vibration amplitude caused by different voltage levels).
2.MTF image conversion generates a probability matrix through state interval division (relative value discretization), andthe effect of amplitude is eliminated through the normalization of probabilities, and the consistency of state transition probabilities is maintained.
Comments 3:The MRAL-Net uses a fixed learning rate (0.0001) and batch size (32). Was hyperparameter tuning (e.g., learning rate schedules, batch size optimization) performed? How were overfitting risks mitigated (e.g., dropout, regularization)?
Response 3:Thank you for pointing this out. We agree this comments.We have clarified and modified it according to your comments. The explanation is as follows:
MRAL-Net uses a fixed learning rate (0.0001) and batch size (32) and does not perform traditional hyperparameter optimizations for the following reasons:
1.Using the Adaptive Optimization Algorithm (Adam), its built-in momentum estimation and parameter-by-parameter learning rate adjustment functions can automatically adapt to gradient changes, reducing the dependence on manually adjusted learning rates.
2.A fixed learning rate of 0.0001 can maintain a fast convergence speed and stability, and avoid oscillation caused by too large learning rate or stagnation caused by too small a learning rate.
3.The training batch uses 32 compared with 16 and 64, and 32 makes the training process converge more quickly and more gently.
MRAL-Net's measures to mitigate the risk of overfitting are as follows:
1.The batch normalization (BN) added to the mixed residual structure normalizes each layer, reduces the shift of internal variables in the calculation process, and the batch normalization has a regularization effect, effectively avoiding the risk of overfitting.
2.Due to the sufficient amount of data and sufficient diversity, there was no fitting problem during the training process.
Changes are as follows:
Revised in lines 348-350:
Due to the sufficient amount of data, the training batch of 32 can ensure the rapid convergence and the robustness after convergence，learning rate is set to 0.0001 to ensure good convergence speed and stability, and to avoid oscillation and stagnation caused by the change of learning rate.
Comments 4:Equation (6)–(8): The derivation of acceleration from FBG wavelength shift lacks clarity. How were parameters like Young’s modulus (E) and cantilever dimensions determined?
Response 4:Thank you for pointing this out. We agree this comments,we have revised them according to your comments and introduced a reference for your reference.we have re-derived the formula and replaced Figure 2, and for the Young's modulus it is determined by the manufacturer, for which we have introduced a reference for your reference.("High-Frequency Optical Fiber Bragg Grating Accelerometer," https://doi.org/10.1109/JSEN.2018.2833885)
Changes are as follows:
Revised in lines 129-144:
The FBG accelerometer converts the acceleration into the axial strain of the FBG by the displacement of the cantilever beam and mass, as shown in Fig. 2(a).Inside there is a metal mass and optical fiber with FBG,the FBG leaves interference fringes on the fiber core by the phase mask method,the metal capillary is used as a cantilever beam,the exterior is encapsulated by a metal case.where the relationship between strain and acceleration is represented by equation (6),where F is the inertial force received by the mass, as shown in Fig. 2(b),It is adsorbed on the surface of the transformer by strong magnetism.S and E are the cross-sectional area of the cantilever beam and the Young's modulus,Since the two FBGs are under the same temperature conditions,Therefore, the effect of temperature on the amount of wavelength change can be ignored,as shown in equation (7),From equation (6) and equation (7),the relationship between the wavelength offset and the acceleration of the two FBGs can be deduced, as shown in equation(8)[24].
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper presents a transformer fault detection model and FBG based system with high prediction accuracy. The work is promising; however, I suggest the following revisions be addressed before the paper can be considered for publication:
- Line 305: In addition to the textual description, it is recommended to include a photograph of the actual experimental setup, as well as a real picture of how the sample is physically fixed to the transformer and in line 125 how the FBG accelerometer is made regarding the materal, the fabrication and packaging process. This would significantly enhance the credibility of the experimental procedure. Additionally, in line 51, other studies have explored the application of FBG sensors (https://doi.org/10.1109/JSEN.2023.3343604, https://doi.org/10.1109/JSEN.2025.3551206). The specific contribution or gap addressed by this paper should be clearly articulated.
- Fig. 2 – FBG Acceleration Sensing Schematic: In addition to the schematic diagram, it would be beneficial to provide real photographs of the actual FBG demodulation system.
- Data Classification: The training dataset is categorized into normal, winding loose, iron core loose, and both winding and core loose conditions. However, these classifications seem vague. It is important to specify the criteria used to define "looseness"—for example, what qualifies as "loose," how it is detected or induced in the transformer, and how the degree of looseness is measured or quantified, and again, it would be better to add real pictures of the actual loose conditions.
- Signal Acquisition: What is the sampling rate used for signal acquisition in the FBG demodulation process? This is critical for evaluating the resolution and fidelity of the captured vibration signals.
- Figures and Equations Formatting: Figures 6 and 7, as well as some equations throughout the manuscript, should be properly centered.
Author Response
Comments 1:In addition to the textual description, it is recommended to include a photograph of the actual experimental setup, as well as a real picture of how the sample is physically fixed to the transformer and in line 130 how the FBG accelerometer is made regarding the materal, the fabrication and packaging process. This would significantly enhance the credibility of the experimental procedure. Additionally, in line 51, other studies have explored the application of FBG sensors (https://doi.org/10.1109/JSEN.2023.3343604, https://doi.org/10.1109/JSEN.2025.3551206). The specific contribution or gap addressed by this paper should be clearly articulated.
