Review of Data-Driven Models in Wind Energy: Demonstration of Blade Twist Optimization Based on Aerodynamic Loads

Abstract

With the increasing use of data-driven modeling methods, new approaches to complex problems in the field of wind energy can be addressed. Topics reviewed through the literature include wake modeling, performance monitoring and controls applications, condition monitoring and fault detection, and other data-driven research. The literature shows the advantages of data-driven methods: a reduction in computational expense or complexity, particularly in the cases of wake modeling and controls, as well as various data-driven methodologies’ aptitudes for predictive modeling and classification, as in the cases of fault detection and diagnosis. Significant work exists for fault detection, while less work is found for controls applications. A methodology for creating data-driven wind turbine models for arbitrary performance parameters is proposed. Results are presented utilizing the methodology to create wind turbine models relating active adaptive twist to steady-state rotor thrust as a performance parameter of interest. Resulting models are evaluated by comparing root-mean-square-error (RMSE) on both the training and validation datasets, with Gaussian process regression (GPR), deemed an accurate model for this application. The resulting model undergoes particle swarm optimization to determine the optimal aerostructure twist shape at a given wind speed with respect to the modeled performance parameter, aerodynamic thrust load. The optimization process shows an improvement of 3.15% in thrust loading for the 10 MW reference turbine, and 2.66% for the 15 MW reference turbine.

1. Introduction

The wind industry is a growing market due to modern efforts to reduce fossil fuel emissions, with a growth in global capacity of 9% in 2022, up to 906 GW. Capacity is expected to continue growing, with an average of 15% per year for several years [1]. In this space, the domain of wind energy research, a foremost objective, is to reduce the levelized cost of energy (LCoE) [2,3,4], with many advancements in the field making wind energy more available, more productive, and cheaper. This can include many technologies or features which improve operation of the turbine, ranging from fatigue monitoring and reduction to structural improvements, aerodynamic improvements and modeling efforts, and materials technologies, and can impact onshore [5] and offshore [6] turbines [7,8].

The wind turbine operates when the wind speed is between the system cut-in and cut-out speed (see Figure 1). The operating objectives depend on the rate speed of the system and the immediate wind speed [9]. In Region 2, where wind speed is below the rated speed, the goal is to maximize power extraction. Controllers adjust the turbine’s rotational speed to match the wind speed, optimizing aerodynamic efficiency. However, this can cause high fluctuations in generator torque and transient loads, negatively impacting the turbine’s mechanical components. Advanced control schemes, like integral synergetic control, enhance power extraction and reduce control input and drive train oscillations. This mitigation extends the turbine’s lifespan by reducing mechanical loads [10]. In Region 3, when wind speed exceeds the rated speed, the focus shifts to limiting power output. This prevents overloading the turbine using complex control mechanisms. The super-twisting sliding mode controller adapts to unknown perturbations with self-tuning gains, maintaining stable power output. This method reduces platform pitch motion and blade fatigue loads, crucial for offshore wind turbines’ stability and durability [11]. Advanced control methods and capabilities have benefitted commercial scale systems by way of increased energy production, load mitigation, and overall net reduced costs [12].

New morphing blade designs, like twisting blades, offer performance improvements over traditional pitch angle and rotor speed control methods. Morphing trailing edge systems use piezoelectric actuators and compliant surfaces to deform the trailing edge, optimizing the lift coefficient and aerodynamic efficiency under varying conditions [13]. Active transformation of the blade twist angle improves aerodynamic performance through computer modeling and experimental work. Data-driven models support the design and control of adaptive aerostructures. They integrate experimental data with low-fidelity BEM and high-fidelity CFD modeling to ensure accuracy and reliability [14]. The European Project “Shape Adaptive Blades for Rotorcraft Efficiency” (SABRE) developed a shape memory alloy (SMA) morphing twist system. This system has demonstrated promising outcomes in aerodynamic-power benefits and reduced acoustic impact. Wind tunnel and whirl tower tests validated this system’s ability to alter the blade’s original twist law and enhance rotor performance in hover and vertical flight [15,16]. The SMA system produces a twist angle of up to 8° per blade radius, translating to potential power savings of 10% in hover and vertical flight [16].

