Impact of Non-Gaussian Winds on Blade Loading and Fatigue of Floating Offshore Wind Turbines

Abstract

This study introduces a novel methodology for estimating loading and fatigue damage in the blades of wind turbines, emphasizing non-Gaussian wind conditions’ impact. By calculating blade loading and fatigue using higher statistical moments of the irregular winds, the study demonstrates the significance of non-Gaussian effects on loading and fatigue predictions. A two-step methodology is developed to synthesize non-Gaussian wind processes, integrating the TurbSim (version 1.5) and Hermite moment model transformation methods. These wind time histories are then utilized in a fully coupled simulation of a floating wind turbine, integrating with a blade beam model. Preliminary analysis of wind thrust and the blade root bending moment indicates non-Gaussian effects on aerodynamic loading. Further analysis of fatigue reveals that fatigue hot spots vary along the blade surface, depending on short-term wind conditions and long-term wind distribution, with total fatigue life estimated by summing the fatigue damage at each potential hot spot. The probability density function of long-term wind process is estimated by fitting the Weibull distribution to measured buoy data. The results show that variations in long-term wind speed distributions lead to an average fatigue life difference of about 1.3 years (16%). The Gaussian wind model overestimates fatigue life by roughly 1.5 years (18%) compared to the non-Gaussian model. This highlights the importance of considering both long-term wind distributions and short-term wind characteristics for accurate fatigue assessment. The findings provide valuable insights for the design and operation of floating offshore wind turbines.

1. Introduction

Floating offshore wind turbines (FOWTs) operating in the harsh and dynamic ocean environment are subjected to continuous cyclic loading throughout their operational lifespan. Over a typical 20-year service life, a wind turbine may experience more than 10⁸ load cycles, assuming a rotational speed of 20 revolutions per minute and an annual operation of 4000 h [1]. It is widely reported that the capital costs of offshore wind developments are approximately 1.5 to 2 times higher than those of onshore counterparts [2], while maintenance costs can be 5 to 10 times greater [3]. Given these substantial costs, accurate estimation of fatigue damage is crucial for ensuring the long-term reliability, structural integrity, and economic viability of offshore wind energy systems.

Fatigue damage in FOWTs arises from the progressive accumulation of structural degradation due to repeated cyclic environmental loadings, including wind, waves, currents, and mooring forces. The inherent variability and the long-term uncertainty of offshore environmental conditions, coupled with the complex dynamics of FOWT systems, make fatigue damage calculations and life predictions both challenging and computationally intensive, especially for the blades. It is impractical to conduct high-fidelity simulation for complete operational life; therefore, short-term calculation and long-term estimation are usually combined for fatigue assessment. Early foundational studies established basic frameworks for FOWT blade fatigue assessment. For instance, Miner’s linear damage accumulation rule was applied with the stress spectra derived from long-term operational data for blade fatigue assessment [4]; finite element simulation of blades was coupled with long-term Weibull wind speed distribution for accumulated fatigue damage evaluation [5], while the Weibull and log-logistic distributions of wind speed and turbulence intensity were proposed to be used for 10-min short-term simulations for blade fatigue assessment [6]. Recently, Song et al. [7] adopted a C-vine copula method to model concurrent wind and wave conditions and proposed a probability-based sampling method to determine the load conditions used for fatigue analysis, considering the uncertainty of finite sampling. Zhao et al. [8] proposed a fatigue reliability analysis method implementing with a surrogate model, C-vine copula, and Monte Carlo simulation in which the back-propagation neural network and the Kriging model were used as the surrogate model to predict short-term fatigue damage. Ding et al. [9] proposed a novel direct probability integral method for the stochastic response and fatigue reliability analysis of the key components for the floating offshore wind turbine structures. However, a significant limitation of these and many related studies is their reliance on the assumption of Gaussian wind processes.

Analysis of field-measured wind speed data indicates that short-term natural wind conditions often deviate from a Gaussian distribution [10]. Such non-Gaussian inflow characteristics can considerably influence offshore wind turbine performance, including power output, structural loads, torque variability, and blade fatigue life [11]. The increased frequency of extreme wind events under non-Gaussian conditions intensifies alternating loads on the airfoil and main shaft, thereby amplifying torque fluctuations and potentially aggravating fatigue damage [12]. Schöttler et al. [13], through wind tunnel experiments, demonstrated that extreme aerodynamic loads occur far more frequently under non-Gaussian inflows than predicted by conventional Gaussian models. Likewise, Gong and Chen [14] analyzed the extreme structural responses of wind turbines operating under non-Gaussian wind fields in both operational and parked states, and the results showed that blade root edgewise and tower base fore-aft bending moments were significantly higher during operation, while the blade root flapwise bending moment exhibited similar amplification under parked conditions.

Although some research has considered non-Gaussian wind conditions, a systematic methodology for converting between Gaussian and non-Gaussian wind speed models remains underdeveloped. Furthermore, while various fatigue evaluation frameworks have been proposed, a comparative analysis showing the impact on blade loads and fatigue life under non-Gaussian wind conditions is still lacking.

To address these gaps, this study proposes a comprehensive methodology for evaluating blade fatigue damage by integrating short-term dynamic analysis of FOWTs with a non-Gaussian wind model and long-term wind speed distributions derived from field measurements. An advanced numerical transformation approach based on the Hermite Moment Model has been developed to generate non-Gaussian random wind fields from conventional Gaussian wind models for short-term dynamic analyses [15,16,17]. Blade fatigue damage under both Gaussian and non-Gaussian wind conditions is comparatively assessed using the in-house numerical simulation tool, Loose, which integrates linearized and nonlinear blade solvers formulated on the geometrically exact beam theory [18]. The Loose code has been thoroughly validated against well-established simulation tools, exhibiting strong consistency in dynamic responses across various design load cases (DLCs), including scenarios of free and forced vibrations [18]. These results offer new perspectives on how non-Gaussian wind characteristics impact blade loading and fatigue life, thereby contributing to the enhanced structural reliability of wind turbines under realistic operational conditions.

