As is common practice in the wind industry, the turbine's SCADA system logged data in 10 min statistics consisting of average, minimum, maximum, and standard deviation values. The dataset included operational parameters such as rotor speed, blade pitch angle, electrical power output, and nacelle direction. Additionally, the available environmental parameters included wind speed, wind direction, and ambient temperature. In this work, only the data corresponding to power-producing conditions were considered and were obtained by filtering data points where the 10 min minimum power was positive. Figure  shows the main operational variables (generator power P, blade pitch β, and rotor speed Ω) as a function of wind speed, illustrating the turbine's performance characteristics.

The wind speed logged by the SCADA system corresponds to a measurement from a nacelle-mounted anemometer to which a transfer function is applied in order to estimate the free-stream wind speed at hub height. There were no meteorological masts or lidar systems in the wind farm to provide independent wind speed measurements. These conditions warrant caution when using the SCADA wind speed for comparison with numerical models, as the transfer function may not accurately represent the real wind conditions.

The terrestrial laser scan was performed while the turbine was parked, with the rotor locked, under low-wind conditions. The scanner was placed at 13 different positions around the turbine, obtaining scans of both the pressure and suction sides of the blade. These scans were aligned into a single reference frame, forming a three-dimensional point cloud. The acquisition primarily targeted one blade (which was oriented vertically and pointing downwards) while also partly capturing the tower, nacelle, hub, and the other two blades. The resulting point cloud is depicted in Fig. , in a referential aligned with the tower axis and centred on the tower base, with the studied blade highlighted. Note that, in this figure, the dataset was downsampled to 10 % of the original points for visualization purposes. The blade region contains approximately 5.29×106 points.

Figure  shows the point cloud in the blade region, in a referential aligned with the blade pitch axis and centred on the blade root. The main limitation of this dataset is that some blade vibrations occurred during the measurement due to the low (but non-zero) ambient wind (especially in the flapping direction, corresponding to the ybld direction). Consequently, the point cloud shows some scatter even after alignment to a consistent reference frame, reflecting the deflections of the blade during the scan. This effect is more pronounced towards the blade tip. This effectively translates to an overestimation of the aerodynamic thickness of outboard blade cross-sections if this effect is not addressed. A strategy to mitigate this effect is presented in Sect. .

SHM data were retrieved from the experimental setup depicted in Fig. . The instrumentation consists of two tower cross-sections, one near the top (cross-section A) and one near the base (cross-section B). Each cross-section includes four measurement locations (identified with “S”), distributed around the inner circumference of the tower and sampled at 5 Hz. The sensor distribution is shown in Fig.  together with the turbine wind rose. At each measurement location, the strain signal is obtained through a bridge circuit. In cross-section A, quarter-bridge configurations are used, with co-located temperature measurements (identified with “T”). In cross-section B, full-bridge configurations are used, consisting of two active and two dummy gauges for temperature compensation.

A previous study used the same instrumentation (but a different monitoring period) to compare different strategies to correct strain gauge drifts and residual thermal effects using measurements during cable untwisting events, when the nacelle rotates 360° to relieve cable torsion. These effects were corrected using the method that led to better results for each cross-section. The corrected stresses were aggregated into 10 min means, and subsequently the bending moments at each cross-section were computed assuming plane stress. Figures  and show the bending moments as a function of the SCADA wind speed, in cross-sections A and B, respectively.

The curves show the typical pattern of increasing bending moments with wind speed until rated power is reached. Beyond rated, the fore–aft moments decrease as pitch control decreases the rotor thrust force, while the side-to-side moments remain roughly constant, as they are dominated by the rotor torque (which is constant for rated power and rotor speed). The scale of bending moments is significantly different between the two cross-sections due to the difference in height. In cross-section A, the fore–aft moment is influenced by the rotor thrust (which has a relatively small lever arm at that height) and the rotor and nacelle overhang moment, while the side-to-side moment is dominated by the rotor torque. In cross-section B, the fore–aft bending moments are much larger, as they are dominated by the lever arm of the rotor thrust, and the side-to-side moments are comparatively small. The scatter in data may be explained by variations in variables such as turbulence intensity or air density, which have a significant effect on the aerodynamic loads. The scatter in MSS at cross-section B, which is noticeably higher, is also attributed to the sensor layout in relation to the most common wind directions (see Fig. ), which causes difficulty in accurately resolving the side-to-side bending moment from the strain gauge measurements.