Response 1:Thank you for pointing this out.We agree with this comment.We have made changes and explanations according to the comments. The explanation for this question is as follows:
In order to enhance the credibility of the experimental procedure, we have attached a photograph of the experimental setup and a real picture of the fixed position of the sensor (Figures4, and 5),And the following explanation was made(Revised in lines 155-158).We provide a description of the materials, manufacturing, and packaging processes of the accelerometer as required (Revised in lines 130-133) and we have explained the specific contributions and problems solved in this article (lines 51-56).
Changes are as follows:
Revised in lines 163 and 165 add Figure 4-5：
Fig. 4 Vibration signal demodulation system
Fig.5 Fixed position of the sensor
Revised in lines (155-158) illustrates Figure 4-5:
The demodulation system of the vibration signal is shown in Figure 4, the NLL, EOM and PG in Figure 3 are integrated in the light source transmitter, the EDFA, Coupler, Circulator and PD are integrated in the demodulation device, the signal acquisition device and the PC are used for signal acquisition, preprocessing and fault diagnosis, and the sensor installation location is shown in Figure 5.
Revised in line 142 modified Figure 2(a) add Figure 2(b)
(a) (b)
Fig. 2. Schematic diagram(a) and physical diagram(b) of FBG acceleration induction
Revised in lines (130-134) describes the materials, fabrication, and packaging of FBG accelerometers:
Inside there is a metal mass and optical fiber with FBG,the FBG leaves interference fringes on the fiber core by the phase mask method,the metal capillary is used as a cantilever beam,the exterior is encapsulated by a metal case.where the relationship between strain and acceleration is represented by equation (6),where F is the inertial force received by the mass, as shown in Fig. 2(b),It is adsorbed on the surface of the transformer by strong magnetism.
Revised in lines (51-56) adds to the contribution of this article and addressed the issues:
Through its anti-interference, high sensitivity and distributed monitoring capabilities, FBG accelerometers solve the problems of electromagnetic interference, environmental adaptability and multi-point deployment in vibration monitoring, Combined with the signal processing method and fault diagnosis model proposed in this paper, it is universally applicable to the fault diagnosis of power transformer vibration signals, which effectively avoids noise interference and improves the accuracy of fault diagnosis.
Comments 2:In addition to the schematic diagram, it would be beneficial to provide real photographs of the actual FBG demodulation system.
Response 2:Thank you for pointing this out.We agree with this comment.We quite agree with your point of view. We have made changes according to the comments.
Changes are as follows:
Revised in line 163 Figure 4：
Fig. 4 Vibration signal demodulation system
Revised in lines (155-157) illustrates Figure 4
The demodulation system of the vibration signal is shown in Figure 4, the NLL, EOM and PG in Figure 3 are integrated in the light source transmitter, the EDFA, Coupler, Circulator and PD are integrated in the demodulation device, the signal acquisition device and the PC are used for signal acquisition, preprocessing and fault diagnosis.
Comments 3:The training dataset is categorized into normal, winding loose, iron core loose, and both winding and core loose conditions. However, these classifications seem vague. It is important to specify the criteria used to define "looseness"—for example, what qualifies as "loose," how it is detected or induced in the transformer, and how the degree of looseness is measured or quantified, and again, it would be better to add real pictures of the actual loose conditions.
Response 3:Thank you for pointing this out.We agree with this comment.The definition of "loose" is indeed important，We have made changes according to the comments.
According to DL/T 573-2021 Power Transformer Maintenance Guidelines and DL/T 573-2010 Power Transformer Maintenance Guidelines。The definition of core loosening is that the loosening of the clamp or core fastening device and the loosening of individual fasteners of the silicon steel sheet lead to core structure loosening, significantly increasing the low-frequency component at 200Hz.Winding loosening refers to the loosening between coils caused by insulation aging, and the composition of 300-600HZ is significantly increased, and the amplitude of 100HZ composition is reduced by about 30%.For the photos of loose windings and cores, because it is difficult to visually observe the looseness, the power transformer needs to be sent back to the manufacturer, and the manufacturer will disassemble the various parts of the transformer, and we cannot keep the photos.
Changes are as follows:
Revised in lines(326-329):Due to the loosening of the clamp or core hold-down device, and the loosening of individual fasteners of the silicon steel sheet, the 200HZ component will increase significantly, and this kind of signal is attributed to the loosening of the core.The loosening between coils caused by aging insulation can lead to a significant increase in the 300-600Hz component, which is attributed to loose windings.
Comments 4:What is the sampling rate used for signal acquisition in the FBG demodulation process? This is critical for evaluating the resolution and fidelity of the captured vibration signals.
Response 4: Thank you for your very valuable comments.
We apologize for any confusion caused by our settings regarding the sampling rate, which may not be apparent, in line 324 we set the sample rate to 10kHZ.
Comments 5:Figures 6 and 7, as well as some equations throughout the manuscript, should be properly centered.
Response 5: Thank you for your very valuable comments. We agree with this comment.We have centered the full-text formula and image based on your opinion.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsMy concerns have been resolved.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe author has addressed my comments, and the manuscript is ready for publication.