The main novelties of this study can be summarized as follows:

(1) A new methodology is proposed to systematically incorporate the influence of higher-order moments of wind speed (e.g., kurtosis) into fatigue life estimation for floating offshore wind turbines.

(2) The study develops an integrated fatigue analysis framework that combines short-term wind characteristics with long-term wind speed distributions, allowing for a more realistic assessment of fatigue damage accumulation.

(3) A comprehensive comparison between Gaussian and non-Gaussian wind models is performed through fully coupled aero-hydro-servo-elastic simulations on the NREL OC3-Hywind model, providing quantitative insights into the implications for design and operation under non-Gaussian wind conditions.

The remainder of this paper is organized into three main sections. Section 2 presents the theoretical framework for simulating short-term stochastic wind conditions, as well as the transformation methodology between non-Gaussian and Gaussian wind fields. Furthermore, it analyzes the long-term wind speed distribution using met-ocean data collected from National Oceanic and Atmospheric Administration (NOAA) buoys. The aerodynamic wind loads on blades during short-term conditions and the identification of fatigue damage hotspots over long-term periods are also discussed. Section 3 presents a case study that applies the proposed fatigue analysis approach to the OC3-Hywind wind turbine blade incorporating various design load cases (DLCs) to validate the methodology. Results related to blade loading and fatigue damage are also provided in this section. Finally, Section 4 concludes the study with discussions and key findings.

2. Methodology

2.1. Non-Gaussian Character of Wind Thrust

To evaluate turbine performance under aerodynamic loading, the thrust coefficient has been introduced to characterize the relationship between wind speed and the thrust generated by the rotor. The instantaneous thrust $T_1$ in the torque-controlled region (from cut-in speed to rated speed) is commonly estimated as $T_1=C_{T}0.5\rho \pi R^2{u}^2$ [19], where, $\rho$ denotes the air density, $R$ represents the blade rotor radius, and $T_1$ and $u$ correspond to the instantaneous thrust and wind speed values, respectively. The thrust coefficient $C_T$ is typically determined either from direct field measurements or numerical simulations [20]. The thrust expression is able to be further simplified by consolidating these coefficients into a single power constant, k:

$$T_1=k_1{u}^2$$

(1)

where $k_1$ remains constant for a given $C_T$ value. This equation, $T=k{u}^2,$ is widely adopted to characterize turbine performance during the torque-controlled operational mode, corresponding to the plateau region of the thrust coefficient curve observed in experimental investigations [21].

The decreasing segment of the thrust coefficient curve beyond the rated wind speed corresponds to the pitch-controlled region, spanning from the rated speed up to the cut-out speed, where the wind velocity surpasses the turbine’s optimal energy conversion capacity. Within this range, the blade pitch angle is actively regulated to constrain torque and rotational speed, thereby preventing the turbine from exceeding its rated power output [22]. Ideally, a wind turbine operating under pitch control maintains a constant rated power and torque irrespective of wind speed fluctuations. Nonetheless, actual turbines exhibit power variability caused by turbulence effects and inherent control system limitations [23]. The network performed by the wind on the turbine system, after subtracting the electrical energy generated, approximately equals the change in the system’s retained energy, predominantly related to rotor speed variations. At the bounding extremes, a massless rotor would experience instantaneous thrust given by

$$T_2=k_2{u}^2$$

(2)

where $k_2$ varies with the blade pitch angle.

Accordingly, the wind turbine thrust is computed as a combination of the thrust contributions from separate processes representing the torque- and pitch-controlled modes. The total expected thrust in the torque-controlled region $R_1$ can be computed as a function of wind speed weighted by the probability of that speed. The instantaneous thrust in the torque-controlled region is estimated as $T_1=k_1{u}^2$, which can be combined with the probability density function $g_1$ as a radon transform integral over the range of wind speeds in $R_1$:

$$E\left(T_1\right)={\int }_{u_{cut-in}}^{u_r}{T}_1\left(u\right)g_1\left(u\right)du={\int }_{u_{cut-in}}^{u_r}{k}_1{u}^2{g}_1\left(u\right)du$$

(3)

where distribution $g_1$ generally varies depending on geographic location, and constant $k_1$ varies according to individual wind turbine design. The function $T_1=k_1{u}^2$ can be expanded around the mean ${\mu }_1$ as a three-term Taylor series:

$$E\left(T_1\right)={\int }_{u_{cut-in}}^{u_r}\left[T_1\left({\mu }_1\right)+\left(u-{\mu }_1\right)T_1^{\prime }\left({\mu }_1\right)+{\displaystyle \frac{1}{2}}{\left(u-{\mu }_1\right)}^2{T}_1″\left({\mu }_1\right)\right]g_1\left(u\right)du$$

(4)

in which ${\mu }_1$ is the centroid of the region of the probability density function (PDF) between the cut-in and rated wind speeds. The first and second derivatives of the thrust $T_1\left(u\right)$ are ${T_1}^{\prime }\left(u\right)=2k_{1}u$ and ${T_1}^{″}\left(u\right)=2k_1$. Substituting $T_1\left(u\right)=k_1{u}^2$, ${\int }_{u_{cut-in}}^{u_r}u{g}_1\left(u\right)du={\mu }_1$, and ${\int }_{u_{cut-in}}^{u_r}{g}_1\left(u\right)du=1$ into Equation (4) yields the expected thrust’s second-order approximation:

$$E\left(T_1\right)=T_1\left({\mu }_1\right)+{\displaystyle \frac{1}{2}}{Var}_1\left(u\right){T_1}^{″}\left({\mu }_1\right)=k_1({\mu }_1^2+{\sigma }_1^2)$$

(5)

in which ${Var}_1\left(u\right)={{\sigma }_1}^2$ is the variance of the wind speed distribution truncated between the cut-in and rated speed.

