the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 17 Jun 2026
An Open-Access Integrated Hierarchical Optimization Framework applied to a 15 MW Medium-Speed Offshore Wind Turbine Drivetrain
Abstract. This work presents an open-access hierarchical, physics-based optimization framework for medium-speed wind turbine drivetrains. The methodology combines mixed-integer architecture exploration with continuous gradient-based refinement, enabling simultaneous optimization of gearbox topology, stage-ratio distribution, gear geometry, shaft sizing, and bearing selection under ISO 6336, ISO 281, and DIN 743 constraints.
Compared to previous design frameworks based on empirical scaling laws, such as WISDEM, the integrated stage-ratio optimization achieved drivetrain mass reductions of approximately 4–5 % while satisfying all design constraints.
Convergence studies demonstrated that the proposed hierarchical optimization strategy efficiently handles the complex mixed-integer design landscape, producing competitive gearbox solutions in <2.5 h on a desktop computer.
Applied to a 15 MW offshore wind turbine, the optimized medium-speed drivetrain achieved a total mass of 274.2 t, corresponding to a 31.5 % reduction relative to the direct-drive reference while maintaining comparable efficiency (97.2 %). The results demonstrate that integrated hierarchical optimization enables competitive drivetrain solutions for next-generation offshore wind turbines.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Wind Energy Science.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
(4057 KB) - Metadata XML
- BibTeX
- EndNote
Status: final response (author comments only)
- RC1: 'Comment on wes-2026-90', Anonymous Referee #1, 20 Jul 2026
-
RC2: 'Comment on wes-2026-90', Anonymous Referee #2, 23 Jul 2026
General Comments
- Overall I feel this is a high quality research paper that discusses the optimization of wind turbine gear boxes, and proposes an optimization architecture that is available for the community to use. In my view there are some minor issues to address, but the paper reads well and presents novel research in an appropriate forum. I am recommending this paper for publication with minor edits.Detailed Review
- Abstract has paragraph breaks, which is not typical in my experience
- Section 1 is strong and clearly identifies a gap in the state of the art, no notes
- Line 51: NVH acronym is introduced without explanation
- Style critique: Section 2 on the literature review is in stark contrast to the well motivated Section 1. The literature review feels dry, and though comprehensive, lacks connection to the point the paper is trying to make. Recommend trying to connect this in a stronger narrative form (eg, what gaps are left in each subsection, what are the limits, how does this paper address them). Lines 75-84 attempt to do this, but it is a little too late in my opinion.
- Generally I think Section 2 is functional and I have no technical concerns.
- Section 3: A conceptual geometry sketch (such as figure 2, though with somewhat improved clarity) would greatly improve reader understanding before diving in to Table 1. A concept sketch also helps to really clarify the design variables in a concise image. Not required for my sign off of the paper, but strong suggestion.
- Eqn 2: Normalized weighted objectives can work, but this is an instance of true multi-objective optimization. No concerns, just noting.
- Table 2 would benefit from a notes or references column like the one presented in Table 3.
- Section 3.2 is clear, no notes
- Figure 1: I havent read the section yet, but this figure does not give me a great understanding of what is going on here. XDSM models would likely be the standard here (though personally I am not a fan of XDSM models without additional annotation and notes), but I think the biggest issue is I don't really understand what is being transferred over between the two columns. There is also no feedback loop, which I would expect for a hierarchial optimization strategy. Hopefully the text will enhance my understanding.
- I'd like to see a little more explanation of the choice of the DE algorithm over something like a Genetic Algorithm, which tends to be more common for this type of problem. Blanket log transformations also can have some consequences (the transformation can sometimes lead to poorly scaled spaces in certain variables), would be nice to see a little more on that as a conditioning strategy.
- No citations from lines 139-164, and there should be (at least citing the sources of the algorithms). I view this as a blocking change to publication, though it is minor
- Section 3.4: This is all valid and are standard tricks to employ, however, this section really needs to be expanded, as the nuances of which constraints this is done for and how will have a significant impact on the final result.
