Optimization of Fused Deposition Modeling Parameters for Mechanical Properties of Polylactic Acid Parts Based on Kriging and Cuckoo Search

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this article, authors proposed an approach combining Kriging and Cuckoo Search algorithms to optimize FDM parameters, enhancing the mechanical properties of PLA 3D printed parts. The methodology effectively identifies the optimal parameters, demonstrating improved tensile strength and reduced experimental costs. Authors also conducted experiments to validate the proposed approach’s accuracy and efficiency.

However, to further improve the manuscript, I have a few suggestions.

 

1)      The writing style of the abstract needs improvement for clarity. For example, sentence from line 7 to line 16 is too long. Authors should break these types of sentences into smaller sentences for better readability and ensure proper punctuation.

2)      The introduction should be rewritten for greater clarity. It would benefit from a more explicit explanation of the scientific gap the authors aim to address. While several related studies are cited, the specific shortcomings of these studies and the significance of this research are not clearly highlighted. The introduction should more effectively convey the gap being filled and the importance of this study in advancing the field.

3)      "et al" should be written as "et al." consistently throughout the manuscript.

4)      The first paragraph of the conclusion reads more like an abstract. It should be rewritten concisely to clearly highlight the key outcomes of the study.

5)      The authors should add proper references for the mathematical expressions used unless they have derived them independently.

6)      It would be beneficial to specify the load cell specifications used for tensile measurements.

In the references section, the formatting needs correction. Some titles are in all caps, while others are in lowercase. This inconsistency should be addressed.

General comment: from a scientific perspective, the manuscript is satisfactory; however, the English requires thorough correction. Sentence structure, punctuation, and overall language quality need to be carefully addressed.

Comments on the Quality of English Language

NA

Author Response

♥ Dear Reviewer:

Thank you very much for your thorough and helpful comments on our manuscript. According to your comments and suggestions, I have revised the manuscript and responded point by point to the comments as following.

In the following content, the blue text is the comment came from you. The black text is the replies and the content revised in the manuscript is marked in red in the revised paper.

Comment 1: The writing style of the abstract needs improvement for clarity. For example, sentence from line 7 to line 16 is too long. Authors should break these types of sentences into smaller sentences for better readability and ensure proper punctuation.

Answer: The author has changed all the cumbersome long sentences in the abstract to more concise short sentences, thereby improving the readability of the sentences.

Firstly, by analyzing FDM principle and its main parameters, printing speed and temperature were selected as research elements, and tensile strength as mechanical performance index. Latin hypercube sampling (LHS) was integrated to generate a limited experimental sample set; Secondly, a Kriging based prediction model for mechanical properties was constructed by learning sample data, and the nonlinear mapping relationship between process parameters and tensile strength was obtained; Then, using the combinations of speed and temperature as design variables and maximizing tensile strength as optimization objective, an optimization model was established, and the optimal process parameters were searched by CS. Finally, experimental verification showed that the Kriging model is correct and effective, and tensile strength of parts printed under the optimal process parameters is significantly improved.

Comment 2: The introduction should be rewritten for greater clarity. It would benefit from a more explicit explanation of the scientific gap the authors aim to address. While several related studies are cited, the specific shortcomings of these studies and the significance of this research are not clearly highlighted. The introduction should more effectively convey the gap being filled and the importance of this study in advancing the field.

Answer: Most existing research determines optimal process parameters through extensive experiments. In order to find the optimal process parameters in continuous intervals and reduce experimental costs, more and more scholars have combined neural networks with intelligent optimization algorithms to optimize FDM process parameters in recent years. However, most of them focus on improving single parameters or the shape accuracy of parts. The main work of this paper is to combine surrogate models and evolutionary algorithms to optimize both speed and temperature parameters simultaneously, thereby improving the mechanical properties of parts.

This section has been revised and supplemented in Introduction in the revised manuscript, and marked in red.

Comment 3: "et al" should be written as "et al." consistently throughout the manuscript.

Answer: Thank you for the professional suggestions. The author has proofread the entire text, and all the "et al" have been written as "et al.", please refer to the revised manuscript..

