Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper applies a genetic algorithm (GA) to design a composite hydraulic cylinder. The topic is interesting and has the potential for significant contribution. However, the following comments should be addressed to improve the quality of the paper:

1. The literature review on the design of composite hydraulic cylinders is insufficient. Specifically, the application of optimization algorithms in the design process is not well-addressed. Please expand the literature review to include relevant studies and highlight the gaps your work aims to fill.

2. Various optimization algorithms are available, such as Particle Swarm Optimization (PSO), Differential Evolution (DE), etc. The authors should discuss why GA was chosen over other algorithms. Highlight its advantages or suitability for this specific problem.

3. Section 2: "Selection of Parameters":

- This section lacks a quantitative analysis of the simulation results used to determine the parameters of the GA. Provide additional data or rationale to support the parameter selection.

- Since all figures are in black and white, it is challenging to interpret Figures 5 to 9. Consider using color figures for clarity.

4. The optimization results are unclear. It is unclear whether the GA determined that 8 layers are optimal or if it was used to select the two best solutions from the five listed in Table 2. Please clarify and revise this section to ensure the methodology and results are transparent.

5. To strengthen the study, include a comparison of GA with another optimization algorithm, such as PSO or DE. This would provide context and validate the performance of GA in this design application.

Other comments

- Revise the decimal notation in the figures (e.g., replace commas with dots for the value of variables NmN_m​).

- Equation 2: Use the multiplication symbol (×) instead of a dot (.) or remove it.

- Use color figures instead of black and white to enhance readability and better illustrate the results.

- Figure 1: Add a legend or annotate the figure to distinguish each type of fiber clearly. For instance, use different markers or line styles for clarity.

- Why do the authors use two colors for arrows in Figure 2?

- Figure 4 looks like a Table. Consider reformatting it as a proper table if it primarily presents tabular data.

Author Response

The paper applies a genetic algorithm (GA) to design a composite hydraulic cylinder. The topic is interesting and has the potential for significant contribution. However, the following comments should be addressed to improve the quality of the paper:

1. The literature review on the design of composite hydraulic cylinders is insufficient. Specifically, the application of optimization algorithms in the design process is not well-addressed. Please expand the literature review to include relevant studies and highlight the gaps your work aims to fill.

Response:

In the text of the manuscript it was added:

Genetic algorithms have proven their usefulness in optimizing elements made of composite materials. In 1995, Le Richie and Haftka [R. Le Riche and R. T. Haftka, “Improved genetic algorithm for minimum thickness composite laminate design,” Compos. Eng., vol. 5, no. 2, pp. 143–161, Jan. 1995.] optimized a flat laminate for four different loading conditions with forces acting in the plane of the element. They tested different types of penalty functions and obtained several variants of layer arrangement for each load case. Soremekun et al. [G. Soremekun, Z. Gürdal, R. T. Haftka, and L. T. Watson, “Composite laminate design optimization by genetic algorithm with generalized elitist selection,” Comput. Struct., vol. 79, no. 2, pp. 131–143, Jan. 2001.] presented different methods of elitist selection and their influence on convergence and results of laminate optimization. They showed that retaining more than one best solution from the previous generation in subsequent generations allows for improving the algorithm's performance, achieving convergence faster and avoiding local optima. Mathias et al. [J. D. Mathias, X. Balandraud, and M. Grediac, “Applying a genetic algorithm to the optimization of composite patches,” Comput. Struct., vol. 84, no. 12, pp. 823–834, May 2006] used a genetic algorithm to optimize composite patches applied to damaged steel structures. The patch application site, its shape, orientation and layer arrangement were subject to optimization. The patch orientation was expressed in a continuous manner, while the layers themselves had dicreet angles. To reduce the computational cost, the memory functionality was implemented in genetic algorithms [C. H. Park, W. Il Lee, W. S. Han, and A. Vautrin, “Improved genetic algorithm for multidisciplinary optimization of composite laminates,” Comput. Struct., vol. 86, no. 19–20, pp. 1894–1903, Oct. 2008], [N. Kogiso, L. T. Watson, Z. Gürdal, and R. T. Haftka, “Genetic algorithms with local improvement for composite laminate design,” Struct. Optim., vol. 7, no. 4, pp. 207–218, Jun. 1994.]. Apart from the optimization of flat laminates, genetic algorithms were also used to design cylindrical elements and storage vessels. Richard and Perreux [F. Richard and D. Perreux, “Reliability method for optimization of [+φ, -φ]n fiber reinforced composite pipes,” Reliab. Eng. Syst. Saf., vol. 68, no. 1, pp. 53–59, Apr. 2000.] presented an analysis of the testing process of composite pipes loaded with internal pressure, taking into account cracking phenomena and statistical uncertainties. Then, they optimized the elements by minimizing the number of layers and searching for the optimal angle of fiber alignment. Messager et al. [T. Messager, M. Pyrz, B. Gineste, and P. Chauchot, “Optimal laminations of thin underwater composite cylindrical vessels,” Compos. Struct., vol. 58, no. 4, pp. 529–537, Dec. 2002.] optimized underwater cylindrical tanks subjected to external pressure. The optimal fiber arrangement was determined by a genetic algorithm coupled with analytical methods for calculating the strength and stability of the elements. The results were validated using FEM calculations and experimental tests. Kim et al. [C.-U. Kim, C.-S. Hong, C.-G. Kim, and J.-Y. Kim, “Optimal design of filament wound type 3 tanks under internal pressure using a modified genetic algorithm,” Compos. Struct., vol. 71, no. 1, pp. 16–25, Oct. 2005.]