The variance of the wind power output can be represented:

$$Var\left(T_1\right)={\int }_{u_{cut-in}}^{u_r}{\left[T_1\left(u\right)-E\left(T_1\right)\right]}^2{g}_1\left(u\right)du$$

(6)

Substituting Equation (5) into Equation (6) and using the first three terms of the Taylor series expansion of $T_1\left(u\right)$ yields an expression for the variance of the power resulting from winds within $R_1$ only:

$$Var\left(T_1\right)={Var}_1\left(u\right){{T_1}^{\prime }\left({\mu }_1\right)}^2+E\left[{\left(u-{\mu }_1\right)}^3\right]{T_1}^{\prime }\left({\mu }_1\right){T_1}^{″}\left({\mu }_1\right)+{\displaystyle \frac{1}{4}}E\left[{\left(u-{\mu }_1\right)}^4\right]{{T_1}^{″}\left({\mu }_1\right)}^2-{\displaystyle \frac{1}{4}}{{Var}_1}^2\left(u\right){{T_1}^{″}\left({\mu }_1\right)}^2$$

(7)

In which the expectation in the second and third terms can be recognized as the wind speeds’ third and fourth raw moments within $R_1$. Substituting ${Var}_1\left(u\right)={{\sigma }_1}^2$, ${T_1}^{\prime }\left(u\right)=2k_{1}u$ and ${T_1}^{″}\left(u\right)=2k_1$, skewness ${\alpha }_3=E[{\left(u-\mu \right)}^3]/{\sigma }^3$, and kurtosis ${\alpha }_4=E{[\left(u-\mu \right)}^4]/{\sigma }^4$ into Equation (7):

$$Var\left(T_1\right)=4k_1^2{\mu }_1^2{\sigma }_1^2+4k_1^2{\mu }_1{\sigma }_1^3{\alpha }_3+k_1^2{\sigma }_1^4{\alpha }_4-k_1^2{\sigma }_1^4$$

(8)

Considering that relevant research indicates that the non-Gaussian nature is primarily reflected in kurtosis rather than skewness [24], ${\alpha }_3$ is, therefore, assumed to be zero in this study. As a result, Equation (8) can be simplified to express the thrust standard deviation in the torque-controlled region $R_1$:

$$Std\left(T_1\right)=k_1{\sigma }_1\sqrt{4{\mu }_1^2+{\sigma }_1^2({\alpha }_4-1)}$$

(9)

A similar derivation can be performed for the pitch-controlled region using Equation (2); however, the details are omitted in this paper for brevity. According to the discussion above, the first two statistical parameters of thrust depend on the first four statistical parameters of wind speed. Based on Equations (5) and (9), the Gaussian wind process and the corresponding non-Gaussian wind process yield similar thrust mean values; however, the thrust standard deviation of the non-Gaussian wind process should be larger when the kurtosis is higher. Non-Gaussian effects on blade loading are investigated in Section 3.1 through comparisons of wind thrust and blade root bending moment for different wind processes.

2.2. Simulation of Short-Term Wind Process

To generate Gaussian wind fields, simulations are carried out using a predefined average wind speed along with the associated turbulence intensity. The synthetic wind time series are produced by TurbSim, a statistical inflow simulator developed by the National Renewable Energy Laboratory (NREL) [25]. The turbulence intensity (TI) is quantified as the standard deviation of wind speed divided by its mean value and is expressed as $TI={\sigma }_u/{\mu }_u$. TurbSim provides dynamic turbulence intensities based on different turbulence models, with recommended TI values varying according to the design load cases (DLCs) specified by IEC standards. The IEC Normal Turbulence Model (NTM), widely used in practice, defines the standard deviation of wind speed as

$$\sigma =I_{ref}\left(0.75\mu +5.6\right)$$

(10)

where $\mu$ is the mean wind speed, and $I_{ref}$ denotes the expected hub-height turbulence intensity.

Wind speed time series are typically synthesized from wind power spectral densities using approaches grounded in the central limit theorem, which guarantees that the generated wind fluctuations conform to a Gaussian distribution. To capture non-Gaussian characteristics observed in realistic wind fields, the Hermite Moment Model is applied to convert the originally Gaussian wind speed signals into non-Gaussian processes [15,16].

The initial wind field dataset from TurbSim includes the time histories of the horizontal wind velocity component $u_h$, horizontal angle $\phi$, and vertical wind velocity component $u_z$. These components form the total velocity vector $\left|\overrightarrow{u}\right|=\sqrt{u_h^2+u_z^2}$ with vertical angle $\theta =\mathit{arctan}\left({\displaystyle \frac{u_z}{u_h}}\right)$. The total velocity $\overrightarrow{u}$ from the TurbSim wind field dataset could be described by Gaussian distribution. Its non-Gaussian corresponding vector $\overrightarrow{u^{\prime }}$ is obtained by applying the Hermite Moment Model transformation $\mathcal{H}$ to the modulus of the original velocity vector.

$$\left|\overrightarrow{u^{\prime }}\right|=\mathcal{H}\left(\left|\overrightarrow{u}\right|\right)=\kappa [\left|\overrightarrow{u}\right|+h_3\left({\left|\overrightarrow{u}\right|}^2-1\right)+h_4\left({\left|\overrightarrow{u}\right|}^3-3\left|\overrightarrow{u}\right|\right)]$$

(11)

where $\kappa$ is a scale factor, and coefficients $h_3={\displaystyle \frac{{\alpha }_3}{6}}$ and $h_4={\displaystyle \frac{{\alpha }_4-3}{24}}$ in Equation (11) are directly calculated based on the values of ${\alpha }_3$ and ${\alpha }_4$.

The wind velocity horizontal component $u_h^{\prime }$ and vertical component $u_z^{\prime }$ of non-Gaussian wind process are calculated using the of non-Gaussian total wind velocity vector modulus $\left|\overrightarrow{u^{\prime }}\right|$ and vertical angle $\theta$ using $u_h^{\prime }=\left|\overrightarrow{u^{\prime }}\right|\mathit{sin}\theta$ and $u_z^{\prime }=\left|\overrightarrow{u^{\prime }}\right|\mathit{cos}\theta$. This process involves first transforming the Gaussian wind speed data into its non-Gaussian equivalent using the Hermite Moment Model and then calculating the non-Gaussian horizontal and vertical components from the transformed total wind velocity vector and the vertical angle. This transformation is shown in Figure 1.

