Spar-type platforms for floating offshore wind turbines are considered suitable for commercial wind farm deployment. To reduce the hurdles of such floating systems becoming competitive, in situ aero-hydro-servo-elastic simulations are applied to support conceptual design optimization by including transient and non-linear loads. For reasons of flexibility, the utilized optimization framework and problem are modularly structured so that the setup can be applied to both an initial conceptual design study for bringing innovative floater configurations to light and a subsequent optimization for obtaining detailed designs. In this paper, a spar floater for a 5 MW wind turbine is used as the basis. The approach for generating an initial but very innovative conceptual floater design comprises the segmentation of the floating cylinder into three parts, the specification of a freer optimization formulation with fewer restrictions on the floater geometry, and the allowance for alternative ballast materials. The optimization of the support structure focuses primarily on cost reduction, expressed in terms of the objective to minimize the floater structural material. The optimization results demonstrate significant potential for cost savings when alternative structural and manufacturing strategies are considered.

With floating support structures for offshore wind turbines, more offshore wind resources can be captured and used for power generation, as around 60 % to 80 % of the ocean areas cannot be exploited with bottom-fixed structures, which are limited to water depths of up to around 50 m

While the spar-buoy concept is already very convenient for volume production and certification due to its simple geometry, this technology has to be further advanced to benefit from a wider range of possible installation sites, simplified handling (both construction, assembly, transport, and installation), reduced levelized cost of energy (LCoE), and improved system motion performance

To obtain an advanced spar-type floater through optimization, most research approaches are based on the common cylindrical spar-type floater shape and utilize gradient-based methods

Thus, this paper aims to demonstrate that through a freer optimization formulation with in situ aero-hydro-servo-elastic simulations, more potential solutions for an advanced spar-type floater design with a higher degree of innovation can be captured, while already including transient and non-linear loads in the analysis. The conceptual design study and optimization approach, applied in this work, focus on hydrodynamic and system-level analyses but do not yet include an optimization of the mooring system. Due to the conceptual character of this study, which precisely targets exploring novel design spaces, stringent limitations on the structure and dimensions are not yet required. The optimization approach followed in this paper is based on an initial design optimization example by

To figure out in detail the required characteristics of such a floating platform, first (Sect.

According to the survey conducted by

As a starting point of the design optimization towards an innovative floating platform for an offshore wind turbine, a traditional spar-buoy FOWT system, taken from phase IV of the OC3 (Offshore Code Comparison Collaboration) project

An aero-hydro-servo-elastic coupled model of dynamics of this reference spar-buoy FOWT system is developed and verified by

The MoWiT model of the OC3 phase IV spar-buoy FOWT system (Sect.

Geometrical definitions of the advanced spar-type floating platform.

Apart from these modifications, which are directly related to advancements in the geometric configuration, the material density of the support structure and the wall thickness of the cylindrical spar-buoy elements are also changed. As the material density of the OC3 phase IV spar-buoy is not explicitly stated in the definition document

Referring here purely to the circumferential walls of the hollow cylindrical or conical elements, as for base and lid, a fixed marginal cap thickness of 0.0001 m is applied, according to the implemented model in the verification study

This results in a structural mass of

This way, a wall thickness of 0.0372 m is obtained for the initially adjusted OC3 phase IV spar-buoy with reduced material density (7850 kg m

Comparison of original and initially adjusted FOWT system parameters.

As the conceptual design (optimization) study does not focus on the mooring system, as already mentioned, and due to the fact that the mooring system itself could be covered in a separate or subsequent detailed design optimization task, any change in the restoring system characteristics due to shifted fairlead positions is prevented by utilizing constant (the original) resulting mooring system properties. This means that – independent of possible attachment points to the reshaped floating platform – the resulting stiffness of each mooring line is taken from the system motion, assuming the original fairlead positions as defined in Sect.

Within this study, the advancements for achieving the conceptual design of an innovative floating platform go beyond the main objectives to reduce the draft of the floater and the cost of the overall system. Further advanced features comprise the investigation of alternative materials, which from an economic point of view are comparable to currently used materials but positively influence the final floater design due to their different material properties and characteristics. Additionally, novel structural approaches, which might be more promising than the common approach of welding cylindrical and tapered sections together and allow a widening of the design space for such innovative floater shapes, are considered. In this conceptual design study, any detailed structural integrity checks are not yet addressed. However, due to the multi-fidelity model, optimization problem, and framework setup, these can be added easily for a more extensive optimization approach in a subsequent detailed design study. The advantage of focusing right now only on hydrodynamics and global system performance without defining any restrictions regarding structural aspects is that floater designs, which would have been discarded when performing structural integrity checks and as they would be impossible to realize with conventional structural approaches, can still be captured as potential solutions when considering different structural realization approaches.