presented an optimization method for the reinforcement of a type 3, composite high-pressure tank. The optimal solution allowing for semi-geodetic winding, and the progressive damage of the material was taken into account in the strength calculations. Xu et al. [P. Xu, J. Zheng, H. Chen, and P. Liu, “Optimal design of high pressure hydrogen storage vessel using an adaptive genetic algorithm,” Int. J. Hydrogen Energy, vol. 35, no. 7, pp. 2840–2846, Apr. 2010.] proposed an adaptive algorithm that had the advantage of faster convergence and better optima finding. This was achieved by varying the mutation and crossover probabilities with the fitness function value.

“The paper [Nikbakht, S., Kamarian, S., Shakeri, M., 2018. A review on optimization of composite structures Part I: laminated composites. Compos. Struct. 195, 158–185. https://doi. org/10.1016/j.compstruct.2019.01.105] provides a comprehensive review of optimisation methods for various composite structures, including composite beams and composite tubes. It can be seen that methods based on Genetic Algorithms and Particle Swarm Optimisation were the most commonly used algorithms. The combination of Particle Swarm Optimisation and Simple Cell Mapping methods, allowed the authors of [Meng-Xin He, Jian-Qiao Sun, Multi-objective structural-acoustic optimization of beams made of functionally graded materials, Composite Structures, Volume 185, 2018, Pages 221-228, ISSN 0263-8223, https://doi.org/10.1016/j.compstruct.2017.11.004] to optimise the material distribution of functionally graded beams. The objective functions were to achieve a design with minimum total mass and maximum emitted power with upper and lower limits of the desired frequencies as constraints. Methods for optimising composite structures based on genetic algorithms in combination with numerical analysis can also be found in the literature. These studies have used composite failure criteria such as Tsai-Wu, Hashin, Maximum Stress and Puck failure criteria as material constraints and mass minimisation, deflection minimisation, buckling load maximisation, material minimisation and load-carrying capacity maximisation as objective functions [Randrup, S. (2015). Optimization of laminated composite structures. Alborg University].”

2. Various optimization algorithms are available, such as Particle Swarm Optimization (PSO), Differential Evolution (DE), etc. The authors should discuss why GA was chosen over other algorithms. Highlight its advantages or suitability for this specific problem.

Response:

In the introduction, a paragraph presenting the advantages of the selected algorithm was added. Other, alternative optimization algorithms were also described.

3. Section 2: "Selection of Parameters":

- This section lacks a quantitative analysis of the simulation results used to determine the parameters of the GA. Provide additional data or rationale to support the parameter selection.

Response:

The main global parameters of the applied algorithm were population size, mutation probability, fraction of the population subject to mutation and maximum mutation angle. Section 2 presents a comprehensive analysis of the impact of these parameters on the ability of the algorithm to achieve convergence (avoiding local minima) as well as on the computational cost. In fact, only a qualitative assessment is presented in the paper. The development of criteria for quantitative analysis of results in multidimensional parameter space is the subject of ongoing research.

- Since all figures are in black and white, it is challenging to interpret Figures 5 to 9. Consider using color figures for clarity.

Response: After considering the reviewer's suggestion, it was decided to leave the figures monochrome. In our opinion, the introduction of colour does not add any new substantive information. The legibility of the figures will be guaranteed by high quality printing.

