Research on rolling bearing fault diagnosis based on multi-dimensional feature extraction and evidence fusion theory

Rolling bearing failure is the main cause of failure of rotating machinery, and leads to huge economic losses. The demand of the technique on rolling bearing fault diagnosis in industrial applications is increasing. With the development of artificial intelligence, the procedure of rolling bearing fault diagnosis is more and more treated as a procedure of pattern recognition, and its effectiveness and reliability mainly depend on the selection of dominant characteristic vector of the fault features. In this paper, a novel diagnostic framework for rolling bearing faults based on multi-dimensional feature extraction and evidence fusion theory is proposed to fulfil the requirements for effective assessment of different fault types and severities with real-time computational performance. Firstly, a multi-dimensional feature extraction strategy on the basis of entropy characteristics, Holder coefficient characteristics and improved generalized box-counting dimension characteristics is executed for extracting health status feature vectors from vibration signals. And, secondly, a grey relation algorithm is used to calculate the basic belief assignments (BBAs) using the extracted feature vectors, and lastly, the BBAs are fused through the Yager algorithm for achieving bearing fault pattern recognition. The related experimental study has illustrated the proposed method can effectively and efficiently recognize various fault types and severities in comparison with the existing intelligent diagnostic methods based on a small number of training samples with good real-time performance, and may be used for online assessment.

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We look forward to receiving your resubmission. Comments to the Author(s) The authors aim to propose an online bearing fault diagnosis, however, the content of the paper did not organise in that way. The content of the paper described a typical bearing faults classification by multi-dimensional features.
1. The paper aims to solve the problem that the traditional time and frequency domain methods are not easy to make an accurate assessment of the health status of rolling bearings. However, the authors did not clearly describe the problems of the traditional time and frequency domain methods. Is that difficulty in extracting useful information from a noisy or nonlinear vibration signal? If yes, please compare/cite the renowned researches in this field.
2. Yager algorithm seems to be the main classifier in the bearing faults classification, however, the description of the Yager algorithm is not available. Please explain how Yager algorithm was adapted into this study.
3. Partial data was used to develop the model, and remaining data was used to test the model. Cross-validation such as k-fold cross-validation is recommended to btain an average accuracy instead of signle accuracy value to test the model ability in actual practical environment.
4. The paper was written in a readable English, but it is not free from grammartical or spelling error such as healthy status vs. health status. Thus, linguistic assistance may required.

Reviewer: 2
Comments to the Author(s) A hybrid method combining Multi-dimensional feature extraction mehtod and gray relation algorithm (GRA) is proposed to realize rolling bearing fault diagnosis. Actually, these algorithms have been used by previous researchers for denoising, signal decomposition and envelope analysis, respectively, which could be found in available literature. All of the algorithms used in the manuscript are proposed by other researchers. This reviewer could not find any novelty of the proposed algorithm from the manuscript.

Reviewer: 3
Comments to the Author(s) The authors of this manuscript proposed a novel rolling bearing fault diagnostic method, in which, multi-dimensional features: entropy characteristics, Holder coefficient characteristics and improved generalized box-counting dimension characteristics were extracted to form the knowledge base. And secondly a gray relation algorithm was used to acquire basic belief assignments, and at last the basic belief assignments were fused through Yager algorithm for achieving bearing fault pattern recognition intelligently. This work has some interesting innovations and conclusions. In my opinion, it can be accepted after minor revisions. The specific needs to be revised are as follows: 1 The grammar and some sentences need further modification and improvement. 2 Some sentences are not concise enough. 3 The bearing data from Case Western Reserve University Bearing Data Center is too old and very easy to classify, hence, I suggest a new dataset to illustrate your model. 4 The time cost of the proposed method is 0.016 seconds. It cannot just rely on this to show that your method is suitable for on-line bearing fault diagnosis.

RSOS-181488.R0
Review form: Reviewer 1 Is the manuscript scientifically sound in its present form? Yes

Recommendation? Accept as is
Comments to the Author(s) All previous comments have been addressed by the authors.

