Performance Prediction Model of Solid Oxide Fuel Cell System Based on Neural Network Autoregressive with External Input Method

Round 1

Reviewer 1 Report

Dear Authors,

the manuscript describe the NNARX method and its application to a SOFC system.

You are kindly suggested to review your original manuscript according to the following comments:

line 73: the authors state: 'The quality prediction performance of the NNARX model of the SOFC system highly depends on architectural parameters'. In order to support the reader, please specify which parameters you refer to.

line 79: please rephrase: ..Taguchi orthogonal (OA)...-> ..Taguchi ortogonal array (OA)...

lines 81-82. The sentence is unclear. Please, rephrase.

line 139: the name of the variables related to the estimated validation prediction and the function of the NNARX structure are missing in the text.

Table 1:

1) please rephrase the caption

2) please rephrase the Levgel-1 and Levgel-2

3) it is unclear what Level-1,-2, and -3 refer to. Please add a description of the data in Table 1

lines 201-202. the sentence is unclear, Please rephrase. Why is it 'unreasonable'?

line 203-204. What is the L9 array? I guess a set of experiments you mention in line 204. Which kind of experiment they are? please specify.

lines 217-218. You mention that the best value for R2 is obtained by applying the approach 1. It is unclear which approach is. Where are the R2 values?

line 224-225: please rephrase.

line 243: the authors state: 'Four factors were conducted according to the parameter structure of NNARX model'. Are these factors the A,B,C,D in Table 1? Please, be clear to help the reader.

line 249: What does A2B2C3D1 refer to? I guess it refers to the combination of A,B,C,D factors in Table 2. Is it correct? in this case, where A=2 and B=2?

lines 273-274. It looks that the content of this sentence has been already stated above.

Table 4: please, set the p-values in scientific format to see some digits.

Lines 277-278. t looks that the content of this sentence has been already stated above.

Best Regards

Author Response

Response to Reviewer 1 Comments

Comments to the Author

Dear Authors, the manuscript describe the NNARX method and its application to a SOFC system. You are kindly suggested to review your original manuscript according to the following comments:

Point 1: line 73: the authors state: 'The quality prediction performance of the NNARX model of the SOFC system highly depends on architectural parameters'. In order to support the reader, please specify which parameters you refer to..

Response 1:

Thanks to the reviewer’s comment, the sentence is revised for readable and marked in red.

Point 2: line 79: please rephrase: ..Taguchi orthogonal (OA)...-> ..Taguchi ortogonal array (OA)...

Response 2:

Thanks to the reviewer’s comment, the statement is revised and marked in red.

Point 3: lines 81-82. The sentence is unclear. Please, rephrase.

Response 3:

Thanks to the reviewer’s comment, the sentence is revised for clearly and marked in red.

 Point 4: line 139: the name of the variables related to the estimated validation prediction and the function of the NNARX structure are missing in the text.

Response 4:

Thanks to the reviewer’s comment, the word is added in manuscript and marked underline in red.

Point 5: Table 1:

1) please rephrase the caption

2) please rephrase the Levgel-1 and Levgel-2

3) it is unclear what Level-1,-2, and -3 refer to. Please add a description of the data in Table 1

Response 5:

• Thanks to the reviewer’s comment, the word is added and marked in red.
• Thanks to the reviewer’s comment, the wrong words are changed and marked in red.
• Thanks to the reviewer’s comment, the Table 1 adds a description of the relevant factors and revised in manuscript in red. Each factor of levels of NNARX model structure parameters selected are described in section 2.2.1, line 168 to line 175 and hidden neurons compute formula according equation (5) and paper references in [32-35].  

Table 1. Factors and levels of NNARX model structure parameter.

Symbol	Factors	Level-1	Level-2	Level-3
A	Hidden neural (hn)	5	10	15
B	Output order (na)	1	3	5
C	Input order (nb)	1	3	5
D	Time delay (nk)	1	3	5

 

Point 6: lines 201-202. the sentence is unclear, Please rephrase. Why is it 'unreasonable'?

Response 6:

Thanks to the reviewer’s comment, the sentence is revised and marked in red for readable.

 

Point 7: line 203-204. What is the L9 array? I guess a set of experiments you mention in line 204. Which kind of experiment they are? please specify. 

Response 7:

Thanks to the reviewer’s comment, the explanation is revised and marked in red and added relevant literatures for readable.

 

Point 8:  lines 217-218. You mention that the best value for R2 is obtained by applying the approach 1. It is unclear which approach is. Where are the R2 values?

Response 8:

Thanks to the reviewer’s comment, the sentence makes confuse easily for reader, so simply modify and marked in red in text. The mathematical formula of R² is described only in this section and computed results shown in Table 5.

 

Point 9: line 224-225: please rephrase.

Response 9:

Thanks to the reviewer’s comment, the sentence is revised for readable and marked in red in text.

Point 10: line 243: the authors state: 'Four factors were conducted according to the parameter structure of NNARX model'. Are these factors the A,B,C,D in Table 1? Please, be clear to help the reader.

Response 10:

Thanks to the reviewer’s comment, the A, B, C, D are really design factors in NNARX model structure shown in Table 1. The sentence is revised for clearly and marked in red in text.

 

Point 11: line 249: What does A2B2C3D1 refer to? I guess it refers to the combination of A,B,C,D factors in Table 2. Is it correct? in this case, where A=2 and B=2?