4. The optimization results are unclear. It is unclear whether the GA determined that 8 layers are optimal or if it was used to select the two best solutions from the five listed in Table 2. Please clarify and revise this section to ensure the methodology and results are transparent.

Response:

The aim of the optimization was to find such a layer arrangement for which the strength coefficient R_T-H would not be exceeded in any of the layers. The number of layers was not imposed, however the smallest number of layers for which the above criterion was met was 8. Table 2 presents the results for which the fitness function values were the lowest. Of these, 3 designs that significantly differed from each other were selected for experimental studies.

 

5. To strengthen the study, include a comparison of GA with another optimization algorithm, such as PSO or DE. This would provide context and validate the performance of GA in this design application.

Response:

The paper did not analyse other optimisation methods for this particular case (optimisation of a composite cylinder structure). It was pointed out that other optimisation methods exist, but the focus was on the method using GA.

Other comments

- Revise the decimal notation in the figures (e.g., replace commas with dots for the value of variables NmN_m​).

Response:

Figures 6, 7, 8, 9, 14 and 17 have been corrected as suggested. A comma has been changed to a dot.

- Equation 2: Use the multiplication symbol (×) instead of a dot (.) or remove it.

Response:

As suggested, the symbol ‘.’ has been replaced. symbol to the ‘×’ symbol.

- Use color figures instead of black and white to enhance readability and better illustrate the results.

Response: After considering the reviewer's suggestion, it was decided to leave the figures monochrome. In our opinion, the introduction of colour does not add any new substantive information. The legibility of the figures will be guaranteed by high quality printing.

- Figure 1: Add a legend or annotate the figure to distinguish each type of fiber clearly. For instance, use different markers or line styles for clarity.

Response

Figure 1 has been corrected. The markers within the groupings have been differentiated.

- Why do the authors use two colors for arrows in Figure 2?

Response:

In Figure 3, two colours of arrows are used to highlight (in red) the start and end of the algorithm.

- Figure 4 looks like a Table. Consider reformatting it as a proper table if it primarily presents tabular data.

Response: The presentation of an individual representing the layering of a winding element in this case better in figure form, since table form can provide missundurstand.

 

Reviewer 2 Report

Comments and Suggestions for Authors

1.      Introduction and motivation

a)      The authors have pointed out the important applications of fiber-reinforced composite materials in mechanical engineering, especially hydraulic components; however, the authors did not justify the reasons why they selected genetic algorithms rather than other optimization algorithms. Please compare the optimization algorithms and discuss the unique advantages of genetic algorithms in fiber-reinforced composites.

b)      The claim that “there are no attempts in the literature to optimize the structure of such a component” may be true. Yet, there are many literatures and algorithms studying the optimization of fiber-reinforced structures with applications in other mechanical components. It is necessary to review these literature and discuss their algorithms.

2.      Technical details

a)      The authors are suggested to indicate how they calculate the maximum strength factor R_T-H? By numerical calculations, finite element simulations, or what?

b)      The selection of initial generations can significantly affect the convergence speed and the computational cost; therefore, they should be selected strategically, such as choosing them based on the basic knowledge and principles of composite structures. How did the authors propose their initial generations?

c)      The authors did not explain the physical meaning of the materials properties presented in Table 1. Additionally, the authors mentioned “the calculations used the orthotropic material model presented earlier”, but specifically, which model were they referring to? Tsai-Hill hypothesis? Please explicitly write this out.

d)      Please compare the R value of the optimized structure with unoptimized composites. In this way, the readers can understand the optimization is useful. I know Section 4 is for this purpose, but adding a few more sentences to compare them and stressing on the advantages of the optimized structures would be beneficial for the impact of this paper.

3.      Minor issues

a)      In Figure 12, the εx and εθ have the same line type and color. Readers cannot distinguish them.

b)      In Figure 14, the y-axis label “0 0,1 0,2 0,3” is confusing for readers. Please change commas to periods. Same for Figure 17.

c)      The language of this manuscript is presented in an understandable manner for me, but some sentences are not in academic writing style, such as the appearance of the second person (“On the market you can find many types…”), and there are some grammatical errors.

Comments on the Quality of English Language

The language of this manuscript is presented in an understandable manner for me, but some sentences are not in academic writing style, such as the appearance of the second person (“On the market you can find many types…”), and there are some grammatical errors.