From the advancements and associated assessment criteria detailed in the following, the modifiable design variables

Based on the derivation of the modified spar-buoy floater model (Sect.

Definition of the seven design variables.

The only structurally related focus considered in this approach is the minimization of the structural cost. This is represented by the objective function

Definition of the 25 inequality constraints.

To achieve a shortened length of the floater, the allowable system draft is limited to the original draft of the OC3 phase IV FOWT as its maximum value, as well as to a recommended minimum value of 15.0 m

The allowable value range for the diameter of each of the BC parts is set from machine epsilon – due to the same modeling feasibility reason – to 120.0 m, leading to the inequality constraints ^{®} floater by Ideol (outer dimensions: 36 m

After all these modifications, the ballast density has to be adjusted to match the original floating equilibrium between buoyancy force, system weight, and downward mooring force so that the original hub height is maintained. To exclude unfeasible system solutions, in which material would have to be removed from the system (realized, for example, by reducing the material density) to meet this equilibrium condition, it has to be ensured that the actual resulting ballast density carries a positive value, which is reflected through inequality constraint

Floating offshore wind project manager at a leading company in offshore industry, personal communication, 6 February 2020.

As particular attention is paid to the global system performance, there are three additional criteria which the FOWT system has to fulfill. For system rotational stability reasons, a maximum total inclination angle of 10.0

The final automated design optimization of the modified reference spar-type FOWT system described in Sect.

System parameters for preprocessing simulations of selected DLCs

When performing an iterative design optimization approach, it is not practical to simulate the full set of DLCs recommended by standards for each design considered. This is not only for reasons of high computational effort, but also due to the fact that not all DLCs may be relevant or design-driving for the specified optimization problem. Thus, in this work, the same approach as taken by

These 54 system simulations have already been performed by

The highest values for the three performance parameters and corresponding DLC simulation cases, based on the modified reference spar-type FOWT system.

Thus, this DLC 1.6 at 11.4 m s

The Python–Modelica framework for automated simulation and optimization, adapted from

The preprocessing DLC simulations (Sect.

Having modeled the reference spar-type FOWT system, described in Sect.

As the simulation tool, Dymola (Dynamic Modeling Laboratory) by Dassault Systèmes

The programming framework is coded in Python. The implemented scripts follow – as detailed in Fig.

To perform the iterative optimization of the reference FOWT system, the optimization algorithm (Sect.

Simulation settings.

From the broad range of available algorithms and methods

Having modeled the FOWT system (Sect.

Development of the design variables within the iterative optimization process: all simulated individuals are represented by light blue crosses and those complying with all constraints by dark blue crosses, the best-performing individual is marked with a yellow filled circle framed in orange, and the value corresponding to the reference FOWT system is plotted as a red line.

Within the iterative optimization algorithm, the values of the design variables for the 60 individuals of the first generation (number 0) are selected by the optimizer based on the specified allowable value ranges. All individuals are simulated in parallel on the available 60 processors and analyzed afterwards by the optimizer with respect to their fitness – meaning the objective function – and their compliance with the constraints based on the resulting time series, evaluated between 200 and 800 s. As simulations may have failed (due to poor performance of instable floating system designs which demonstrate a negative metacentric height), the simulated time is checked against the specified simulation stop time (800 s according to Table

Having evaluated the simulated individuals of generation 0, the optimizer selects the design variables for the individuals of the next generation (number 1), again in accordance with the specified allowable value ranges, but also based on the fitness and constraint compliance rate of each of the previous individuals, using the tournament selector for evaluating the dominance. Then, the loop of simulating individuals, evaluating each system with respect to the objective function and constraints, and re-selecting values for the design variables of the individuals of the next generation is repeated as long as the number of executed simulations is still below the specified total number of simulations of 10 000. This iterative optimization algorithm ends when the stop criterion is reached; the final results are now available.

The optimization run takes about 31 d and 11 h and comprises 10 011 individuals simulated in total, ranging from generation 0 up to generation 166, with full populations up to and including generation 165.

Development of the constraints within the iterative optimization process: all simulated individuals are represented by light cyan crosses and those complying with all constraints by dark bluish green crosses, the best-performing individual is marked with a yellow filled circle framed in orange, and the maximum allowable value is plotted as a red line.

Key figures of the exemplary potential innovative floater geometries.

In Fig.

Similarly, Fig.

As presented and mentioned in Sect.

Exemplary potential innovative floater geometries selected from the individuals complying with all constraints: the individuals complying with all constraints are represented by unfilled light blue circles, the best-performing individual is marked with a dark blue filled circle, and the value corresponding to the reference FOWT system is plotted as a red filled circle with the associated shape drawn with a red line.

Pendulum-stabilized innovative floating platform concepts.

