Lidar-based virtual load sensors for mooring lines using artificial neural networks

Floating offshore wind turbines are equipped with a variety of sensors, which are measuring data, valuable for the control and monitoring of the turbine. However, reliable measurements are difficult or costly for some physical quantities. This includes load estimates for mooring lines and fairleads. In this study, we investigate an approach using wind speed measurements from a forward-looking nacelle-based lidar as inputs to long short-term memory networks to estimate fairlead tensions. Nacelle-based lidar wind speed measurements on floating offshore wind turbines are influenced by platform motions, in particular by the rotational pitch displacement and the surge displacement of the floater. Therefore, the lidar wind speed measurement contains information about the dynamic behavior of the floater. In turn, the floater’s dynamics determine the fair lead loads. Thus in this study, we directly use the lidar-measured line of sight (LOS) wind speeds to estimate mooring line tensions. The model training data is obtained using the aero-elastic wind turbine simulation tool openFAST in combination with the numerical lidar simulation framework ViConDAR. Results show, that lidar-based virtual load sensors can reproduce mean fairlead tension as well as low-frequency fluctuations, with varying accuracy dependant on the combination of input features. For the model which is only using LOS wind speed measurements as input a normalized root mean squared error of 0.55 was obtained.


Introduction
With many countries worldwide having ambitious targets for offshore floating wind turbine (FOWT) installations and a pipeline of upcoming projects, the installed capacity of FOWT is expected to increase significantly in this decade.Forecasts expect the global installed floating wind capacity to reach 16.5 GW by 2030 [1].With the large-scale commercial deployment of FOWTs comes the need for reliable load-monitoring solutions.FOWTs are equipped with a variety of sensors, which are measuring data, valuable for the control and monitoring of individual turbines and farms.However, reliable measurements are difficult or costly for some physical quantities.In these cases, the use of a virtual sensor is a promising alternative.Mooring lines are a critical component of FOWTs, and their failure can be catastrophic.Apart from extreme loads, fatigue is one of the relevant mechanical failure modes for mooring lines and fairleads (see e.g.[2]).Therefore, load estimates of mooring lines and fairleads of floating offshore wind turbines are of high interest for monitoring applications.However, in practice mooring line loads are difficult to measure.
In this study, we investigate an approach using wind speed measurements from a forwardlooking nacelle based lidar as input to a neural network to estimate fairlead tensions.As shown in [3], nacelle based lidar measurements on FOWTs are influenced by platform motions, in particular the fore-aft motion of the nacelle.Therefore, the lidar wind speed measurement contains information about the inflow as well as the dynamic behavior of the floater.In turn, the fairlead loads are determined by the floater's dynamics and position.Thus, we can directly use the lidar-measured LOS wind speeds to estimate the loads on the mooring lines.
In short, the objectives of our work are: • to develop a virtual sensor model for fairlead tensions based on nacelle based lidar wind measurements, • to verify the model performance against simulation results, • and to evaluate the damage equivalent loads (DELs) from virtual sensors and reference time series.

Nacelle based lidar measurements on FOWT
Lidar measurements from nacelle based lidar systems on FOWTs are affected by floater motions.As investigated in [3], different effects of motion influence can be distinguished.Rotational motions of the floater-tower assembly cause tilted beam geometries compared to a fixed system, resulting in changing LOS velocity measurements.Tilted beam geometries also cause a shift of the lidar focus points in space.In the presence of a turbulent wind field, this change in measurement position results in variations in the measured wind speed.In addition, the rotational and translational motions of the floater cause significant nacelle translational velocities.Since the nacelle based lidar system follows the translational motion of the nacelle in space, these velocities are superimposed on the measurements.A detailed discussion of individual influencing parameters and quantification of effects can be found in [4].In this study, we take advantage of the motion-induced effects in lidar measurements by using LOS velocities measurements as input to the load prediction model.