Advanced modeling tools are essential to support blade research, development, and implementation, particularly for morphing and other advanced blade designs. Traditional aerodynamic models rely on traditional momentum theories. These theories lack the ability to effectively simulate the modern wind turbines complex flow regimes—necessitating empirical corrections that limit accuracy and reliability [17]. As wind turbines grow larger and more flexible, especially offshore, the interaction between aerodynamic forces and structural dynamics becomes complex. High-fidelity large-eddy simulations (LESs) and aero-servo-elastic solvers accurately capture these interactions [18]. Computational fluid dynamics (CFD) is extensively used for evaluating novel turbine designs. However, modern turbines’ complexity demands new tools to enhance accuracy. Multidisciplinary design optimization (MDO) approaches integrate Reynolds-averaged Navier–Stokes solvers with numerical optimization methodologies [19]. The offshore wind industry’s rapid expansion, with turbines becoming taller and moving into deeper waters, complicates modeling. This requires accounting for large-scale atmospheric variability and complex sea conditions, which classical boundary layer turbulence theories and simpler models cannot adequately address [20]. Financial and operational risks associated with wind power plant development necessitate highly accurate modeling and simulation to mitigate risks and ensure performance [21]. Innovations in modeling tools are crucial to characterize unique challenges of the offshore environment. Developing and validating new aerodynamic models and simulation tools is essential to predict next-generation wind turbine performance and reliability accurately.

One of the foremost avenues of investigating improvements for wind turbines is in power generation. The total available amount of capturable power is well known through the Betz limit [22], and efficiency improvements at many stages of turbine design allow progressively more of this theoretical limit to be captured in real systems [23]. Fatigue is also an ongoing point of interest for wind turbine research [24,25,26], as reduction in fatigue allows the system to operate for more total time, increasing the total energy generated per system and reducing maintenance costs during that operation time. Similarly, structural and material considerations [27] also contribute to the reduction in LCoE by increasing uptime, reducing maintenance or manufacturing costs [28], and improving power output.

Data-driven methods, then, provide a novel avenue to pursue these reductions in LCoE, and thereby push the envelope on wind energy technology, as demand for the industry is expected to grow. In wind energy, as well as aerodynamics overall, there are several avenues for data-driven modeling to provide potential benefits. Aerodynamics research is already making use of data-driven methods for the purposes of systems identification [29,30], that is, the identification of relationships between input data and output data, and feature extraction [31], the identification of features in the data [32]. Reduced-order data-driven modeling provides a significant reduction in computational expense over traditional methods, such as computational fluid dynamics (CFD), and provides approaches to aerodynamics problems where CFD is too expensive to accomplish.

Connecting these aerodynamic modeling advantages to wind energy, the prior review conducted by Pandit et al. provides a possible foundation for examining many of the applications of data-driven models in wind turbines but is narrowed to focus on the implementation of supervisory control and acquisition data (SCADA) systems and their use in data-driven models. Their paper places strong emphasis on condition monitoring as a task for these models, while also briefly discussing the importance and application of performance monitoring to pair with it. The review features a notable highlight in that, until recent years, classification-based models, in the context of SCADA data, have historically been the subject of much greater attention than regression-based models [33].

With this foundation of condition monitoring and performance monitoring as a branching-off point, there exist several groups of research efforts to examine as a way to gain insight into the present state of data-driven models in wind turbine research. For the scope of this review, condition monitoring is a collection of applications and topics which pertain to the health of the turbine system and its subsystems. This includes fault detection, fault classification, fault prediction, icing, fatigue, and more. The condition monitoring efforts mentioned in [33] are several such efforts. Performance monitoring, within the scope of this review, pertains, then, to power curve prediction, controls applications, turbine state modeling, and other such tasks.

In addition to the above tasks, wake modeling is another branch of wind energy that is utilizing data-driven methods. For the purposes of this paper, wake modeling encompasses any task or topic that contributes to the interdisciplinary efforts between aerodynamics and mathematics and aims to better model the complex downstream flow states of a fluid system. This notably includes many more topics than just wind energy, however, and this paper will only cover its intersection with wind turbine flows.

With this context in mind, this review highlights specific applications in wind turbine research and examines how various data-driven models are currently being used to conduct research on the topic. Beyond that, this paper looks at the trends in current research spaces for data-driven wind turbine applications and looks ahead to where these efforts are heading and where they are needed.

2. Data-Driven Methods in Wind Energy

Data-driven methods include a variety of mathematical techniques which utilize data collection, application of datasets, or in some way deal with data as part of their use. This more general description is intentionally vague to encompass many related, yet distinct, techniques that fall under the term. More narrowly, data-driven methods typically involve “learning” information from prepared datasets, through tasks such as regression, classification, and more, for the purposes of identifying relationships and complex patterns in data. A notable advantage of this is that, depending on the problem, such techniques may reduce computational expense or complexity over other methods.

The following section includes a description of various data-driven methods which feature prominently in the literature for wind energy, as a summary of the features and advantages of such methods.

