Machine Learning-Based Prediction of 2 MW Wind Turbine Tower Loads During Power Production Based on Nacelle Behavior

Abstract

The cost of a wind turbine support structure is high and this support structure is difficult to repair, especially for offshore wind turbines. As such, the loads and stresses that occur during the actual operation of wind turbines must be monitored from the perspective of maintenance planning and lifetime prediction. Strain measurement methods are generally used to monitor the load on a structure and are highly accurate, but their widespread implementation across all wind turbines is impractical due to cost and labor constraints. In this study, a method for predicting the tower load was developed, using simple measurements applied during power generation, for onshore wind turbines. The method consists of a machine learning model, using the nacelle displacement and nacelle angle as inputs, which are highly correlated with loads at the bottom of the tower. Nacelle displacements can be derived from accelerations, which are already monitored in regard to most wind turbines; the nacelle angle can be calculated from the nacelle angle velocity, measured with a gyroscope. The low-frequency components that cannot be captured with these parameters were predicted using the operational condition data used for wind turbine control. Additionally, the prediction accuracy was increased by creating and integrating separate machine learning models for each typical vibration component. The method was evaluated through the aeroelastic simulation of a 2 MW wind turbine. The results showed that the fatigue and extreme loads of the fore–aft and side–side bending moments at the bottom of the tower can be predicted using operational conditions and nacelle accelerations, and the prediction accuracy in regard to the high-frequency components can be increased by adding the nacelle angle velocity into the model. Furthermore, the fatigue loads of the torsional torque can be evaluated using the nacelle angle velocity. The proposed method has the ability to predict the loads at the bottom of the tower without any, or with only a few, additional sensors.

1. Introduction

1.1. Background

As the pursuit of comfort using science and technology exceeds the carrying capacity of Earth and the natural environment deteriorates, there is a need for technology that can help maintain both human living standards and the natural environment. Renewable energy is central to addressing this challenge, with wind power generation emerging as one of the most successful technologies. A key challenge in regard to wind power generation is its dependence on environmental factors, including wind conditions, ground conditions, corrosion, temperature, and sea conditions (if offshore), which vary with the installation site. Therefore, a more detailed maintenance plan is required in regard to wind power infrastructure. However, human-only monitoring of the relevant factors is difficult due to the increase in the number of facilities, which has occurred based on demand, and due to the development of offshore wind turbines, which are difficult to access. As such, demand is growing for monitoring technologies that can increase the cost efficiency and reliability of monitoring. Advancements in data storage (e.g., cloud computing), communication (e.g., high-speed wireless), and analysis technologies (e.g., artificial intelligence) are strengthening the foundation for improving monitoring systems.

The wind turbine support structure, i.e., the tower and foundation, is one of the most important components in the monitoring of a wind turbine, as it differs from site to site and is challenging to replace and monitor. The cost of the support structure is high for offshore wind turbines, which is important from the perspective of assessing the lifetime remaining and for lifetime extension of the structure. The use of strain measurement methods is common and they are highly accurate when used to monitor the structural health of a wind turbine. However, measuring the strain is often difficult, in terms of the cost and labor requirements, when evaluating each wind turbine. Furthermore, measuring and maintaining the underwater structure of offshore wind turbines is difficult or impossible.

Within this context, virtual sensing technology, which is used to estimate the load and stress on wind turbine support structures from other measured values without measuring the strain in the relevant areas, is important. Extensive research has been conducted on this topic. The developed methods can be broadly divided into two categories: estimating the statistical values, such as the damage equivalent load, and estimating the time histories. The former has been studied more [1], but the focus on the latter has recently been increasing.

1.2. Studies on Statistical Value Prediction

Pandit et al. [1] provided a comprehensive review of SCADA data applications for wind turbine monitoring. They discussed the state-of-the-art advancements, challenges, and the potential for future improvements, emphasizing the importance of leveraging operational data for cost-effective performance monitoring. Mehlan et al. [2] introduced a digital twin approach for the virtual sensing of wind turbine hub loads and drivetrain fatigue damage. By utilizing SCADA and condition monitoring system data, they estimated the aerodynamic loads and monitored the drivetrain fatigue, showcasing its potential use for predictive maintenance. Some statistical estimation methods solely rely on standard SCADA data. For instance, Cosack et al. [3] used a neural network to evaluate the main fatigue loads experienced by a wind turbine, including the tower, and validated their results with actual measurements. They proposed a data-driven monitoring approach that eliminated the need for expensive load measurement devices, demonstrating its feasibility for fatigue monitoring in practical applications. Movsessian et al. [4] examined the effectiveness of feature selection and dimensionality reduction. Their study shows that careful feature selection significantly improves prediction accuracy and computational efficiency. Nielsen et al. [5] developed a surrogate model to estimate extreme tower loads using the random forest algorithm, which has the potential to efficiently replace computationally intensive physics-based simulations, while maintaining high accuracy.

Studies have also been conducted to increase prediction accuracy by considering tower acceleration and wave height data, in addition to SCADA data. Santos et al. [6] investigated the fatigue load at the bottom of the towers of large monopile wind turbines. They found that, unlike standard-sized monopile wind turbines, more fatigue damage occurs in the side–side direction and during idling, and considering tower acceleration and wave height data, in addition to SCADA data, is effective in increasing the accuracy of these predictions. In addition, Santos et al. [7] increased the prediction accuracy and made the conservative assessment by adopting a physics-informed machine learning model that incorporates physical laws into the neural network. This integration of physics knowledge helped improve the generalization capability of the model, making it more reliable in varying conditions.