A visual inspection of the different scans revealed that individual scans predominantly covered either the low-pressure (LP) side or the high-pressure (HP) side of the blade. The scans were manually classified accordingly and processed separately for each blade side. For each side, the scatter due to blade vibrations was mitigated using a consensus-based alignment procedure described here. In this context, the alignment can be interpreted as estimating, for each scan, a rigid in-plane translation that minimizes the distances between the scan points and a common reference curve (the consensus), based on nearest-neighbour correspondences.

An initial smooth consensus curve was first fitted to the points. Each individual scan cross-section was then aligned to this consensus by estimating a rigid translation in the cross-section plane, computed by minimizing distances to nearest-neighbour correspondences with the consensus curve. After translating all scans, the consensus curve was refitted to the aligned data. This align-refit procedure was repeated iteratively until the consensus curve stabilized. The resulting consensus curves were not used directly as final geometric representations, but only as intermediate constructs to achieve consistent alignment of the individual scans. Figure  illustrates the aligned cross-section point clouds for a representative spanwise station, highlighting the substantial reduction in scatter achieved through the alignment process in comparison with the data in Fig. .

Following the consensus-based alignment, each of the selected 39 spanwise stations is represented by an aligned two-dimensional point cloud describing the local blade cross-section. At this stage, points from all retained scans were pooled together, yielding a single aggregated representation of the section geometry. The next step was to fit an airfoil shape to the aligned point cloud.

To constrain the fitted shapes to physically realistic profiles and to improve computational efficiency, a predefined database of candidate airfoils was defined, based on two airfoil families which were specified by the manufacturer (also including circular airfoils and mixtures of circular airfoils with the specified families to better capture the region near the root). Each airfoil geometry was stored in normalized form (unit chord with the leading edge at the origin) and discretized using 200 points along the contour. These candidate airfoils are expected to cover the range of airfoil shapes used along the blade span.

For each spanwise station, every candidate airfoil in the database was evaluated independently. The evaluation consisted of fitting the candidate airfoil to the section's point cloud through a transformation with four parameters: a scale factor c, an in-plane rotation angle αx, and translations tx and ty in the xbld and ybld directions, respectively. This transformation and its parameters are depicted in Fig. . For each candidate airfoil, the transformation parameters were adjusted to minimize a fitting error between the transformed airfoil contour and the measured point cloud. The best-fitting airfoil was then selected based on the lowest fitting error. This procedure was repeated for all spanwise stations.

The optimal set of parameters fitting each candidate airfoil shape to each spanwise station's point cloud was obtained by minimizing a nearest-neighbour distance measure between them. For each measured point, the Euclidean distance to the closest vertex of the discretized airfoil contour was computed. A Huber loss function was applied to the resulting distance vector to reduce sensitivity to outliers and poorly resolved regions, and the mean Huber loss was used as the objective function. The resulting bounded nonlinear optimization problem was solved with respect to the four transformation parameters using the gradient-based optimization algorithm L-BFGS-B . The process was stopped automatically when further parameter updates produced no meaningful reduction in the fitting error or when the estimated local slope of the objective indicated that a minimum had been reached.

Thus, this procedure selected the best-fitting airfoil shape from the database for each spanwise station and provided an estimate of each station's scale, orientation, and position. Examples of fitted airfoil shapes at two representative blade sections are compared with the aligned point cloud in Fig. .

