A New Latin Hypercube Sampling with Maximum Diversity Factor for Reliability-Based Design Optimization of HLM
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper presents a novel Latin Hypercube Sampling with Maximum Diversity Factor to improve performance in quantifying uncertainty and reducing computation time. However, following are some comments for the authors,
1. The novelty of this research is not clear from the abstract and its reflection can be improved in the conclusion section as well.
2. Some of the sentences in the paper are long in length and have complex structure, which makes them hard to follow.
3. Some references are cited at multiple places in the introduction section. It would be better to cite one paper at one place.
4. Sub figures of Figure 1 are not explained in the text.
5. The explanation of the results presented in the tables can be improved.
6. Figure 4 is can be improved, because it is blurred in the present form.
7. Is there any unit of the parameters presented in the Tables?
8. Each figure's results should be explained separately for clarity.
Author Response
The paper presents a novel Latin Hypercube Sampling with Maximum Diversity Factor to improve performance in quantifying uncertainty and reducing computation time. However, following are some comments for the authors,
1. The novelty of this research is not clear from the abstract and its reflection can be improved in the conclusion section as well.
Answer: Thank you for your suggestion. We have improved the abstract and conclusion.
2. Some of the sentences in the paper are long in length and have complex structure, which makes them hard to follow.
Answer: Thank you for your suggestion. We have improved and proofreading by an expert.
3. Some references are cited at multiple places in the introduction section. It would be better to cite one paper at one place.
Answer: Thank you for your suggestion. We have improved.
4. Sub figures of Figure 1 are not explained in the text.
Answer: Thank you for your suggestion. We have corrected.
5. The explanation of the results presented in the tables can be improved.
Answer: Thank you for your suggestion. We have improved.
6. Figure 4 is can be improved, because it is blurred in the present form.
Answer: Thank you for your suggestion. We have improved.
7. Is there any unit of the parameters presented in the Tables?
Answer: Thank you for your suggestion. We have added.
8. Each figure's results should be explained separately for clarity.
Answer: Thank you for your suggestion. We have added more explanation.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper introduces a novel Latin Hypercube Sampling method, termed LHSMDF, for uncertainty quantification and computational time reduction in reliability-based design optimization. The method has demonstrated satisfactory performance in the testing of mechanical components and has been applied in the design of a six-bar high-lift mechanism. It enhances the reliability of the mechanism while ensuring the precision and accuracy in the manufacturing process. However, there are areas that require improvement, including:
1. ‘The definition of Mm is presented in Fig 2’, I think it is the definition of d.
2. Although the LHSMDF method mentioned in Section 2.2.1 can improve computational efficiency, it does not provide specific quantitative data on computational time and efficiency gains. This may make it challenging to evaluate the method's performance and reliability in practical applications.
3. Section 4.2 lacks a comparative and analytical discussion on uncertainty quantification methods. There is no detailed comparison of the advantages and disadvantages of LHS and ATLBO-DA methods with other uncertainty quantification methods and optimization algorithms. For instance, a discussion on the merits and drawbacks of other uncertainty quantification methods (such as Monte Carlo simulation) compared to the LHSMDF method is not provided. This may make it difficult to assess the applicability and effectiveness of these methods.
4. Other sampling methods should be compared, such as orthogonal sampling, stratified sampling, and optimized Latin hypercube sampling.
5. How can we determine that Pf, calculated using the LHS and LHSMDF methods, is more accurate? Generally, a benchmark is obtained using Monte Carlo simulations with a very large number of samples (over 1E7 generally). Thus, the resulting higher efficiency can also be problematic.
6. Currently, for reliability problems, there are adaptive sampling methods with higher local sensitive sampling density, such as active learning Bayesian methods and Kriging methods. These methods actively seek sampling points near the failure domain or around G(x) = 0. How do you evaluate these methods?
7. Formatting: 1. There are many unnecessary spaces in the abstract, please check and correct them. 2. The font of the caption for Figure 2 is different; please ensure consistency. 3. Please maintain consistency in the parentheses format within the text, as there is inconsistency between lines 153 and 158. 4. Lines 177 and 178 (O2B) are unclear due to formatting issues. 5. In line 190, please ensure the units are consistent, such as 0° to 360°. 6. Please maintain consistency in italicizing variables throughout the article. For example, in line 257, (τ) should be italicized. 7. Please enhance the clarity of (b) in Figure 4.