Some researchers have recorded partial strain measurements to evaluate fatigue at points where the strain was not measured. Ziegler et al. [8,9] developed a method for predicting fatigue loads at the cross-sections in a monopile foundation at any height, by measuring the strain on one cross-section in the tower and applying simulation results and the k-nearest neighbor regression algorithm. The study confirmed that strain measurements at a single level can be used to effectively extrapolate the fatigue loads throughout the tower, reducing the need for extensive monitoring setups.

Pacheco et al. [10] developed a method for evaluating the level of damage of all the wind turbines in a wind farm and for all time periods, by using tower strain data for a limited number of wind turbines and time periods. Santos et al. [11] estimated quasistatic thrust loads using 1 s SCADA data and used nacelle acceleration to estimate the fatigue loads at the bottom of the tower, for an entire wind farm, using limited turbine strain data. Avendano-Valencia et al. [12] created a model for predicting the fatigue load on a wind turbine subjected to wake turbulence, based on the load on the adjacent wind turbine. They applied Gaussian Process Regression, which demonstrated robust performance in modeling the complex interdependencies between wake effects and fatigue loads, further enhancing prediction accuracy.

1.3. Studies on Time–History Prediction

Many studies have focused on predicting the time histories of the loads and stresses on wind turbine support structures, using the mode expansion method and based on acceleration data acquired from multiple cross-sections in a tower. Iliopoulos et al. [13] predicted the acceleration at any location on a monopile foundation, the results of which were in agreement with both the time history and frequency distribution. They found that the method could be applied in various situations, such as during operation, idling, and emergency shutdown [14]. Maes et al. [15] used a similar method to evaluate the strain on turbine support structures, but found a problem with the integral required in the evaluation process, which increased the error in regard to the quasistatic component, and prevented an evaluation from taking place. Noppe et al. [16] overcame this problem by creating a neural network model that predicts thrust loads using the strain at the bottom of the tower and 1 s SCADA data. The quasistatic strain is then predicted from the thrust loads. Iliopoulos et al. [17] extended their method and divided the frequency range into three bands using bandpass filters, proposing a method for predicting the frequency band below 0.2 Hz caused by thrust forces using the strain at the bottom of the tower, for predicting the frequency band from 0.2 to 0.5 Hz caused by the tower’s first mode of oscillation and wave loads using the acceleration at the tower top, and for predicting the frequency band above 0.5 Hz caused by wind turbulence and higher modes of rotor rotation using the acceleration at the middle of the tower. Henkel et al. [18] demonstrated with measured data that the mode expansion method is effective when used for measuring underwater and underground monopile foundations.

The mode expansion method has also been applied for the evaluation of jacket foundations. Augustyn et al. [19] showed that the accuracy of the displacement estimation for jacket foundations was increased when considering the local brace vibration mode and wave-induced vibrations, using wave height data and Ritz vectors. Henkel et al. [20] predicted the quasistatic frequency band below 0.2 Hz, using the strain measured at the jacket top, and the dynamic frequency band, using the acceleration measured in regard to the tower. Partovi-Mehr et al. [21] also predicted the quasistatic component from the strain at the bottom of the tower and predicted the dynamic component from the acceleration of the tower. Skafte et al. [22] proposed a method for predicting the low-frequency vibrations caused by waves, using Ritz vectors and high-frequency vibrations, based on the acceleration of marine structures other than wind turbines.

In addition to mode expansion methods, Branquard et al. [23] proposed a method to assess the structure of wind turbines using an extended Kalman filter; Bilbao et al. [24] developed a method using a Gaussian process latent force model; Wei et al. [25] constructed a method using satellite positioning data and a Kalman filter; and Pimenta et al. [26] created a method based on physical equations for floating wind turbines.

1.4. Study Objectives

Despite the many virtual sensing methods that have been developed for monitoring wind turbine support structures, the models that predict statistical values can only predict either fatigue or extreme values. Additionally, these models are unsuitable for detailed analysis. Difficulties are also encountered when predicting the time history using modal expansion, because acceleration measurements are required at multiple tower heights and strain data are needed to evaluate the low-frequency components. A method using Ritz vectors was proposed for evaluating low-frequency components, but can only be used when wave loads are the main factor. This method is not applicable when wind loads are the main factor.

To overcome these issues, we developed a virtual sensing method that uses nacelle behavior to predict the load at the bottom of the tower. Nacelle behavior is the displacement in two directions (fore–aft and side–side) and the angle in three directions (nodding, rolling, and yawing). We propose calculating these displacements by integrating the translational acceleration, captured with acceleration sensors, and the angular speed, captured with gyro sensors. Most wind turbines are already equipped with acceleration sensors, so only a gyro sensor needs to be added to measure the nacelle behavior, so this method is easier than the conventional method of installing acceleration sensors at multiple cross-sections in the tower. Here, the same problem arises during integration as with conventional methods, i.e., the large error in regard to the low-frequency component. Whereas researchers have often obtained additional strain measurements, we propose using operating condition data, i.e., power, generator speed, and pitch angle, to address the problem. Measuring strain is difficult, but the operational conditions of wind turbine structures are already being monitored for control purposes, so no additional sensors need to be added. We compared the accuracy of linear and nonlinear machine learning models, as well as creating separate models for each frequency band, corresponding to specific physical phenomena. In addition, most previous studies only predicted the bending moment in regard to wind turbine towers; however, we also predict the torsional torque, enabling a more comprehensive evaluation of the tower.