Finally, the fitting results are related to the aerodynamic parameters which need to be input in the aeroelastic models. Firstly, the fitted scale parameter directly provides a local chord estimate. In addition, translation parameters tx and ty yield an estimate of the aerodynamic centre (assumed to be at 25 % of the chord), which can be used to derive spanwise trends in the section reference line (blade curvature and sweep). Finally, although the rotation angle αx is evidently related to the local twist angle, the twist definition requires some care. It is necessary to ensure that the zero-twist reference is consistent with that used in numerical models, as even small twist offsets cause significant changes in performance . The twist angle is defined as the angle between the chord line and the rotor plane. Since the laser scan includes points in the nacelle and tower, the twist can be rigorously determined as depicted in Fig. .

The figure depicts a clipped view of the point cloud, in the referential aligned with the blade axis, showing all points with zbld/R<0.25. Since the laser scan includes points in the nacelle and tower, the definition of the rotor plane is non-ambiguous. The figure also shows the fitted airfoil at the zbld/R=0.25 station, along with its chord line. The angle between the chord line and the rotor plane is the sum of the local twist angle at that station θ(zbld) with the blade pitch angle β. The figure also shows that θ(zbld)+β is equal to αx(zbld)+90°. This yields the following expression for the local twist angle: 5θ(zbld)=αx(zbld)+90°-β.

With αx(zbld) obtained from the airfoil fitting procedure and β known from the SCADA data at the time of the scan, this expression allows the calculation of the twist distribution along the blade span with a zero-twist reference consistent with that used in numerical models.

Chord and twist distributions used in the numerical models were derived from the laser scan, where the estimates at discrete spanwise stations were smoothed to reduce the effect of fitting noise. Figure  compares the final chord and twist distributions with the laser scan estimates.

The determination of the spanwise airfoil shapes required a more manual approach based on the fitted airfoils and engineering judgement. Apparent thickness fluctuations between adjacent stations were treated as scan-induced noise; therefore, contiguous regions were constrained to share a single airfoil shape and to follow a monotonic thickness reduction toward the tip. The resulting spanwise distribution of airfoil thickness is shown in Fig. , where regions of constant thickness correspond to regions with the same airfoil type. The high variations near the root reflect the difficulty of fitting the airfoil shape in that region, where the blade geometry is more complex and does not follow typical aerodynamic shapes. However, this region's contribution to the overall aerodynamic performance is small and is not expected to affect the results.

The interaction of the wind with the turbine is calculated in the AeroDyn module, which employs the blade element momentum (BEM) theory , with additions and corrections for effects such as tower shadow, tip losses, and hub losses. The blades are discretized into a finite number of nodes, where the chord, twist, curvature, and sweep are specified. Each section is associated with an airfoil, for which the lift and drag coefficients as a function of angle of attack are provided as input. The tower drag is modelled with a constant drag coefficient of Cd=0.5. The lift and drag forces are calculated at each blade element based on the local relative velocity and user-specified airfoil polars. These forces are then integrated along the blade span to obtain the aerodynamic loads, which are passed to the structural module for load and response calculations.

The airfoil polars were generated using XFOIL and the usual corrections and extrapolations. For each airfoil shape used in the model, the local Reynolds number was determined based on the average chord length, the inflow velocity (calculated from the rated wind speed and rotor speed, assuming an axial induction factor of 1/3), and the kinematic viscosity of air at 15 °C. The corresponding Mach number was also computed, using the local inflow speed and the speed of sound at 15 °C. XFOIL was then used to compute the polars over a range of angles of attack from -20 to 20°, with transition to turbulence forced at 10 % of the chord to reflect the typically high surface roughness of wind turbine blades. As XFOIL provides polars for two-dimensional flow, three-dimensional corrections were subsequently applied: the Du-Selig method for lift and the Eggers method for drag . Finally, the polars were extrapolated to cover the full angle of attack range (-180 to 180°) using the Viterna method . These steps were automated using the openfast-toolbox package .

The structural response to the applied loads is calculated with the ElastoDyn module, which employs a combined modal and multi-body formulation. The modal formulation is used to model both the tower and the three blades, allowing for the calculation of loads and displacements as a function of time. The key inputs are the mass and stiffness distributions of the components, as well as the mode shapes of the considered modes (two fore–aft and side-to-side modes for the tower and two flapwise and one edgewise modes for each blade). The nacelle and hub are modelled as rigid bodies.