Comments for author File: Comments.pdf
Minor revisions
Author Response
This paper introduces a novel Latin Hypercube Sampling method, termed LHSMDF, for uncertainty quantification and computational time reduction in reliability-based design optimization. The method has demonstrated satisfactory performance in the testing of mechanical components and has been applied in the design of a six-bar high-lift mechanism. It enhances the reliability of the mechanism while ensuring the precision and accuracy in the manufacturing process. However, there are areas that require improvement, including:
- The definition of Mmis presented in Fig 2’, I think it is the definition of d.
Answer: Thank you for your suggestion. We have improved.
- Although the LHSMDF method mentioned in Section 2.2.1 can improve computational efficiency, it does not provide specific quantitative data on computational time and efficiency gains. This may make it challenging to evaluate the method's performance and reliability in practical applications.
Answer: Thank you for your suggestion. We have added computational time in Table 1-4 and added more explanation in the discussion part.
- Section 4.2 lacks a comparative and analytical discussion on uncertainty quantification methods. There is no detailed comparison of the advantages and disadvantages of LHS and ATLBO-DA methods with other uncertainty quantification methods and optimization algorithms. For instance, a discussion on the merits and drawbacks of other uncertainty quantification methods (such as Monte Carlo simulation) compared to the LHSMDF method is not provided. This may make it difficult to assess the applicability and effectiveness of these methods.
Answer: Thank you for your suggestion. We have added experimental results by MCS.
- Other sampling methods should be compared, such as orthogonal sampling, stratified sampling, and optimized Latin hypercube sampling.
Answer: Thank you for your suggestion. We have added testing with OLHS.
- How can we determine that Pf, calculated using the LHS and LHSMDF methods, is more accurate? Generally, a benchmark is obtained using Monte Carlo simulations with a very large number of samples (over 1E7 generally). Thus, the resulting higher efficiency can also be problematic.
Answer: Thank you for your suggestion. This is our aim.
- Currently, for reliability problems, there are adaptive sampling methods with higher local sensitive sampling density, such as active learning Bayesian methods and Kriging methods. These methods actively seek sampling points near the failure domain or around G(x) = 0. How do you evaluate these methods?
Answer: Thank you for your suggestion. Due to the limitation of the present study, we can extend to address the issue in the future.
- Formatting:
- There are many unnecessary spaces in the abstract, please check and correct them.
Answer: Thank you for your suggestion. We have addressed.
- The font of the caption for Figure 2 is different; please ensure consistency.
Answer: Thank you for your suggestion. We have addressed.
- Please maintain consistency in the parentheses format within the text, as there is inconsistency between lines 153 and 158.
Answer: Thank you for your suggestion. We have addressed.
- Lines 177 and 178 (O2B) are unclear due to formatting issues.
Answer: Thank you for your suggestion. We have addressed.
- In line 190, please ensure the units are consistent, such as 0°to 360°.
Answer: Thank you for your suggestion. We have addressed.
- Please maintain consistency in italicizing variables throughout the article. For example, in line 257, (τ) should be italicized. 7. Please enhance the clarity of (b) in Figure 4.
Answer: Thank you for your suggestion. We have improved.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsIn this manuscript, a new Latin hypercube sampling strategy is proposed and integrated into the reliability-based design optimization for the issue of a six-bar high lift mechanism. The inconsistency of the symbol system used in this paper leads to confusion in understanding. Besides, some concepts and definitions related to reliability or optimization are incorrect. The reviewer would like to point out several key mistakes for the authors to improve this manuscript.
1. The symbol “n”. There are many “n”s having different meanings in this paper. For instance, in Line 129 it stands for the dimensionality of input random variables, while it becomes the number of g functions in Eq. (20), or the sampling number in Tables 1 to 3.