Comment 4: The first paragraph of the conclusion reads more like an abstract. It should be rewritten concisely to clearly highlight the key outcomes of the study.

Answer: Based on the reviewer's suggestion, the author has rewritten the conclusion.

In this paper, a methodology that integrates CS with Kriging for the devise and majorization of the FDM process parameters has been developed and verified. Compared with the majority of experimental approaches, the proposed surrogate model can effectively illustrate the impact of process parameters on the performance within a continuous range. The consequence of the project demonstrate that the proposed means is more effective, and it can cut down the experimental cost and enhance the efficiency of the optimization of FDM process parameters.

The optimal process parameters obtained in this paper are as follows: the printing velocity is 31 mm/s, the printing temperature is 225 °C, and the corresponding maximum tensile strength is 37.47MPa. Meanwhile, thanks to the high degree of accuracy of the Kriging method and the CS as well as the merit of having few parameters that need to be finely adjusted, the proposed method has great capability and can be redouble extended and used to the performance-improvement-oriented optimization of process parameters.

Comment 5: The authors should add proper references for the mathematical expressions used unless they have derived them independently.

Answer: The algorithm formulas for Kriging and CS in this article refer to references [26] and [27], therefore, the author has added corresponding references in the revised manuscript. In addition, a description and discussion of Latin Hypercube Sampling (LHS) have been added, along with references [28].

Comment 6: It would be beneficial to specify the load cell specifications used for tensile measurements.

Answer: Tensile strength of various samples was conducted using Microcomputer controlled electronic universal testing machine (TEM104C, Shenzhen Wance Testing Machine Co., Ltd.). The load cell used was an American AiLogics force sensor (Model: DBSL-1t).

Tensile strength of various samples was conducted using Microcomputer controlled electronic universal testing machine (TEM104C, Shenzhen Wance Testing Machine Co., Ltd.), as shown in Figure 4. The load cell used was an American AiLogics force sensor (Model: DBSL-1t).

 

With kindest regards.

I hope that the responses are acceptable to your kind comments. I look forward to hearing from you. Thank you very much for your patient work.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Interesting study of using simulation approach to find optimum process parameters that could yield the best tensile strength performance from 3D printed PLA. The simulation results are also verified with experiments, which yield relatively high accuracy between both approaches.

However, some issues need to be addressed, primarily as follow, and the rest in the PDF attached:

1. The literature reviewed in the introduction lacks critical analysis, merely describing what different authors have done. The literature review should become the basis to identify research gaps and formulate the resulting objectives and methodology in the present study.

2. As a result from (1), the problem statement/motivation of this study is unclear. The justifications behind selection of methodologies, materials, parameters, etc. are not provided, e.g. What are the advantages of Krigning and CS compared to other approaches? What are the limitations of other approaches? etc... These should be determined from analysis of literature (research gap).

3. The description of methodology needs to be improved, particularly on LHS. Based on the results, LHS is an important tool to extract the 40 sets of parameters for training and testing with Krigning and CS, but the methodology/procedure of LHS is not described in the methodology section.

 

Please also address other comments in the PDF attached.

Comments for author File: Comments.pdf

Author Response

♥ Dear Reviewer:

Thank you very much for your helpful comments on our manuscript. According to your comments and suggestions, I have revised the manuscript and responded point by point to the comments as following.

In the following content, the blue text is the comment came from you. The black text is the replies and the content revised in the manuscript is marked in red in the revised paper.

Comment 1: The literature reviewed in the introduction lacks critical analysis, merely describing what different authors have done. The literature review should become the basis to identify research gaps and formulate the resulting objectives and methodology in the present study. The problem statement/motivation of this study is unclear. The justifications behind selection of methodologies, materials, parameters, etc. are not provided, e.g. What are the advantages of Krigning and CS compared to other approaches? What are the limitations of other approaches? etc... These should be determined from analysis of literature (research gap).

Answer: Thank you for the academic suggestions, most existing research determines optimal process parameters through extensive experiments. In order to find the optimal process parameters in continuous intervals and reduce experimental costs, more and more scholars have combined neural networks with intelligent optimization algorithms to optimize FDM process parameters in recent years. However, most of them focus on improving single parameters or the shape accuracy of parts. The main work of this paper is to combine surrogate models and evolutionary algorithms to optimize both speed and temperature simultaneously, thereby improving the mechanical properties of parts.

