Floating wind turbines must withstand a unique and challenging set of loads from the wind and ocean environment. To de-risk development, accurate predictions of these loads are necessary. Uncertainty in modeling predictions leads to larger required safety factors, increasing project costs and the levelized cost of energy. Complex aero-hydro-elastic modeling tools use many input parameters to represent the wind, waves, current, aerodynamic loads, hydrodynamic loads, and structural properties. It is helpful to understand which of these parameters ultimately drives a design. In this work, an ultimate and fatigue-proxy load sensitivity analysis was performed with 35 different input parameters, using an elementary effects approach to identify the most influential parameters for a case study involving the National Renewable Energy Laboratory (NREL) 5 MW baseline wind turbine atop the OC4-DeepCwind semisubmersible during normal operation. The importance of each parameter was evaluated using 14 response quantities of interest across three operational wind speed conditions.

The study concludes that turbulent wind velocity standard deviation is the parameter with the strongest sensitivity; this value is important not just for turbine loads, but also for the global system response. The system center of mass in the wind direction is found to have the highest impact on the system rotation and tower loads. The current velocity is found to be the most dominating parameter for the system global motion and consequently the mooring loads. All tested wind turbulence parameters in addition to the standard deviation are also found to be influential. Wave characteristics are influential for some fatigue-proxy loading but do not significantly impact the extreme ultimate loads in these operational load cases.

The required number of random seeds for stochastic environmental conditions is considered to ensure that the sensitivities are due to the input parameters and not due to the seed. The required number of analysis points in the parameter space is identified so that the conclusions represent a global sensitivity. The results are specific to the platform, turbine, and choice of parameter ranges, but the demonstrated approach can be applied widely to guide focus in parameter uncertainty.

It is projected that over 8 GW of floating wind energy will be installed by 2027

Not all inputs have an equal impact on the FOWT loads, and different types of loads are more sensitive to different inputs. Most modeling parameters have some uncertainty associated with them. This uncertainty could be due to inaccuracy in defining the parameter, physical statistical variability in the parameter, or changes in time throughout the life of a project. The impact of this uncertainty should be assessed for uncertainty in the ultimate and fatigue loads on the structure. It is helpful to understand which modeling inputs are really driving the uncertainty, so the analysis can be focused and efficient.

Sensitivity studies have previously been done for land-based and offshore wind turbines. One approach to assessing sensitivity is the elementary effects (EE) method. This method has commonly been used in the wind industry, where variance-based sensitivity approaches are difficult, given the complexity of the modeling. The EE method is sometimes called a screening method and can effectively identify the set of the most influential parameters, but it does not consider any coupling of inputs

In 2018, Robertson et al. used EE to assess the significance of 18 turbulent wind-inflow-related parameters for three different wind speed ranges on a land-based National Renewable Energy Laboratory (NREL) 5 MW baseline wind turbine. They found that shear and turbulence levels in the main wind direction were the most important parameters impacting the turbine loads

Wind turbine simulations are very complex, with a huge number of highly coupled input parameters. The EE approach with independent radial perturbations has been thoroughly tested for effects at the turbine level in the papers cited above. This process was extended to the farm level, with an emphasis on wake effects, in a 2021 project

Offshore wind energy deployments introduce a wide range of additional input parameters for the ocean environment and in the complex support structures. A 2023 study assessed the sensitivity of dynamic modal parameters to four modeling inputs: wind speed, rotor speed, nacelle yaw angle, and mean sea level for the fixed-bottom Block Island wind turbines

A 2022 study used the EE method to look at the sensitivity of fatigue to a broad set of continuous and discrete parameters, including cycles to failure curves for the tower and monopile

Floating platforms introduce more complexity. Not only are new modeling parameters involved, but the critical response can involve a new range of motions. It is predicted that FOWT costs can potentially be reduced more than 3 times by 2030 compared to 2021 costs

A demonstration of this is shown below. Section

The EE method tested with previous sensitivity studies was extended to a semisubmersible floating wind platform. A range of input parameters was selected, focusing on inputs previously identified as having a strong sensitivity and adding new offshore and floating support-structure-specific variables. The tested ranges of the input variables were chosen based on possible or expected levels of uncertainty. The study was conducted for an operating wind turbine in three different wind conditions: below rated, near rated, and above rated. These conditions correspond to wind speeds of 8.0, 12.0, and 18.0 m s

The wind turbine chosen in this study is the NREL offshore 5 MW baseline wind turbine. This device has open-source characteristics and has been used in many research efforts. It was designed to be representative of commercial turbines to help enable and advance conceptual design studies. The turbine features an upwind three-bladed rotor and uses variable speed and collective pitch control

The platform used in the study is the OC4-DeepCwind semisubmersible designed for the DeepCwind Consortium and adapted for a collaborative verification and validation project