Mooring line loads
Mooring lines are used for station keeping and stabilization of FOWTs and are located submerged underwater.They are susceptible to fatigue due to repeated loading cycles caused by different environmental conditions.It is therefore important to be able to measure dynamic line loads.However, the harsh marine environment makes it difficult to install sensors and maintain their accuracy over long periods.Although mooring lines perform critical functions, the lack of sensors makes them difficult to monitor and to assess the lifetime of individual lines.Depending on the stabilization needed by the station-keeping system and sea-bed characteristics, the shape and design of the mooring lines change.Current floater designs make use of taut or catenary mooring lines to achieve stability and station keeping.While taut lines are pre-tensioned, catenary lines provide stability only with their weight.Thus, governed by the principles of catenary shape, the mooring lines will go through dynamic loading based on the motions of the platform.For a catenary mooring line, the vertical and horizontal force at the fairlead can be represented as a fairlead tension force.Due to changing environmental conditions like waves, currents, and wind, the response of the FOWT and dynamic mooring tension will change as well [5,6].Some of these changes could be captured by using the LOS measurements of the lidar as input to virtual load sensor models.

Virtual sensors
Measurements of physical parameters are required for the efficient operation, control, and monitoring of operational wind turbines.In cases where direct measurements through sensors are impossible or impractical, the use of virtual sensors is an alternative.Instead of measuring the quantity of interest directly, virtual load sensor concepts are used to estimate this quantity indirectly, taking available measurement data as input, and modeling the required quantity.The model mapping the input data to the prediction can in principle be of different nature.In cases where the physical relationship between the input quantity and the output is known a physical model can be employed.An overview of modeling approaches for mooring line loads based on physical principles can be found in [7].
In cases where the exact relationship between input and output is unknown or can not be described sufficiently through a physical model, the use of data-driven models is a promising alternative.This is the case for fairlead tension predictions based on lidar inflow measurements as an input.
The potential of data-driven approaches for modeling virtual sensors in wind energy applications has already been demonstrated by different studies.In [8] several measurable predictor signals have been used to train neural networks, predicting the load of a wind turbine gearbox in six degrees of freedom.In [9] different network designs have been investigated for the prediction of blade root bending moments, wake center detection, and blade tip-tower clearance.

Methodology
A numerical approach is employed for the provision of model training data, as well as the demonstration of the prediction performance.We use the aero-elastic wind turbine simulation tool openFAST [10] in combination with the numerical lidar simulation framework ViConDAR [3,11] to create the input and output variables for the neural network.
Synthetic turbulent wind fields are created using the open-source turbulence code TurbSim [12].Relevant FOWT responses, including mooring line loads, are simulated using the aero-elastic simulation code openFAST version 3.2.1.Simulated wind fields and turbine dynamics are further used as input to the open-source numerical lidar simulator.Here, virtual lidar measurements under the influence of all six degrees of freedom are created.Mooring line loads and corresponding lidar measurements are then used to train neural networks for the prediction of fairlead tensions.Finally, we evaluate the predictions of the neural networks against the simulated time series.Figure 1 shows an overview of the approach.

Wind field generation
A set of 100 synthetic wind fields is created using the open-source turbulence code TurbSim [12] which employs the Veers method [13] for turbulence creation.For each wind field, the mean wind speed is randomized between 4ms -1 and 20ms -1 .Additional wind field parameters are summarized in table 1.

FOWT model
The University of Maine VolturnUS-S reference floating wind turbine [14] is a semisubmersible floating substructure in combination with the International Energy Agency (IEA) 15-240-RWT 15 MW reference wind turbine [15].The floater is designed as a steel structure comprised of three radial and one central cylindrical floating body, while the turbine tower is connected to the central column.Station keeping is realized through three chain catenary mooring lines of 850m length and a mass of 685kgm -1 , attached to the three radial floating bodies.Figure 2 (right) shows a sketch of the floater geometry, the fairlead positions, and the mounting position of the lidar.All details on the floater and mooring line design parameters can be found in [14].In total, a set of 1050 simulation samples is created, while the wind field is randomly sampled from the set of 100 wind fields described above.The wind direction is randomly sampled between -180 deg and +180 deg.To minimize the influence of transient effects each simulation is created with a total length of 1200s while the first 600s are discarded.