Dynamic mode decomposition (DMD). DMD, introduced by Peter J. Schmid and Joern Sesterhenn [34,35,36], is a dimension-reduction technique for time series data. DMD identifies modes with specific oscillation frequencies and decay/growth rates, which are the normal modes in linear systems or the approximations of Koopman operator modes and eigenvalues in general cases. DMD captures modes with explicit temporal behaviors and features, including damped or driven sinusoidal patterns, hence DMD differs from other dimension-reduction methods such as the principal component analysis (PCA).

Artificial neural networks (ANNs). ANNs are a branch of machine learning models that consist of interconnected groups of artificial neurons [37], where each connection can transmit a signal from one neuron to another and be controlled by activation functions.

Convolutional neural networks (CNNs). CNNs are a specialized type of artificial neural network designed for processing data that has a grid-like topology, such as images [38]. CNNs employ a mathematical operation called convolution and are particularly effective for tasks involving image recognition, classification, and analysis. CNNs can efficiently handle the spatial hierarchy in data by filtering inputs for useful information and, thus, reducing the dimensions of the data, making them easier to analyze.

Bidirectional gated recurrent units (BiGRUs). This method is a sequence processing model that consists of two gated recurrent units [39,40,41], one taking the input in a forward direction, and the other in a backwards direction. It is a bidirectional recurrent neural network with only the input and forget gates.

Gaussian process regression (GPR). A method of interpolation based on Gaussian process governed by prior covariances, GPR is a nonparametric, Bayesian approach to regression that provides a probabilistic method to infer predictions [42]. It models the underlying function that generates the data as a Gaussian process, characterized by its mean and covariance functions.

The decision tree method. Decision tree is a machine learning algorithm used in applied statistics for both classification and regression tasks [43,44]. It models decisions and their possible consequences by splitting data into branches at decision nodes, based on feature values. Each node represents a feature in the dataset, each branch represents a decision rule, and each leaf node represents an outcome. Decision trees work by repeatedly partitioning the dataset into subsets based on the feature that results in the highest information gain or the biggest reduction in impurity. This process continues recursively until a stopping criterion is met.

The random forest method (RF). RF is a powerful ensemble learning technique for both classification and regression tasks [43,44]. It operates by constructing a multitude of decision trees at training time and outputting the mode of the classes (for classification) or mean prediction (for regression) of the individual trees. RFs improve upon the simplicity of decision trees by adding randomness and bootstrapping (sampling with replacement) to the tree-building process, which helps in reducing overfitting and ensures better generalization to unseen data.

2.1. Wake Modeling

Wake modeling, in this context, involves (1) a farm-scale interaction between multiple wind turbines, where the aerodynamic wake of one turbine influences the performance of downwind turbines, and (2) a turbine-scale investigation of how the flow field of wind evolves after its interaction with a turbine. This is an interdisciplinary topic which touches on aerodynamics such as fluid–structure interactions and turbulent flow analysis. While wake modeling remains an area of interest for several different, wider topics, for the scope of this paper, its intersection with data-driven modeling efforts accommodates several notable approaches and outcomes, including flow prediction.

Naseem Ali and Raúl Bayoán utilized dynamic mode decomposition (DMD) to forecast wake states, with the intent to assist controls systems to adjust farm-scale system according to predicted power output. This particular effort currently shows an approximate 15% error between predictive and actual fluctuating velocities, and future work intends to better capture nonlinearities [45]. In a similar effort, H. Zhang et al. utilized a sparsity-promoting DMD method to improve the computational efficiency of standard DMD methodology in numerical simulations, via reduction in the number of required modes for reconstruction of the wake [46]. Both methods take advantage of data-driven modeling’s ability to reduce complexity of the problem, and further take advantage of DMD’s particular features to enable forecasting of states.

Guo Nai-Zhi, Zhang Ming-Ming, and Li Bo investigated wind turbine wake using an RF approach to determine the relationship between local inflow parameters and the wake expansion rate. The paper took in SCADA data, filtered them for inflow data at the upwind turbine, then utilized that as the inflow conditions for the model. It then used a genetic algorithm (GA) to solve an optimization problem regarding the RMSE between the measured rate and calculated rate to find the optimal wake expansion rate for the time domain. By doing so, the paper presented a data-driven model which combines machine learning and analytical models, for an improvement in RMSE of 20% [47].