Author Response

1. Introduction and motivation
2. a)      The authors have pointed out the important applications of fiber-reinforced composite materials in mechanical engineering, especially hydraulic components; however, the authors did not justify the reasons why they selected genetic algorithms rather than other optimization algorithms. Please compare the optimization algorithms and discuss the unique advantages of genetic algorithms in fiber-reinforced composites. ML

Response:

The paper did not analyse other optimisation methods for this particular case (optimisation of a composite cylinder structure). It was pointed out that other optimisation methods exist, but the focus was on the method using GA. The Introduction was extended and other optimisation methods were described.

 

1. b)      The claim that “there are no attempts in the literature to optimize the structure of such a component” may be true. Yet, there are many literatures and algorithms studying the optimization of fiber-reinforced structures with applications in other mechanical components. It is necessary to review these literature and discuss their algorithms.

Response:

The Intorduction section describes known, other optimisation methods:

Genetic algorithms have proven their usefulness in optimizing elements made of composite materials. In 1995, Le Richie and Haftka [R. Le Riche and R. T. Haftka, “Improved genetic algorithm for minimum thickness composite laminate design,” Compos. Eng., vol. 5, no. 2, pp. 143–161, Jan. 1995.] optimized a flat laminate for four different loading conditions with forces acting in the plane of the element. They tested different types of penalty functions and obtained several variants of layer arrangement for each load case. Soremekun et al. [G. Soremekun, Z. Gürdal, R. T. Haftka, and L. T. Watson, “Composite laminate design optimization by genetic algorithm with generalized elitist selection,” Comput. Struct., vol. 79, no. 2, pp. 131–143, Jan. 2001.] presented different methods of elitist selection and their influence on convergence and results of laminate optimization. They showed that retaining more than one best solution from the previous generation in subsequent generations allows for improving the algorithm's performance, achieving convergence faster and avoiding local optima. Mathias et al. [J. D. Mathias, X. Balandraud, and M. Grediac, “Applying a genetic algorithm to the optimization of composite patches,” Comput. Struct., vol. 84, no. 12, pp. 823–834, May 2006] used a genetic algorithm to optimize composite patches applied to damaged steel structures. The patch application site, its shape, orientation and layer arrangement were subject to optimization. The patch orientation was expressed in a continuous manner, while the layers themselves had dicreet angles. To reduce the computational cost, the memory functionality was implemented in genetic algorithms [C. H. Park, W. Il Lee, W. S. Han, and A. Vautrin, “Improved genetic algorithm for multidisciplinary optimization of composite laminates,” Comput. Struct., vol. 86, no. 19–20, pp. 1894–1903, Oct. 2008], [N. Kogiso, L. T. Watson, Z. Gürdal, and R. T. Haftka, “Genetic algorithms with local improvement for composite laminate design,” Struct. Optim., vol. 7, no. 4, pp. 207–218, Jun. 1994.]. Apart from the optimization of flat laminates, genetic algorithms were also used to design cylindrical elements and storage vessels. Richard and Perreux [F. Richard and D. Perreux, “Reliability method for optimization of [+φ, -φ]n fiber reinforced composite pipes,” Reliab. Eng. Syst. Saf., vol. 68, no. 1, pp. 53–59, Apr. 2000.] presented an analysis of the testing process of composite pipes loaded with internal pressure, taking into account cracking phenomena and statistical uncertainties. Then, they optimized the elements by minimizing the number of layers and searching for the optimal angle of fiber alignment. Messager et al. [T. Messager, M. Pyrz, B. Gineste, and P. Chauchot, “Optimal laminations of thin underwater composite cylindrical vessels,” Compos. Struct., vol. 58, no. 4, pp. 529–537, Dec. 2002.] optimized underwater cylindrical tanks subjected to external pressure. The optimal fiber arrangement was determined by a genetic algorithm coupled with analytical methods for calculating the strength and stability of the elements. The results were validated using FEM calculations and experimental tests. Kim et al. [C.-U. Kim, C.-S. Hong, C.-G. Kim, and J.-Y. Kim, “Optimal design of filament wound type 3 tanks under internal pressure using a modified genetic algorithm,” Compos. Struct., vol. 71, no. 1, pp. 16–25, Oct. 2005.]

presented an optimization method for the reinforcement of a type 3, composite high-pressure tank. The optimal solution allowing for semi-geodetic winding, and the progressive damage of the material was taken into account in the strength calculations. Xu et al. [P. Xu, J. Zheng, H. Chen, and P. Liu, “Optimal design of high pressure hydrogen storage vessel using an adaptive genetic algorithm,” Int. J. Hydrogen Energy, vol. 35, no. 7, pp. 2840–2846, Apr. 2010.] proposed an adaptive algorithm that had the advantage of faster convergence and better optima finding. This was achieved by varying the mutation and crossover probabilities with the fitness function value.