Lidar configuration
The lidar configuration considered is based on commercially available lidar systems as they are used for wind turbine control purposes.The beam configuration represents a fixed beam lidar system with 4 beams, arranged in a squared pattern.The opening angle (angle to the center line) of four beams is set to  ≈ 12.5°and the angle around the center line is set to  = 45°, 135°, 225°, 315°.The LOS measurements from 4 beams are taken sequentially with a temporal distance of   = 0.25.The duration of a full scan is 1s and the measurement range is set to 300m.The beam range gate length is set to 30 m and discretized by 10 points along the range gate.Additionally, Gaussian white noise of   = 20 is added to each measurement.The lidar pattern and corresponding coordinate system are shown in figure 2 (left).

Network design
We use long short-term memory (LSTM) networks [16] for the prediction of mooring line loads.LSTM networks are a specific type of recurrent neural networks which are widely used for prediction tasks with sequential input data such as time series data.This network type is capable of capturing long-term dependencies in time series data.The lidar and wave time series represent information of the wind and wave field several seconds before it reaches the FOWT and affects the target loads.Therefore, a time dependency between input and target signals can be expected.To represent this time dependency, an LSTM network architecture was chosen for the prediction task in this work.Figure 3 shows the structure of the network used.

Feature and target selection
The objective of this study is not to find an ideal virtual load sensor model for mooring line loads but to investigate the value of lidar inflow measurements for the estimation of mooring line loads.Therefore, the feature selection is done manually and focused on the use of lidar LOS measurements in combination with additional measurement signals as input features.Four different models are created.
The first model does only take the four LOS measurements of the lidar and the yaw position of the nacelle as an input.The nacelle yaw is taken into account because the lidar measurements do not contain any information about the global wind direction.In the second model, we include the wave elevation as an additional feature to add information about the hydrodynamic conditions to the model.Wave elevation measurements by wave buoys or wave radar systems are potentially available in future floating wind farms.The third model takes the lidar measurements as well as the rotational floater displacement in pitch and roll direction as inputs.In real applications, inclination signals can be available through inertial measurement units in the lidar device itself or the FOWT assembly.The last model serves as a baseline model for the lidar based models and uses the x-and y-positions in global coordinates as inputs.Accurate position measurements are potentially available through differential global navigation satellite systems in real floating wind farms.The fairlead tension of the three fairleads is selected as model targets, while one separate model is trained for each fairlead tension sensor.100-600 530

Model Performance
We evaluate the model performance using two different metrics.The accuracy of the time series prediction is evaluated using the RMSEN metric.The RMSEN is the root mean squared error between the predicted and the true target time series, normalized by the standard deviation   of the reference time series.It is calculated by: where  pred is the predicted time series value,  is the corresponding reference value and  is the number of data points in the sequence.Considering the possible use and application of the investigated virtual load sensors, the second evaluated metric is DEL.DELs are used for monitoring fatigue loads and estimation of remaining lifetimes.The calculation is based on a rain flow counting algorithm, counting the number of cycles   with load amplitudes   .  for each sample sequence is calculated by: where  ref is number of reference cycles and  is the Wöhler coefficient.Following the recommendation of [18] the Wöhler coefficient for a studless mooring chain is assumed to be  = 3.The number of reference cycles  ref for a reference cycle frequency of 1Hz is chosen to be 600.