Response 11:

Thanks to the reviewer’s comment, the OA matrix symbol in Table 2 was modified within level number to avoid confusion. The A, B, C, D are design factors and Arabic numeral is level of each factor as shown in Table 1. The A2B2C3D1 means the combination of experimental number in OA5 for (A) hidden units (hn=10, level-2), (B)output order (na=3, level-2), (C)input order ( nb=5, level-3) (D)time delay (nk=1,level-1). Table 2 is revised to clearly as below:

 

Point 12: lines 273-274. It looks that the content of this sentence has been already stated above.

Response 12:

Thanks to the reviewer’s comment, the statement maybe redundant and delete for clearly.

  

Point 13:Table 4: please, set the p-values in scientific format to see some digits.

Response 13:

Thanks to the reviewer’s comment, the value has revised based on comment.

 

Point 14: Lines 277-278. t looks that the content of this sentence has been already stated above.

Response 14:

Thanks to the reviewer’s comment, the statement maybe redundant and delete for clearly.

Author Response File: Author Response.pdf

Reviewer 2 Report

The submitted article is original and I suggest it for publication after some changes.

 

Lines 73-75 Which background do you mean about “ a very limited technical background”? I would disagree with this sentence if it is related to the technical background of the SOFC performance model. On my opinion ANN are useful to define black box models when it is not possible to define a mathematical model, but it is necessary to know which variables could describe the problem;

 

Lines 100-103 Please modify the sentence. When I read the first time the entire section, I was looking for the description of the long-term test. It seemed also that ref 31 describes only the SOFC cell. When I read more times this chapter I realized that ref 31 do not explain only SOFC cells but also performed the long-term test.

 

Lines 112-113 Is sccm standard cubic centimeters per minute? Please use SI units.

 

Line 121 why training phase and validation phase was defined in this way? Why dataset was not split randomly?

 

Line 160 Were data of each variables normalized? If yes, why normalization did you use? Also I would suggest to show a figure of the ANN proposed.

 

Line 200 It seems something is missing, the sentence starts with “ and”

 

Line 275 which is the value of p-value? I think it is not 0 but very close, use scientific notation

 

Line 331 It seems that ANN has not predict correctly some values between 0.804 and 0.805, is it correct? Did you investigate why?

Author Response

Response to Reviewer 2 Comments

Comments to the Author

The submitted article is original and I suggest it for publication after some changes.

Point 1: Lines 73-75 Which background do you mean about “ a very limited technical background”? I would disagree with this sentence if it is related to the technical background of the SOFC performance model. On my opinion ANN are useful to define black box models when it is not possible to define a mathematical model, but it is necessary to know which variables could describe the problem;

Response 1:

Thanks to the reviewer’s comment, this sentence focused on accurate NNARX model structure parameter selection can help the prediction performance for SOFC system more efficiently. The sentence is revised to avoid confusion and marked in red.  

Point 2: Lines 100-103 Please modify the sentence. When I read the first time the entire section, I was looking for the description of the long-term test. It seemed also that ref 31 describes only the SOFC cell. When I read more times this chapter I realized that ref 31 do not explain only SOFC cells but also performed the long-term test.

Response 2:

Thanks to the reviewer’s comment, the sentence is revised and marked in red.

Point 3: Lines 112-113 Is sccm standard cubic centimeters per minute? Please use SI units.

Response 3:

Thanks to the reviewer’s comment, the sccm is indeed standard cubic centimeters per minute. According the comment suggestion, the statement is revised in SI units and marked in red.

Point 4: Line 121 why training phase and validation phase was defined in this way? Why dataset was not split randomly?

Response 4:

Thanks to the reviewer’s comment, according to the literature of Ljung [32] presented, once the dataset have been collected then after separated data to identify the process efficiently, to the first two thirds were to estimate the model parameter and remaining one third of data were for model validation. Randomly divided dataset are suitable for discontinuous and insufficient to avoid miss information; however, the voltage dataset of SOFC system are sufficient and continuity time-series. All information of degraded performance in SOFC system has been included in dataset. Thus, the dataset divided into selected according the definition of literature proposed and not randomly in this work.

The added cited literature has been listed in reference and described as below:

[32] L. Ljung, “System Identification: Theory for User,” Prentice –Hall, Upper Saddle River, 1999.

Point 5: Line 160 Were data of each variables normalized? If yes, why normalization did you use? Also I would suggest to show a figure of the ANN proposed.

Response 5:

Thanks to the reviewer’s comment, the dataset were normalized in the prior of identification by zero-mean normalization and ANN of ARX model architecture is added in figure 3 based on the comment. 

Point 6: Line 200 It seems something is missing, the sentence starts with “ and”

Response 6:

Thanks to the reviewer’s comment, the statement has revised for readable and marked in red.

Point 7: Line 275 which is the value of p-value? I think it is not 0 but very close, use scientific notation

Response 7:

 Thanks to the reviewer’s comment, the value has revised based on comment.

Point 8: Line 331 It seems that ANN has not predict correctly some values between 0.804 and 0.805, is it correct? Did you investigate why?

Response 8:

Thanks to the reviewer’s comment, the results of optimal set (A2B3C3D1) during multi-step process have been demonstrated that the performance metric shown in Table 5 about RMSE, MAE, MAPE and R2 are very well than original OA5. From the figure 9 shows the results of regression values close to 1 provide the output best performance. For realizing clearly, we plot all the multi-step error of optimal test model as below shown, thus, the obvious error during 950 to 1000 hours but still within adequate and reasonable.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Dear Authors,

thanks a lot for the answers to my comments.

The original manuscript has been reviewed accordingly and I have no comments on the actual version of the paper.

 

Best regards