DeepCwind floating offshore wind platform

The numerical modeling was performed using OpenFAST version 3.3.0 for the aero-hydro-servo-elastic analysis. The turbulent inflow wind was generated using TurbSim. The hydrodynamic forces on the floating platform were calculated in the HydroDyn module using a combination of potential flow coefficients and viscous-drag elements. The irregular wave field was generated using the JONSWAP spectrum, and the current was depth independent. Note that wave stretching was not included, with drag forces only applied up to the mean free surface; this will lead to an underprediction of second-order wave forces and a reduced sensitivity to the hydrodynamic forces near the waterline. Steady current was applied as a simple superposition on the wave velocities. No vortex shedding forces associated with the steady current are modeled. The first- and second-order potential flow calculations were performed using the panel method code WAMIT. The mooring system was modeled using the lumped-mass-dynamics-based MoorDyn module. The substructure was treated as rigid, but the tower and blades were compliant, and their deflections were calculated using the ElastoDyn module. Previous analysis of the NREL 5 MW baseline wind turbine has shown that the higher-fidelity BeamDyn solver produces results that are generally aligned with the lower-fidelity ElastoDyn solver. The largest difference for this turbine is that BeamDyn does predict a small amount of blade torsion not captured by ElastoDyn, but this is generally compensated for by the active blade-pitch controller. The aerodynamic forces were calculated in the AeroDyn module, using blade element momentum theory with unsteady aerodynamics and tower forces. The turbine was controlled using the ServoDyn module, using the baseline controller for the NREL 5 MW turbine atop the OC4-DeepCwind semisubmersible with a Bladed-style dynamic link library.

Each simulation was run for a 10 min time series with a 1 min transient removed from the results. This transient period was selected based on time series of the nominal load case for each of the three conditions. The time of the transient period was reduced by using initial surge and pitch values near their expected mean values for each wind speed. IEC recommends using at least six 10 min simulations, with potentially more depending on the specific FOWT and site

The EE method was outlined by Max Morris in 1991 for general computational experiments. The key advantage is one factor is adjusted at a time, reducing the total number of simulations required for a sensitivity assessment

A modification of the original technique uses radial perturbations of all parameters for a sufficiently large number of starting points. This radial EE method was described and tested by Robertsen et al. in 2018 and is used here

Three-parameter representation of input parameter hyperspace with a set of starting points and individual parameter perturbations, adapted from

In this work, the size of the perturbations was held constant, to

Irregular wave conditions and turbulent wind conditions require a seed for the pseudo-random number generator (pRNG) for phase information. There can be variation in loads based only on the seed, so a sufficient number of seeds should be tested to ensure the influence in the seed does not mask the influence of the parameter variation. IEC recommends a minimum of six seeds may be higher depending on the specific device and environmental condition

The output quantities of interest (

There are likely large differences in the output loads based on the wind speed condition. For ultimate loads, the maximum value experienced is a key concern, so if sensitivity is high, but the total load is still low, it is not important. To account for this, the ultimate sensitivity value includes the addition of the output for the nominal value of all input parameters corresponding to the wind speed (

Wind condition probability used for the fatigue-proxy elementary effects sensitivity calculation.

To identify which input parameters contributed to the highest sensitivity, significant events were defined following Eqs. (

Table

Modeling input parameters for sensitivity analysis (italic, wind and aerodynamics; plain, system and structure; bold, sea state and hydrodynamics).

For each input parameter, the potential range of uncertainty and a nominal value were selected. The ranges are based on either statistical variation in time or uncertainty. These values are shown in Table

Modeling input parameter ranges and nominal values for below-rated (BR), near-rated (NR), and above-rated (AR) wind speed bins (italic, wind and aerodynamics; plain, system and structure; bold, sea state and hydrodynamics). If only one value is given, it applies to all three wind conditions.

Continued.

In general, the variables are independent of each other. The exception to this is coupling between wind and wave misalignment, significant wave height, and peak wave period. The maximum significant wave height is a function of the wind and wave misalignment; waves can potentially be larger when the misalignment is small. Both the minimum and maximum wave periods are functions of the wave height.

The first 16 parameter ranges were based on the ranges from previous EE studies with some adjustments for an offshore wind environment

The justifications for the new floating-offshore-specific parameter range selections are as follows:

The significant wave height, peak period, and spectral shape factor are used to define the JONSWAP wave spectrum, as given by Eq. (

It should be noted that the previous work identifying the importance of this parameter included a wave stretching model. In this analysis without wave stretching it is expected that the significance will be reduced.

Wave height dependence on misalignment and wave period dependence on wave height from aggregate values (black) used from US East Coast (blue), West Coast (green), and Gulf Coast (red) comprehensive sites

A total of 14 quantities of interest were selected to evaluate the importance of each input parameter. Table

Output quantities of interest for load identification (italic, rotor-specific; roman, global system).