Results and discussion
Results are only presented for fairlead 1 tension, because no statistical differences in the prediction accuracy of the three fairlead tensions were observed.Figure 4 (top) shows an exemplary time series of model predictions and corresponding reference time series for the four evaluated models.Additionally, the power spectral density (PSD) of the prediction and the reference time series is shown for each model (bottom).It can be seen that the predictions made purely based on lidar data provide a representation of the mean fairlead tensions and the low-frequency fluctuations with an RMSEN of 0.55 across all validation sample sequences.Higher frequencies, above 0.05 Hz, are not represented by the lidar only model.This can be explained by the lidar LOS one wind speed time series and PSD plot in figure 5.The lidar measurements do not show a distinct representation of the wave excitation.Consequently, the model is not able to predict the wave frequencies in the fairlead tension accurately.
The second model presented in figure 4 includes the wave elevation as an input feature to the model.Thus, wave frequencies are better represented by the model.Similarly, the model using the lidar measurements and the floater rotational displacements can capture low-frequency fluctuations as well as higher frequencies corresponding to wave excitation.Finally, the positionbased model shows similar performance as the two aforementioned models.Frequencies up to 0.3 Hz are well captured, while higher frequencies due to the structural dynamics of the assembly are not captured.It should be noted that the choice of spatial wind field grid resolution can influence the representation of floater dynamics at different frequencies in the simulated lidar measurements.More detailed analysis and verification with real measurement data are needed to confirm the results of this initial study.Additionally, the shown example represents a sample with high prediction accuracy of the lidar only and lidar + wave model.Other testing samples show less agreement between predictions and references for these models.The shown sample is marked as a red dot in figures 6 and 7.
To analyze the performance of the different models systematically, the RMSEN values for model predictions as a function of wind direction is calculated and shown in figure 6   values for lidar only and lidar + wave models are characterized by high scatter between the individual testing samples.The mean RMSEN for the lidar + pitch + roll model over all testing samples is slightly lower compared to the other two models including lidar measurements.This can be attributed to better capturing of pitch and roll dynamics content in fairlead tensions.
The model with position data as input shows slightly better performance with lower RMSEN values and less scatter.Figure 7 shows the calculated DELs for all models in relation to DELs calculated from the reference time series for the fairlead 1 tension.While all models underestimate the

Conclusions and future work
In this work, we have developed a virtual sensor model for fairlead tensions of FOWTs using inflow information from a nacelle-based lidar.An LSTM network structure was trained for different combinations of input features.Our work shows that nacelle-based lidar inflow measurements from FOWT contain valuable information about the FOWT dynamics.This information can be used for load predictions of fairlead tensions via a representative simulation model.Compared to predictions made from FOWT position data, lidar-based predictions show higher uncertainties.Nevertheless, the approach could be used as a reference for position-based models or in cases where accurate position measurements are not available.Future work on the topic will systematically analyze the ability of nacelle-based lidar systems to capture individual floater DoF in different frequency regions, relevant to mooring line loads.Additionally, we will investigate the use of lidar inflow information for the time ahead forecasting of mooring line loads.In this context, especially the forecasting of extreme loads could be of high relevance.

Figure 1 .
Figure 1.Mooring line virtual load sensor approach

Figure 2 .
Figure 2. Left: Lidar Pattern and coordinate system for lidar simulation.Right: UMaine VolturnUS-S floater set-up, top view.

Figure 4 .
Figure 4. Time series example of standardized prediction and reference time series for fairlead 1 tension (top).PSD of prediction and reference time series (bottom).

Figure 5 .
Figure 5. Standardized time series and PSD of one LOS measurement sample.

Table 1 .
Turbulent wind field parameters

Table 2 .
Model features [9].2.Hyperparameter tuningFollowing the approach of[9]two types of hyperparameters are distinguished.One set of parameters is determining the architecture and training characteristics of the LSTM model.Another set of parameters defines the number of training data sequences and the window length of the input and target time series.All training parameters are summarized in table 3. Parameters were optimized using a Bayesian optimization approach.The optimization was performed using the experiment manager functionality of the MATLAB statistics and machine learning toolbox[17].All training parameters as well as the optimized values of the best-performing model are summarized in table3.The adaptive moment estimation (ADAM) algorithm was used for training the model parameters.With the given hyperparameters, the training time for one virtual load sensor model is approximately 1 hour while the prediction of a ten-minute target sequence takes below 1s.