To validate the proposed technique, results are shown using measurements taken at an offshore wind turbine. The monitored turbine is installed on a jacket and instrumented with strain gauges at the interface between transition piece and tower (Fig. b). The measured strains are converted into bending moments in the fore–aft and side–side directions using the turbine yaw in the SCADA. The quasi-static contribution of the thrust load to the measured bending moment Mtn,m is obtained by using a Butterworth filter of the fourth order on the recorded bending moments in a frequency range from 0 to 0.2 Hz. This frequency band is defined in a way so that the filtered signal is not influenced by the first natural frequency (0.31 Hz) since this is unrelated to any SCADA signal anyway. This is shown by the red solid line in Fig. a. The targeted quasi-static load (filtered) no longer contains the effects of structural dynamics and rotor harmonics.

The resulting signal is then transformed into thrust load Ft,m, using the distance between the sensors (location of the measured bending moment) and the hub (location of acting force) . To match the time steps of the SCADA data, the obtained thrust load is down-sampled using an antialiasing filter to a time frame of 1 s and additionally averaged over 10 min.

As the turbine is installed on a jacket, the role of wave loading in the bending moment is assumed to be negligible.

Every wind turbine is installed with a SCADA system. The main purpose of the SCADA system is to monitor and control plants, for which reason it records continuously. The main advantage of using SCADA data is the default availability. However, the correct calibration and quality of the sensors is not guaranteed over the entire lifetime. A common example is the anemometer to measure wind speeds and wind directions. It is installed behind the rotor and known for its high uncertainties due to poor calibrations. Moreover, the quality and accuracy of the data can differ among the different manufacturers. A proper preprocessing of the SCADA data and associated filtering process is advised. In this case, the preprocessing and filtering process consisted in exclusion of improbable and unrealistic values for wind speed (outside interval [0; 50] ms-1) and for generated power (outside interval [-0.1; 1.25] ⋅Prated) and periods of constant wind speed from the dataset. In total, less than 0.2 % is removed.

For this research a subset of 1 year of both 10 min statistics and 1 s signals of SCADA data was available. The subset consisted in both cases of measurements for wind speed, rotor speed, generated power, blade pitch angle, yaw angle and ambient temperature. Figure a shows the power curve obtained with 1 s and 10 min SCADA, respectively in blue and purple. The lines indicate the median value of the dataset, while the surface spans from the 5th to the 95th percentile of the data. The power curve shows a much higher variability for 1 s SCADA then for 10 min SCADA. The same difference in variability can be observed in Fig. b and c, where 1 s and 10 min averages of measured thrust load are plotted versus the 1 s and 10 min SCADA parameters wind speed and generated power, respectively. The present variability in 1 s data is not only the result of noise but is mainly due to the inertias within the controlling system and the wind turbine. For example, when the wind speed increases, the power output increases only a few seconds after. These inertias result in time delays of up to several seconds between, for example, the wind speed and the generated power. These delays are not considered constant over time and will differ for every SCADA parameter. Moreover, they last for only a couple of seconds and in consequence they cannot be observed within 10 min averages.

Measurements of air pressure are available from a nearby met mast (15 km). Using the ambient temperature (from the SCADA dataset), the air density ρ is calculated using Eq. (), where p is air pressure (Pa), T is ambient temperature (K) and Rspecific is the specific gas constant for dry air (287.058 Jkg⋅K). ρ=pRspecificT

A crucial part in the model creation is the parameter selection. Input parameters are chosen based on their Pearson correlation and mutual information to the thrust load. The Pearson correlation between a thrust signal and all considered SCADA signals is calculated using Eq. (), in which X‾ is the mean value of the signal X . R(X,Y)=∑i=1n(xi-X‾)(yi-Y‾)∑i=1n(xi-X‾)2∑i=1n(yi-Y‾)2

Since the problem we are facing is not necessarily linear, an analysis to identity and quantify possible chaotic or nonlinear dependence is recommended as well. A possible measure is mutual information, a measure of dependence based on information theory and the notion of entropy. The mutual information I(X;Y) between two signals X and Y is determined with Eq. () , using the probability density functions f(x), g(y) and h(x,y). To obtain these probability density function estimations, a histogram-based estimation as explained by with bin widths defined using the interquartile range of the data, as suggested by , is implemented. Opposed to Pearson correlation coefficients, mutual information does not have a general maximum value indicating perfect dependence between two signals. Therefore, the resulting mutual information should be normalized first. This is carried out by dividing by the joint entropy of the two signals , as indicated by Eq. (). Inormalized(X;Y)=∑x∈X∑y∈Yh(x,y)log⁡h(x,y)f(x)g(y)-∑x∈X∑y∈Yh(x,y)log⁡h(x,y)=I(X,Y)H(X,Y)

The calculation of Pearson correlation and mutual information is performed for operational data only, both 1 s data and 10 min data, for a period of 2.5 months. During this period the full wind speed range is covered, as shown by Fig. . Additionally, the datasets are divided into two subsets: data when the turbine was operating below rated operation (64 % of 10 min and 62 % of 1 s operational data) and at rated operation (36 % of 10 min and 38 % of 1 s operational data).