S. Ashwin Renganathan et al. also attempted to model the wake flow fields of a turbine farm, utilizing wind LIDAR measurements to improve accuracy over “incomplete and noisy” experimental data. In this paper, several machine learning methods were utilized in tandem. A neural network (NN) was first used to compress the data state-space by several orders of magnitude. Then, GPR was applied to map that state space. The paper thus presented a predictive wake model which drastically saves on computational expense, with the intent being that the data-driven methods create low-expense, accurate wake models that can be used in real time [48]. Here, again, the particular features of data-driven methods, this time NN and GPR, were used to enable prediction of a complex system by reducing the complexity of the data.

A novel data-driven method for reducing the computational expense of wake modeling was also presented by J. Steiner, R. Dwight, and A. Viré. The method described in their work generates data using high-fidelity large eddy simulations (LESs) and applies this data to a lower-fidelity Reynolds-averaged Navier–Stokes (RANS) model as a correction term derived through regression modeling. This approach is intended to take advantage of the preferable computational performance of the RANS model, while still maintaining some of the quality of data from the LES method [49].

Overall, the research presented shows a directed effort towards reduction in complexity and computational expense presented by the turbulent flow field problem. Corroborating this, Martin Geibel and Galih Bangga, in their research on wake reconstruction, explicitly stated that their results reduced dimensionality of the flow data, through use of a particular ANN [50]. Generally, this feature is the one of the most advantageous to the application of wake modeling and flow data.

The literature overall indicates that a growing body of work exists that seeks to apply the particular advantages that data-driven methods provide in terms of computational expense to the problem of wake modeling in wind turbines and wind farms, extending to a strong foundation of work beyond that discussed above [51,52,53,54,55,56]. Wake, as a complex and high-dimensional problem, stands to benefit greatly from faster, cheaper modeling techniques offered by data-driven methods, particularly due to the turbulent flow use case. These benefits apply to both individual wind turbines [57], and to full wind farms [58], where knowledge of a turbine’s performance downwind from wake effects can impact power generation of the farm [59]. Notably, modal decomposition techniques [45,46] and deep learning techniques, particularly GPR [48] and NN approaches [57,60,61], are currently under thorough investigation by the literature for wake applications.

2.2. Performance Monitoring

Performance monitoring is another ongoing avenue of research for data-driven modeling in the wind turbine space. For the purposes of this paper, performance modeling is classified here as any task where data-driven models are utilized to observe, predict, control, and optimize the performance of individual turbines, or turbine farms, referencing tasks as such as in [33]. One such use case of this technology is in power capture, as an example, being used at least as early as 2011 in predictive control schemes to optimize power capture using a neural network [62]. Performance monitoring typically involves an examination of specific performance parameters of the turbine, such as power capture and vibration, often with the intent of controlling these values or otherwise manipulating turbine features. Applications here range from optimization of power capture to accounting for changes in environmental and turbine conditions in a controls system.

R. Pandit, D. Infield, and M. Santos examined the impact of a variety of environmental conditions on a GPR data-driven model describing the power curve of a turbine. They found that many known environmental factors do significantly influence the ability of a data-driven model to describe the power curve, with the strongest influence being turbulence intensity. Inclusion of this environmental feature improved model accuracy by approximately 15% [63]. By using GPR, this effort correlates a variety of complex systems and influences to achieve accuracy gain over traditional analytical methods, taking advantage of the strengths of the GPR method in reduction in complexity.

Another method to improve the modeling of a turbine power curve was presented in the paper by Wang, Y. et al. for modeling power output to wind speed with a single wind speed input. The proposed method is a combination of several data-driven methods: extreme learning machines, channel attention, CNN, and Huber loss. Through the sequential application of these techniques, the method produces a power curve that outperforms traditional models. The authors of the paper noted that, through the testing of several data-driven methods, the ability of CNN to fit nonlinear data is a key feature in its ability to perform above other techniques, such as artificial neural networks (ANNs) [64].

A more modern effort for the active control of wind turbine parameters, as compared to [62] as aforementioned, is discussed in a paper by R. Dinkla et al. This effort uses a model predictive control method, specifically subspace predictive control, to contribute to a closed-loop controller for the blade pitch actuation. The goal of this effort is to improve the performance of the blade pitch controller by reducing the total amount of pitch actuation, by incorporating detected future wind disturbances instead of traditional methods, with the added benefit of improving data efficiency of the controller through less requisite data retention [65]. Data-driven methods here are incorporated to predict states and improve data efficiency specifically, enabling real-time controls applications.