2. What is the meaning of “var 1” and “var 2” in Eq. (3)? The variance? Of what?
3. The definition of the reliability index in Eq. (20) is wrong.
4. Please check the distribution of F. The current expression is F ~ N(14.01×105, 3.11×104), but I guess it should be like F ~ N(14.01e5, 3.11e4). Meanwhile, what’s the meaning of “(pf = 0.0926)” in Line 275? The failure probability? Via what methods? Monte Carlo simulation?
Some technical issues:
1. There is no theoretical proof on the new Latin hypercube sampling strategy. However, this is the backbone of the work and should be illustrated in detail.
2. Continuously, the failure probabilities in the three test examples are too big. For such issues there are many advancing point selection strategies, e.g., importance sampling, GF-discrepancy minimization, line sampling, etc.
3. The reviewer can only see the Gaussian distribution utilized in all presented examples. Please add more applications considering other distributions.
Author Response
In this manuscript, a new Latin hypercube sampling strategy is proposed and integrated into the reliability-based design optimization for the issue of a six-bar high lift mechanism. The inconsistency of the symbol system used in this paper leads to confusion in understanding. Besides, some concepts and definitions related to reliability or optimization are incorrect. The reviewer would like to point out several key mistakes for the authors to improve this manuscript.
- The symbol “n”. There are many “n”s having different meanings in this paper. For instance, in Line 129 it stands for the dimensionality of input random variables, while it becomes the number of gfunctions in Eq. (20), or the sampling number in Tables 1 to 3.
Answer: Thank you for your suggestion. We have addressed the mistake.
- What is the meaning of “var 1” and “var 2” in Eq. (3)? The variance? Of what?
Answer: Thank you for your suggestion. We have added an explanation.
- The definition of the reliability index in Eq. (20) is wrong.
Answer: Thank you for your suggestion. We have addressed the mistake.
- Please check the distribution of F. The current expression is F~ N(14.01×105, 3.11×104), but I guess it should be like F ~ N(14.01e5, 3.11e4). Meanwhile, what’s the meaning of “(pf = 0.0926)” in Line 275? The failure probability? Via what methods? Monte Carlo simulation?
Answer: Thank you for your suggestion. We have addressed the mistakes.
Some technical issues:
- There is no theoretical proof on the new Latin hypercube sampling strategy. However, this is the backbone of the work and should be illustrated in detail.
Answer: Thank you for your suggestion. We have addressed the issue by adding more comparative experiments in Table 1-4.
- Continuously, the failure probabilities in the three test examples are too big. For such issues there are many advancing point selection strategies, e.g., importance sampling, GF-discrepancy minimization, line sampling, etc.
Answer: Thank you for your suggestion. We have addressed the issue by adding more comparative experiments with OLHS in Table 1-3.
- The reviewer can only see the Gaussian distribution utilized in all presented examples. Please add more applications considering other distributions.
Answer: Thank you for your suggestion. Due to the limitations of the present study, we can extend to address the issue in the future.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThe paper in its current form is of low quality, and does not warrant journal publication.
The title is misleading. At first I thought that HLM stands for Hierarchical Linear Models (there is also a HLM software - see: https://ssicentral.com/index.php/products/hlm-general/ )
Consider instead "A New Latin Hypercube Sampling with Maximum Diversity Factor for Reliability-Based Design Optimization" or "A New Latin Hypercube Sampling with Maximum Diversity Factor for Reliability-Based Design Optimization with Applications"
The authors define too many abbreviations in the text which makes reading difficult. Limit them to only 2 or 3 which occur multiple times in the text.
On line 128 there is an equation embedded in the text, but subscripts (or lack of) and fonts do not match equation (3).
Line 144-145 reads "...which is expected to better reflect." This sentence is incomplete
Figure 3: Please use accepted notations for pin joints and for ground pin joints. It was nowhere explained in the paper which link is associated with the flight control surface of the aircraft and where the input is. Best is if you can show a drawing of the real mechanism with the flight-control surfaces and input actuator visible.
Lines 216-217: "...to create a visual mechanism" What is a visual mechanism??
Line 261: "The resultant tensile stress at the highest stress point is given by Equation (25)" Note that Equation (25) is the von Misses equivalent stress (no a "resultant tensile stress"), valid for ductile steel, but not for some cast irons.