The resulting Pearson correlation and mutual information between the measured thrust load and several SCADA parameters for all datasets is depicted in Fig. .

Focusing first on the results for the total operational dataset, a high Pearson correlation can be found for rotor speed (0.8871 and 0.8935 for 10 min and 1 s data, respectively), generated power (0.7513 and 0.7497) and to a lesser extent wind speed (0.5082 and 0.4829). When looking at the results of mutual information for the total operational datasets, the highest dependencies are again found for wind speed (0.3934 and 0.1068 for 10 min and 1 s data, respectively), generated power (0.3453 and 0.1904) and rotor speed (0.2888 and 0.1217). Interestingly, a relatively high value is also found for the blade pitch angle (0.2330 and 0.1186). In the case of the operational data below rated power, the values for Pearson correlation and mutual information are even higher for rotor speed (0.9383 and 0.9622 for Pearson correlation and 0.4660 and 0.2161 for mutual information), generated power (0.9396, 0.9603, 0.5158 and 0.2811) and wind speed (0.9417, 0.9086, 0.4342 and 0.1057). Here, the values for mutual information of pitch angle decreased to 0.2075 and 0.1103 for the 10 min and 1 s datasets, respectively, since the pitch angle does not vary a lot as long as generated power is below rated. Conversely, operational data at rated power reveal a high Pearson correlation of the blade pitch angle (0.9499 and 0.9298) and wind speed (0.8898 and 0.8194). The same observation is made for the results of mutual information: 0.4492 and 0.1268 for the blade pitch angle and 0.3804 and 0.0793 for the wind speed. This difference in behavior is explained as follows. Once the turbine reaches its rated power value, the only parameter acting to vary wind speed and thrust load will be the blade pitch angle. Hence a significantly lower correlation and mutual information for the rotor speed (0.1562, 0.1385, 0.0333 and 0.0098) is found. However generated power is still correlated to thrust load with a significant value in the case of 10 min averages (0.6354). The value for mutual information in the case of 10 min data is significantly higher as well (0.1308). Figure c reveals a very steep curve between thrust and generated power once rated power is reached.

In the results of Pearson correlation (Fig. , left) negative values are the result of an additive inverse relationship between the depicted parameter and the thrust load. For a turbine operating below rated power, a higher wind speed results in a slightly lower blade pitch angle and an increased thrust load. Therefore, a decreasing blade pitch angle (due to an increase in wind speed) leads to a higher thrust load. Hence, a negative value for Pearson correlation between pitch angle and thrust load when the turbine is operating below rated power is expected. Once rated power is reached, increasing wind speeds result in higher blade pitch angles, slightly increasing generated power and decreasing thrust loads (Fig. b). Accordingly, an increase in blade pitch angle and generated power (thanks to an increase in wind speed) enforces a decrease in thrust load. And thus, a resulting negative Pearson correlation between thrust load and wind speed and generated power and pitch angle for operational data at rated power is consistent.

It is obvious the turbine reacts differently to varying wind speeds depending on the operational state. Once rated power is reached, the relation of the thrust load to the depicted SCADA parameters often differs. This leads to lower correlation values for the total dataset in comparison to the operational states separately. In the case of the pitch angle, the correlation is even nonexistent when looking at the total operational dataset. However, when taking into account the existing nonlinearities, as with mutual information, the blade pitch angle is clearly correlated with the thrust load based on the total operational dataset as well.

In general the values for Pearson correlations and clearly for mutual information are less considering 1 s averages compared to 10 min averages. This can be explained by the present time delays of several seconds between parameters, as a result of the inertias present within the system. When calculating the autocorrelation between the thrust load signal and shifted SCADA signals, the biggest time shift was found for the pitch signal and corresponded to -3 s.

For the continuation of this research, only the yaw angle will not be considered as an input parameter due to its small correlation and mutual information (0.0598, 0.0596, 0.0403 and 0.0367 for Pearson correlation of 10 min and 1 s datasets and mutual information of both datasets, respectively) with the thrust load.

According to , thrust loads are influenced by air density. While changes in the depicted SCADA variables happen within seconds, air density changes on a different timescale (several hours). Instead of including air density in the set of input parameters, it is accounted for as a correction of the modeled thrust load F^T: F^T,corr=ρF^T.

The simulated data are obtained by using the software FAST v8 , offered by the National Renewable Energy Laboratory (NREL). The chosen simulated turbine is the NREL 5.0 MW baseline wind turbine, installed on an OC3 Monopile RF configuration. All simulation specifications are kept as proposed by the software for use of this turbine type. This means that turbulence and irregular waves are also accounted for. To make sure the full wind speed range is sufficiently covered in the simulation data, several input wind files with varying average wind speed between 3 and 25 ms-1 are generated using TurbSim. Each wind speed is accounted for equally. In essence, the wind distribution is thus considered uniform.