- Figure 2 comes too late, and is too cluttered for it to be helpful as presented (what are the triangles?). Recommend a rethink on this figure to present a specific thing (eg, design variables, gearbox position, etc.). Dont be afraid to split into two or more figures if needed.
- Table 5: Unintroduced acronyms (DLC, NTM, ETM, EDC...)
- Sections 4.3.1, 4.3.2, and 4.3.3 felt a little like a rehash of previous sections
- Table 6 is fine, but lacks the context for me to understand it
- Table 7 would benefit from figures mentioned in my above comments
- Figure 5 is interesting, but I dont know what the labels are (db, epsilon, x_s, x_p). Its possible they were mentioned in the earlier paper, but would be nice to have more explaination in the figure label of what I'm looking at. It looks cool though
- Figure 6: again, I feel I'm lacking some context for this. Legends are also illegible due to font size.
- Figure 11 has overlapping text labels, but otherwise this is a great figure (python has a label offset term you can pass in, or you can directly pin the text box on x,y coordinates)
- Figure 12 image resolution is poor on the version I have (in python, export as pdf or svg, or increase the dpi value)
- Figure 13 also has resolution issues (but this is also a great figure)
- Body of the paper is strong and forms a complete narrative in my view
- Tables A1 and A2 appear before the Appendix header
- Appendix A1 is helpful, but I still feel the presentation of design variables needs to be improved (ie, copying A1 into the body of the paper would not be sufficient in my view). I think this specific presentation makes sense as an Appendix
- I actually would prefer to see Appendix 4 (and maybe Appendix 5) in the body of the paper, but I think it is fine as AppendixCritical Issues
- Overall I feel the optimization is presented well, but I think the missing piece is the foundation explaining the design variables in the model. IE, show me a picture of the system being optimized, clearly identify the design variables (whether they be discrete or continuous), group them into sets, and then show how the optimizer goes through them. In the early part of the paper, I felt this was the most critical weakness. I would recommend that the authors make a pass at improving this, but I do feel the paper does currently clear the bar for publication.
- Generally it would be nice to see some stronger justification for algorithm choices (DE vs GA, SLSQP vs IP, etc.). However, authors could justifiably state this is beyond scope of the current work.
- Citations need to be added in Section 3.3
- Section 3.4 needs to be expanded to show what constraints have been modified and how, unless these can be cited in published literature.
- Generally I feel the figures need more explicit context and framing in the narrative. At times reading the paper feels like an overwhelming amount of data that as a reader I'm not sure how to interpret. I advise either 1) expand explanations in the narrative for the figures or 2) consider removing some of the figures (and maybe tables). These should support the core narrative the authors are trying to tell, but at times this thread is lost.Final Thoughts
- Overall I feel this is a strong and well written paper that deserves to be published
- This is an appropriate forum for publication
- I am returning to the editor a recommendation of accept with minor revisions
- I would be happy to review again, but I doubt it will be necessary
- Sorry for the slow review, I enjoyed reading this paper!Citation: https://doi.org/10.5194/wes-2026-90-RC2
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 67 | 12 | 4 | 83 | 4 | 6 |
- HTML: 67
- PDF: 12
- XML: 4
- Total: 83
- BibTeX: 4
- EndNote: 6
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1. The optimization framework is essentially quasi-static. How would the optimized drivetrain change if dynamic load amplification and drivetrain dynamics were considered?
2. The internal load calculation assumes equal load sharing among planetary gears. How does this assumption affect the optimization results?
3. OpenFAST loads are directly used as boundary conditions. How sensitive are the optimization results to the fidelity of the applied drivetrain loads?
4. The fatigue methodology is insufficiently described. Please clarify how fatigue loads and bearing lifetime are calculated.
5. The framework is validated against KISSsoft and WISDEM only. I suggest discussing the expected performance compared with multibody dynamics tools？