In the remainder of this paper, the proposed method is outlined in Section 2, the target wind turbine and loads in regard to the case study are described in Section 3, and the details of the implementation of the case study are described in Section 4. The prediction results for the case study are provided in Section 5. Then, a summary of the study, the prospects for the application of the proposed method to offshore wind turbines, and the potential for further development of the proposed method are described in Section 6.

2. Methodology

2.1. Input Data

Data are collected to create a prediction model, which can be created through the use of simulations or measurements. The parameters according to which data can be collected are shown in

Table 1. Parameters for which data were collected.

Objective variable	Bending moment of target tower cross-section (fore–aft and side–side directions) Torsional torque of target tower cross-section
Explanatory variable	Nacelle acceleration (fore–aft and side–side directions) Nacelle angular velocity (nodding, rolling, yawing) Operating condition (power, pitch angle, generator speed)

. Data on all of these variables do not need to be collected; the objective variable is the monitoring of the load for the wind turbine in question and the explanatory variables are determined based on the objective variable and the required accuracy, with reference to the results from the case study, as detailed in Section 5. In addition, it is necessary to collect data on the typical conditions (such as wind conditions), within the target operating conditions.

The nacelle acceleration and nacelle angular velocity need to be converted into the nacelle displacement and nacelle angle. The calculation process is shown in Figure 1. The nacelle acceleration is integrated twice and the nacelle angular velocity is integrated once. As the level of integration increases the error in the low-frequency components, a high-pass filter is used to remove these low-frequency components. The cutoff frequency of the high-pass filter depends on the accuracy of the measurement and should be set as low as possible without increasing the error due to integration.

2.2. Determination of Explanatory Variables

The explanatory variables are determined by checking their correlation with each objective variable. The variables that are highly correlated with the objective variable are selected, but because the highly correlated variables could differ with the frequency band, the decision is made by considering the frequency band that relates to the desired increase in the prediction accuracy. If the number of explanatory variables is too high, the prediction accuracy may not improve due to overfitting, so care is needed when selecting the explanatory variables.

2.3. Determination of Frequency Band

The factors that cause fluctuations in the tower load to be evaluated are as follows:

• Fluctuation frequency of external forces, such as wind speed;
• Rotor rotation frequency;
• Blade passing frequency and its harmonics;
• Natural tower frequency;
• Natural drivetrain frequency.

We determined how to divide the frequency band by focusing on the factors that strongly impacted the tower load.

2.4. Selection of Machine Learning Models

Various machine learning models are available, and the model that provides high predictive accuracy differs depending on the objective and explanatory variables. Multiple evaluation metrics, such as analysis time and ease of interpreting the results, could also be used to verify the accuracy of the model. The model is tested using limited data, and a machine learning model that suits the purpose is selected.

2.5. Creation of a Machine Learning Model

In general, a machine learning model is created by dividing the data into training and test data. The prediction model is developed using the training data and the prediction accuracy is evaluated using the test data. However, if all the data are randomly divided into training and test data, the data for adjacent time periods may be similar and may not be completely independent, leading to an overestimation of the prediction accuracy. Therefore, some ingenuity is required, such as dividing the data into 10 min intervals and separating the data into training and test sets.

In this study, in addition to the usual method of creating a prediction model for full frequency bands (full frequency band model), we propose a method of dividing the objective and explanatory variables into frequency bands according to the physical phenomena, creating a prediction model for each and, finally, integrating them (each frequency band model). Our aim, here, is to avoid a situation where the prediction of the frequency band with the strongest impact is prioritized and the prediction accuracy for the other frequency bands deteriorates, due to a model being created for all the frequency bands at once. The workflow of the analysis is shown in Figure 2. The frequency band division is applied as described in Section 2.3.

3. Case Study Conditions

This section describes the wind turbine and loads in the case study.

3.1. Wind Turbine

The target wind turbine was a 2 MW downwind turbine, manufactured by Hitachi, Ltd. (Tokyo, Japan) [27], intended for installation on land, and its specifications are shown in

Table 2. The wind turbine’s general specifications.

Manufacturer	Hitachi, Ltd.
Model	HTW2.0–86
Rotor diameter	86 m
Rotor position	Downwind
Rated power	2 MW
Number of blades	3
Tilt angle	−8 deg
Corning angle	5 deg
Hub height	78 m
Power control	Pitch, variable speed

. In this study, we prioritized confirming the feasibility of the method and, thus, used onshore wind turbines, which have relatively simple behavior and condition settings. We discuss the application of this method to offshore wind turbines, which have a greater requirement for this technology, in Section 6.2.

