An Extreme Learning Machine for the Simulation of Different Hysteretic Behaviors

Round 1

Reviewer 1 Report

A novel method based on a combination of extreme learning machine (ELM) and least-squares support vector machine (LS-SVM) is presented for the simulation of hysteresis with different properties. This manuscript is with novelty. Some minor issues should be revised before its acceptance.

 

1.       The internal uncertainties and external disturbance of the model should be given.

 

2.       The description of the experiment is too little, it should be supplemented and explain what factors in the actual experiment are ignored by the simulation.

 

3.       The regularization can be referred to some recent progress, such as “A novel uncertainty-oriented regularization ……”, etc.

 

4.       Does model uncertainty have an impact on the results? Authors can be referred “A novel load-dependent sensor placement method ……”.

 

5.       Why is the internal and external relationship of the experimental and simulated curves like Figure 13?

 

6.       All the pictures in this manuscript are not clear enough. Please polish them.

 

7.       Future research efforts can be appropriately predicted.

Author Response

Dear Editor,

Thank you for giving us the opportunity to submit a revised draft of our manuscript titled “An Extreme Learning Machine for the simulation of different hysteretic behaviors”, Manuscript Number: applsci-1986613, to Applied Sciences. We appreciate the time and effort that you and the reviewers have dedicated to providing your valuable feedback on our manuscript. We are grateful to the reviewers for their insightful comments on our paper. We have been able to incorporate changes to reflect the suggestions provided by the reviewers. We highlighted the changes by using the track changes mode in MS Word within the manuscript.

Here is a point-by-point response to the reviewers’ comments and concerns:

Comments and Suggestions for Authors

A novel method based on a combination of extreme learning machine (ELM) and least-squares support vector machine (LS-SVM) is presented for the simulation of hysteresis with different properties. This manuscript is with novelty. Some minor issues should be revised before its acceptance.

1. The internal uncertainties and external disturbance of the model should be given.

These have been elaborated in the revised version as much as possible.

2. The description of the experiment is too little; it should be supplemented and explain what factors in the actual experiment are ignored by the simulation.

 

The authors did not conduct any experiments in this research study. The experimental data was extracted from other research studies, and they were cited accordingly.

 

3. The regularization can be referred to some recent progress, such as “A novel uncertainty- oriented regularization ……”, etc.

This has been elaborated in the revised version as much as possible.

4. Does model uncertainty have an impact on the results? Authors can be referred “A novel load-dependent sensor placement method ……”.

This has been elaborated in the revised version as much as possible.

5.      Why is the internal and external relationship of the experimental and simulated curves like Figure 13?

The curves compare the experimental results of Ref. [33] with the output obtained from this article. In Figure 13, the response of the proposed ELM-SVM model has been compared with the experimental data that has not already contributed to the training phase.

6.      All the pictures in this manuscript are not clear enough. Please polish them.

The pictures in this article have been revised, and polished pictures have been replaced.

7.      Future research efforts can be appropriately predicted.

The following paragraph has been added to the end of the conclusion section:

The proposed ELM-SVM model has been assessed on different hysteretic behaviors from different fields of engineering in this paper. However, further assessments and application of this proposed model on hysteresis control and compensation remain open for future research.

 

Reviewer 2 Report

(1) Many expressions in English need to be improved.

(2) In general, the least square method will result in over-fitting. Why use the extreme learning machine?

(3) Many symbols need to be explained. For example, in equations (1)-(3) and “pf” on line 3 of section 2. The description of section 2 is unclear.

(4) In section 3, the extreme learning machine with only one hidden layer has calculation cost less than those with many hidden layers, but its simulation accuracy will be worse than the others. Check equation (6) and provide relevant conditions.

(5) Also many symbols need to be explained in section 4. Check equation (11). The “y” may contain noises and thus the solution to (11) will be unreliable. The description of section 4 is unclear.

(6) How to convert the multi-value mapping of hysteresis relation into a single-value mapping?

(7) How to use the neural network of the extreme learning machine to predict outputs corresponding to inputs which are untrained?

(8) How to combine the extreme learning machine with the least-square support vector machine?

(9) In figures 5-14, what are the experimental data from? Please explain the experiment. The hysteresis behavior depends on simultaneously displacement and velocity. Please explain that in the relevant description and results. What are the extreme learning machine and support vector machine used in section 6? Please provide them in details.

