A Streamlined Polynomial Regression-Based Modeling of Speed-Driven Hermetic-Reciprocating Compressors

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In their submitted manuscript, Jay Wang and Wei Lu addressed the phenomenological modeling of the performance of hermetic reciprocating compressors driven by variable-speed electric motors. To this end, they conducted univariate and bivariate polynomial regression analyses to determine the dependence of volumetric and isentropic efficiency on the compression ratio and motor rotational speed. They used the experimental results for estimating statistical models from Ji Wang's research team, published in the journal Energy Conversion and Management. The similarity of the names Jay Wang and Ji Wang is interesting. I noticed it because this article is actually a continuation of the previously mentioned work by Ji Wang's group.

While this article is well-written, it lacks creativity, both in the research method used and in its conclusions. Univariate polynomial regression (i.e., a statistical technique used to model a non-linear relationship between a single independent variable and a dependent variable by fitting a polynomial equation to the data) is certainly not original. The same is true for bivariate polynomial regression.

Engineers know that in this type of compressor, the thermal impact depends primarily on the piston speed (shaft rotation speed), the compression ratio, and cylinder cooling. Therefore, the conclusions drawn are substantively correct, but they do not inform readers about the new research methodology or the innovative method of conducting numerical studies. The presented results may be of interest only to engineers interested solely in the Bitzer 4HTE-20K CO₂ compressor, used commercially. The comparative analysis presented in Figures 12 and 13, intended to demonstrate that statistical models are superior to physical models, is unfair because statistical models are merely a way of treating experimental data. Please indicate in the manuscript text what the term "old prediction" means - statistical or theoretical (Figures 12 and 13). This paper also frequently contains the same misspellings. Using the definite article "the" followed by a symbol f is not proper because the words and symbols serve different functions.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

1. The manuscript highlights limitations in existing compressor models, the novelty could be stated more explicitly. Please clarify how this 1-D + 2-D polynomial regression approach differs from prior manufacturer-based correlations and physics-based efficiency modeling.
2. The reasoning behind selecting third-order and mixed-term polynomials is not clearly explained. Please justify the choice mathematically or through model selection criteria
3. A brief sensitivity analysis showing how coefficient variations affect prediction, especially at low frequencies, would provide confidence in model robustness.
4. The current study focuses on a single Bitzer CO₂ compressor. Please discuss broader applicability to other refrigerants, compressor sizes, or manufacturers.
5. The manuscript uses manufacturer software outputs for fitting. It would help to explicitly state the number of operating points and data granularity used in regression development.
6. Validation is performed against one publicly-available dataset. Consider adding additional independent test cases or provide a justification for why this single dataset is sufficient.
7. The model improves accuracy below 40 Hz, but the physical reasons are briefly mentioned. Providing a deeper engineering interpretation of why performance prediction difficulties arise at low speeds would enhance understanding.
8. Alongside max ±10% error, presenting RMSE or MAPE values and error histograms would offer a clearer view of prediction accuracy.
9. Define clearly whether predictions remain reliable outside the selected operating envelope ( <25 Hz or >70 Hz, or suction/discharge extremes).
10. Given the number of polynomial terms, a short note on overfitting prevention or validation partitioning would be valuable.
11. A brief comparison with machine learning models (SVR, ANN) or physics-enhanced hybrid models would help contextualize why polynomial correlations were preferred.
12. Although the method is “streamlined,” providing a remark on computational time vs physics-based models could support claims of efficiency.
13. Highlight which terms in the polynomial relations have physical interpretation vs purely empirical fitting to strengthen the model’s scientific grounding.
14. Ensure all variables have units upon first appearance, particularly in the mathematical model section (some equations appear without explicit units).
15. Add a sentence on measurement/model uncertainty, particularly refrigerant property estimation from CoolProp/RefProp.
16. Some figures contain overlapping trends and small labels. Consider increasing contrast, label size, and axis annotations for improved readability.
17. Equations (15–16) defining operational zones are introduced abruptly. Briefly justify these limits or cite the source for these constraints.
18. The paper notes lubrication/flow challenges at low speed. Including a citation or short explanation strengthens this claim.
19. It would be helpful to outline potential extensions, such as incorporating valve dynamics, thermal losses, or motor efficiency into the regression model.
20. The manuscript is generally clear, but a light English editing pass (clarity, grammar, removing repetition in Results/Discussion) would improve flow and readability.
21. A brief discussion on whether future learning-based approaches (DDPG, TD3) could complement the proposed polynomial model for real-time compressor optimization would be valuable. Cite this paper:

https://link.springer.com/article/10.1007/s41315-025-00475-x

Comments on the Quality of English Language

N/A

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors provided comprehensive explanations of their research and simultaneously improved the readability of the submitted manuscript. The editorial board of a scientific journal may consider publishing it. Regrettably, the authors focused exclusively on developing phenomenological models, which are not universal.

Reviewer 2 Report

Comments and Suggestions for Authors

After deep reviewing, I confirm that the authors have addressed all my previous comments and suggestions. The manuscript has improved significantly in quality and clarity. I have no further concerns and recommend the paper for acceptance.