3.2. Target Loads

The loads evaluated included three-directional moments at three tower height sections, as shown in Figure 3, namely the bottom, middle, and top of the tower, at 0, 38.3, and 75.8 m above the ground, respectively. The wind turbine was assumed to be generating power. The cost of the foundation accounts for a large proportion of the overall cost of a wind turbine, especially for offshore wind turbines. Our analysis focused on the loads at the bottom of the tower, as reducing these loads is important. The coordinate system was common in regard to the three height sections, with the X, Y, and Z directions being the horizontal rotor axial, the horizontal lateral, and the vertical direction, respectively. The bending moment in the Y direction, M_YT, is the bending moment in the fore–aft direction of the wind turbine, and the bending moment in the X direction, M_XT, is the bending moment in the side–side direction. We focused on the M_YT in the analysis, because the M_YT is larger compared to the M_XT for the target wind turbine and target operating condition. The M_XT progressively increases for wind turbines and during idling⁶. The moment in the Z direction, M_ZT, is the torsional torque around the tower axis and is particularly important for turbines with jacket foundations. To distinguish between the loads at each height, the loads at the bottom of the tower are denoted by M_YTb, M_XTb, and M_ZTb; the loads at the middle of the tower by M_YTm, M_XTm, and M_ZTm; and the loads at the top of the tower by M_YTt, M_XTt, and M_ZTt. In the figures, M_YT and M_XT were normalized using the designed maximum load of the vector composite and M_XYT and M_ZT were normalized using the designed extreme value load of M_ZT (maximum absolute value) for each cross-section.

4. Case Study

4.1. Input Data

4.1.1. Aeroelastic Analysis

We could have used different measurements as input data, but we prioritized the feasibility of the method and instead used the results of the aeroelastic analysis. Aeroelastic analysis was conducted using Bladed version 4.2.0.83 software [28], considering five vibration modes for the blades (three flapwise modes and two edgewise modes) and seven vibration modes for the tower (three fore–aft direction modes, three side–side direction modes, and one torsional mode). The wind conditions for the aeroelastic analysis are shown in

Table 3. The wind parameter values used in the aeroelastic simulations.

Mean wind speed [m/s]	8, 14
Turbulence intensity (Iref) [−]	0.12, 0.14, 0.16, 0.18
Wind shear exponent (α) [−]	0.14, 0.2, 0.33, 0.5
Turbulence seed [−]	1~6

. The average wind speed was set to 8 m/s for optimal operation efficiency and 14 m/s for the rated output operation. A total of 192 cases were analyzed for 10 min each, with two average wind speeds, four turbulence intensities, four wind shears, and six turbulence seeds.

4.1.2. Time History and Power Spectral Density

The results of the two aeroelastic analysis cases (average wind speed of 8 m/s and 14 m/s) were standardized by subtracting the mean and dividing by the standard deviation, and the time history and power spectral density of the M_YTb and each explanatory variable were compared.

The nacelle X acceleration (Figure 4, average wind speed 14 m/s) has a higher frequency component than M_YTb, and the correlation between them is low. The nacelle X displacement (Figure 5, average wind speed 14 m/s) is strongly correlated with the tower’s first natural frequency of 0.34 Hz (and at frequencies below that), which is the main vibration component of M_YTb. However, the correlation is weak at frequencies above that. The nacelle nod angle (Figure 6, average wind speed 14 m/s) is highly correlated with the high-frequency components above 0.8 Hz, compared with the nacelle X displacement. The hub thrust load F_XN (Figure 7, average wind speed 14 m/s) is strongly correlated with the low-frequency components below 0.1 Hz and with the high-frequency components above 0.8 Hz, but is weakly correlated with the tower’s first natural frequency of 0.34 Hz. The pitch angle (Figure 8, average wind speed 14 m/s) was negatively correlated with the low-frequency components and the correlation was high at frequencies below 0.05 Hz. The power (Figure 9, average wind speed 8 m/s) is highly correlated with the components at frequencies below 0.05 Hz. The generator speed (Figure 10, average wind speed 8 m/s) is highly correlated with the low-frequency components below 0.05 Hz.

These findings show that the low-frequency components of M_YTb, below 0.05 Hz, are highly correlated with the pitch angle during optimal operation at 8 m/s and with the power and generator speed during the rated output operation at 14 m/s. Using these values may enable predictions to be made across the entire wind speed range. The nacelle X displacement and the nacelle nod angle more effectively predict the tower’s first natural frequency than the hub thrust load, F_XN, used in previous studies. The high-frequency components above 0.8 Hz more strongly correlate with the nacelle nod angle than with the nacelle X displacement.

4.1.3. Data Correlation

In this section, we outline our examination of the correlation between the objective and explanatory variables. The objective variables included the nine loads described in Section 3.2. The explanatory variables included four operating conditions, fifteen nacelle behavior variables, and four hub center loads. The Pearson correlation coefficients, which were determined based on the aeroelastic analysis results for 10 min periods with average wind speeds of 8 m/s and 14 m/s, are shown in Figure 11 and Figure 12, respectively.

(1)

Correlation with Operating Conditions

The following parameters were examined as operating conditions: power, pitch angle, generator speed, and yaw misalignment. M_YTb and M_YTm are highly correlated with the output and generator speed at 8 m/s and with the pitch angle at 14 m/s. The reason for this finding is likely because the power and generator speed change but the pitch angle remains constant in the low wind speed range, where the aim is to produce as much power as possible. Conversely, in the high wind speed range, where the turbine operates at the rated power and rotational speed, the power and generator speed remain constant but the pitch angle changes. By combining these operating conditions, predictions could be possible for the entire wind speed range. M_YTt does not correlate highly with the operating conditions because M_YTb and M_YTm are considerably affected by the thrust force, which is the total force applied to the rotor, whereas M_YTt is strongly affected by the bending moment, which is the imbalance of the forces applied to the rotor. The operating conditions are highly correlated with the former, but weakly correlated with the latter.