This section has been revised and supplemented in Introduction in the revised manuscript, and marked in red. Regarding the advantages of Kriging and CS, the author conducted research on the comparison between Kriging and neural networks, as well as the comparison between CS and GA and PSO. The corresponding literature has been added to the introduction.

The above studies conducted a large number of experiments through trial and error, and then selected better process parameters in discrete intervals. Its disadvantage is that the results are not optimal, and the experimental cost is huge.

However, there is still little research on combining surrogate models and evolutionary algorithms to optimize printing speed and temperature in order to improve the mechanical properties of FDM parts.

In this paper, printing velocity and nozzle temperature are the parameters employed for examination, while tensile strength acts as the response index for analysis. Subsequently, an optimization framework based on the Kriging method and CS algorithm is put forward to optimize the process parameters of FDM for the printing of PLA parts. By integrating Latin Hypercube Sampling (LHS) with experimental analysis to generate sample data, a Kriging model is constructed based on this sample data for predicting tensile strength. Then, based on the Kriging forecast model, CS is utilized to seek out the optimum solution. The proposed method plays a significant role in enhancing the mechanical properties of 3D printed polymer components and facilitating the in-depth application of 3D printing technology.

Comment 2: The description of methodology needs to be improved, particularly on LHS. Based on the results, LHS is an important tool to extract the 40 sets of parameters for training and testing with Krigning and CS, but the methodology/procedure of LHS is not described in the methodology section.

Answer: In response to reviewer’s opinions, the authors added a description of methodology LHS.

Latin Hypercube Sampling (LHS) is a method of approximating random sampling from multivariate parameter distributions, and can ensure that each of the input variables has all portions of its range represented[28]. Therefore, LHS is used to generate a limited number of training and testing samples, and then the mechanical strength of the printed specimens corresponding to each sample point is calculated through sample printing and performance experiments, thereby generating a Kriging training and testing sample set.

Comment 3: FDM should be defined in full here, not just short form. Specify the material for the aerospace parts in this case. Polymers? Metals? alloys? CS should be defined in full here, not just short form..

Answer: In response to reviewer’s opinions, the authors have revised the title of the paper to “Optimization of fused deposition modeling parameters for mechanical properties of polylactic acid parts based on Kriging and cuckoo search”.

Comment 4: What are adhesive materials?

Answer: Adhesive materials are materials that can be bonded together.

Comment 5: 'Clamped' is not a suitable word to be used here.

Answer: During printing, the filament is rolled in two feeding rods and sent to the printing nozzle through a feeding mechanism.

Comment 6: The material is in filament form, not wire. Please change the description in the image.

Answer: The image has been modified to the following image.

Comment 7: What are the criteria for the optimal process parameters and that of the mechanical properties?

Answer: In the author's opinion, the optimal process parameters mentioned in this article are the FDM process parameters corresponding to the parts with the best mechanical properties, especially tensile properties, that can be printed.

Comment 8: Why are the specimens undeformed after tensile tests?

Answer: All the specimens were pulled apart, but the author only placed them together to show the situation after the fracture.

Comment 9: Y-axis should be labelled as Tensile strength (MPa).

Answer: The image has been modified to the following image.

Fig. 7.  The predicted and expected values of Kriging.

Comment 10: Minimum or maximum? In Table 2.

Answer: Thank you very much for your suggestion. The author has made revisions to Table 2..

Table 2 Optimization results and validation

Optimal parameters	Maximum σ by CS	The corresponding σ by experiment	Relative error
(31 mm/s, 225℃)	37.47MPa	38.27 MPa	2.09%

Comment 11: What do the authors mean by 'foretell patterns'? What do the authors mean by 'redouble extended'?

Answer: In response to reviewer’s opinions, the author has rewritten the conclusion.