The tower mass and stiffness distributions were calculated based on the tower geometry provided by the manufacturer. The equivalent information was not available for the blades, so the blade mass and stiffness distributions were scaled from the IEA 3.4 MW reference turbine . The mass distribution scaling was performed knowing the total blade mass, while the stiffness distribution scaling was performed to preserve the ratio of stiffness to mass along the span. Since this work focuses on the 10 min means of loads and performance, and dynamic structural response is not studied, the structural properties of the blades have a negligible impact on results, and the scaling approach is justified.

The drivetrain is modelled as a torsional spring whose parameters were directly copied from the IEA 3.4 MW reference turbine. The gearbox efficiency was calculated based on the SHM-measured aerodynamic power (calculated from the SHM-measured rotor torque and the SCADA-measured rotor speed) in comparison with the generator power.

Although the details of the controller are proprietary and were not provided by the manufacturer, SCADA data allow for a satisfactory characterization of the controller behaviour. The controller was modelled using ROSCO , an open-source wind turbine controller modelling tool developed by NREL. For a clearer controller characterization according to the logic inherent to ROSCO, the tip speed ratio (TSR) λ and the generator torque QG are now introduced through Eqs. () and () (where ηG is the generator efficiency, obtained from manufacturer data sheets).

6λ=ΩRV7QG=PΩηG

The characterization of the controller set points defined in the numerical model and their inference from SCADA data are summarized in Fig. , which shows scatterplots of pitch, generator torque, TSR, and rotor speed versus wind speed, as well as the set points in dashed black lines and the regions of operation according to the nomenclature used by .

The different regions are numbered in increasing order of wind speed and are modelled with different control strategies, which are now described. Region 1 corresponds to wind speeds below cut-in, where the turbine is not in operation. In regions 1.5, 2, and 2.5, the pitch angle follows a look-up table as a function of wind speed, while the generator torque is the controlled variable. The torque controller aims to maintain rotor speed at its minimum and maximum values Ωmin and Ωmax in regions 1.5 and 2.5, respectively. In region 2, it aims to keep TSR constant at an optimal value λopt that maximizes power production. In region 3, the generator torque is constant and equal to its rated value QG,rated, while the pitch angle is the controlled variable. Since the rotor speed is also constant and equal to its rated value, this translates to constant rated power.

Figure  shows scatterplots of generator power, pitch angle, and rotor speed versus wind speed, comparing values measured by SCADA against numerical simulation results. Overall, the plot shows a good agreement between the simulations and the measurements, although there are some discrepancies to be noted. The generator power vs. wind speed plot reveals that the model slightly overpredicts power capture below rated wind speed, while the rated power is well predicted, since it is imposed by the controller. Inversely, the pitch angle is well captured below rated, where it is set by the controller, while above rated the model overpredicts the pitch angle. The rotor speed is well captured in all regions of operation, again because it is regulated by the controller (either by setting the value of Ω directly or by controlling the TSR in region 2).

The comparison with SCADA data is useful to validate the controller model and perform an initial assessment of the model, but it does not allow a complete evaluation of model accuracy, since it does not provide enough insight into the underlying aerodynamic loads. Furthermore, the power and pitch discrepancies could be attributed to a variety of effects. A further model evaluation and analysis of possible error sources is performed using the SHM measurements, as described in the next section.

A further assessment of the baseline model is provided by comparing simulated loads against the experimentally obtained loads using the strain gauges in the SHM system described in Sect. . It is emphasized that, while SCADA data are ubiquitous and relatively easy to obtain, measurements of structural loads are rarer, making this additional dataset valuable to help disentangle different modelling uncertainty sources, which are unclear from SCADA data alone.