For M_XT, M_XTt is highly correlated with the power and generator speed at 8 m/s, but this is not the case for M_XTb and M_XTm. At 14 m/s, the heights are low, so predicting the M_XT across the entire wind speed range from the operating conditions is difficult. The correlation between M_ZT and the operating conditions is weak, so predicting the M_ZT is difficult.

(2)

Correlation with Nacelle Behavior

In regard to the nacelle behavior, five variables were investigated in regard to the axial and rotational behavior around the three axes, as shown in Figure 3, excluding the behavior in the Z-axis direction, where the changes were minimal. We also investigated the displacement/angle, velocity/angular velocity, and acceleration/angular acceleration of each of the variables. The velocity/angular velocity and acceleration/angular acceleration are not highly correlated with the nacelle behavior, but some displacements/angles are highly correlated. M_YTb and M_YTm are highly correlated with the X displacement and nod angle, but M_YTt is not. M_XTb and M_XTm are highly correlated with the Y displacement and roll angle, but M_XTt is not. M_ZTb, M_ZTm, and M_ZTt are highly correlated with the yaw angle.

(3)

Correlation with Hub Center Load

Previous studies have predicted the loads at the bottom of the tower using the thrust force, F_XN, of the rotor. M_YTb and M_YTm are strongly correlated with F_XN, but the correlation with the nacelle X displacement is stronger. As such, M_YTb and M_YTm can be more accurately predicted using the nacelle X displacement.

4.1.4. Nacelle Behavior Calculation

Integration was required to calculate the nacelle displacement and nacelle angle, which are highly correlated according to the findings in Section 4.1.3, using the nacelle acceleration and nacelle angular velocity as inputs. We performed this integration using Equation (1):

$$y\left(i\right)=y\left(i-1\right)+{\displaystyle \frac{x\left(i\right)+x\left(i-1\right)}{2}}\times \left(t\left(i\right)-t\left(i-1\right)\right), y\left(0\right)=0$$

(1)

where y is the variable after integration, x is the variable before integration, t is time, and i is the time step.

A third-order Butterworth high-pass filter with a cutoff frequency of 0.1 Hz was used to remove the low-frequency components. The cutoff frequency was set based on the findings in prior studies [21,24], but the cutoff frequency can be lowered if the noise performance of the accelerometer is improved [17]. In this study, the consistency of the power spectral density in regard to the operating conditions and M_YTb decreased above 0.05 Hz (see Section 4.1.2), and the prediction accuracy can be improved if the cutoff frequency is lowered to approximately 0.05 Hz.

4.2. Determination of Explanatory Variables

The explanatory variables for each objective variable were determined, as shown in

Table 4. Explanatory variable sets.

	MYT	MXT	MZT
OpeCon	Power, Pitch, Gen. Speed	Power, Pitch, Gen. Speed	Power, Pitch, Gen. Speed
OpeCon + Displacement	Power, Pitch, Gen. Speed, Nacelle X Displacement	Power, Pitch, Gen. Speed, Nacelle Y Displacement	Power, Pitch, Gen. Speed, Nacelle Y Displacement
OpeCon + Displacement + Angle	Power, Pitch, Gen. Speed, Nacelle X Displacement, Nacelle Nod Angle	Power, Pitch, Gen. Speed, Nacelle Y Displacement, Nacelle Roll Angle	Power, Pitch, Gen. Speed, Nacelle Y Displacement, Nacelle Yaw Angle

, based on the results described in Section 4.1.2 and Section 4.1.3. The explanatory variables were defined for the moment directions (MYT, MXT, and MZT) of the objective variable and did not change according to height (bottom, middle, or top). The explanatory variables were determined following three methods, according to the ease of measurement: the first involved considering the operating condition only (OpeCon), the second considered the operating condition and nacelle displacement (OpeCon + Displacement), and the third included the operating condition, nacelle displacement, and nacelle angle (OpeCon + Displacement + Angle). The operating conditions were determined using three variables: the power, pitch angle, and generator speed. The nacelle displacement and nacelle angle were the variables that were most strongly correlated, according to the Pearson correlation coefficient (Figure 11 and Figure 12).

The operating conditions of a wind turbine must be controlled and data are generally acquired on these conditions. In regard to the nacelle displacement, the nacelle acceleration is already measured for many wind turbines in order to monitor their condition. No additional sensors need to be installed as the nacelle acceleration can be converted into the nacelle displacement (see Section 4.1.4). The nacelle angle is difficult to determine using the existing sensors, but a gyroscope could be added to the nacelle to increase its predictability (see Section 4.1.4). This would be easier than recording acceleration measurements at multiple tower heights and measuring the strain on the tower, as conducted in previous studies.

4.3. Determination of Frequency Band

The frequency band division method used in this study is shown in

Table 5. Frequency band division method.