The paper [Nikbakht, S., Kamarian, S., Shakeri, M., 2018. A review on optimization of composite structures Part I: laminated composites. Compos. Struct. 195, 158–185. https://doi. org/10.1016/j.compstruct.2019.01.105] provides a comprehensive review of optimisation methods for various composite structures, including composite beams and composite tubes. It can be seen that methods based on Genetic Algorithms and Particle Swarm Optimisation were the most commonly used algorithms. The combination of Particle Swarm Optimisation and Simple Cell Mapping methods, allowed the authors of [Meng-Xin He, Jian-Qiao Sun, Multi-objective structural-acoustic optimization of beams made of functionally graded materials, Composite Structures, Volume 185, 2018, Pages 221-228, ISSN 0263-8223, https://doi.org/10.1016/j.compstruct.2017.11.004] to optimise the material distribution of functionally graded beams. The objective functions were to achieve a design with minimum total mass and maximum emitted power with upper and lower limits of the desired frequencies as constraints. Methods for optimising composite structures based on genetic algorithms in combination with numerical analysis can also be found in the literature. These studies have used composite failure criteria such as Tsai-Wu, Hashin, Maximum Stress and Puck failure criteria as material constraints and mass minimisation, deflection minimisation, buckling load maximisation, material minimisation and load-carrying capacity maximisation as objective functions [Randrup, S. (2015). Optimization of laminated composite structures. Alborg University].

 

2. Technical details
3. a)      The authors are suggested to indicate how they calculate the maximum strength factor R_T-H? By numerical calculations, finite element simulations, or what?

Response:

The manuscript has been supplemented with a paragraph on the method of determining the strength factor. The strength calculations themselves were performed using a numerical script based on the classical laminate theory. The script was written in Wolfram Mathematica software.

1. b)      The selection of initial generations can significantly affect the convergence speed and the computational cost; therefore, they should be selected strategically, such as choosing them based on the basic knowledge and principles of composite structures. How did the authors propose their initial generations?

Response:

In order to avoid local optima, as well as to allow the algorithm to find non-obvious solutions, it was decided not to excessively restrict either the first generation or any subsequent ones. The only restrictions resulted from the manufacturing technology and were the necessity of having layers in twin pairs (±α), and a minimum layer angle of 20 degrees.

1. c)      The authors did not explain the physical meaning of the materials properties presented in Table 1. Additionally, the authors mentioned “the calculations used the orthotropic material model presented earlier”, but specifically, which model were they referring to? Tsai-Hill hypothesis? Please explicitly write this out.

Response:

The manuscript has been supplemented with information on how the strength coefficient was determined in accordance with the Tsai-Hill hypothesis.

1. d)      Please compare the R value of the optimized structure with unoptimized composites. In this way, the readers can understand the optimization is useful. I know Section 4 is for this purpose, but adding a few more sentences to compare them and stressing on the advantages of the optimized structures would be beneficial for the impact of this paper.

Response:

Meaningful comparison between optimized and non-optimized laminates seems to be an impossible task. The results of such a comparison will depend on the structure of such non-optimized laminate. If one assume that non-optimized means meeting strength conditions, but having a non-optimal number of layers, then it will be characterized by very low values of the strength coefficient R. The process of selecting a non-optimized structure would require decisions to be made by the designer, the accuracy of which would depend on his knowledge and experience.

 

3. Minor issues
4. a)      In Figure 12, the εx and εθ have the same line type and color. Readers cannot distinguish them.

Response:

The description in Figure 12 has been corrected.

17. b)      In Figure 14, the y-axis label “0 0,1 0,2 0,3” is confusing for readers. Please change commas to periods. Same for Figure 17.

Response:

This has been corrected.

1. c)      The language of this manuscript is presented in an understandable manner for me, but some sentences are not in academic writing style, such as the appearance of the second person (“On the market youcan find many types…”), and there are some grammatical errors.

Response:

This has been corrected.

The language of this manuscript is presented in an understandable manner for me, but some sentences are not in academic writing style, such as the appearance of the second person (“On the market you can find many types…”), and there are some grammatical errors.

Response:

This has been corrected.