Line 280-284: The performance function, g(X), for all test problems is given by: EQUATION (28) where Sigma_a represents the allowable stress of the connecting rod. A contradiction here!!!!
Not clear why the cantilever and connecting rod were introduced! These examples were not fully developed.
REGARDING CONNECTING RODS, PLEASE NOTE THAT THEY FAIL MAINLY DUE TO BUCKLING IN PLASTIC RANGE (JOHNSON PARABOLA) - SEE ALSO PICTURES:
https://en.m.wikipedia.org/wiki/File:Bent_connecting_rod_1.JPG
https://en.m.wikipedia.org/wiki/File:Bent_connecting_rod_2.JPG
Not clear what Figures 5 and 7 show. Two overlapped positions of the optimized mechanism in Figure 3? Please use accepted symbols for joints and ground joints.
REFERENCES:
Use the Cite function in Google Scholar to verify references. I found three references (and for sure there are more) where you used the given names and abbreviated names with initials.
Ref. 8 should be: Mardani Najafabadi, M. and Taki, M., 2020. Robust data envelopment analysis with Monte Carlo simulation model for optimization the energy consumption in agriculture. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, pp.1-15.
Ref. 10 should be: Abyani, M. and Bahaari, M.R., 2020. A comparative reliability study of corroded pipelines based on Monte Carlo Simulation and Latin Hypercube Sampling methods. International Journal of Pressure Vessels and Piping, 181, p.104079.
Ref. 14 should be: Liaw, H.C., Shirinzadeh, B. and Smith, J., 2008. Robust motion tracking control of piezo-driven flexure-based four-bar mechanism for micro/nano manipulation. Mechatronics, 18(2), pp.111-120.
Comments on the Quality of English Language
I doubt this manuscript was read by all co-authors.
Author Response
1.The paper in its current form is of low quality, and does not warrant journal publication.
Answer: Thank you for your suggestion. We have upgraded the paper to meet with the quality of this journal.
- The title is misleading. At first I thought that HLMstands for Hierarchical Linear Models(there is also a HLM software - see: https://ssicentral.com/index.php/products/hlm-general/ )
Consider instead "A New Latin Hypercube Sampling with Maximum Diversity Factor for Reliability-Based Design Optimization" or "A New Latin Hypercube Sampling with Maximum Diversity Factor for Reliability-Based Design Optimization with Applications"
Answer: Thank you for your suggestion. The title of the present paper fits with our research aims.
- The authors define too many abbreviations in the text which makes reading difficult. Limit them to only 2 or 3 which occur multiple times in the text.
Answer: Thank you for your suggestion. The abbreviations have limited for some necessary in used to make the size of this paper is in compact as much as possible.
- On line 128 there is an equation embedded in the text, but subscripts (or lack of) and fonts do not match equation (3).
Answer: Thank you for your suggestion. We have corrected.
- Line 144-145 reads "...which is expected to better reflect." This sentence is incomplete
Answer: Thank you for your suggestion. We have addressed.
- Figure 3: Please use accepted notations for pin joints and for ground pin joints. It was nowhere explained in the paper which link is associated with the flight control surface of the aircraft and where the input is. Best is if you can show a drawing of the real mechanism with the flight-control surfaces and input actuator visible.
Answer: Thank you for your suggestion. We have corrected.
- Lines 216-217: "...to create a visual mechanism" What is a visual mechanism??
Answer: Thank you for your suggestion. We have corrected.
- Line 261: "The resultant tensile stress at the highest stress point is given by Equation (25)" Note that Equation (25) is the von Misses equivalent stress (no a "resultant tensile stress"), valid for ductile steel, but not for some cast irons.
Answer: Thank you for your suggestion. We have corrected.
- Line 280-284: The performance function, g(X), for all test problemsis given by: EQUATION (28) where Sigma_a represents the allowable stress of the connecting rod. A contradiction here!!!!
Answer: Thank you for your suggestion. We have corrected.
- Not clear why the cantilever and connecting rod were introduced! These examples were not fully developed.
Answer: Thank you for your suggestion. We have addressed.