Looking at the floater geometries presented in Fig.

The development of the objective function within the iterative optimization process, as presented in Fig.

Development of the objective function within the iterative optimization process: all simulated individuals are represented by light green crosses and those complying with all constraints by dark green crosses, the best-performing individual is marked with a yellow filled circle framed in orange, and the value corresponding to the reference FOWT system is plotted as a red line.

The individual with the minimum structural material volume yields a reduction of more than 31 % compared to the original (modified) reference spar-type floating platform, for which it must be noted that it has neither been designed with the same design requirements nor yet been optimized. The fact that this optimum solution is just found in the last generation states that the optimizer still tries to improve the result for the objective function since no convergence tolerance has been specified as a stop criterion, and the 10 000 simulations have to be completed. Evaluation of the individuals corresponding to the first 10 minimum objective function results yields – as some individuals yield the same objective function value – 16 individuals with just a

The geometry of the best-performing floater shape is shown schematically in Fig.

The best-performing floater geometry (black) in comparison to the original shape (red).

Key figures of the best-performing floater design.

Overall, the shape of the optimized conceptual floater design rather resembles a thick submerged barge-type floater, hanging below the upper column element. The constriction in the tapered part is significant and would not be directly feasible, both from a manufacturing point of view and with respect to structural integrity. The reason for the current shape obtained is the connection of the upper column to the upper BC part, which, however, is, as well as the middle BC part, negligible. Thus, for this floater configuration, the tapered part could directly connect the end of the upper column with the top of the lower BC part. The change in required structure material would not be that significant; however, the related change in the displaced water volume has to be taken into account by adjusting the structure mass and by carefully evaluating the system performance due to the shifted center of buoyancy. This realization by means of a tapered section, however, comes with a large diameter change and corresponding large taper angle, which may be critical for both hydrodynamic load calculations and manufacturing, as discussed in more detail in Sect.

The highest values for the three performance parameters and corresponding DLC simulation cases, based on the best-performing floating system.

Finally, with the conceptual design solution for the innovative FOWT platform obtained from the optimization run, the DLCs that are selected for the preprocessing automated system simulations for choosing the most critical DLC (as presented in Sect.

A shift in the criticality of the DLCs is observed: the smallest change in the criticality order of the 54 environmental conditions happens in the horizontal nacelle acceleration. Still, the cases of DLC 1.6 at cut-out wind speed, as well as around rated wind speed, are the most critical, but the DLC used within the iterative optimization algorithm is still among the first 10, with an acceleration value that is almost 12 % lower compared to the maximum obtained from all simulated DLCs. This, however, is itself more than 17 % below the maximum allowable horizontal nacelle acceleration and, hence, uncritical, which – on a side note – is not the case for the original floating spar-buoy wind turbine system. A significant increase in the resulting performance values and a considerable change in the degree of criticality of the environmental conditions are obtained for the mean translational motion. Here, the selected DLC for the optimization process drops from the original sixth position to the 22nd, while it is just 10 % below the highest value achieved, which is still less than half of the maximum allowable value and, hence, again uncritical. However, the most severe shift in the criticality of the DLCs happens in the total inclination angle. As indicated in Sect.

In addition to the results presented, analyzed, and discussed in Sect.

First of all, the duration of the optimization simulations needs to be dealt with. If an additional stop criterion based on a realistic convergence tolerance had been specified, only a fraction of the 10 000 simulations would have had to be simulated as the convergence tolerance would have been reached already after around 40 generations. Thus, the conceptual design study would have required just less than a quarter of the actual spent time. However, even around 181 h – which is more than a week – is still too long for just a conceptual design study, which should take no more than 2 d. The reason behind the currently quite long time required does not lie in the multi-fidelity framework and fully modular optimization problem setup, but rather in the developmental stage of the numerical model for a FOWT system

An 800 s load case simulation with a FOWT in an irregular sea state and with turbulent wind conditions takes about 4.5 h, which is about 20 times as much as the time to be simulated.

. While for bottom-fixed wind turbine systems, real-time capability of the numerical models based on MoWiT has already been achievedBased on the findings of the DLC simulations with the best-performing conceptual FOWT system design (Sect.

Considering the wide design space – especially the broad allowable value ranges for the structural diameters – and the extreme environmental conditions included in the DLC simulations, some refinements in the model with respect to the hydrodynamic calculations are suggested.

