Partial Discharge Signal Denoising Algorithm Based on Aquila Optimizer–Variational Mode Decomposition and K-Singular Value Decomposition
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper proposed denoising method using AO-VMD and K-SVD algorithms. In the manuscript authors demonstrated excellent noise reduction. The proposed algorithm outperform other denoising strategies.
The manuscript is well organized and scientifically sound. It meets the requirement for publication.
Author Response
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Reviewer 2 Report
Comments and Suggestions for AuthorsPaper Summary: Partial Discharge Signal Denoising Algorithm Based on AO-VMD and K-SVD
The article deals with a new method, which is composed of two algorithms, for detecting partial discharges (PD) in insulation of electrical equipment. He approaches the problem as follows:
1 – A signal without PD noise is generated;
2 – Noise is added to this signal from step 1;
3 – The AO-VMD algorithm is applied to remove a portion of the noise;
4 – The K-SVD algorithm (singular value decomposition (SVD)
) is applied to remove the remainder of the noise from step 3, reconstructing the original PD signal.
Thus, the article is basically composed of two algorithms. The first algorithm is Variational Mode Decomposition (VMD), which is an improvement on the Empirical Modal Decomposition (EMD) algorithm for filtering noise in signals. The VMD will decompose a real-valued signal into K modes. The sum of these K modes must be equal to the original signal. In this way, an optimization problem with an equality constraint is generated, but using the Lagrangian with a penalty factor α, this problem is converted into an unconstrained problem. In this way, the meta-heuristic optimization algorithm Aquila Optimizer (AO), which is based on the hunting behavior of eagles, is employed to search for optimal solutions, with the aim of optimizing the parameters K and α. Thus, the noisy signal is decomposed into several modes and reconstructed, while still maintaining some level of noise.
The second algorithm is K-SVD (singular value decomposition), which is a dictionary learning algorithm and which will also solve an optimization problem with the objective of reconstructing the original PD signal. That is, a signal is compressed and represented by a sparse linear combination of basis functions (known as atoms) that are collected in a dictionary. Thus, this algorithm contains two main components, the creation of this dictionary and the sparse decomposition over it.
To prove the efficiency of the proposed method, computational simulations are carried out with 4 different types of functions that will be added with two different types of noise. In addition to this simulation, a field test is carried out with a real PD signal. Initially, the authors show how the AO-VMD algorithm is superior for removing certain noise from a signal, compared to other methods such as Fast Fourier Transform (FFT), Short-Time Fourier Transform (STFT) and EMD. Because all three of these methods were not able to remove the noise and at the same time maintain some characteristic of the original PD signal. In Figure 7, the authors illustrate how AO-VDM achieves both goals. Finally, in Figure 8, it is illustrated how the K-SVD algorithm manages to reconstruct the original PD signal quite faithfully, observing how they overlap and their spectrum is very similar.
Another simulation carried out by the authors is to compare the proposed method with other methods found in the literature. Figure 10 contains an illustration of this result. Showing that the proposed method can very efficiently remove noise from a signal. The method that came closest to it was the Wavelet transform method, but this still maintains some noise in the time domain. And in Figure 11 you can find the results of the four metrics used in the work, root mean square error (RMSE), signal-to-noise ratio (SNR), waveform similarity coefficient (NCC), and noise reduction ratio (NRR). In all these metrics, with the exception of RMSE, the method proposed by the authors obtained better results than those compared.
Finally, this same comparison of the proposed method with other methods in the literature was carried out with a real PD signal. Once again, K-SVD proved to be superior, with only the Wavelet transform method having similar results.
Regarding some errors: Check the “Notes paper applsci-2892483-peer-review-v1” attached file, there are several errors that can and need to be corrected.
Regarding organization: The article is well-organized with an explanatory summary. However, I missed the introduction of a brief paragraph describing each topic section to make it easier to read the article and search for information.
Regarding grammar: The text is in readable English, is well written with small inconsistencies, and is as easy as possible to understand.
Regarding the Figures and Tables sampled in the text: Check the file “Notes paper applsci-2892483-peer-review-v1”. In general, many Figures need to be improved, as their quality is very poor to view.
Regarding the conclusion: It is consistent with the objective that was presented during the work. It showed that the proposed method was superior for removing noise in PD signals.