Recommendation?
Major revision is needed (please make suggestions in comments)

Comments to the Author(s)
In the revised manuscript, there seems to be no response to the questions raised before. The following questions are outstanding. 1. The authors aim to propose an online bearing fault diagnosis. However, the content of the paper did not organise in that way. 2．According to the extracted features, the good classification results can be achieved by using Holder coefficients. As shown in Figure 5, Holder coefficients are completely separable under different operating conditions. 3. From the characteristics of different fault level of severity, the fusion features seem indistinguishable. Because there is a common overlap and confusion area between the 3 characteristics.

04-Dec-2018
Dear Dr Ying, The Subject Editor assigned to your paper ("Research on rolling bearing fault diagnosis based on multi-dimensional feature extraction and evidence fusion theory") has now received comments from reviewers. We would like you to revise your paper in accordance with the referee and Associate Editor suggestions which can be found below (not including confidential reports to the Editor). Please note this decision does not guarantee eventual acceptance.
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Once again, thank you for submitting your manuscript to Royal Society Open Science and I look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. Comments to the Author(s) In the revised manuscript, there seems to be no response to the questions raised before. The following questions are outstanding. 1. The authors aim to propose an online bearing fault diagnosis. However, the content of the paper did not organise in that way. 2．According to the extracted features, the good classification results can be achieved by using Holder coefficients. As shown in Figure 5, Holder coefficients are completely separable under different operating conditions. 3. From the characteristics of different fault level of severity, the fusion features seem indistinguishable. Because there is a common overlap and confusion area between the 3 characteristics.

Reviewer: 1
Comments to the Author(s) All previous comments have been addressed by the authors.
1. The paper aims to solve the problem that the traditional time and frequency domain methods are not easy to make an accurate assessment of the health status of rolling bearings. However, the authors did not clearly describe the problems of the traditional time and frequency domain methods. Is that difficulty in extracting useful information from a noisy or nonlinear vibration signal? If yes, please compare/cite the renowned researches in this field. Answer: The background introduction of the paper has been modified, thanks for your advice! 2. Yager algorithm seems to be the main classifier in the bearing faults classification, however, the description of the Yager algorithm is not available. Please explain how Yager algorithm was adapted into this study. Answer: The description of the Yager algorithm has beed added in the paper, thanks for your advice! 3. Partial data was used to develop the model, and remaining data was used to test the model. Cross-validation such as k-fold cross-validation is recommended to obtain an average accuracy instead of signle accuracy value to test the model ability in actual practical environment. Answer: The modification has been made in the paper.
The diagnostic results from Table 2 show that the detecting success rate for bearing faulty conditions can reach 100%, with the total fault pattern recognition success rate almost 99.09% based on a small number of training samples, which shows a certain improvement in diagnostic accuracy compared with the existing intelligent diagnostic methods from references [33], [34] and [35]. The time cost of the proposed method through a laptop computer with a 4.0 GHz dual processor for one Test Case is only 0.016 seconds. The time consumption of the proposed approach is encouraging, and the proposed method may be suitable for on-line bearing fault diagnosis. For supplementary verification, the k-fold cross validation is performed for those 550 data samples and the average success rate is 100% for 10-fold cross validation, and the average success rate is 99.98% for 5-fold cross validation. 4. The paper was written in a readable English, but it is not free from grammartical or spelling error such as healthy status vs. health status. Thus, linguistic assistance may required. Answer: The linguistic modification has been made in the paper. Thanks for your advice!