Frequency Band	Target	Filter Name
<0.1 Hz	Wind speed fluctuation, LPF range in calculating nacelle displacement and angle	BPF1
0.1~0.6 Hz	1 P at rated rotation speed (0.275 Hz), first tower (0.34 Hz)	BPF2
0.6~1.2 Hz	3 P at rated rotation speed (0.825 Hz)	BPF3
1.2~2.1 Hz	6 P at rated rotation speed (1.65 Hz), first drivetrain torsion (1.65 Hz)	BPF4
2.1~3.0 Hz	9 P at rated rotation speed (2.47 Hz), second and third tower (2.3~2.8 Hz)	BPF5

. Because a high-pass filter with a cutoff frequency of 0.1 Hz is applied when calculating the nacelle displacement and nacelle angle (see Section 4.1.4), the frequencies below 0.1 Hz were divided. In addition, the frequencies were divided according to the rotor rotation frequency 1 P at the rated rotation speed, the blade passing frequency 3 P, which is three times that of the frequency, and its harmonics, as well as the natural frequencies of the tower and the drivetrain. A third-order Butterworth filter was used as the bandpass filter.

4.4. Machine Learning Model Selection

We examined the prediction accuracy and analysis time of various models to select the appropriate models. Here, the neural network was not included. The Python 3.8.10 wrapper Pycaret, a tool for automating ML workflows, was used in this study.

Table 6. Performance of machine learning models.

Model	MAE	MSE	RMSE	R2	RMSLE	MAPE	TT (s)
Extra Trees Regressor	0.101	0.017	0.131	0.954	0.028	0.028	0.443
Random Forest Regressor	0.105	0.018	0.135	0.952	0.029	0.029	0.982
CatBoost Regressor	0.116	0.021	0.146	0.944	0.031	0.031	0.926
Light Gradient Boosting Machine	0.118	0.022	0.148	0.942	0.032	0.032	0.159
Extreme Gradient Boosting	0.117	0.022	0.149	0.942	0.032	0.032	0.242
Gradient Boosting Regressor	0.123	0.024	0.154	0.937	0.033	0.033	0.434
Linear Regression	0.125	0.025	0.157	0.935	0.034	0.034	0.623
Least Angle Regression	0.125	0.025	0.157	0.935	0.034	0.034	0.070
Bayesian Ridge	0.125	0.025	0.157	0.935	0.034	0.034	0.070
AdaBoost Regressor	0.128	0.026	0.160	0.932	0.035	0.035	0.215
Ridge Regression	0.128	0.026	0.160	0.932	0.035	0.035	0.071
Decision Tree Regressor	0.140	0.035	0.186	0.909	0.040	0.038	0.074
K-Nearest Neighbor Regressor	0.459	0.337	0.581	0.108	0.122	0.125	0.073
Lasso Regression	0.476	0.354	0.595	0.066	0.124	0.130	0.073
Elastic Net	0.476	0.354	0.595	0.066	0.124	0.130	0.070
Lasso Least Angle Regression	0.476	0.354	0.595	0.066	0.124	0.130	0.070
Orthogonal Matching Pursuit	0.476	0.354	0.595	0.066	0.124	0.130	0.071
Dummy Regressor	0.491	0.379	0.616	−0.001	0.128	0.133	0.127
Huber Regressor	0.500	0.409	0.640	−0.080	0.132	0.134	0.073
Passive Aggressive Regressor	0.576	0.547	0.730	−0.447	0.151	0.151	0.069

shows the results of the evaluation of each machine learning model when the objective variable was M_YTb and the explanatory variables were the three operating conditions (power, pitch angle, and generator speed) and the nacelle displacement (nacelle X displacement). We used the 10 min data from the aeroelastic analysis, with an average wind speed of 14 m/s. Here, as evaluation indices, we used the mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), coefficient of determination (R²), log mean squared error (RMSLE), mean absolute percentage error (MAPE), and training time (TT).

Models that use ensemble learning and decision trees ranked highly. This finding was thought to be because of the nonlinear behavior that was output and because the rotational speed was limited to a rated value and because the pitch angle was only adjusted when the energy above a certain level was used as input data. Decision trees are excellent at reproducing these types of phenomena. In this study, we used a nonlinear model called the extra trees regressor (ET), which combines decision trees and ensemble learning, using bagging to balance analysis accuracy and analysis time, as well as a linear model called linear regression (LR), which is simple and produces results that are easy to interpret.

4.5. Machine Learning Model Creation

Figure 13 shows the workflow that we followed for creating the machine learning model used in this study. The aeroelastic analysis results were divided into a training and a test dataset. However, rather than randomly dividing the data, the cases involving turbulence seeds 1 to 4 and 5 to 6 were used as the training and test datasets, respectively. This avoided splitting the data in a similar state at close times into training and test datasets. A machine learning model was developed using the training dataset, and the model was evaluated using the test dataset.

5. Evaluation of the Prediction Results

This section presents the results from a case study, based on the settings presented in Section 3 and Section 4.