Regarding a possible improvement: Finally, I missed a comparison of the computational effort of this method with others, since to apply it, several optimization problems are solved, which I imagine is computationally expensive. The Wavelet transform method obtained a similar result, and is perhaps simpler to apply.
In summary, the work is interesting and very relevant to the issue of noise removal in PD signals. He brought a good bibliographical review, a new method and made comparisons of this method with others previously published. The method was applied to both computationally generated signals and a real signal, showing the effectiveness of noise removal in both cases.
However, as listed in this review, some issues need to be clarified and some corrections need to be made. All these corrections are in the “Notes paper applsci-2892483-peer-review-v1” file.
Comments for author File: Comments.pdf
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsI have the following comments and recommendations for the paper:
— Abstract: There are many (many!) abbreviations that are not defined here (AO-VMD, K-SVD, etc.), and many of them are not probably known to all readers. Moreover, the work procedure is not explained sufficiently clearly in my opinion. Therefore, the abstract is not readable and must be totally rewritten.
— Introduction: Here, the abbreviations are well defined. The introduction itself seems to me quite brief, however, there are sufficient number of references here. However, I am a little in a doubt whether the state-of-the-art is sufficiently described here in these several paragraphs only.
— Basic theory: First of all, the equations are typed quite nicely. However, some symbols should be better explained because they could be unfamiliar to readers (e.g., ||^2_2, s.t. (subject to?), delta_t, µ^^ (Fourier transformation, how precisely?)). Generally speaking, I expected a little more detailed and clearer description.
— Line 66: “where” should not be indented, use \noindent
— 2.1.2, using the Aquila optimizer: There are really many meta-heuristic and non-meta-heuristic optimization algorithms nowadays. How can you be sure that the chosen AO one is the optimal selection for your problem? Did you try other algorithms as well?
— 106: Use \noindent as well
— 107: How the standard deviation (sigma) is defined?
— 112: Please cite where the Sparse Dictionary Learning can be found for a first info about this method.
— 119, 136: Again, \noindent
— 137: Please cite where Frobenius norm can be found. And why this norm has been selected? (The norms could be more precisely defined in the paper, in my opinion.)
— (10) and (12): “subject to” should be written in Roman letters (not Italics, they are not variables)
— IMPORTANT: Regarding all figures: They are too small. Why didn't use the full page width? In the MDPI template, it is possible:
\begin{figure}[H]
\begin{adjustwidth}{-\extralength}{0cm}
\centering
\scalebox{}{\includegraphics{}}
\end{adjustwidth}
\caption{This is a wide figure.\label{}}
\end{figure}
or
\begin{figure}[H]
\begin{adjustwidth}{-\extralength}{0cm}
\resizebox{\textwidth+\extralength}{!}{\includegraphics{}} %+ OK!
\end{adjustwidth}
\caption{}
\label{}
\end{figure}
%\unskip
(You can learn it from the MDPI template…)
— Flowcharts in Figure 1 and Figure 2 have different style. Maybe the style could be uniform in one article…
— Please cite Short-Time Fourier Transform (not all readers know it)
— Figure 6 is really small, please use the full page width as recommended above.
— The same for Figure 9.
— Equation (14): When I program such relation, I always include some correction (repairing) of the denominator to prevent a division by a very small number (or even zero). How do you operate this?
— Figure 10 is small, Figure 11 is extremely small, please enlarge!
— Figure 13 represents the achievements of this article very well (and please enlarge it as well).
— Again regarding abbreviations (305--307). They are defined here, OK. However, the Abstract is frequently used alone, without the rest of the paper. Therefore, really, I think the Abstract should be autonomous, independent on the abbreviations defined elsewhere.
— 308: Please delete a remainder of the template (Appendix A)!
— References looks well.
Generally, it is clear that the authors are well-founded and the suggested method is working as shown in Figure 13, e.g. However, the paper needs many improvements in the way how it is written and how the things are explained.
Comments on the Quality of English LanguageIt seems to me that English is quite OK.
Author Response
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Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThis work is scientifically very sound. The analysis and methods are confirmed by means of numerical simulation and measurements.
For the additional benefit of the readers could you please show the accuracy and convergence for the optimized number of K modal functions, when this number is reduced by 10%, as well as when
it is somewhat increased (increased by 10% with respect to the determined optimal K).
Author Response
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Author Response File: Author Response.pdf
