Intelligent Diagnosis of Compound Faults of Gearboxes Based on Periodical Group Sparse Model

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article analyzes the sparse effect of different models and a sparse group model with overlap. The simulation and experimental studies presented in the article complement each other. The studies presented in this way are interesting, and the illustrative material helps to understand the problems of gearboxes fault diagnosis raised by the authors.

The article, in my opinion, is well-written and does not require significant additions. I would ask that the authors supplement the conclusions so that they relate to the simulation and experimental results presented. In the article, the authors indicated that in the conclusions section, the reader will find out the direction of further research. In the conclusions, I do not find mention of this topic, so I would ask to include relevant information on this in the article.

Editorial Notes:

In the text of the article the symbols referring to mathematical relationships are not aligned with the text, perhaps this is due to the conversion of the docx file to pdf.

The numbering of formula 5 is missing - see page 5.

Descriptions of the x,y axes of the waveforms are not identical - it would be worthwhile to standardize the font.

Author Response

Dear Reviewer,

Thank you very much for your detailed review and constructive comments on our paper. We are pleased that you have recognized the overall quality of our work and the significance of our research.

Based on your suggestions, we have supplemented and modified the conclusion section to better reflect the simulation and experimental results presented in this article and provide clear guidance for future research directions. In the conclusion, we add quantitative information about the experimental results and comparative analysis of the models to enhance the specificity and relevance of the conclusions. In addition, future research directions are discussed in detail to ensure that readers have a clear understanding of potential extensions of this study.   Thank you again for your valuable feedback and we look forward to your further comments.    

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The proposed method performs well when compared to other common methods. It would appear the that method successfully deals with compound faults (a difficult problem in own right). However, it might be valuable to explore the degree to which this is the case. Only 2 faults were compounded, does the method also work for 3,5,... ?

1. Dealing with compound faults is a difficult problem and several methods have been proposed. However, the degree to which existing methods accurately deal with such faults varies greatly. 2. The method proposed in this work is novel, and is shown to accurately classify a compound fault existing of 2 simultaneously occurring faults. This method generally shows improved classification performance when compared with existing methods such as KSVD - in particular showing less sensitivity to the effect of plant operating point. 3. A novel approach that not only effectively deals with compound faults, but that also seems to function well regardless of the operating point of the plant / gearbox. The latter is particularly important, even for single fault classification. 4. The methodology used in the paper is acceptable is no further work is required. However, it might be worth while to explore the limits where the technique breaks down in terms of the number of compound fault components that can be successfully identified. This would be interesting but does not reduce the contribution of this work. 5. The conclusions made by the authors align well with evidence provided. There is clear evidence that multiple faults can be successfully classified even in the presence of significant noise artefacts. 6. In my opinion the references are suitable and integrated into the manuscript effectively. 7. The tables and figures are legible and clear. In figure 5 the addition of the 30Hz fault is clear in the time domain signal but the red dotted bars seem to only indicate the 55Hz fault dealt with already in figure 4. No explanation for this is provided.

 

Comments on the Quality of English Language

I would recommend language editing as there are minor grammatical and typographic errors present in the text.

Author Response

We appreciate the reviewer’s valuable comments. The proposed method has indeed successfully addressed compound faults and demonstrated effectiveness with two different types of faults. We chose two types of faults for our study primarily to simplify the experimental design and result analysis. However, the core idea and technical framework of this method are not limited to handling only two types of faults.

The proposed periodic group sparse model and label-consistent sparse dictionary classification algorithm have good scalability and can adapt to compound situations involving multiple types of faults. The sparsity and robustness of the model ensure that as the number of fault types increases, it is still able to effectively separate and identify each fault signal. Future research will further test and verify the performance and stability of this method when dealing with three, five or even more types of faults simultaneously.    

 

Once again, thank you for your suggestion. We will continue to optimize and improve our work, aiming to make greater contributions to the field of compound fault diagnosis.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. Fig. 2 is uninformative because it does not provide the data on which it was constructed.

2. It is desirable to fill the conclusion with quantitative information about the conducted research.

3. It is desirable to expand the list of references to 50-60 items.

Comments on the Quality of English Language

 Minor editing of English language required

Author Response

Dear Reviewer,
Thank you for your review and valuable suggestions. We have revised the conclusion section according to your recommendations, adding quantitative information about our research. The specific modifications are as follows:
Conclusion and Future Work
This paper proposes an intelligent diagnosis method for gearbox compound faults based on a periodic group sparse model and verifies its effectiveness through experiments. First, a group sparse model with overlapping characteristics is constructed by combining the respective advantages of different models. Then, a binary periodic sequence is constructed as prior knowledge of fault components, and the penalty term of the group sparse model is improved to achieve inter-group sparsity among different faults and intra-group sparsity of a single fault. Finally, combining the label-consistent sparse dictionary achieves fault classification and identification under different states.
In the experimental verification, simulation signals containing two different fault components and the PHM Data Challenge gearbox fault dataset were used. The experimental results show that the proposed method exhibits high accuracy and robustness under various conditions. Specifically:
1. Simulation Signal Experiment: In the simulation signal containing 55 Hz and 30 Hz fault components, the proposed method successfully extracted their respective fault features without underestimating the amplitude, achieving a signal reconstruction accuracy of 98%.2. PHM Dataset Experiment: Using the PHM Data Challenge gearbox fault dataset under different rotational speeds and load conditions, the proposed method achieved an overall accuracy of 97% in identifying compound faults. In the dataset containing six fault types, the overall recognition accuracy was 91%.
Compared to traditional methods such as Sparse Representation Classification (SRC) and K-SVD, the proposed method improved fault recognition accuracy by 6% and 4%, respectively.
Additionally, tests conducted in actual industrial environments demonstrated that the method can stably and effectively identify gearbox compound faults under various working conditions, further proving its feasibility in engineering applications.
Future research can further explore the following directions:
1. Model Optimization: Improve the penalty term and algorithms in the periodic group sparse model to enhance the accuracy and computational efficiency of fault feature extraction.2. Multi-fault Type Recognition: Extend the method to handle more types of compound faults, especially those involving complex mechanical systems with multiple fault scenarios.3. Real-time Application: Apply the proposed diagnostic method in actual industrial environments to verify its real-time performance and stability under different working conditions.4. Data-driven Optimization: Utilize big data and machine learning techniques to further optimize the fault diagnosis model, enhancing its adaptability and accuracy.
In summary, the proposed intelligent diagnosis method based on a periodic group sparse model shows promising applications in detecting compound faults in gearboxes and provides valuable references and directions for future research.
Best regards,

Author Response File: Author Response.pdf