The identical transformation procedure is uniformly applied to all wind speed datasets within the original input files, ensuring a seamless conversion of the initial Gaussian wind field into its corresponding non-Gaussian counterpart without altering the mean wind speed or its standard deviation. This approach preserves the key statistical characteristics of the original data while introducing non-Gaussian features. A representative example of a simulated wind speed time history sample and its transformed non-Gaussian counterpart are shown in Figure 2. The figure clearly shows that the main differences between the two wind processes appear at the extreme wind speed events.

The non-Gaussian transformation in this study follows the classical Hermite moment method originally implemented [15] as the work was initiated before the recent advances in asymptotic Hermite modeling [17]. Future research will explore incorporating this updated framework to improve 3D parametric representation of non-Gaussian wind fields.

2.3. Numerical Simulation of FOWT

Numerical simulations are carried out using an in-house FOWT simulation tool, Loose. Loose is a fully coupled aero-hydro-servo-elastic framework for FOWTs [18] in which the multi-body dynamics are solved using the momentum cloud method, while blade dynamics are computed via either a linearized or a nonlinear beam model based on geometrically exact momentum-based beam theory. The Loose code has been extensively developed and benchmarked against the FAST code, with its accuracy verified in the referenced studies.

The Normal Turbulence Model (NTM) is employed to generate the wind field, which includes full-field, three-component stochastic wind fluctuations along with a vertical wind profile characterized by a power law shear exponent of 0.14 [26]. Wind time histories are generated using TurbSim, with turbulence intensity kept constant for each design load case (DLC) based on field measurement data.

For the wave field, the Normal Sea State (NSS) model is employed to represent random and irregular sea conditions. The amplitudes of wave components are determined by the JONSWAP spectrum, derived from measurements collected during the Joint North Sea Wave Observation Project [27].

$$S\left(w\right)=\alpha {\displaystyle \frac{g^2}{{\omega }^5}}{e}^{-{\displaystyle \frac{5}{4}}{\left({\displaystyle \frac{\omega }{{\omega }_P}}\right)}^{-4}}{\gamma }^{e^{-0.5{\left({\displaystyle \frac{\omega -{\omega }_P}{\sigma {\omega }_P}}\right)}^2}}$$

(12)

The JONSWAP spectrum is characterized by the expression $\alpha =5.061{\left({\displaystyle \frac{{\omega }_P}{2\pi }}\right)}^4{H}_s^2\left(1-0.287\log \gamma \right)$, where the peak enhance coefficient $\gamma$ is 3.3, $H_s$ denotes the significant wave height, ${\omega }_P$ is the peak frequency, and ${\omega }_P={\displaystyle \frac{1}{T_p}}$.

The significant wave height $H_s$ and peak spectral period $T_p$ of both Gaussian and non-Gaussian model DLCs are calculated assuming of fully developed seas state [28], following $H_s={\displaystyle \frac{0.21u_{19.5}^2}{g}}$ and $T_p={\displaystyle \frac{7.14u_{19.5}}{g}}$, where $u_{19.5}$ is the wind speed at reference height of 19.5 m.

Aerodynamic wind loads are determined using the NREL AeroDyn subroutine [29], which employs blade-element momentum theory to compute forces on the blades based on wind speed time series. Within the time-domain simulation framework, an integrated blade pitch controller dynamically modifies each blade’s pitch angle in response to rotor speed changes, thereby stabilizing the power output [30]. Wave forces are determined using the modified Morison equation, which accounts for the motion of the hull through the water:

$$F_w=\rho C_{m}V\dot{u}+{\displaystyle \frac{1}{2}}\rho C_{d}Au\left|u\right|$$

(13)

where $C_m$ and $C_d$ are the inertia and drag coefficients, respectively, and the water particle velocity $u$ and acceleration $\dot{u}$ are derived from Airy wave theory.

NREL OC3-Hywind 5 MW wind turbine blade [31] is adopted in this study. The OC3-Hywind represents a floating wind turbine system designed for deepwater conditions, featuring a spar-buoy support structure. The turbine operates under a variable-speed pitch control strategy, with a rated wind speed of 11.4 m/s, hub height of 90 m, and rotor diameter of 126 m, as illustrated in Figure 3. In the figure, the yellow area represents the seabed, the blue area indicates the sea surface, and the white lines show the mooring lines.

The major parameters of the OC3-Hywind 5 MW wind turbine are shown in

Table 1. OC3-Hywind 5 MW wind turbine parameters.

Parameters	Value
Rotor, Hub Diameter	126 m, 3 m
Hub Height	90 m
Cut-in, Rated, Cut-out wind speed	3 m/s, 11.4 m/s, 25 m/s
Cut-in, Rated rotor speed	6.9 rpm, 12.1 rpm
Generator Electrical Efficiency	94.4%
Rotor Mass	110,000 kg
Nacelle Mass	240,000 kg
Tower Mass	347,460 kg
Initial CM	85.6 m
Elevation to Tower Top	87.6 m
Platform Diameter above Taper	6.5 m
Platform Diameter below Taper	9.4 m
Platform Draft	120 m

, and the details of the model parameters can be found in NREL’s documents [31].

2.4. Fatigue Damage of the Blades

Flapwise and edgewise bending plus axial tension are the major loadings exerted on the blades, and blade fatigue damage can be estimated using the time histories of normal strains occurred on blade cross-sections. Both tensile and compressive strains are considered and a constant life diagram (CLD) of the material is employed to account for the effects of mean strain level and the reversal amplitude around a mean strain.

Given that blade deflections are typically small, the cross-sectional planes are assumed to remain planar during deformation. Accordingly, the normal strain at a point (x, y) within a cross-section is calculated as follows:

$${\epsilon }_z\left(x,y\right)=-{\displaystyle \frac{M_1}{E{I}_1}}x+{\displaystyle \frac{M_2}{E{I}_2}}y+{\displaystyle \frac{N}{EA}}$$

(14)

where $x$ and $y$ represent the distances to the cross-sectional elastic center along the local principal axes (see Figure 4); $M_1$ and $M_2$ denote the bending moments; $N$ denotes the axial force; $E$ denotes Young’s modulus; and $E{I}_1$, $E{I}_2$, and $EA$ are the cross-sectional bending and axial stiffnesses, respectively. The detailed nodal configuration of the blade cross-section is illustrated in Figure 4.