Similar controls-oriented efforts can be seen in work by Yang Liu et al. [66], who also designed a data-driven pitch controller to reduce computational expense of the system model, as well as in work by Jingjie Xie et al. [67], who used an NN-based adaptive controls algorithm to manage pitch and torque control. The efforts mentioned in [65,66,67] take advantage of the reduction in computational expense that data-driven methods provide, as does the work by M. Nouri Manzar and A. Khaki-Sedigh [68]. Their effort, too, involved the use of a data-driven model to enable active control of pitch and torque control schemes through reduction in computational expense, for the controller to operate in real-time. Data-driven models also contribute to other controls applications in wind energy due to their reduction in the complexity of problems, such as the work carried out by Jian Yang et al. [69], where a model for fatigue load distribution was utilized to optimize active power dispatch to a wind turbine farm, combining wake research with performance control.

Other facets of performance provide more niches for data-driven models. In the work by S. P. Mulders et al., a data-driven approach for the calibration of internal controller models was presented. The calibration algorithm uses turbine operating data to calibrate the internal model. While this effort is foremost intended to assist in ensuring the performance of the turbine is optimal by calibrating the internal model to match the actual operating parameters of turbine, it should be noted that this calibration process also accounts for turbine degradation [70].

Overall, performance monitoring applications in the literature lack a clear direction as a body of work that the other applications investigated appear to possess. Specific applications, however, do show a few trends; efforts to support wind turbine controls systems are ongoing, leveraging the lowered computational expense offered by data-driven methods to enable either real-time control and optimization mechanisms [65,66,67,68], or to assist in the development and utilization of novel control methods besides pitch and torque controls [69,70]. Significant effort is also present toward characterization of the power curve and other performance factors of a turbine, instead utilizing data-driven methods to capture complex relationships that modern models lack, such as turbulence and various environmental factors [71,72,73,74]. Data-driven methods also have found applications in a predictive capacity, combining the two prior advantages of reduced computational expense and capturing complex relationships into real-time tasks across several performance modeling applications outside of controls [71,75,76]. Notably, many data-driven methods presently used in performance modeling applications are machine learning techniques such as NN [72,73,74], or GPR [63].

2.3. Condition Monitoring

Condition monitoring involves a breadth of subjects, including the long-term examination of the health and integrity of the turbine, the classification of anomalies turbines experience in operation, the detection of faults as they occur, and the prediction of when and how such issues arise. For the purposes of this paper, condition monitoring is classified here as any task that involves the observation or influencing of turbine health, operational status, or anomalies in the turbine systems, referencing such as in [32].

Among the various condition monitoring applications of data-driven models in wind turbines, a common use case is that of fault detection. However, within this broader scope, a variety of more specific applications can also be delineated. Namely, this includes applications such as detection, to find issues when they occur [77], diagnosis, to classify issues [78,79], and prediction, to determine when an issue may occur [78,80,81,82]. The purpose of these tasks, as stated by J.-Y. Hsu et al., is to “provide technicians early warnings, improve equipment efficient, and decrease system downtime of wind turbine operation [33]” or, more broadly, to reduce LCoE through system maintenance cost and overall system efficiency and uptime.

In the same paper by J.-Y. Hsu et al., two data-driven models were trained to detect and classify anomalies in wind turbine operation, one decision tree model, and one random forest (RF) model. Their process to develop these models also examined machine learning algorithms including neural network (NN), support vector machine (SVM), boosting tree, and the general chi-square automatic interaction detector, concluding that the random forest (RF) model produced the most accurate results. Validation tests of the final models showed 92.68% accuracy for the decision tree model, and 91.98% accuracy for the random forest model [83].

Multiple papers by L. Xiang et al. [84,85] describe an effort to use a convolutional neural network (CNN) model with an attention mechanism (AM) in the application of fault detection. The effort in [84] implements a “long- and short-term memory network” in the CNN, with weighting influenced by the AM, to run alongside the operation of the turbine, and predict when its condition will violate set parameters that denote a fault or anomaly. In [85], the effort continued by implementing “two bidirectional gated recurrent unit[s]”, and both displayed results through utilization of the model on SCADA datasets of real turbine operation. It is of note that the primary feature these models examine is operational temperature, unlike many similar fault detection efforts. Unlike the data-driven methods in previous applications, it should be noted that many of the methods here utilize the advantages that various data-driven methods provide for rapid and accurate classification, with many data-driven methods such as NN and decision tree methods being well suited to classification tasks.

The fault detection system described by S. Cho et al. is specific to hydraulic blade pitch subsystems. The system uses a Kalman filter to estimate the current operating conditions of the subsystem, and an artificial neural network (ANN) to diagnose fault types. Notably, while the Kalman filter is used in detection of the fault, this ANN system falls under a classification framework, and is capable of classifying six specific types of faults. Validation tests in the paper show an approximate 97% accuracy of the system [86].

