An Open-Access Integrated Hierarchical Optimization Framework applied to a 15 MW Medium-Speed Offshore Wind Turbine Drivetrain

Mehlan, Felix C.; Nejad, Amir R.

doi:10.5194/wes-2026-90

Preprints

https://doi.org/10.5194/wes-2026-90

Preprints

17 Jun 2026

| 17 Jun 2026

Status: a revised version of this preprint is currently under review for the journal WES.

An Open-Access Integrated Hierarchical Optimization Framework applied to a 15 MW Medium-Speed Offshore Wind Turbine Drivetrain

Felix C. Mehlan and Amir R. Nejad

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.

Received: 18 May 2026 – Discussion started: 17 Jun 2026

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.

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Felix C. Mehlan and Amir R. Nejad

Status: final response (author comments only)

RC1:
'Comment on wes-2026-90', Anonymous Referee #1, 20 Jul 2026

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？

Citation: https://doi.org/10.5194/wes-2026-90-RC1
- AC1:
  'Reply on RC1', Felix Christian Mehlan, 18 Aug 2026
  We would like to thank the Editor and the Reviewers for their constructive comments and suggestions. We have revised the manuscript accordingly and believe that the changes have improved its presentation. Below, we provide a point-by-point response to all comments and describe the corresponding revisions made to the manuscript.
  The optimization framework is essentially quasi-static. How would the optimized drivetrain change if dynamic load amplification and drivetrain dynamics were considered?
  The optimization framework is indeed quasi-static to enable repeated iterations of the optimization loop with reasonable computational costs. As part of the MADE4WIND project, a separate high-fidelity multibody system (MBS) model of the optimized drivetrain has also been developed. This model includes shaft and planet-carrier flexibility, gear meshing and bearing models to capture to represent internal drivetrain dynamics with a high fidelity. The computational cost of the MBS simulations is approximately 12-15 h for a single 3600 s design load case, which makes direct integration into the optimization loop impractical. The present framework therefore uses quasi-static load calculations for design-space exploration, while the MBS model is used for a verification step for selected optimized designs. Dynamic effects may alter local peak loads and load sharing among planet gears and could therefore affect safety margins. Quantifying such changes is the subject of ongoing validation work within the MADE4WIND project. We added section “4.1.3 Validation against multi-body simulation” to better state the limitations and scope of the current work.
  
  The internal load calculation assumes equal load sharing among planetary gears. How does this assumption affect the optimization results?
  The quasi-static internal load model assumes equal nominal sharing among the planets; however, the gear strength calculations do not use the nominal load directly. A mesh load-sharing factor K_gamma according ISO 6336, is applied to account for unequal load distribution among the planets. This increases the design load used in the gear strength calculations relative to ideal equal sharing. Preliminary simulation results with the MBS model reveal that the assumed values of K_gamma = [1.20, 1,35] for N_P = [4, 5] are conservative and yield safe designs, however, this is part of ongoing work.
  
  OpenFAST loads are directly used as boundary conditions. How sensitive are the optimization results to the fidelity of the applied drivetrain loads?
  We agree that the optimized drivetrain depends on the fidelity of the applied boundary loads. In the current framework, torque and rotor loads from OpenFAST simulations are treated deterministically and uncertainty in aeroelastic load calculation is not propagated through the optimization. Because the governing gear, bearing, and shaft constraints scale differently with transmitted load, changes in the applied load spectrum can alter not only component dimensions but also the active constraints and therefore the preferred stage-ratio distribution. The current study should therefore be interpreted as conditional on the prescribed load set. Reliability-based optimization methods could address the challenge of uncertainty propagation, which we see as a potential extension of our work. We extended section 3.3 with a brief discussion on this topic.
  
  The fatigue methodology is insufficiently described. Please clarify how fatigue loads and bearing lifetime are calculated.
  Section 3.3 was expanded to include more details on the stress cycle counting methods, gear loads and bearing lifetime calculations.
  
  The framework is validated against KISSsoft and WISDEM only. I suggest discussing the expected performance compared with multibody dynamics tools?
  As discussed in answer to the first question, validation against multibody simulation models is subject of ongoing work. Added section “4.1.3 Validation against multi-body simulation” for clarity.
  
  Citation: https://doi.org/10.5194/wes-2026-90-AC1
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 Appendix
Critical 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
- AC2:
  'Reply on RC2', Felix Christian Mehlan, 18 Aug 2026
  We would like to thank the Editor and the Reviewers for their constructive comments and suggestions. We have revised the manuscript accordingly and believe that the changes have improved its presentation. Below, we provide a point-by-point response to all comments and describe the corresponding revisions made to the manuscript.
  Abstract has paragraph breaks, which is not typical in my experience
  Abstract breaks have been removed.
  
  Section 1 is strong and clearly identifies a gap in the state of the art, no notes
  Agreed
  
  Line 51: NVH acronym is introduced without explanation
  NVH explanation added
  
  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.
  Section 2 has been revised to provide a clearer narrative connecting the different areas of gearbox optimization research. The revised literature review now discusses the limitations and remaining gaps of the individual approaches as they are introduced.
  
  Generally I think Section 2 is functional and I have no technical concerns.
  Agreed
  
  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.
  
  A new conceptual gearbox geometry sketch (Figure 1) has been added, illustrating the drivetrain configuration and design variables.
  
  Eqn 2: Normalized weighted objectives can work, but this is an instance of true multi-objective optimization. No concerns, just noting.
  
  We agree that the problem is inherently multi-objective. The revised manuscript explicitly refers to the formulation as a scalarized multi-objective optimization problem, where the weighting parameter w is used to address the trade-off between the design objectives of weight and efficiency.
  