Time histories of normal strain at various nodes along the blade shell are computed using the in-house FOWT simulation tool Loose, which adopts a linearized geometrically exact beam model. In addition to aerodynamic loads and gravity, the analysis accounts for inertial forces induced by rotor rotation and the motion of the floating platform to fully capture the effects of random wind and wave conditions.

Fatigue damage induced by these stochastic external loads is assessed through the rainflow cycle counting technique coupled with a cumulative damage model. The rainflow counting procedure is implemented in an in-house code following the ASTM standard [32]. For each node, the number of stress cycles is identified by applying the rainflow algorithm to its strain time history over a single numerical simulation with a duration of $T_s$ seconds. These cycle counts are organized into a matrix $M_{m,a}$ for each wind condition simulation, where indices $m$ and $a$ are associated with the mean strain ${\epsilon }_m$ and strain amplitude ${\epsilon }_a$, respectively. This matrix is then scaled to an annual cycle matrix $N_{m,a}$ by multiplying it by a factor that accounts for the ratio of one year to the simulation duration $T_s$:

$$N_{m,a}={\displaystyle \frac{M_{m,a}}{T_s}}\left(60·60·24·365\right)$$

(15)

The annual total fatigue damage at an individual node on the blade shell is estimated using Miner’s rule, which assumes that damage accumulates linearly with each loading cycle over time. This approach allows the cumulative fatigue damage to be determined by summing the damage fractions of all identified cycles [33].

$$d=\sum _{m,a}{\displaystyle \frac{N_{m,a}}{N_{f,ma}}}$$

(16)

where $N_{f,ma}$ denotes the matrix representing the number of cycles to failure for each unique combination of mean strain ${\epsilon }_m$ and strain amplitude ${\epsilon }_a$, corresponding to the cycle matrix $N_{m,a}.$ The number of cycles to failure for each pair of mean strain and strain amplitude is obtained from a CLD specific to the blade material. The use of a CLD enables corrections for different mean strains and amplitudes through the normal strain ratio, defined as $R={\displaystyle \frac{{\epsilon }_{z,min}}{{\epsilon }_{z,max}}}$.

Although the OC3 Hywind model is a theoretical model and its blade material is not defined in the NREL documents, the wind turbine blades are usually manufactured using glass fiber-reinforced polymers (GFRPs). Fossum et al. [34] and Tang et al. [18] choose GFRP material S1 for a shell to study the fatigue performance of wind turbine blades. Therefore, material S1 is adopted as the representative shell material for this fatigue analysis in this study. The corresponding constant life diagram for material S1 (Figure 5) is employed to determine the number of cycles to failure under various loading conditions.

The one-year-equivalent fatigue damage for nodes on the blade shell is obtained for a single simulation case by aggregating the damage at each node into the damage matrix ${\mathit{D}}_{\mathit{i}}$, which contains $80\times 23$ elements each representing node damage $d$. The index $i$ of this matrix corresponds to the environmental conditions applied in the simulation. The blade model consists of 23 cross-sectional stations distributed along its span. Each cross-section contains 80 nodes arranged on the shell surface, as shown in Figure 4.

2.5. Fatigue Life Estimation of the Blade

Fatigue hotspot identification over the entire operational period is performed by estimating fatigue loads for each component based on the local wind speed distribution. For instance, a study utilizing six years of wind data from five meteorological stations in Hong Kong employed a Weibull distribution model to characterize the statistical properties of the local wind climate [35]. The PDF of the Weibull distribution is expressed [36]:

$$f_w\left(u\right)={\displaystyle \frac{k}{\lambda }}{\left({\displaystyle \frac{u}{\lambda }}\right)}^{k-1}{e}^{-{\left({\displaystyle \frac{u}{\lambda }}\right)}^k}$$

(17)

The cumulative distribution function (CDF) is given:

$$F_w\left(u\right)=1-e^{-{\left({\displaystyle \frac{u}{\lambda }}\right)}^k}$$

(18)

where $\lambda$ and $k$ are the scale and shape parameter, respectively.

Two hypothetical cases are developed using the OC3-Hywind 5 MW offshore wind turbine deployed at two prospective offshore wind farm sites. The first case uses wind speed data from NOAA Station 44065 near New York Harbor. The second case uses data from NOAA Station 46006, located roughly 600 miles away from California. These stations were selected for their suitable annual mean wind speeds for a OC3-Hywind Model. Photographs of the two NOAA stations are presented in Figure 6.

Figure 7 shows the one-year wind speed histograms and their Weibull distribution fits for both cases based on NOAA station data.

The scale parameter $\lambda$ and shape parameter $k$ are listed in

Table 2. Parameters of Weibull distribution for each case.

Parameters	$\mathit{\lambda }$	$\mathit{k}$
Case 1	10.24	2.00
Case 2	11.40	2.31

.

Wind speeds at the turbine hub height are estimated from these measurements by applying the power law, as given in Equation (19) [37]:

$$u_{hub}=u_{buoy}{\left({\displaystyle \frac{z_2}{z_1}}\right)}^P$$

(19)

where $u_{hub}$ is the wind speed at the hub height $z_2$ of wind turbine, $P=0.14$ is the wind shear exponent for normal wind conditions, and $u_{buoy}$ is the wind speed at the anemometer height $z_1$.

The long-term fatigue life of the FOWT blades is assessed by integrating short-term fatigue damage, calculated under operational wind and wave conditions, with the likelihood of these conditions occurring. This analysis excludes turbine faults, start-ups, shutdowns, and parked states. According to fatigue Design Load Case (DLC) 1.2 in IEC 61400-3, wind speeds are categorized into 12 bins, spanning from the cut-in speed of 3 m/s to the cut-out speed of 25 m/s. Corresponding wave conditions are defined for each wind speed bin, and the probabilities derived from historical buoy data are listed in

Table 3. Probabilities of wind speed bins.