In this paper, a methodology that integrates CS with Kriging for the devise and majorization of the FDM process parameters has been developed and verified. Compared with the majority of experimental approaches, the proposed surrogate model can effectively illustrate the impact of process parameters on the performance within a continuous range. The consequence of the project demonstrate that the proposed means is more effective, and it can cut down the experimental cost and enhance the efficiency of the optimization of FDM process parameters.

The optimal process parameters obtained in this paper are as follows: the printing velocity is 31 mm/s, the printing temperature is 225 °C, and the corresponding maximum tensile strength is 37.47MPa. Meanwhile, thanks to the high degree of accuracy of the Kriging method and the CS as well as the merit of having few parameters that need to be finely adjusted, the proposed method has great capability and can be extended and used to the performance-improvement-oriented optimization of process parameters.

Comment 12: These values should be mentioned in the abstract.

Answer: In response to reviewer’s opinions, the authors added “the printing velocity is 31 mm/s, the printing temperature is 225 °C, and the corresponding maximum tensile strength is 37.47MPa” in the abstract.

Abstract: As an emerging rapid manufacturing technology, 3D printing has been widely applied in numerous fields such as aerospace, shipbuilding and wind power, by virtue of its advantage in efficiently fabricating components with complex structures and integrated functions. In response to the problems of poor mechanical properties and difficulty in selecting process parameters for fused deposition modeling (FDM), this paper analyzed the principle of FDM and proposed a parameters optimization method based on Kriging and Cuckoo Search (CS) algorithm aimed at improving the mechanical properties of 3D printed polylactic acid (PLA) parts. Firstly, by analyzing FDM principle and its main parameters, printing speed and temperature were selected as research elements, and tensile strength as mechanical performance index. Latin hypercube sampling (LHS) was integrated to generate a limited experimental sample set; Secondly, a Kriging based prediction model for mechanical properties was constructed by learning sample data, and the nonlinear mapping relationship between process parameters and tensile strength was obtained; Then, using the combinations of speed and temperature as design variables and maximizing tensile strength as optimization objective, an optimization model was established, and the optimal process parameters were searched by CS. The optimal printing velocity is 31 mm/s and printing temperature is 225 °C, and the corresponding maximum tensile strength is 37.47MPa. Finally, experimental verification showed that the Kriging model is effective, and tensile strength of parts printed under the optimal process parameters is significantly improved..

 

 

With kindest regards.

I hope that the responses are acceptable to your kind comments. I look forward to hearing from you. Thank you very much for your patient work. At last, thank you for your arduous work and instructive advice, and I hope that the corrections will meet with approval.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The authors predicts the optimum FDM parameters via experiment dan computational. However, there are several thing that could be done to improve the paper.

1.  The description and discussion of Latin hypercube sampling (LHS) are very limited. Please explain more about this.

2.  Please discuss more the evaluation of Kriging. Reablity evaluation and kriging model parameters can be explored.

3. Please explain each Figure in more detailed manner.

Author Response

♥ Dear Reviewer:

Thank you very much for your thorough and helpful comments on our manuscript. According to your comments and suggestions, I have revised the manuscript and responded point by point to the comments as following.

In the following content, the blue text is the comment came from you. The black text is the replies and the content revised in the manuscript is marked in red in the revised paper.

Comment 1: The description and discussion of Latin hypercube sampling (LHS) are very limited. Please explain more about this.

Answer: Latin Hypercube Sampling (LHS) is a method of approximating random sampling from multivariate parameter distributions, and can ensure that each of the input variables has all portions of its range represented[28]. Therefore, LHS is used to generate a limited number of training and testing samples, and then the mechanical strength of the printed specimens corresponding to each sample point is calculated through sample printing and performance experiments, thereby generating a Kriging training and testing sample set.

In response to reviewer’s opinions, the authors added a description of methodology LHS.

Latin Hypercube Sampling (LHS) is a method of approximating random sampling from multivariate parameter distributions, and can ensure that each of the input variables has all portions of its range represented[28]. Therefore, LHS is used to generate a limited number of training and testing samples, and then the mechanical strength of the printed specimens corresponding to each sample point is calculated through sample printing and performance experiments, thereby generating a Kriging training and testing sample set.

Comment 2: Please discuss more the evaluation of Kriging. Reablity evaluation and kriging model parameters can be explored.