  Table 2 would benefit from a notes or references column like the one presented in Table 3.
  The variable bounds are referencing the default values from KISSsoft, as stated in the table caption.
  
  Section 3.2 is clear, no notes
  Agreed
  
  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.
  Figure 1 has been replaced with a revised flowchart of the hierarchical optimization framework. Feedback paths and more information on the transferred variables, objectives and constraints were added. The description in Section 3 has been revised accordingly.
  
  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.
  
  Revised section 3.5 with additional justification for the selection of DE. DE was selected here because it provides a population representation with relatively few tuning parameters and performed robustly in the convergence studies presented section 4.3. We also acknowledge that alternative population-based method such as GA, could be applied, however a systematic algorithm comparison is beyond the scope of this work. More justification on the log-transformation was added to section 3.5. Since the stage ratios are of comparable magnitude and constrained by narrow upper and lower bounds, the transformation does not introduce strongly disparate variable scales.
  
  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
  
  Added references for DE, Sobol sampling, SLSQP, JAX and SciPy implementations.
  
  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.
  
  Expanded section 3.4 to describe the differentiable reformulations required for the gradient-based optimization. Table 3 was added to summarize modified operations, mathematical formulations and numerical tolerances, and the specific component calculations in which they are applied. The numerical approximations were verified against the original calculations and the parameters were selected such that the resulting residual errors remain below 1e-9.
  
  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.
  
  Figure 2 has been replaced by two figures: (1) A conceptual gearbox geometry sketch (Figure 1) illustrating the drivetrain configuration and design variables. (2) revised flowchart of the hierarchical optimization framework (Figure 2)
  
  Table 5: Unintroduced acronyms (DLC, NTM, ETM, EDC...)
  
  Added definitions of DLC, NTM, ETM, EDC to table caption.
  
  Sections 4.3.1, 4.3.2, and 4.3.3 felt a little like a rehash of previous sections
  
  sections 4.3.1-4.3.3 have been revised to reduce repetition with the methodology.
  
  Table 6 is fine, but lacks the context for me to understand it
  
  Added more context to the table caption.
  
  Table 7 would benefit from figures mentioned in my above comments
  
  Added reference to the new Figure 1, illustrating the design variables in the table caption
  
  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
  
  Added variable description to the table caption
  
  Figure 6: again, I feel I'm lacking some context for this. Legends are also illegible due to font size.
  
  Revised Figure 6 to reduce clutter, increase font size and better highlight areas of distinct normal module values with dashed lines. Also added more detail to the table caption.
  
  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)
  
  Fixed the overlapping labels.
  
  Figure 12 image resolution is poor on the version I have (in python, export as pdf or svg, or increase the dpi value)
  
  Re-printed figure 12 in .eps-format for higher resolution
  
  Figure 13 also has resolution issues (but this is also a great figure)
  Re-printed figure 13 in .eps-format for higher resolution
  
  Body of the paper is strong and forms a complete narrative in my view
  Agreed
  
  Tables A1 and A2 appear before the Appendix header
  
  Moved Tables A1 and A2 further down
  
  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
  Presentation of the design variables has been revised with an added Figure 1, as discussed in the response to earlier questions.
  
  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 Appendix
  Thank you for the suggestion. We prefer to keep this part in the appendix, as it mostly covers calculations based on ISO standards and we would like to focus the methodology section on the novel optimization framework.
  
  Critical 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.
  The beginning of Section 3 has been revised to provide the missing foundation for the optimization framework. Figure 1 was added, which illustrates the system being optimized and identifies the system-level, discrete stage-level, and continuous stage-level design variables. Figure 2 then shows how these variable groups are passed through the three nested optimization layers and how optimized quantities are returned between them.
  
  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.
  Provided further justification for the solver choices based on the characteristics of the respective optimization layers in section 3.5. DE is used for the non-convex and locally non-smooth outer and discrete optimization problems, while SLSQP is applied to the differentiable, constrained continuous subproblem, where analytical gradients are available through automatic differentiation. Other algorithms, such as GA and IP, could also be considered, however, a systematic comparison of optimization algorithms is beyond the scope of the present study. The suitability and convergence behavior of the selected algorithms are further examined in Sections 4.3 and 4.4.
  
  Citations need to be added in Section 3.3
  Added references for DE, Sobol sampling, SLSQP, JAX and SciPy implementations
  
  Section 3.4 needs to be expanded to show what constraints have been modified and how, unless these can be cited in published literature.
  Expanded section 3.4 to describe the differentiable reformulations required for the gradient-based optimization. Table 3 was added to summarize modified operations, mathematical formulations and numerical tolerances, and the specific component calculations in which they are applied. The numerical approximations were verified against the original calculations and the parameters were selected such that the resulting residual errors remain below 1e-9.
  
  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.
  Tables and figures have been edited (in particular Fig 1 and 2) to provide a better narrative. Figure captions and the surrounding discussion have been expanded to provide clearer context. Redundant methodological descriptions have been reduced, where possible. We hope that these changes will improve the reader’s flow.
  
  Citation: https://doi.org/10.5194/wes-2026-90-AC2

Felix C. Mehlan and Amir R. Nejad

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Short summary

This study presents a new open-access framework for designing offshore wind turbine drivetrains. The method automatically explores different gearbox layouts and component sizes to find lighter and more efficient designs while satisfying engineering safety requirements. Applied to a 15 megawatt offshore wind turbine, the optimized drivetrain achieved a 31.5 % lower mass than a direct-drive reference design while maintaining similar efficiency.


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