5.1. Prediction Accuracy of Each Frequency Band Model

Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18 show examples of the prediction models created for each frequency band. The objective variable was the fore–aft bending moment at the bottom of the tower, M_YTb; the explanatory variables were the operating conditions, nacelle displacement, and nacelle angle; and the machine learning model was LR. In each figure, (a) is the coefficient importance calculated by multiplying the proportional constant of the LR model by the standard deviation of the variable, (b) compares the time history of the predicted values with the true values, (c) is the correlation, and (d) compares the power spectral density. The prediction model for frequencies below 0.1 Hz is shown in Figure 14. Almost no vibration components are present in this frequency band because a high-pass filter was applied when calculating the nacelle displacement and nacelle angle (see Section 4.1.4). As the nacelle displacement and nacelle angle do not contribute to the prediction, the operating conditions are used for the prediction. The models for 0.1 Hz and above are shown in Figure 15, Figure 16, Figure 17 and Figure 18. The operating conditions minimally contribute to the predication, whereas the contribution of the nacelle displacement is high in the low-frequency models, and the contribution of the nacelle angle is high in the high-frequency models.

Figure 19a–c shows the coefficient of determination (R²) for each frequency band model for the tower’s base load. The horizontal axis shows the explanatory variables and the type of machine learning model. The results of the fore–aft bending moment, M_YTb, are shown in Figure 19a. The model for the frequency bands below 0.1 Hz is accurate with the operating conditions only, which increases further when the machine learning model is changed from linear LR to nonlinear ET. The reason why the nonlinear model has a higher R2 is because the power and generator speed are rated above a certain wind speed and the pitch angle changes only above a certain wind speed, so they behave nonlinearly. For models with frequency bands above 0.1 Hz, the prediction accuracy is higher for the lower frequency bands when only the nacelle displacement is used; when the nacelle angle is added, the prediction accuracy is close to one for all the frequency bands.

The results for the side–side bending moment, M_XTb, are shown in Figure 19b. The model accuracy for the frequency band below 0.1 Hz is relatively high with the operating conditions only, but the accuracy is not higher than that of M_YTb. The model with frequency bands above 0.1 Hz has higher prediction accuracy with the nacelle displacement than with M_YTb; by adding the nacelle angle, the accuracy of all the frequency band models is close to one.

The results for the torsional torque, M_ZTb, are shown in Figure 19c. The model for the frequency band below 0.1 Hz has low prediction accuracy when using the explanatory variables considered in this study. The models for the frequency band above 0.1 Hz have low prediction accuracy when using the operating conditions and nacelle displacement, but, when the nacelle angle is used, the prediction accuracy is close to one for all the frequency band models.

Figure 19d–f shows the coefficient of determination (R²) for each frequency band model for the loads on the middle of the tower. Although some differences can be noted, the trend is the same as for the loads on the bottom of the tower.

Figure 19g–i shows the coefficient of determination (R²) for each frequency band model for the loads at the top of the tower. The results of the fore–aft bending moment, M_YTt, are shown in Figure 19g. The prediction accuracy of the model with a frequency band below 0.1 Hz is low when using the explanatory variables included here. For models with a frequency band of above 0.1 Hz, the prediction accuracy increases with the addition of the nacelle angle. The results of the side–side bending moment, M_XTt, are shown in Figure 19h. The prediction accuracy of the model with the frequency band below 0.1 Hz was high when including only the operating conditions, due to the contribution of the power. For the models with frequency bands above 0.1 Hz, the prediction accuracy was increased by adding the nacelle angle. The results of the torsional torque, M_ZTt, are shown in Figure 19i, showing a trend similar to that of the torsional torque at the bottom and middle of the tower.

5.2. Tower Load Prediction Accuracy

Figure 20, Figure 21, Figure 22 and Figure 23 are examples of the results produced by the tower load prediction models. The objective variable was the fore–aft bending moment, M_YTb, at the bottom of the tower and the explanatory variables were the operating conditions and the nacelle displacement. Figure 20 shows the full frequency band model using LR (see Section 2.5), which was generally accurate below 0.5 Hz, but showed substantial deviations above 0.5 Hz. Figure 21 shows each frequency band model using LR (see Section 2.5); the prediction accuracy above 0.5 Hz was higher than that of the full frequency band model. Figure 22 shows the full frequency band model using ET and Figure 23 shows each frequency band model using ET. As with LR, the prediction accuracy at high frequencies was higher for each frequency band model.

The prediction accuracy of each model is shown in Figure 24, Figure 25 and Figure 26. The evaluation was performed with three indices using all the test data: the coefficient of determination R², the ratio of the predicted to the true value of the fatigue damage equivalent load when the SN curve slope m was 4 (DEL), and the ratio of the predicted to the true value in terms of the maximum absolute value. The reference lines at 1.00 indicate the predicted and the true values are identical.

Figure 24a–c depicts the results for the fore–aft bending moment at the bottom of the tower, M_YTb. Even when the operating conditions were the only explanatory variables (Figure 24a), the prediction accuracy was high. However, the three indices became approximately one after adding the nacelle displacement to the explanatory variables (Figure 24b) and using the nonlinear ET model and each frequency band model. The prediction accuracy increased further when the nacelle angle was added to the explanatory variables (Figure 24c), and the three indices became approximately one even when the linear LR model was used.

Figure 24d–f shows the results for the side–side bending moment at the bottom of the tower, M_XTb. When the operating conditions were the only explanatory variables (Figure 24d), the prediction accuracy was low. However, fatigue and extreme loads were generally predicted when the nacelle displacement was added to the explanatory variables (Figure 24e), and a further increase in the predication accuracy was achieved by adding the nacelle angle (Figure 24f).