For an accurate representation of the hydrodynamic loads on the floating structure, the hydrodynamic coefficients have to be recalculated for each specific diameter. This is already done for the horizontal added mass coefficient and the total inertia force since the MacCamy–Fuchs approach is applied to each column element separately. However, the horizontal drag coefficient is currently not altered from the original value of 0.6, which is a valid assumption for large diameters already at low flow velocities, whereas for small-diameter structures, a horizontal drag coefficient around twice as large might be applicable

For more extreme environmental conditions with extreme waves and structures similar to those obtained with the optimization run that tend to have a large diameter directly at or close to the top of the BC, the upper surface of such a large diameter cylinder might become dry. This event has to be accounted for when calculating the added mass and damping coefficients in order to not overestimate the heave and pitch added mass and, thus, not underestimate the horizontal nacelle acceleration in the case of more energetic sea states.

The applied MacCamy–Fuchs approach is in principle only valid for cylinders with vertical walls and not for cylinders with abrupt diameter changes, leading to conical sections or even large horizontal surfaces anywhere along the column (the latter one, however, is considered again by means of the vertical Froude–Krylov excitation force, as discussed previously). If the MacCamy–Fuchs approach is applied to conical structures, in particular the high-frequency wave loads will be underestimated. This could be of the order of magnitude of up to 8 % or 14 % for a cone angle of around 6.7 or 12.2

As expected and as addressed and discussed in Sect.

In this paper, an automated optimization approach is applied to a spar-type FOWT system to develop a conceptual innovative floating platform design, which is optimized with respect to the change in hydrodynamics and their impact on the main system performance, while structural, manufacturability, or other constraints are not considered, whereas other advancements are facilitated. This approach, following a freer optimization formulation with in situ aero-hydro-servo-elastic simulations to include transient and non-linear loads already in the system analyses, is taken in order to be able to explore novel design spaces that can be better from a hydrodynamic point of view and show potential for more cost-efficient design solutions but may require novel structural approaches. The application is based on the OC3 phase IV reference spar-buoy FOWT system. This, however, is modified by dividing the spar-buoy base column into three distinct partitions so that sufficient buoyancy as well as a deep center of gravity can be obtained. Furthermore, the wall thickness is adjusted based on a common ratio of the support structure's structural mass to the displaced mass of water. The optimization focuses on the minimization of the steel volume of the floater, which represents an approximation of the capital expenditure of the floating platform. In addition, constraints regarding the outer dimensions (meaning the allowable value ranges of the design variables), the global fully coupled system performance, the system draft, the ballast, and the geometric integrity are defined, whereby advanced features – such as alternative ballast materials or novel structural approaches – are incorporated into the definition of the value ranges of the design variables and ballast density. Having selected, based on preprocessing automated system simulations, one DLC that is most critical for the constrained system performance criteria, the iterative optimization run is performed, utilizing the Python–Modelica framework for automated simulation and optimization, as well as using the genetic algorithm NSGA-II as the optimizer. The analysis of the optimization simulation results shows that the individuals that comply with all prescribed constraints aggregate as for their objective function values to an asymptote. The applied iterative optimization algorithm presented in this study yields a conceptual floating support structure design that has a more than 31 % reduced structure material volume compared to the original floating platform, meets all global performance criteria for the considered critical DLC, has an overall draft of 36.8 m, utilizes MagnaDense or high-density concrete as ballast material, and resembles a thick submerged barge-type floater. Based on the applied hydrodynamic and system-level analyses, an optimized initial innovative floater design is obtained, which has to be further refined by incorporating structural checks into the optimization process but can be realized by means of alternative structural approaches that utilize, for example, trusses or tendons instead of solely welding cylindrical sections together. Thus, the presented approach of expanding the design space and purposefully leaving out basic manufacturability constraints in the conceptual design study lets the optimizer explore novel configurations that are not necessarily covered by conventional floater manufacturing techniques. The results of the presented conceptual design optimization exhibit similarities to recent innovative design solutions, such as Stiesdal's TetraSpar and Saipem's Hexafloat, which emphasizes the potential for the industry.

The OC3 phase IV FOWT system consists of the NREL (National Renewable Energy Laboratory) 5 MW reference wind turbine

Main properties of the OC3 phase IV FOWT system

The code is not publicly accessible since it is embedded in the libraries developed at Fraunhofer IWES. However, MoWiT may be made available free of charge for academic use.

The data are not publicly accessible since they are embedded in the data depository at Fraunhofer IWES. However, MoWiT may be made available free of charge for academic use so that the data can be reproduced.

ML conceived and realized the work, performed the research, developed and applied the design optimization approach, analyzed the results, and wrote the paper. MC and AK supervised the work and reviewed the paper.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This research was partially supported by the Renewable Energy Marine Structures (REMS) Centre for Doctoral Training (CDT) and the German Fraunhofer Institute for Wind Energy Systems (Fraunhofer IWES).

This work was partially supported by grant EP/L016303/1 for Cranfield University, University of Oxford and University of Strathclyde, Centre for Doctoral Training in Renewable Energy Marine Structures – REMS (

This paper was edited by Katherine Dykes and reviewed by four anonymous referees.