the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Jul 2025
Surrogate-Based Design Optimization of Floating Wind Turbines in Time Domain
Abstract. Floating wind turbine (FWT) design involves higher costs and greater uncertainty than onshore or fixed-bottom offshore turbines due to low technology maturity, limited operational experience, and harsh marine environments; these factors have led to conservative design practices. To address these challenges, we introduce a novel two-step deterministic surrogate-based optimization framework that enables efficient time-domain design optimization for FWTs. In the first step, analytical design constraints are applied to refine the design space and establish a feasible region. In the second step, a surrogate model is trained on high-fidelity aero-hydro-elastic simulations, covering the reduced design space defined from step 1. During an optimization run, the surrogate model replaces computationally expensive direct time-domain analyses, capturing the dynamic response of the system with significantly reduced computational effort. This approach effectively balances model fidelity and computational cost, bridging the gap between conceptual and detailed design phases for floating wind structures. We demonstrate the framework on a semisubmersible platform (UMaine VolturnUS) coupled with the IEA 15 MW reference wind turbine, a representative large-scale FWT. Two primary design variables – the buoyancy column diameter and the overall floater radius – are optimized to minimize the levelized cost of energy (LCOE) of the system. The optimization incorporates global structural limit state constraints covering ultimate (ULS), fatigue (FLS), and serviceability (SLS) requirements to ensure the design’s structural feasibility. The surrogate-assisted optimization yields a design that achieves a LCOE of 176.9 /MWh, which is a 3.7 % reduction in LCOE relative to the baseline, with feasibility validated against all ULS, FLS, and SLS criteria. These results highlight the framework’s potential to reduce FWT costs and improve design reliability by enabling time-domain optimization without excessive computational expense.
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
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RC1: 'Comment on wes-2025-115', Anonymous Referee #1, 04 Aug 2025
The paper investigates the potential for optimizing floating wind turbines (FWTs) through a novel two-step hybrid optimization framework. This framework introduces innovation by combining design space reduction with surrogate-based modelling to enhance computational efficiency.
In the first step, the design space is reduced by applying design constraints aimed at excluding infeasible solutions. During this phase, the design variable vector Xᵈ (representing buoyancy column dimensions and floater radius) and the environmental condition vector Xᵉ are defined. Additionally, analytical design constraints are introduced based on the floater’s dynamic behaviour and overall geometric limitations.
In the second step, a surrogate model based on feedforward neural networks is trained using aero-hydro-servo-elastic simulations. This surrogate model enables efficient evaluation of the system’s dynamic performance, significantly reducing computational cost. The design space and environmental conditions are further refined using Latin Hypercube Sampling.
The framework is demonstrated using the UMaine VolturnUS semisubmersible platform coupled with the IEA 15 MW Reference Wind Turbine (RWT). The optimization design variables include the external column diameter and floater radius. The objective is to minimize the Levelized Cost of Energy (LCOE), subject to constraints related to ultimate loads, serviceability, and fatigue performance.
Comments and suggestions:- The introductory part on the differences between design approaches is interesting and relevant to the study. It is suggested to further expand that section and also add additional references.
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The method is overall interesting. However, claiming that it is general for FOWT is too pretentious as this stage since there are design variables in the rotor (especially large and very flexible ones) and in the coupling between the rotor and the floater/moorings that still need to be proven as feasible with surrogate models. It is recommended that the paper title and abstract more clearly convey the fact that the procedure is so far applied only to floater design (and also assuming only some of the design variables).
- The authors should better clarify the criteria with which the constraints in Table 5 have been selected.
- To enhance the impact of the study, it is suggested that the authors give an estimation of the saving in terms of computational cost with respect to a direct optimization using the complete model in the time domain. In other words, the reader should understand better why it is important to have the two steps separately and use the surrogate model then: how long did this process take, with respect to using the complete model in HAWC2, run for several DLCs and seeds with different geometries? Are we getting the same accuracy? Is it worth it in terms of cost vs. accuracy?