The output parameters of interest for this research are specified in Table . As the results obtained using simulated data will be used to be compared to real-life data, only comparable parameters for the SCADA data and the measured bending moment are worked with and indicated in Table .

The air density is kept constant during the simulations. Therefore, the applied corrections for air density did not influence the results.

To train the model, a dataset with a total simulated time of ca. 2.5 days is used. Additionally, the model is validated on an additional simulated dataset with a total simulated time of ca. 1.5 days. These data are not used to train the model and can thus be used as a complete independent validation set.

Results are shown in Fig. . A good match between modeled thrust load F^T and simulated thrust load FT,s can be found during both training and validation phases (Fig. a, b). Figure c shows the relative error Δϵ between simulated and modeled thrust load (Δϵ=abs(FT,s-F^T)FT,s) versus wind speed for the test set during the training phase and the total dataset during the validation phase. The line indicates the median value of the relative error, calculated for each wind speed bin of 0.5 ms-1. The surface spans from the 5th to the 95th percentile of the data. In general, the relative error of both datasets barely exceeds 10 %, except for very low wind speeds. Here, a higher relative error is found due to the lower absolute values of the thrust load. For higher wind speeds, errors increase. Starting from 12 ms-1 an increasing variability in relative error can be observed for increasing wind speed. A similar behavior was found for the training and the validation set during the training phase. This indicates the training set was representative for the validation set, the test set and the total dataset during the validation phase.

Four time series spanning 10 min during the validation phase are shown in Fig. , two while operating below rated power (Fig. a, c) and two while operating at rated power (Fig. b, d). The time series of 10 min with the highest averaged absolute error between simulated and modeled thrust loads below rated and at rated power are shown in Fig. c and d, respectively. In all cases a very good match is found. This is represented by a low value for the averaged absolute relative error (MRE) for those time series (MRE > 4,5 %).

The proposed modeling method is also tested on an operating wind turbine. Thrust loads are measured using strain gauges, installed at the interface between tower and transition piece, as explained in Sect. . A model is trained using 2 weeks of 1 s data. Moreover, this model is validated on a dataset of 1 year, including the 2 weeks of training data.

Results are shown in Fig. . A good match between measured thrust loads FT,m and modeled thrust loads F^T can be found during both training and validation phases. Although above roughly 18 ms-1, the modeled thrust curve shows less variability than the measured curve, meaning the difference between the 5th and the 95th percentile of modeled thrust is lower than the difference between the 5th and the 95th percentile of measured thrust (Fig. a, b). Figure c shows the relative error (Δϵ=abs(FT,m-F^T)FT,m) of the test set during the training phase, being 15 % of the total training set of 2 weeks, and the total dataset during the validation phase of 1 year of operation. Again, the line indicates the median value, calculated for every wind speed bin of 0.5 ms-1. The surface spans from the 5th percentile to the 95th percentile of the data. A similar behavior among the training, validation and test set during the training phase was obtained. In general, the relative error does not exceed 15 %. Moreover, with a median value barely exceeding 5 %, results are promising. In general, the errors are increased with respect to the results using FAST (as shown in Fig. c). The errors obtained for lower wind speeds up to 10 ms-1 are increased due to offsets, the mean differences between measured and modeled values, present in the results. When looking at the long-term validation set, the errors are increased with respect to the test set during the training phase due to bigger mean differences. Furthermore, the errors obtained for wind speeds higher than ca. 18 ms-1 are slightly higher due to the loss of variability in the tail of the thrust curve. Again, an increasing variability in relative errors can be observed for increasing wind speeds, starting from ca. 12 ms-1.

To illustrate these observations, four time series of 10 min are shown in Fig. . Two of them show operation below rated power (a and c), while the other two show operation at rated power (b and d). The time series depicted in Fig. c and Fig. d show 10 min with the highest averaged absolute error when operating below or at rated power, respectively. An offset can be observed in (a, c), while the loss of variability can be observed in (d). The values of the averaged absolute relative error indicate the match is still acceptable (MRE < 6.5 %). As explained, the resulting errors are influenced a lot by present offsets between the measured and the modeled thrust load signal. However, these offsets will not influence a fatigue assessment performed according to common practice in industry. This practice consists of cycle counting of the stress signals and transforming the cycle counts into damage using the Miner's rule. Since during this practice only the size of the cycles matters, the fatigue assessment is not influenced by the mean value of the cycles.

Calculating the Pearson correlation and the mutual information between the measured and modeled thrust load signals for the same period of 2.5 months (see Sect. ) results in 0.9962 and 0.2740, respectively. These increased values for 1 s data signals indicate that a lot of the present variability in the thrust load can be explained by combining several SCADA parameters and allowing some latency between the different signals. When looking at only one parameter, the difference in value for thrust measurements occurring for the same value of that parameter cannot be explained. When considering more parameters, this difference might already be explained by a different value of another parameter. Therefore, the resulting correlation between the measured thrust load and only one parameter is lower than between the measured thrust load and a combination of multiple parameters, as performed by the neural network.