The blade root bending moment, yaw-bearing bending moment, tower base bending moment, low-speed shaft bending moment, and watch circle each have components in two directions. For ultimate loads, the value of each quantity was taken as the maximum vector magnitude. For fatigue-proxy loads, a load rose approach was used. The cycles were divided into 12 directional bins (15

The heel angle is a combination of the pitch and roll angle and was combined at every time step for both ultimate and fatigue-proxy loads following Eq. (

In total, 324 000 OpenFAST and 72 000 TurbSim simulations were run following the quantities in Eq. (

Ultimate EE value stacked histograms divided into wind speed conditions for 14 quantities of interest; the red line marks the threshold for the significant EE value.

Fatigue-proxy EE value stacked histograms divided into wind speed conditions for 14 quantities of interest; the red line marks the threshold for the significant EE value.

The histograms in Figs.

The ultimate values shown in Fig.

The bar graphs in Figs.

Floating offshore wind turbine ultimate load EE sensitivity, divided by load type; the solid bars correspond to turbine-specific responses, and the hatched bars correspond to global system responses (input parameter colors: red, inflow wind; magenta, aerodynamic forces; black, system and structure; blue, sea state; cyan, hydrodynamic forces).

Looking at the ultimate load sensitivity in Fig.

Looking at Fig.

Floating offshore wind turbine fatigue-proxy load EE sensitivity, divided by load type; the solid bars correspond to turbine-specific responses, and the hatched bars correspond to global system responses (input parameter colors: red, inflow wind; magenta, aerodynamic forces; black, system and structure; blue, sea state; cyan, hydrodynamic forces).

Convergence of the ultimate response sensitivity due to the number of random seeds.

The presented results in Sect.

Given the very large number of inputs, outputs, starting points, and wind speeds, it is difficult to look at the influence of the seed number for each input and output combination individually. Some examples of seed convergence for input and output combinations that led to a large number of significant sensitivity are shown in Figs.

Ultimately, the important criterion is that the identified most influential input parameters are not dependent upon the seeds used. This means that the bar plots in Figs.

Convergence of the fatigue-proxy response sensitivity due to the number of random seeds.

The ultimate load sensitivity for some important input parameters is almost independent of the number of seeds, including

The fatigue-proxy load sensitivity results converge much quicker than the ultimate load sensitivity results. Even for

The sensitivity results are determined to be converged after 90 seeds for ultimate loads and after 30 seeds for the fatigue-proxy loads. This process is likely load case and device dependent, so it should be performed independently for each application of the EE sensitivity analysis approach. The results shown in Figs.

Convergence of the ultimate response sensitivity due to the number of input parameter hyperspace starting points.

Convergence of the fatigue-proxy response sensitivity due to the number of input parameter hyperspace starting points.

The radial one-at-a-time perturbation method looks at the uncoupled sensitivity at a single point in the parameter hyperspace, within the ranges defined. Each point, chosen following the Sobol sequence, likely has a different local sensitivity value. To get a picture of the true sensitivity across the full domain, a sufficient number of starting points must be used. It should be noted that, while the process treats the inputs as fully uncoupled (with the exception of wave misalignment, height, and period), there are likely some combinations of inputs that would not be physically expected, and the sensitivities at these points can still influence the findings.

The number of necessary starting points is a function of the local second partial derivatives. When the derivative changes sharply through the domain, more starting points are needed for converged identification of the most important inputs. Similarly to the method of determining seed convergence, the sufficient number of starting points was determined by calculating the number of significant events per input using a range of 1 to

In this case, the sets of

For the ultimate load convergence, shown in Fig.

For the fatigue-proxy load convergence shown in Fig.

This work used a radial EE approach to identify which numerical modeling input variables have the most important effects on ultimate and fatigue-proxy loading of the DeepCwind floating platform supporting the NREL 5 MW offshore wind turbine. The standard deviation of the load was used as a proxy for the fatigue. This simplification quantifies load variability but likely underpredicts the sensitivity to input parameters which strongly influence load frequency. Non-linear fatigue paths were not included in this method at all. All modeling parameters have a range of validity, and this process can determine which uncertainty ranges should be assessed in greater detail. A total of 35 input parameters were tested and evaluated using 14 output responses. The results were delineated by output to understand which specific input and response relationships have the highest sensitivity. The required number of seeds used for stochastic irregular waves and turbulent wind environments was assessed to ensure that the variability due to seed was not influencing the conclusions. The required number of starting points in the parameter range domain was also assessed to ensure that the sensitivity assessment approximated a global sensitivity. In total, 324 000 OpenFAST simulations and 72 000 TurbSim simulations were run, spanning three different operating wind speed conditions.