Author Response

Dear Editor,

Thank you for giving us the opportunity to submit a revised draft of our manuscript titled “An Extreme Learning Machine for the simulation of different hysteretic behaviors”, Manuscript Number: applsci-1986613, to Applied Sciences. We appreciate the time and effort that you and the reviewers have dedicated to providing your valuable feedback on our manuscript. We are grateful to the reviewers for their insightful comments on our paper. We have been able to incorporate changes to reflect the suggestions provided by the reviewers. We highlighted the changes by using the track changes mode in MS Word within the manuscript.

Here is a point-by-point response to the reviewers’ comments and concerns

 

Comments and Suggestions for Authors

• Many expressions in English need to be improved.

The English of the paper has been improved.

(2) In general, the least square method will result in over-fitting. Why use the extreme learning machine?

In extreme learning machine models, some parameters are chosen randomly. As explained in the article, the deteriorating stopping operator is used to convert the multi-value mapping into a single-valued mapping. Inspiring by the extreme learning machine model, the free parameters of DS neurons are set randomly. The role of the extreme learning machine model is only in the random selection of parameters.

As in LS-SVM the number of adjustable parameters depends on the training sample number, and there is a regularization parameter  in its formulation, it is not prone to overfitting. Thus, the proposed ELM-SVM benefits this property.   

(3) Many symbols need to be explained. For example, in equations (1)-(3) and “pf” on line 3 of section 2. The description of section 2 is unclear.

The symbols in this section were explained, and the unclear ones were corrected. DS operator has been proposed in Ref. [22]. Hence, in section 2 of the manuscript, the DS operator has been introduced briefly, and the readers refer to Ref. [22] for more details.

(4) In section 3, the extreme learning machine with only one hidden layer has calculation cost less than those with many hidden layers, but its simulation accuracy will be worse than the others. Check equation (6) and provide relevant conditions.

The equations of the ELM in the manuscript were redundant. Thus, they have been removed in the revision. The only similarity between the conventional ELM and the proposed ELM-SVM model is to randomly set the free parameters of the first hidden layer in both models. There exists a clear explanation in this regard in the manuscript. 

(5) Also, many symbols need to be explained in section 4. Check equation (11). The “y” may contain noises and thus the solution to (11) will be unreliable. The description of section 4 is unclear.

Section 4 has been revised to be clear.

(6) How to convert the multi-value mapping of hysteresis relation into a single-value mapping?

As discussed in section 5 in the ELM-SVM model, the main role of the first hidden layer that enjoys the DS neurons is to convert the hysteresis into a one-to-one mapping. This converted one-to-one mapping is learned by the subsequent LS-SVM layer in the model.

(7) How to use the neural network of the extreme learning machine to predict outputs corresponding to inputs which are untrained?

In this manuscript, the conventional ELMs have not been directly adopted in ELM-SVM model. In ELM-SVM model the free parameters of the first hidden layer that includes DS neurons have been set randomly as in ELM.

(8) How to combine the extreme learning machine with the least-square support vector machine?

ELM-SVM Model has been described in section 5. The architecture of the proposed model has been depicted in Figs 3 & 4.

(9) In figures 5-14, what are the experimental data from? Please explain the experiment. The hysteresis behavior depends on simultaneously displacement and velocity. Please explain that in the relevant description and results. What are the extreme learning machine and support vector machine used in section 6? Please provide them in details.

In this article, the experimental data of other authors have been used, which are referenced by mentioning the source. And the results obtained from the proposed model have been compared with them, and their results are shown in the article.

 

 

Reviewer 3 Report

The paper presents a very interesting topic. The methodology is clearly described and the results are shown. 

Author Response

 

	Yes	Can be improved	Must be improved	Not applicable
Does the introduction provide sufficient background and include all relevant references?	(x)	( )	( )	( )
Are all the cited references relevant to the research?	(x)	( )	( )	( )
Is the research design appropriate?	( )	(x)	( )	( )
Are the methods adequately described?	( )	(x)	( )	( )
Are the results clearly presented?	(x)	( )	( )	( )
Are the conclusions supported by the results?	(x)	( )	( )	( )

Comments and Suggestions for Authors

The paper presents a very interesting topic. The methodology is clearly described and the results are shown. 

No actions needed

Round 2

Reviewer 2 Report

Several expressions may need to be improved further. Coordinate labels of some figures need to be added.

Author Response

Thnak you.  We addressed those minor changes that you had requested.