- A more critical discussion on the expected sensitivity of the results to the initial modelling choices, such as the selection of variables and constraints, would be valuable. Additionally, presenting the trends of key load responses in the optimized configuration compared to the baseline would help strengthen the analysis.
Citation: https://doi.org/10.5194/wes-2025-115-RC1 -
RC2: 'Comment on wes-2025-115', Anonymous Referee #2, 02 Sep 2025
Major Comments
- The paper presents an interesting and promising optimization concept that aims to reduce the design space exploration of FOWTs for generating surrogate models to support design optimization. This is a valuable direction, and the approach has potential to be quite impactful.
- The most notable contribution seems to be the proposed two-step approach and the development of the surrogate model. At present, however, the details provided may not be sufficient for readers to fully understand or replicate the methodology. In particular, the rationale behind specific design choices and the interpretation of the optimization results could be expanded to improve clarity and accessibility.
- The computational cost of constructing the surrogate model is not fully described, apart from mentioning that a supercomputing cluster was required. More context here (e.g., runtime, resources, or scaling considerations) would help readers assess the feasibility of applying this approach in other settings. Relatedly, it would be helpful to know how the surrogate model itself (and the resulting optimal design) was verified.
- The description of the high-fidelity database could be clarified further. For instance, it is not entirely clear how environmental and design-based samples were combined. Since this step appears central to constructing a reliable surrogate, additional details would strengthen the paper and improve reproducibility.
- The discussion of LCOE uncertainties is thoughtful. This raises the question of whether structural mass might serve as a more robust figure of merit with less uncertainty. Additionally, it would be useful to clarify whether (and how) AEP changes with the platform model.
- The sensitivity study could benefit from additional explanation. For example, how should the reader interpret the results shown in Figure 9? What is the reference for the reported errors?
- Figure 6 appears to play an important role in reducing the design space, but its meaning is somewhat difficult to interpret. For example, are the shown samples infeasible? How do the subfigures (a)–(f) relate to each other, and what do the different colors indicate? Adding clarification to the caption or text would improve readability.
- The process for building a Latin hypercube sampling from the feasible design space is not currently described, but seems to be an essential step in the study. Including this would strengthen the methodological transparency.
- The discussion of the final design optimization and results could be enriched. For example: which constraints are active? Which design variables changed, and why? What impact did these changes have on cost and constraints? Providing this interpretation would help highlight the significance of the results.
Minor Comments
- The first sentence of the abstract highlights uncertainty, but this theme does not appear again later in the paper. A more consistent discussion might improve the narrative.
- The phrase "buoyancy column diameter" could be made clearer, as technically all columns provide buoyancy.
- Tables and figures are sometimes referenced far from where they appear in the text, which can disrupt the flow of reading.
- The definitions of design constraints could be presented more clearly. The $g_i$ functions may not be necessary for readers, and plain language explanations might be more effective. Variable definitions should ideally appear in the captions if they are used within the tables (e.g., Tables 5 and 10). Additionally, the placement of these two tables feels quite far apart.
- "System stability" appears in the constraints with only one citation and minimal explanation. More context would be helpful here.
- The discussion of six random seeds is not entirely clear. Is this applied for each environmental case?
- Table 6 lists several optimization algorithms, but it is not clear which one was actually used in the study. If only one is applied, it may be best to focus on that rather than listing all.
- For the DEL calculations, it would be valuable to explain the assumption that each sample is equally likely, as this may not be obvious to readers.
- The distributions of the environmental parameters are not described. Were they fitted to metocean data? Including this information would be helpful.
- Section 3.6: the sentence beginning “SLS is defined as the maximum…” is difficult to parse and could be revised for clarity.
Style Comments
- Both “FOWT” and “FWT” are used; standardizing terminology would improve consistency.
- Sideways tables can be challenging to read. If possible, reformatting them would enhance readability.
- Figure labels should be consistent with the text size. At present, Figures 4–9 are difficult to read.
Citation: https://doi.org/10.5194/wes-2025-115-RC2
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