A Piecewise Particle Swarm Optimisation Modelling Method for Pneumatic Artificial Muscle Actuators
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis manuscript proposes a parameter identification for nonlinear pneumatic artificial muscle. The method was evaluated by comparing modeling errors with other popular modeling methods. It can be understood that the objective of this study is to improve modeling accuracy with reduced computational costs.
1. The method has only been verified through experiments using one specific PAM, and its versatility remains questionable. This is because, in PAMs that use the compressibility of fluids, the impact of inertia and elasticity that governs their behavior varies more or less depending on the size.
2. Some parts of the paper should be improved to provide more straightforward explanations, using formulas and tables rather than just sentences.
- The PSO optimization function in Section 2.2 should be provided in the equation.
- Are there precise descriptions of linear and inflation/deflation models using equations in Section 3?
- In Section 3.1, please provide a table of model parameters of each model, which are obtained from model generation. Otherwise, readers cannot know the difference among models. Computational costs should also be itemized in the table for comparison.
- The differences in the types of input waves used in the experiment are not clear. Is it possible to summarize the properties of the input waveforms in a table, such as profile, amplitude, frequency, and median?
- The comparison with other methods described in the third paragraph of Section 4 could be summarized in a table or graph so that the differences in modeling accuracy and computational cost (even qualitative if information is difficult to obtain) are apparent.
3. The rapid sin wave error graph in Figure 5-12 is strange and should be revised. Also, it would be better to add figure numbers and titles to each figure. Otherwise, seeing the figures in column or row order is confusing.
4. Does gravity factor into account in the model? The PAM is not necessarily oriented vertically in a specific application, but can the proposed method still be applied?
Comments on the Quality of English LanguageThe only thing that bothered me was the use of British English in some parts.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe article proposes the use of particle swarm to identify the model parameters of a Pneumatic Artificial Muscle Actuator.
The approach is interesting but it has serious drawbacks that should be solved.
1. When piecewise models are defined are more than 3 parameters to be optimized, please define clearly the parameters optimized by the PSO in this case.
2. There are several variables that can be used to separate the models in the piecewise definition, please define clearly.
3. Please, formally define with equations the piecewise model
4. The optimization problem should be clearly described: optimization variables, constraints, fitness function
5. Indicate in a table the parameters obtained as result of the optimization process
6. Compare the experimental results with the figures provided by FESTO, I mean figures h[%]-F
Other minor comments:
1. Some figures are blurry Fig 1 and Fig 2
2. Figure "Rapid Sin Wave Error" is not ok please review
3. Legend in fig 4 is not complete, yellow is missing
4. PSO has been used for other related optimization problems in robotics, references could be made to other works to illustrate the usefulness and extend the applicability, for example:
Bayona, E., Sierra-García, J. E., & Santos, M. (2024). Comparative Analysis of Metaheuristic Optimization Methods for Trajectory Generation of Automated Guided Vehicles. Electronics, 13(4), 728.
Lu, J., & Zhang, Z. (2021). An improved simulated annealing particle swarm optimization algorithm for path planning of mobile robots using mutation particles. Wireless Communications and Mobile Computing, 2021(1), 2374712.
Comments on the Quality of English LanguageMinor editing of English language required
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe quality of the paper has improved thanks to the revisions made in response to the reviewers' comments. Figure 4-11 is still of poor quality, even though Figure number 5-12 is incorrect to begin with. I recommend the authors correct and revise them before final publication.
Author Response
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Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsReviewer Comment 1: When piecewise models are defined are more than 3 parameters to be optimized, please define clearly the parameters optimized by the PSO in this case.
Author Response: A brief paragraph has been added clarifying how the parameters for each piecewise model are generated. (Section 2.3, lines 223-226)
Reviewer response:
The optimization sequence is not totally clear yet. For example lets assume there are 3 models, when the model 1 is optimized what values (P1-P3) are set in models 2-3 ???
Reviewer Comment 2: There are several variables that can be used to separate the models in the piecewise definition, please define clearly.
Author Response: Equations 14, 15 and 16 have been added to better present the piecewise model definition, showing the variable used for model separation is U(t), the input to the system. In the case of this system this would be the voltage input value to the proportional pressure
regulator. Additionally, the number of model sections is now defined as a value n for each of the different models generated in section 3.1 (Section 3.1, lines 292-293, lines 298-299, and lines 302-303) and the description of the input ranges decided upon for the model generation was amended to better incorporate these equations (Section 3.1, lines 306-307).
Reviewer comment: Now the separation variable is clear. But the description of the selection of intervals K1, K2,....Kn-1 could be improved.
In 305-306 appears: increases, the density of these intervals 305 was chosen to increase across the stroke length. These input ranges were decided as 𝐾1=306 1.05,𝐾2=2.35,𝐾3=3.15,𝐾4=3.95,𝐾5=4.75.
This decission is taken by the user or by the optimizer ? These K values are obtained with some equation?
Reviewer Comment 3: Please, formally define with equations the piecewise model.
Author Response: Equations 14, 15 and 16 have been added to formally define the piecewise model and better represent the model separation. Additional text to better put these added equations into the context of the section was added. (Section 2.3, lines 223-236)
Reviewer response:
Equation 16 is not well formalized please improve. equations 15 and 16 provide the same output and it is incorrect, the y(t) should be decomposed in two variables xinf and xdef. The current equation (16) does not says that.
Comments on the Quality of English LanguageMinor editing of English language required
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