In addition to the efforts described in greater detail above, the literature presents other such efforts regarding fault detection. Yanjie Guo et al. proposed a data-driven method for fault diagnosis for turbine drive trains, citing robustness to “harmonic interference and background noise”, for a more efficient method than traditional methods [87]. Mengshi Li et al. also proposed a data-driven model for fault diagnosis, this time examining the drive train, actuators, and sensors for faults across the turbine system, similarly citing “robustness to noise”, as well as an applicability to a wide range of turbine systems, given availability of appropriate data [88]. Similar to [87], research by Zhen Xu et al. incorporated data fusion into its approach to fault diagnosis on the drive chain [89].

Bilal, Adjallah, and Sava proposed the groundwork for a fault classification method through analysis of a variety of data types for a particular wind farm [90]. J. Man, Z. Zhang, and Q. Zhou presented a framework to predict wind turbine shutdowns through data-driven predictive analytics [91]. Jaclyn Solimine and Murat Inalpolat presented a data-driven, acoustics-based method to detect damage to the turbine blades, reaching between 89% and 99.8% detection accuracy depending on the type of fault [92]. D. Yu et al. proposed a “deep-belief network” data-driven method for fault detection and classification which is not only compared to traditional models, but also to a selection of multiple existing data-driven models as well to emphasize its accuracy over previous methods [93], a comparison illustrating just how well adapted data-driven modeling is to fault detection as an application, and how populous it has become in the space.

Despite the relative abundance of fault detection and fault classification research efforts, other niches exist in condition monitoring applications, such as health monitoring and icing prediction. For health monitoring, in work by Zhe Song et al., SCADA data were used to monitor and predict wind turbine health states. In particular, the bin method, Copula method, and normal distribution method were examined and evaluated for their performance, with the examined framework showing the Copula method to be promising, despite the limited access to SCADA data by the project [94].

Further fault detection and classification efforts are strongly represented in the literature [95,96,97,98,99]. In fact, the effort spent towards fault detection applications is the most represented topic among those reviewed by volume.

Another application is in icing problems [100,101,102,103,104]. In a paper by Y. Wu, H. Yuan, and T. Wen, a hybrid data-driven and simulation method was proposed to predict icing on wind turbine blades. Physical laws regarding the growth of icing on the blade were used to set up a simulation, and then that simulation was used to generate the data for a polynomial regression model. This regression model associates a variety of parameters, such as wind speed, to the accumulation of ice. The intention of this effort, then, was for use in a predictive capacity to predict when icing will cause problems for turbines already in operation [100].

The literature for condition monitoring applications of data-driven methods trend clearly and strongly toward fault detection and fault classification [83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99], taking advantage of the classification domain of data-driven methods instead of the regression of previous applications. Many of the papers reviewed proposed similar but distinct solutions to both broad and niche aspects of wind turbine operation in the space, covering much of the potential research space, varying by either type of solution presented or specificity of the application at hand. It is, therefore, the opinion of the authors that this is a saturated research area. Other condition monitoring efforts are present in the literature, such as those of fatigue and icing accommodations [31,69,100,101,102,103,104], yet fault detection and classification make up the largest portion of the literature out of all topics reviewed, indicating that there is some potential research yet available that is either overshadowed or pushed out of view by the overrepresentation of fault detection applications. Notably, fault detection applications utilize particular data-driven methods with advantages in classification, such as SVM [79], random forest [83], and NN [99].

2.4. Other Data-Driven Efforts

As noted, not all current research fits neatly into the above common categories. Several such articles were focused on determining operational parameters during dynamic conditions [105,106]. J. Yan et al. utilized a long-term short-term (LTSM) neural network (NN), hybridized with a database of physical, dynamic operation characteristics to assist simulation of wind turbine operations, stated by the authors to often be “physical simulation models”. The direct benefit of this research was intended to be an improvement in simulation accuracy and reduction in computational expense for these simulations, with the proposed method seeing a 99.8% accuracy in determining power output, and an 88.5% accuracy in tower root load [105]. Similarly, the efforts of Dong, X., et al. sought to assist in determining a wind turbine’s operational parameters during dynamic operating conditions through the use of a neural network. Unlike the previous effort, this was intended to augment a lack of obtainable measurements in a turbine during active dynamic operation “under severe disturbance”, rather than in simulation [106].

Unlike the previously discussed efforts, some research is directed towards improvement of the available data-driven modeling methods available in the field, rather than towards a specific application. M. Tan and Z. Zhang proposed a random sampling method for wind turbine data-driven models, radially uniform sampling. The intent of the algorithm, as with most sampling algorithms, was to obtain a randomly sampled data subset which would accelerate the training process with minimum loss of accuracy. The paper compared the sampling method in five different data-driven methods, including SVM and NN, where the proposed sampling method outperformed traditional sampling methods in the accuracy of the trained models [107].