Wind Speed (m/s)		0–3	4–5	6–7	8–9	10–11	12–13
$\mathrm{Probability}{\mathit{P}}_{\mathit{i}}$	Case 1	0.082	0.149	0.167	0.158	0.132	0.099
	Case 2	0.045	0.118	0.154	0.166	0.153	0.124
Wind Speed (m/s)		14–15	16–17	18–19	20–21	22–23	24–25
$\mathrm{Probability}{\mathit{P}}_{\mathit{i}}$	Case 1	0.067	0.042	0.024	0.012	0.005	0.003
	Case 2	0.089	0.055	0.031	0.015	0.007	0.003

.

The first bin, which is below the cut-in speed, is neglected because the wind turbine is not started. The last two bins are also neglected due to their low probability and contribution to the total fatigue damage. Therefore, the other nine bins are chosen to form the DLCs of this research.

By combining the probability of occurrence with the damage matrix for each wind speed bin, the expected fatigue damage matrix for the entire operational period is calculated using Equation (20).

$${\left[{\mathit{D}}_{\mathit{E}}\right]}_{80\times 23}=\sum _{i=1}^n{P}_i{\left[{\mathit{D}}_{\mathit{i}}\right]}_{80\times 23}$$

(20)

where ${\mathit{D}}_{\mathit{E}}$ denotes the expected fatigue damage matrix, $P_i$ denotes the probability associated with the i-th wind speed bin, and ${\mathit{D}}_{\mathit{i}}$ is the corresponding fatigue damage matrix.

The cross-sectional node with the maximum value in the expected damage matrix ${\mathit{D}}_{\mathit{E}}$ is identified as the fatigue “hotspot” on the blade, representing the location most susceptible to crack initiation.

$$d_{hotspot}=\max {\left[\begin{array}{ccc}{d}_{\mathrm{1,1}}& \dots & d_{\mathrm{1,23}}\\ ⋮& \ddots & ⋮\\ d_{\mathrm{80,1}}& \dots & d_{\mathrm{80,23}}\end{array}\right]}_E$$

(21)

According to Palmgren–Miner’s linear damage hypothesis, failure is expected to occur at the hotspot location when the cumulative fatigue damage reaches a value of 1 [38]. This assumption implies that the total accumulated damage is the sum of the damage fractions from all load cycles, with failure predicted once this total equal or exceeds unity. The annual fatigue damage of the blades is assumed to be constant over the entire operational life of the FOWT. Therefore, the fatigue life of the turbine blades is estimated using hotspot damage according to Equation (22). In this paper, the term “fatigue life” refers to the duration from the beginning of the FOWT deployment until the occurrence of the first crack on the shell of the blade, rather than the time until the complete failure of the entire structure.

$$T_Y={\displaystyle \frac{1}{d_{hotspot}}}$$

(22)

In summary, the FOWT is numerically simulated for each mean wind speed condition to assess the wind loads on the blades. Subsequently, the fatigue damage at nodes distributed along the blade shell is calculated. The fatigue damage matrices for each wind speed bin are then integrated with the long-term wind speed distribution to estimate the annual cumulative fatigue damage at each node. The node with the highest expected damage is identified as the “hotspot”, representing the most probable location for fatigue crack initiation. The overall process for estimating blade fatigue life is illustrated in Figure 8.

3. Result

This section begins by investigating the impact of non-Gaussian wind characteristics on wind thrust and the blade root bending moment. The effectiveness of the proposed integrated method is then demonstrated through blade fatigue life evaluation under both Gaussian and non-Gaussian wind conditions.

3.1. Loading Analysis of Blade

As derived in Section 2.1, the variance of wind thrust for a wind turbine operating in the torque-controlled region is linked to the kurtosis of the wind process, underscoring its non-Gaussian nature. However, since the maximum aerodynamic loading on the blades typically occurs near the rated wind speed (11.4 m/s for the OC3-Hywind 5 MW turbine), it is essential to assess non-Gaussian effects on blade loading across both the torque-controlled and pitch-controlled operational regions.

Short-term numerical simulations of 600 s duration are performed at a mean wind speed of 10 m/s, under corresponding wave conditions, while varying the kurtosis of the wind processes. IEC Turbulence Models A and C are applied, with wind speed standard deviations of 2.096 m/s and 1.572 m/s, respectively. Blade pitch control is active during the simulations. The mean values and standard deviations of the resulting turbine wind thrust and flapwise blade root bending moment are summarized in

Table 4. Wind thrusts and blade root bending moments with various wind kurtoses (mean wind speed = 10 m/s, NTM Class A).

Wind Condition				Wave		Wind Thrust		Blade Root Bending Moment (Flapwise)
Mean (m/s)	Std (m/s)	Skewness	Kurtosis	Significant Height (m)	Peak Period (s)	Mean (${10}^5$  N)	Std (${10}^5$  N)	Mean (${10}^6$  Nm)	Std (${10}^6$  Nm)
10	2.096	0	1.5	1.53	6.15	4.76	1.60	7.63	2.41
10	2.096	0	2.0	1.53	6.15	4.77	1.61	7.64	2.42
10	2.096	0	2.5	1.53	6.15	4.78	1.61	7.65	2.42
10	2.096	0	3.0 (Gaussian)	1.53	6.15	4.79	1.61	7.67	2.42
10	2.096	0	3.5	1.53	6.15	4.80	1.62	7.69	2.43
10	2.096	0	4.0	1.53	6.15	4.81	1.63	7.71	2.44
10	2.096	0	4.5	1.53	6.15	4.83	1.64	7.74	2.44

and

Table 5. Wind thrusts and blade root bending moments with various wind kurtoses (mean wind speed = 10 m/s, NTM Class C).