The bending moments at section A are analysed in Fig. . The fore–aft bending moment MFA is overpredicted by the model across the full wind range, although the trend is well captured. The side-to-side bending moment MSS matches well for almost the entire wind speed range, with a slight overprediction at high wind speeds. Figure  shows the bending moments at section B. The fore–aft bending moment MFA is again overpredicted, especially in below-rated conditions, while there is reasonable agreement in the side-to-side bending moment MSS. Overall, the fore–aft bending moments have higher errors than the side-to-side moments. The most relevant error is in the fore–aft bending moment at section B below rated wind speed, since it corresponds to an overprediction of the highest magnitude loads experienced by the turbine. Fore–aft bending moments are primarily driven by the rotor thrust, which suggests that the model overpredicts thrust, especially below rated wind speed. This hypothesis is further explored in the next section.

A further comparison is made between experimental and simulated rotor thrust and torque, depicted in Fig. . The experimental values were derived from the tower bending moments according to the method in Sect. . The simulated values were calculated from the OpenFAST outputs of rotor thrust and torque coefficients. These results summarize the findings from the previous section, providing a more direct insight into the rotor aerodynamic loads: the thrust is slightly overpredicted below rated wind speed, while the torque is reasonably well captured.

The above results were obtained assuming steady-wind conditions, often a preferred simulation strategy due to the lower computational cost and post-processing complexity. However, turbulence is always present in real wind conditions, and some of the discrepancies between the simulated curves and the experimental measurements (which correspond to 10 min averages under turbulent wind) may be explained by the effect of turbulence. To assess this, additional simulations were performed including turbulence in the wind field, with turbulence intensities of 5%, 10%, and 15% (corresponding to realistic values of turbulence intensity at the site, as logged by the SCADA system). Turbulent simulation results are compared with the steady-wind results in Figs.  and for operational and structural data, respectively.

The comparison with SCADA data shows that the effect of turbulence is relevant only in regions where the controller laws change abruptly, such as around the point where rated power is reached. In these regions, turbulence smooths the transition between different controller regimes, yielding results that are closer to the experimental data. However, away from these regions, the effect of turbulence is negligible, and the steady-wind simulations provide a good approximation of the mean behaviour.

The comparison with SHM data shows a similar trend, where turbulence has a smoothing effect around transition regions. This is especially relevant in the rotor thrust, since this variable peaks around rated wind speed. The apparent overestimation of maximum thrust in the steady-wind simulations is mitigated when turbulence is included, yielding results that are closer to the experimental data. However, below rated wind speed, the thrust is still overpredicted.

Overall, the experimental trends observed in both SCADA and SHM data are well captured by the baseline simulations, indicating that the main physical phenomena are represented adequately and supporting the modelling approach. Furthermore, the rotor thrust and torque, estimated with the methods in Sect. , served as useful variables to characterize the rotor, summarizing the findings from the tower bending moment comparison and providing a more direct insight into the rotor aerodynamic loads, even without blade instrumentation. This is particularly relevant for the thrust, which is the main driver of the largest tower loads and is not measured in SCADA.

The main observed discrepancies between the model results and the measurements are summarized as follows:

a slight overprediction of power capture below rated wind speed,

These discrepancies, though small in magnitude, are consistent across both datasets (SCADA and SHM), suggesting inaccuracies in the model rather than errors in the measurements. Furthermore, they appear over the entire wind speed range, rather than being concentrated around specific operating points, indicating that the errors are of a systematic nature and have an underlying physical cause.

The errors suggest an overprediction of the aerodynamic loads: the thrust and power are overpredicted below rated, and the pitch angle is overpredicted above rated, indicating that the simulated turbine maintains rated power with more pitch (i.e. a greater reduction in aerodynamic efficiency) than in reality. This may be explained by modelling errors in the interaction between the wind and the rotor or by errors in modelling the wind field. In other words, there are several model inputs which may explain the observed discrepancies, which motivates a parameter study to assess the sensitivity of the model to selected uncertainties, as described in the next section.