Reviewer: 2
Comments to the Author(s) A hybrid method combining Multi-dimensional feature extraction mehtod and gray relation algorithm (GRA) is proposed to realize rolling bearing fault diagnosis. Actually, these algorithms have been used by previous researchers for denoising, signal decomposition and envelope analysis, respectively, which could be found in available literature. All of the algorithms used in the manuscript are proposed by other researchers. This reviewer could not find any novelty of the proposed algorithm from the manuscript. Answer: With the development of artificial intelligence, the procedure of rolling bearing fault diagnosis is more and more treated as a procedure of pattern recognition, and its effectiveness and reliability mainly depend on the selection of dominant characteristic vector of the fault features. In the paper, a novel diagnostic framework for rolling bearing faults based on multi-dimensional feature extraction and evidence fusion theory, is proposed to fulfill the requirements for effective assessment of different fault types and severities with real-time computational performance.  Table 2 show that the detecting success rate for bearing faulty conditions can reach 100%, with the total fault pattern recognition success rate almost 99.09% based on a small number of training samples, which shows a certain improvement in diagnostic accuracy compared with the existing intelligent diagnostic methods from references [33], [34] and [35]. The time cost of the proposed method through a laptop computer with a 4.0 GHz dual processor for one Test Case is only 0.016 seconds. The time consumption of the proposed approach is encouraging, and the proposed method may be suitable for on-line bearing fault diagnosis. For supplementary verification, the k-fold cross validation is performed for those 550 data samples and the average success rate is 100% for 10-fold cross validation, and the average success rate is 99.98% for 5-fold cross validation.

Reviewer: 3
Comments to the Author(s) The authors of this manuscript proposed a novel rolling bearing fault diagnostic method, in which, multi-dimensional features: entropy characteristics, Holder coefficient characteristics and improved generalized box-counting dimension characteristics were extracted to form the knowledge base. And secondly a gray relation algorithm was used to acquire basic belief assignments, and at last the basic belief assignments were fused through Yager algorithm for achieving bearing fault pattern recognition intelligently. This work has some interesting innovations and conclusions. In my opinion, it can be accepted after minor revisions. The specific needs to be revised are as follows: 1 The grammar and some sentences need further modification and improvement. Answer: The linguistic modification has been made in the paper. Thanks for your advice! 2 Some sentences are not concise enough. Answer: The related modification has been made in the paper. Thanks for your advice! 3 The bearing data from Case Western Reserve University Bearing Data Center is too old and very easy to classify, hence, I suggest a new dataset to illustrate your model. Answer: This bearing database from Case Western Reserve University Bearing Data Center is a classical database, which has been widely used for testing the effectiveness of the proposed diagnostic methods by researchers, seen in "Reference". And in order to comparison with the existing intelligent diagnostic methods, we used this bearing database to test our proposed method. Thanks for your advice! Manuscript title: Research on rolling bearing fault diagnosis based on multi-dimensional feature extraction and evidence fusion theory Dear editor, Thank you for your useful comments and suggestions on our manuscript. We have modified the manuscript accordingly, and the detailed corrections are listed below: Reviewer(s)' Comments to Author: Reviewer comments to Author: Reviewer: 2 Comments to the Author(s) In the revised manuscript, there seems to be no response to the questions raised before. The following questions are outstanding. 1.The authors aim to propose an online bearing fault diagnosis. However, the content of the paper did not organise in that way. Answer: We have modified our paper title from "Research on rolling bearing on-line fault diagnosis based on multi-dimensional feature extraction and Dempster-shafer Evidence theory" into "Research on rolling bearing fault diagnosis based on multidimensional feature extraction and evidence fusion theory" so as to fit for the content of the paper. 2.According to the extracted features, the good classification results can be achieved by using Holder coefficients. As shown in Figure 5, Holder coefficients are completely separable under different operating conditions. Answer: From Fig.4, Fig.5 and Fig.6, the Holder coefficient characteristics show a better inter-class separation and intra-class polymerization than entropy characteristics and improved generalized box-counting dimension characteristics extracted from the bearing vibration signals with different fault types. We have modified this part in paper.
3. From the characteristics of different fault level of severity, the fusion features seem indistinguishable. Because there is a common overlap and confusion area between the 3 characteristics. Answer: From Fig.4, Fig.5 and Fig.6, the Holder coefficient characteristics show a better inter-class separation and intra-class polymerization than entropy characteristics and improved generalized box-counting dimension characteristics extracted from the bearing vibration signals with different fault types. However, from Fig.8, Fig.9 and Fig.10, the improved generalized box-counting dimension characteristics show a better inter-class separation than entropy characteristics and Holder coefficient characteristics extracted from the bearing vibration signals with different severities. As entropy characteristics, Holder coefficient characteristics and improved generalized boxcounting dimension characteristics show their strengths and weaknesses in classifying