Figure 24g–i shows the results for the torsional torque at the bottom of the tower, M_ZTb. The prediction accuracy did not increase when the operating conditions were the only explanatory variables (Figure 24g) or when the nacelle displacement was added (Figure 24h). The R² did not increase when the nacelle angle was added (Figure 24i) because the low-frequency components below 0.1 Hz could not be predicted (see Section 5.1); however, the fluctuation components above 0.1 Hz were predicted, so the fatigue load could be predicted.

Figure 25 depicts the results for the middle of the tower, which are similar overall to the results for the bottom of the tower.

Figure 26a–c shows the results for the fore–aft bending moment at the top of the tower, M_YTt. The prediction accuracy did not improve when the operating conditions were the only explanatory variables (Figure 26a) or when the nacelle displacement was added (Figure 26b). However, the fatigue load could be evaluated in general when the nacelle angle was added (Figure 26c). Figure 26d–f shows the results for the side–side bending moment at the top of the tower, M_XTt. A general prediction could be produced using only the operating conditions (Figure 26d), and the prediction accuracy increased when the nacelle angle was included (Figure 26f). Figure 26g–i shows the results for the torsional torque at the top of the tower, M_ZTt, which are equivalent to the results for the torsional torque at the bottom and middle of the tower.

6. Conclusions and Future Works

6.1. Summary of the Results

A method for predicting three wind turbine tower loads (fore–aft bending moment, side–side bending moment, and torsional torque) was developed based on machine learning and simplified measurements of the nacelle behavior, without relying on strain measurements. Specifically, the machine learning model uses nacelle behavior as the input, which is strongly correlated with the tower load. The method was evaluated using aeroelastic analysis of a 2 MW onshore wind turbine. The main findings are summarized as follows:

(1)

The fore–aft and side–side bending moments at the bottom of the tower are not highly correlated with the nacelle acceleration, angular acceleration, velocity, or angular velocity. However, the fore–aft and side–side bending moments are highly correlated with the nacelle displacement and the nacelle angle. This correlation is particularly strong for the nacelle displacement with the low-frequency components and for the nacelle angle with the high-frequency components;

(2)

A high-pass filter must be applied when calculating the nacelle displacement and the nacelle angle from the measurements obtained with an accelerometer and gyroscope, which prevents the prediction of low-frequency components. Operating condition data, such as the power, generator speed, and pitch angle, were used to compensate for this limitation; in this way, the low-frequency components of the fore–aft bending moment at the bottom of the tower could be predicted, in general;

(3)

The prediction accuracy of the low-frequency components of the fore–aft bending moment at the bottom of the tower was increased using operating condition data and by changing the machine learning model from linear to nonlinear. However, nonlinear models should be used with caution as they may overpredict high-frequency components;

(4)

The fatigue and extreme loads of the fore–aft and side–side bending moments at the bottom of the tower can be predicated using operating condition and nacelle acceleration data. In addition, the prediction accuracy of high-frequency components increases when including nacelle angle velocity data;

(5)

The fatigue load of the torsional torque may be evaluated using nacelle angular velocity (yaw angular velocity) data. However, the prediction accuracy of the extreme load is lower because low-frequency components cannot be predicted using operating condition, nacelle acceleration, or nacelle angle velocity data.

Our results indicate that the bending moments in two directions at the bottom of the tower can be predicted with operating condition and nacelle acceleration data, which are already measured in regard to most wind turbines. Adding nacelle angle velocity data could increase prediction accuracy and enable the evaluation of the fluctuating components of torsional torque.

6.2. Prospects for Offshore Wind Turbines

The feasibility of our proposed method was verified using onshore wind turbines. However, this technology is more applicable for offshore wind turbines, where the cost of the wind turbine support structure is relatively high and maintenance is difficult. Here, we describe the prospects in regard to three types of foundations, namely monopile, jacket, and floating foundations, because the behavior and conditions of offshore wind turbines differ depending on the foundation type, as follows:

(1)

Monopile foundation: The effects of waves on the foundation must be evaluated. However, the load on the foundation could be similarly predicted because the foundation has the same structure as an onshore wind turbine tower;

(2)

Jacket foundation: This foundation is highly rigid and is not easily affected by waves, so the load at the tower base does not substantially differ from that of an onshore wind turbine. However, evaluating the torque applied in regard to the bottom of the tower is likely to be more important;

(3)

Floating foundation: The load on floating offshore wind turbines is dominated by low-frequency vibrations with large vibration amplitudes, so measuring the nacelle behavior requires ingenuity, such as measuring lower frequency vibrations and the contribution of gravitational acceleration to acceleration measurements.

6.3. Development Potential in Terms of This Method

The following measures could be considered for the further development of this method:

(1)

This method can be verified using actual measurements. The measurement accuracy must be verified for detecting the target phenomenon and the cutoff frequency of a high-pass filter when calculating the nacelle displacement and nacelle angle (see Section 4.1.4);

(2)

Its application to offshore wind turbines should be considered. In this case, the points mentioned in Section 6.2 must be considered;

(3)

We only analyzed power generation, but whether this technology can also be used during idling and emergency shutdown should be confirmed;

(4)

We calculated the nacelle displacement and nacelle angle based on the nacelle acceleration and nacelle angle velocity, but the related prediction accuracy could be increased if these parameters are measured directly using GPS or other means.