A parametric study was performed to assess the sensitivity of the model to selected uncertainties. A list of parameters which may explain the observed discrepancies was compiled, and each parameter was perturbed individually around the baseline model while keeping all other settings fixed. Parameters characterizing the blade geometry were varied in a range much larger than the expected uncertainty in the laser-scan-based estimates to represent typical uncertainties when laser scans are not available. The parameters considered and their perturbations are listed in Table .

The physical meaning of the selected parameters and their possible relationship with the observed discrepancies are now described.

Chord scale kc. As aerodynamic forces are proportional to the blade chord, changes in chord have a direct impact on the rotor's energy capture and loads, suggesting the possibility that the model inputs overestimate the real chord. The chord scale kc was introduced as a multiplicative factor applied to the entire chord distribution along the blade span, defining new chord distribution c′(zbld)=kcc(zbld).

It should be noted that other parameters not studied here may also play a role in the observed discrepancies, such as wind shear, drivetrain/generator efficiency, and air density. Nevertheless, the five selected parameters are expected to be the main sources of uncertainty for a typical aeroelastic model.

The results of the parametric study are summarized in Fig. , where each row of plots corresponds to one of the parameters listed in Table . The three columns correspond to selected outputs as a function of wind speed: generator power, pitch angle, and fore–aft bending moment in cross-section B. Each plot compares simulation results using different parameter values against experimental measurements. The generator power and pitch angle plots are cropped to the wind speed ranges where the respective variables are not set by the controller to focus on the regions where the parameter perturbations have an effect (i.e. below rated for power and above rated for pitch angle). It should be noted that the last row of the plot, which considers variations in the wind speed scale, has the SCADA wind speed V on the x axis, and not the corrected wind speed V′, to facilitate comparison.

Overall, the figure shows that all parameters have a significant effect on the outputs considered within the ranges studied. In principle, this might allow the tuning of these parameters to match the measurements more closely, but the realism of the required perturbations must be assessed to determine whether these parameters are plausible explanations for the observed discrepancies.

The first two rows in Fig.  show the effect of variations in blade geometry through the chord scale kc and the twist offset Δθ. Both parameters are effective in reducing the observed discrepancies. However, the chord scale necessary to match the measurements (around kc=0.9) implies a reduction in chord which is much larger than the expected uncertainty in laser-scan-based estimates. Similarly, the twist offset necessary to match the measurements (around Δθ=2°) is also larger than the expected uncertainty in the twist measuring method (described in Fig. ). In summary, the chord and twist can be tuned to match SCADA and SHM measurements, but the required perturbations are too large to be plausible, given the use of laser scans. This highlights the value of laser scans to reduce uncertainties in blade geometry when validating aeroelastic models, avoiding an incorrect attribution of discrepancies to uncertainties in blade geometry.

The third row in Fig.  shows the effect of variations in airfoil polars through the polar degradation factor δp. It should be noted that, although the polars are based on the laser-scanned airfoil shapes, they are more uncertain than the chord and twist since they are calculated using XFOIL with additional corrections and extrapolation methods, which may have limitations. Therefore, the polar degradation factor is a more plausible parameter to explain the observed discrepancies. However, the required degradation (around δp=0.15) is relatively high, suggesting that other sources of uncertainty may also be relevant.

The fourth and fifth rows of the plot show the effect of yaw misalignment and a scale factor in the measured wind speed, reflecting possible errors in the wind field characterization, a realistic source of uncertainty since the wind field is not measured directly at the rotor, and nacelle-mounted sensors are prone to errors. Both parameters are effective in bringing the simulations closer to the measurements, although an improved match in the power, pitch, and below-rated bending moment comes at the expense of a worse match in the above-rated bending moment.

In summary, the parametric study shows that several parameters can be tuned to reduce the observed discrepancies between the baseline model and the experimental measurements. However, some of these parameters require perturbations larger than the expected uncertainties in the baseline model, suggesting that they are not plausible explanations for the discrepancies. Other parameters, such as the polar degradation factor and wind field characterization, are more plausible sources of uncertainty, although they may not fully explain the discrepancies on their own. This highlights the complex interplay of uncertainties in aeroelastic modelling and the need for comprehensive validation studies using multiple data sources.