While not necessarily in the field of aerodynamics, related data-driven modeling efforts also contribute to economic considerations for the broader field of wind energy, such as site management, siting, and optimization of wind farms. A study by A. P. Reiman et al. presented data-driven turbine models for distributed wind, with a strong emphasis on siting and economic studies. The data-driven methodology here was a variety of regression models intended for use in economic studies relating turbine size, power generation, costs, and power storage [108].

2.5. Future of Data-Driven Research

Several strong trends emerge from review of the literature. First, wake modeling is a growing research area, with both a strong foundation of established work and clear advantages for utilization of data-driven methods. Able to effectively utilize multiple types of data-driven methods such as modal decomposition and deep learning methods, efforts such as [46,47,48,49,50] push forward understanding of wake modeling techniques, while efforts such as [61] apply those techniques in practice, such as to turbine farms. As such, there is a growing disparity between the bodies of work for the two, with more effort currently directed at the former. While somewhat unsurprising, given that the former is developing the tools to be used in the latter, this opens up the opportunity for the utilization of those developed data-driven methods as tools in future work. Overall, wake modeling efforts are already strong, are growing, and show opportunity for new avenues of research off the backs of recent research.

Second, in the space of condition monitoring applications, fault detection is strongly represented. In fact, it is the most strongly represented application in all of the reviewed literature, if including the related categories of fault classification and fault prediction [83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99]. This strong representation forms a foundation for any work in the field but leaves little room for innovation to the base concept aside from novel modeling techniques and more niche applications. This may imply that the next step for research efforts in this field is to try for refinement, that is, to improve detection and classification accuracy over previous data-driven methods, or to synthesize existing data-driven methods for further advantages.

Lastly, performance monitoring applications are not strongly correlated as a category, reaching various disparate controls, performance, and predictive applications. While wake modeling and fault detection can benefit from a body of work dedicated to the advancement of similar research, performance monitoring has a weaker foundation to build from, despite the relatively older age of the topic. A significant body of work will be required before performance monitoring topics become as well founded as the other topics reviewed, but does stand to gain from doing so, as shown by the predictive controls [65,66,67,68,69,70] and power curve modeling [71,72,73,74] topics reviewed.

2.6. Implications to Adaptive Aerostructures

In previous work by the authors [6,109,110,111], aerostructures with adaptive twist capabilities were explored. Region 2 was considered for optimization of a twist profile with respect to power capture, at a variety of wind speeds for a 20 kW reference turbine [6]. A segmented approach was considered for implementation in a physical turbine blade, and several methods of bridging an idealized twist profile and segmented blade profile were investigated for best performance [109]. Our work with this model suggests improvements in wind capture of up to 13% and reductions in thrust load up to 70%.

Computer simulation models are crucial to the advancement of adaptive aerostructures. Still, there is a critical need for aerodynamic modeling tools that are efficient and accurate. To realize the adaptive technology in practice, the authors are studying a data-driven approach to model arbitrary performance parameters using a segmented twist profile. The efforts toward this are detailed here as an example of data-driven modeling in the space of wind turbine research.

3. Methodology

A linear segmented approach, as detailed in [110,111], is utilized to map performance parameters of interest to twist profiles using a variety of data-driven modeling techniques. A segmented approach is chosen to reduce the number of independent variables in the cost function to a user-defined amount, which can be modulated in future work. The cost function to be examined is defined, in region 3 operation only, as

$$P=f\left(u,\phi \left(u,\left\{\Delta {\theta }_i\right\}\right),\left\{\Delta {\theta }_i\right\}\right),$$

(1)

where $P$ is the performance parameter of interest, $\left\{\Delta {\theta }_i\right\}$ are the changes in twist relative to the original twist profile at the actuation points, henceforth referred to as actuation twist, and $\phi$ is the pitch angle at the root, which is determined by the turbine controller as part of region 3 operation to constrain power capture at rated power and is assumed to be a function of relative twists. Lastly, $u$ is the wind speed, assuming a nonturbulent, steady flow.

To acquire the data needed to build the data-driven models, in the general case, simulations are run using simulation software on a selected turbine of interest. For each simulation, a twist profile is generated using a uniform distribution for the value of each actuation twist, which is applied to the rest of the discrete points on the blade data sheet through linear interpolation. This is independently performed a user-selected number of times for each given wind speed, which are randomly selected through a normal distribution. An additional value set of zero in all actuation twists is also included at each wind speed, for later comparison. Each simulation is allowed to ready a steady state, and the output values of the simulation are recorded as periodic, time-averaged data. The output must necessarily include both the performance parameter(s) of interest, and the pitch.