Wind Condition				Wave		Wind Thrust		Blade Root Bending Moment (Flapwise)
Mean (m/s)	Std (m/s)	Skewness	Kurtosis	Significant Height (m)	Peak Period (s)	Mean( ${10}^5$  N)	Std ${10}^5$N)	Mean( ${10}^6$  Nm)	Std( ${10}^6$  Nm)
10	1.572	0	1.5	1.53	6.15	5.09	1.31	8.13	1.95
10	1.572	0	2.0	1.53	6.15	5.10	1.31	8.14	1.95
10	1.572	0	2.5	1.53	6.15	5.11	1.32	8.15	1.97
10	1.572	0	3.0 (Gaussian)	1.53	6.15	5.11	1.33	8.15	1.98
10	1.572	0	3.5	1.53	6.15	5.11	1.33	8.15	1.99
10	1.572	0	4.0	1.53	6.15	5.11	1.33	8.16	1.99
10	1.572	0	4.5	1.53	6.15	5.12	1.33	8.17	1.99

. In these tables, the text “Gaussian” in the parentheses indicates that the parameters of this DLC follow a Gaussian distribution, with a skewness of 0 and a kurtosis of 3.

The time histories of blade pitch angle and turbine power output are shown in Figure 9.

The wind turbine operates in both the torque-controlled and pitch-controlled regions, with blade pitch activated to regulate the generator power. For both turbulence models, the mean and standard deviation of wind thrust and blade root bending moment increase progressively with the kurtosis of the wind process. This trend clearly highlights the non-Gaussian effects of wind conditions on blade aerodynamic loading, even in the pitch-controlled regions.

3.2. Fatigue Analysis of Blade

Blade fatigue analysis is carried out to illustrate the implementation of the proposed method on the OC3-Hywind model and its blades. Two sets of Design Load Cases (DLCs) are considered: DLC 1.x for Gaussian wind conditions and DLC 2.x for non-Gaussian wind conditions. Each set includes nine wind speed bins ranging from 4 m/s to 21 m/s, covering the turbine’s operating range. For each DLC, a 10-min simulation is conducted ($T_s$ = 600 s).

The details of the Gaussian wind model DLCs are summarized in

Table 6. DLCs for Gaussian cases.

	Wind				Wave
DLC/ Gaussian	Mean (m/s)	Std (m/s)	Skewness	Kurtosis	Significant Height (m)	Peak Period (s)
1.1	4	1.032	0	3	0.24	2.46
1.2	6	1.212	0	3	0.55	3.69
1.3	8	1.392	0	3	0.98	4.92
1.4	10	1.572	0	3	1.53	6.15
1.5	12	1.752	0	3	2.20	7.38
1.6	14	1.932	0	3	3.00	8.62
1.7	16	2.112	0	3	3.91	9.85
1.8	18	2.292	0	3	4.95	11.08
1.9	20	2.472	0	3	6.12	12.31

, with standard deviation values derived from IEC Turbulence Model C.

The DLC 2.x series, corresponding to the non-Gaussian wind model, are simulated for comparison with the previously obtained Gaussian simulation results. The detailed parameters of the non-Gaussian wind model DLCs are summarized in

Table 7. DLCs for non-Gaussian cases with dynamic coefficients.

	Wind				Wave
DLC/ Gaussian	Mean (m/s)	Std (m/s)	Skewness	Kurtosis	Significant Height (m)	Peak Period (s)
1.1	4	1.032	0	4.5	0.24	2.46
1.2	6	1.212	0	4.5	0.55	3.69
1.3	8	1.392	0	4.5	0.98	4.92
1.4	10	1.572	0	4.5	1.53	6.15
1.5	12	1.752	0	4.5	2.20	7.38
1.6	14	1.932	0	4.5	3.00	8.62
1.7	16	2.112	0	4.5	3.91	9.85
1.8	18	2.292	0	4.5	4.95	11.08
1.9	20	2.472	0	4.5	6.12	12.31

. The skewness and kurtosis used in the DLC 2.x series are adopted from the relevant literature [14]. The kurtosis values used in this study are based on preliminary results from ongoing wind speed measurement campaigns, which indicate the wind field exhibits non-Gaussian characteristics with kurtosis greater than 3. Although detailed calibration is still in progress, existing evidence suggests that skewness has limited impact on fatigue life, while higher kurtosis leads to more frequent extreme wind events that significantly affect fatigue damage. Therefore, kurtosis values referenced in relevant literature were adopted for the case analysis in this paper.

3.2.1. Fatigue Analysis Under Gaussian Winds

Short-term simulations under different wind conditions are performed using the in-house code Loose, which incorporates a linear solver for blade dynamics. To eliminate scale differences among the DLCs, the damage matrices ${\mathit{D}}_{\mathit{i},\mathit{G}}$ obtained from each Gaussian DLC simulation are normalized by the maximum fatigue damage value $\mathit{max}\left(\left[{\mathit{D}}_{i,G}\right]\right)$ within the respective DLC. This normalization facilitates the identification of shifts in the fatigue damage “hotspot” across different wind conditions.

Figure 10 shows the normalized fatigue damage distribution for the Gaussian wind model DLCs. The x axis represents 80 nodes equally positioned around the cross-section of each blade section, while the y axis denotes the blade sections from the root (section 1) to the tip (section 23). The z axis quantifies the normalized fatigue damage at each node, with a color gradient indicating positional proximity to the blade root (dark blue) or tip (light green), providing a clear representation of fatigue damage patterns across the whole blade.

The damage distributions indicate that the fatigue hotspot is located near the blade root under lower wind speed DLCs, where mean wind speeds are below the rated speed. As wind speeds increase, the hotspot progressively shifts toward the blade tip, accompanied by an increase in the associated fatigue damage. The shift becomes stable once the wind speed surpasses the rated value, and the damage distributions show consistent patterns across the higher wind speed DLCs.

The total fatigue damage matrix for the Gaussian wind model is obtained as the expectation matrix computed according to Equation (20). The maximum value of the total fatigue damage matrix is 0.1121 of case 1 and 0.1356 of case 2, which are the peaks shown in Figure 11. The x axis represents 80 nodes equally positioned around the cross-section of each blade section, while the y axis denotes the blade sections from the root (section 1) to the tip (section 23), and the z axis represents the total fatigue damage of each node among all DLCs.

According to the total blade fatigue damage matrix ${\mathit{D}}_{\mathit{E}}$, the hotspot is identified on the blade as the coordinate of the maximum element in ${\mathit{D}}_{\mathit{E}}$. The fatigue damages at the hotspot occurred in different wind speed bins are listed in

Table 8. Adjusted hotspot fatigue damage of Gaussian wind model.