The evaluated input parameters included wind and water environment descriptions, structural properties, and aerodynamic and hydrodynamic modeling coefficients. All parameter ranges were assessed to cover the possible variation due to changes in time, uncertainty in construction, or uncertainty in accuracy.

It was found that ultimate load EE values were highly stratified by wind speed; depending on the output load, either the above-rated or the near-rated condition contributed the most extreme load sensitivity. Significant fatigue-proxy EE values, however, were not clearly split by wind condition.

The EE approach has been shown to be effective for screening the most influential modeling parameters for FOWT load assessment. For the combination of the NREL 5 MW offshore wind turbine on the DeepCwind semisubmersible, the input parameters contributing to the highest sensitivity in ultimate loads are as follows:

primary,

secondary,

tertiary,

primary,

secondary,

tertiary, sheer,

Similarly to previous analyses with land-based wind turbines, the turbulent wind speed standard deviation in the main direction (

Mooring loads and device watch circles are dominated by the current. Almost no significant events in these outputs come from the wind or wave variables. When it comes to mooring design, a significant effort should be made to assess the true range of current speeds and directions.

With the exception of the horizontal center of mass, the system mass, inertia, and structural properties have a lower impact on the loads; environmental condition variability seems to be much more important. This is likely a platform-specific conclusion; the DeepCwind semisubmersible is a relatively stable design with a relatively large water-plane area and resonant frequencies outside of the main wave and wind energy. The one structure parameter that does have a high relative sensitivity is the horizontal system center of mass in the wind direction. This value is less important for the fatigue-proxy cyclic amplitudes but is by far the main driver for the extreme platform heel angle and, subsequently, the tower base bending moment.

While the wave misalignment angle, height, and period do have a meaningful influence on some fatigue-proxy values, it is somewhat surprising how little of an impact the wave conditions have on the extreme ultimate loads. The wave input perturbations contribute far fewer significant events than the current inputs and even fewer compared to the turbulent wind characteristics. This would indicate that significantly more emphasis should be placed on understanding the wind environment rather than the wave environment for an offshore wind site assessment for this floater. Future analyses that include idling conditions past the cut-out wind speed may find that wave inputs are more influential. It is likely that without the aerodynamic damping of the operational turbine, changes in the wave height and period may lead to more considerable changes in the ultimate loads on the platform. It is still logical that the waves are more influential for fatigue loading than for ultimate loading. Potential wave over-topping and slamming events could also be design drivers for platform stiffener design; however, these loads are difficult to understand using mid-fidelity modeling tools.

The method employed in this project can be used as an important step in the design process. The results identify which input parameter uncertainty ranges need to be given particular attention. The conclusions should be treated as unique to the individual platform and turbine, as well as the selected parameter ranges, and it is recommended that nonoperational load cases are also considered.

Figure

Fatigue-proxy EE value histograms divided by the wind speed condition for 14 quantities of interest with a zoomed-in

Figures

Figure

Figure

Figures

Seed convergence of the platform heel due to the system horizontal center of mass (blue line: nominal starting point, red line: perturbation in

Seed convergence of the low-speed shaft bending moment due to the turbulent wind speed standard deviation in the main wind direction (blue line: nominal starting point, red line: perturbation in

Seed convergence of the nacelle acceleration due to the turbulent wind speed standard deviation in the main wind direction (blue line: nominal starting point, red line: perturbation in

Seed convergence of the yaw-bearing yawing moment due to the turbulent wind speed standard deviation in the main wind direction (blue line: nominal starting point, red line: perturbation in

The OpenFAST and TurbSim models used in the study and the open-format versions of the summary plots found in the report can be publicly found at

Almost a total of 400 000 simulations were run (OpenFAST and TurbSim), resulting in a large set of input files and output data. This full set cannot be shared for practical reasons. Interested parties may contact the authors for additional information.

This project was conceptualized by JJ and AR, who provided oversight and coordination of all aspects. Initial parameter ranges were selected by KS and AR. The numerical model execution was performed by WW. The draft was prepared by WW with review and editing from JJ, AR, and KS.

At least one of the (co-)authors is a member of the editorial board of

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

We would like to thank Lu Wang of NREL for performing the potential flow calculations for the OC4-DeepCwind platform used in this analysis.

A portion of the research was performed using computational resources sponsored by the Department of Energy's Office of Energy Efficiency and Renewable Energy located at NREL.

This work was authored by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the US Department of Energy (DOE) under contract no. DE-AC36-08GO28308. Funding has been provided by the DOE Wind Energy Technologies Office. The views expressed in the article do not necessarily represent the views of the DOE or the US Government. The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for US Government purposes.

This research has been supported by the Wind Energy Technologies Office (grant no. DE-AC36-08GO28308).

This paper was edited by Julia Gottschall and reviewed by Erin Bachynski-Polić and one anonymous referee.