Answer: Kriging is a type of interpolation function model based on statistical discipline, and is widely used as a popular type of surrogate models for approximating expensive black box functions in engineering design and optimization. When predicting the information of a certain point, it is necessary to estimate the unknown information of the point by linear combination of the information in a certain range of the point, and it is not affected by random error. Kriging model has good global convergence and high fitting accuracy, and has high nonlinear approximation ability. The author added an evaluation description of Kriging in the revised manuscript.

Kriging is a type of interpolation function model based on statistical discipline, and is widely used as a popular type of surrogate models for approximating expensive black box functions in engineering design and optimization. When predicting the information of a certain point, it is necessary to estimate the unknown information of the point by linear combination of the information in a certain range of the point, and it is not affected by random error. Kriging model has good global convergence and high fitting accuracy, and has high nonlinear approximation ability. Kriging model y(x) can be expressed as the sum of a parameterized linear regression model and a non-parametric random process[26].

In addition, the tuning of kriging hyper-parameters has a direct and influential impact on its approximating capability. It always requires numerical optimization of the nonlinear and multi-modal likelihood function to obtain the optimal kriging hyper-parameters based on the maximum likelihood estimation (MLE) theory. The author has conducted in-depth research on this part of the work in published academic papers, and a cuckoo search based approach is proposed and applied to the optimization of kriging hyper-parameters to ensure and improve the approximation ability of the kriging surrogate model.

Comment 3: Please explain each Figure in more detailed manner.

Answer: Thank you for the professional suggestions from the reviewer. The author has revised and provided detailed descriptions of the images in the entire text.

 With kindest regards.

I hope that the responses are acceptable to your kind comments. I look forward to hearing from you. Thank you very much for your patient work.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Authors have thoroughly addressed all my concerns, resulting in significant improvements to the manuscript. The revised version reflects clarity, precision, and a well-structured presentation of the research. I recommend it for publication.

Author Response

Dear reviewer,

Thank you very much for agreeing to publish this manuscript and for your constructive comments and suggestions in the past. These are all important to the authors. Thank you again.

Reviewer 2 Report

Comments and Suggestions for Authors

Acceptable response by the authors. Just a minor revision required for the abstract, in particular the last sentence:

 

'Finally, experimental verification showed that the Kriging model is effective, and tensile strength of parts printed under the optimal process parameters is significantly improved.'

 

1. Define 'effective' in this case, perhaps mentioning the numerical value of the relative error between the simulated and experimental results, and mention that it is within acceptable range.

 

2. Define 'significantly improved' in this case. Put a numerical value/objective assessment to signify this improvement.

Author Response

♥ Dear Reviewer:

Thank you very much for accepting and recognizing the authors' previous response. Regarding the second round of comments, I have revised the manuscript and responded to the comments as following.

In the following content, the blue text is the comment came from you. The black text is the replies and the content revised in the manuscript is marked with a yellow background in the revised paper.

Comment: 'Finally, experimental verification showed that the Kriging model is effective, and tensile strength of parts printed under the optimal process parameters is significantly improved.'

1. Define 'effective' in this case, perhaps mentioning the numerical value of the relative error between the simulated and experimental results, and mention that it is within acceptable range.
2. Define 'significantly improved' in this case. Put a numerical value/objective assessment to signify this improvement..

Answer: The comments are crucial for improving the rigor of this article. Therefore, based on the reviewer's comments, the author has made revisions to the abstract and provided additional explanations in the main text.

In Abstract：

Finally, compared to test data, the relative prediction error of Kriging model is 0.62%, and the optimal strength (38.27MPa) increased by about 12.7% compared to the average value (33.97MPa) of experimental data. It can be seen that the Kriging model is effective, and the tensile strength of parts printed under the optimal process parameters is significantly improved.

In Case study：

The optimal strength (38.27MPa) increased by about 12.7% compared to the average value (33.97MPa) of 40 sets of experimental data.

With kindest regards.

I hope that the responses are acceptable to your kind comments. I look forward to hearing from you. Thank you very much for your patient work.

Author Response File: Author Response.docx