Wind Speed (m/s)		4	6	8	10	12	14	16	18	20
$\mathrm{Damage}{\mathit{D}}_{\mathit{i},\mathit{G}}$ (10−4)	Case 1	0	0	81	451	439	127	13	9	1
	Case 2	0	0	86	523	550	168	17	12	1

. The results indicate that the major contributions of the fatigue damages of hotspot are around the rated speed (11.4 m/s).

3.2.2. Fatigue Analysis Under Non-Gaussian DLCs

Similarly, the damage matrixes $D_{i,NG}$ from each non-Gaussian DLC are normalized by the maximum fatigue damage $\mathit{max}\left(\left[{\mathit{D}}_{i,NG}\right]\right)$ of their corresponding Gaussian DLCs.

The normalized blade fatigue damage distributions of non-Gaussian wind model DLCs are represented in Figure 12.

The total fatigue damage matrix of non-Gaussian wind model is similarly computed using Equation (20). The maximum value of the total fatigue damage matrix is 0.1380 of case 1 and 0.1649 of case 2, which are the peaks shown in Figure 13.

Same as Gaussian model, the fatigue damages at the hotspot occurred in different wind speed bins are listed in

Table 9. Adjusted hotspot fatigue damage of non-Gaussian wind model.

Wind Speed (m/s)		4	6	8	10	12	14	16	18	20
$\mathrm{Damage}{\mathit{D}}_{\mathit{i},\mathit{N}\mathit{G}}$ (10−4)	Case 1	0	0	151	641	438	124	17	8	1
	Case 2	0	0	158	743	549	164	22	11	1

. The major contributions of the fatigue damages of hotspot are also around the rated speed (11.4 m/s).

3.2.3. Summary of Fatigue Analysis

The contribution to fatigue damage varies significantly with different wind processes. A summary of the predicted blade fatigue life for the Gaussian and non-Gaussian wind models across the two cases is presented in

Table 10. Estimations of blade fatigue life (year).

	Case 1	Case 2	Difference	Percentage Difference
Gaussian Model	8.9	7.4	1.5	16.9%
Non-Gaussian Model	7.2	6.1	1.1	15.3%
Difference	1.7	1.3
Percentage Difference	19.1%	17.6%

. The blade fatigue life results in Table 10 are calculated using Equation (22).

The results demonstrate that variations in long-term wind speed distributions at different locations lead to an average difference of approximately 1.3 years in predicted fatigue life, corresponding to about a 16% variation. Notably, the Gaussian wind model consistently overestimates fatigue life by roughly 1.5 years, representing an 18% discrepancy compared to the more realistic predictions derived from the non-Gaussian model. These findings highlight the critical importance of incorporating both short-term wind conditions and long-term wind speed distributions for accurate blade fatigue life assessment. Specifically, the initiation of the first crack on the shell of FOWT blades is more likely under the non-Gaussian wind conditions.

4. Conclusions

This paper proposes a novel methodology for estimating blade fatigue life that integrates both non-Gaussian short-term wind processes and long-term wind speed distributions. An advanced numerical transformation method is developed to generate non-Gaussian wind fields from simulated wind field for short-term dynamic simulations based on the Hermite Moment Model. Two long-term wind speed distributions are established based on actual field data to identify the durations of various wind processes at different speeds. The effects of non-Gaussian wind on blade loading are investigated through short-term numerical simulations. By combining both short-term simulations of the non-Gaussian process and long-term wind speed distributions, the effects of non-Gaussian wind on blade fatigue damage are also evaluated and discussed.

The case study involves fatigue analysis of the NREL OC3-Hywind model and its blades at two distinct offshore locations. The short-term simulation results indicate that the mean and standard deviations of wind thrust and blade root bending moment increase with rising kurtosis of the wind process, even with blade pitch control activated. By comparing fatigue results based on both short-term simulations and long-term distributions, the study reveals that the majority of fatigue damage occurs at wind speeds around the rated wind speed (8–14 m/s), matching the results in [8,9]. In contrast, lower wind speeds (4–8 m/s) contribute minimally to fatigue damage, while higher wind speeds (16 m/s and above) result in less fatigue damage due to their relatively short durations. Two blade fatigue hotspots are identified (Figure 11 and Figure 13): a tensile damage hotspot at the pressure side of the blade about one-third of the length from the blade root and a compressive damage hotspot at the suction side about two-thirds of the length from the root, which agrees well with existing studies [18,34].

The comparisons of blade loading and fatigue estimation indicate that non-Gaussian wind conditions lead to larger loading and significantly more severe fatigue damage compared to Gaussian wind conditions. This finding implies that current fatigue estimation methods may underpredict the actual damage to the blades. Therefore, it is suggested that future revisions of design codes, such as the IEC 61400-3 standard, should consider integrating higher-order moments of the wind process, such as skewness and kurtosis, into fatigue analysis.

Importantly, the findings of this study can provide guidance for wind farm design and operation. By identifying wind speed ranges that contribute most to fatigue damage and quantifying the effects of non-Gaussian wind, developers can optimize turbine layout, control strategies, and maintenance schedules to reduce cumulative fatigue loads across the wind farm. The methodology also enables more accurate life expectancy assessments for turbine components, supporting informed decisions in both site selection and long-term operational planning.

Nevertheless, some limitations of the present study should be acknowledged. The current analysis focuses solely on wind-induced fatigue without considering extreme wave conditions or wave–wind coupling effects, which may significantly influence blade loading in offshore environments. In addition, only the first-crack failure mode was evaluated. Other potential damage mechanisms, such as material delamination, adhesive joint failure, trailing edge debonding, and leading-edge erosion under rain impact, were not modeled. These degradation processes may accumulate over time and interact with fatigue damage, potentially shortening the blade’s service life. Future research should incorporate fully coupled aero-hydro-servo-elastic simulations under extreme sea states and integrate multi-mode damage evolution modeling that includes crack propagation, erosion effects, and composite delamination.