- REGARDING CONNECTING RODS, PLEASE NOTE THAT THEY FAIL MAINLY DUE TO BUCKLING IN PLASTIC RANGE (JOHNSON PARABOLA) - SEE ALSO PICTURES:
https://en.m.wikiped-ia.org/wiki/File:Bent_connecting_rod_1.JPG
https://en.m.wikipedia.org/wiki/File:Bent_connecting_rod_2.JPG
Answer: Thank you for your suggestion. We have added more explanation of the test problem.
- Not clear what Figures 5 and 7 show. Two overlapped positions of the optimized mechanism in Figure 3? Please use accepted symbols for joints and ground joints.
Answer: Thank you for your suggestion. We have added more explanation of the figures.
- REFERENCES:
Answer: Thank you for your suggestion. We have corrected all mistakes.
Use the Cite function in Google Scholar to verify references. I found three references (and for sure there are more) where you used the given names and abbreviated names with initials.
Ref. 8 should be: Mardani Najafabadi, M. and Taki, M., 2020. Robust data envelopment analysis with Monte Carlo simulation model for optimization the energy consumption in agriculture. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, pp.1-15.
Ref. 10 should be: Abyani, M. and Bahaari, M.R., 2020. A comparative reliability study of corroded pipelines based on Monte Carlo Simulation and Latin Hypercube Sampling methods. International Journal of Pressure Vessels and Piping, 181, p.104079.
Ref. 14 should be: Liaw, H.C., Shirinzadeh, B. and Smith, J., 2008. Robust motion tracking control of piezo-driven flexure-based four-bar mechanism for micro/nano manipulation. Mechatronics, 18(2), pp.111-120.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors have made significant improvement and the manuscript can be published now.
Author Response
The authors have made significant improvement and the manuscript can be published now.
Answer: Thank you for your acceptance.
Reviewer 2 Report
Comments and Suggestions for AuthorsCan be prepared for publish
Author Response
Can be prepared for publish
Answer: Thank you for your acceptance.
Reviewer 3 Report
Comments and Suggestions for AuthorsIt is improved to be ready for publication.
Author Response
It is improved to be ready for publication.
Answer: Thank you for your acceptance.
Reviewer 4 Report
Comments and Suggestions for AuthorsThe authors define way too many abbreviations throughout the text, which make reading the paper difficult!
Not clear how the 6-bar linkage kinematic design can capture reliability aspects. One would think that force and moment loading (including variable loading) are the causes of failure on a flight control mechanism - see for example Alaska Airlines Flight 261. The mechanism solutions in figures 5 to 9 seem disproportionate.
The authors should drop this 6-bar linkage example and focus on the connecting rod and cantilever beam.
* Use accepted terminology please:
equation 25 is the "equivalent stress" NOT "combined stress"
use "side constraints" instead of "Limitation of the design variable"
Comments on the Quality of English Language
The authors define way too many abbreviations throughout the text, which make reading difficult.
Author Response
difficult!
Answer: Thank you for your suggestion. We have limited the necessary abbreviation. We try to balance the word counting and difficulty of reading.
Not clear how the 6-bar linkage kinematic design can capture reliability aspects. One would think that force and moment loading (including variable loading) are the causes of failure on a flight control mechanism - see for example Alaska Airlines Flight 261. The mechanism solutions in figures 5 to 9 seem disproportionate.
The authors should drop this 6-bar linkage example and focus on the connecting rod and cantilever beam.
Answer: Thank you for your suggestion. Your concerns are necessary for dynamic design, but the limitation of this study focus on kinematic design can disturb with uncertainty due to link length tolerance. Your concern is our aim in designing the HLM in the future.
* Use accepted terminology please:
equation 25 is the "equivalent stress" NOT "combined stress"
use "side constraints" instead of "Limitation of the design variable"
Answer: Thank you for your suggestion. We have corrected it all.
Round 3
Reviewer 4 Report
Comments and Suggestions for AuthorsThe authors' responses are superficial, and do not address the criticisms formulated.
Overall, the paper lacks substance and I do not support its publication.
Comments on the Quality of English LanguageN/A