For the specific analysis presented here, OpenFAST (v3.5.3. United States Department of Energy National Renewable Energy Laboratory) is used as the modeling software, and the distribution of wind speeds uses a mean at 15 m/s and variance of 1.5 m/s. This places the operation of the turbine in region 3, which is the focus of this effort. Furthermore, here, the process is repeated using a 10 MW [112] and 15 MW [113] reference turbine, to ensure its generalizability, and focuses on rotor thrust load as the performance parameter to be examined, due to its relevance in fatigue research. The simulations are run using three actuation points and three randomized distributions per wind speed. Thus, the cost function becomes

$$T=f\left(u,\phi \left(u,\Delta {\theta }_1,\Delta {\theta }_2,\Delta {\theta }_3\right),\Delta {\theta }_1,\Delta {\theta }_2,\Delta {\theta }_3\right),$$

(2)

where $T$ is the aerodynamic thrust load. For the models presented, 400 simulations were run, and 10% of the data generated were set aside for validation. Each simulation is a continuous operation of the turbine from startup, lasting through the system, reaching steady state, and output data are taken as a periodic average value during that steady-state period. Specifically, OpenFAST output data are batch-generated using a Python script with the above criterion, that is, Python scripting was used to control OpenFAST while generating 400 simulation iterations with the stated variation in wind speed and twist configuration, recording the time-averaged output data alongside the twist and wind speed input configurations. This is conducted individually for each reference turbine, as each turbine requires an independent set of data for an independent set of models. The data generated are then used as training data for several data-driven methods, namely, SVM, NN, decision tree, and GPR. MATLAB’s regression modeling tool is used for this task, importing the output and input datasets from the Python script. Training data, here, are the subset of data used for initial modeling, while test data are the subset of the original data retained to evaluate the performance of the developed models, by examining predictions for data points not within the training subset. Once each model is trained, they are evaluated through set-aside test data, and compared to evaluate the optimal modeling process. The overall methodology is described in its entirety in Figure 2.

4. Results

In building a model from the data, several data-driven methods were examined. Shown in

Table 1. 10 MW turbine model RMSE results.

	Training Data
	Decision Tree	SVM	Neural Network	GPR
Pitch (°)	1.4327	0.12141	0.54099	0.019475
Thrust Load (N)	18,881	17,635	3105.6	483.04
	Test Data
	Decision Tree	SVM	Neural Network	GPR
Pitch (°)	1.0738	0.12149	0.67701	0.0092139
Thrust Load (N)	19,982	28,100	4186.3	473.74

are the various approaches tested, and their relative performance as evaluated via RMSE, for the 10 MW reference turbine. This process was then repeated for the 15 MW turbine, presented in

Table 2. 15 MW turbine model RMSE results.

	Training Data
	Decision Tree	SVM	Neural Network	GPR
Pitch (°)	1.4142	0.15206	0.016374	0.015752
Thrust Load (N)	30,819	3012.5	6193.7	905.24
	Test Data
	Decision Tree	SVM	Neural Network	GPR
Pitch (°)	1.2089	0.10908	0.016508	0.013788
Thrust Load (N)	27,067	2835	5860.7	649.35

.

For modeling the pitch on the 10 MW turbine, the RMSE of the GPR model was 6.25 and 13.2 times smaller than the next best performing model, SVM, for the training and test data, respectively, with even larger improvements in accuracy over NN and decision tree models. For the 15 MW turbine, the RMSE of the GPR model was 9.65 and 7.91 times smaller than the SVM model, for the training and test data, respectively, again with larger improvements in accuracy over NN and decision tree models.

For modeling the performance parameter of interest, the rotor thrust, on the 10 MW turbine, the RMSE of the GPR model was 6.43 and 8.84 times smaller than the next best performing model, NN, for the training and test data, respectively, with larger improvements in accuracy over SVM and decision tree models. For the 15 MW turbine, the RMSE was 3.33 and 4.37 times smaller than the next best performing model, SVM, for the training and test data, respectively, with larger improvements in accuracy over SVM and decision tree models. Therefore, overall, the models developed show a clear advantage in terms of accuracy in favor of GPR as the appropriate data-driven model for this application, being several times more accurate than all other models in all cases.

4.1. Optimization of Thrust Load

To demonstrate the application of this process, an optimization problem was run using the developed models to predict optimal performance of the performance parameter, aerodynamic rotor thrust loading, at various wind speeds for this particular configuration. The process utilized particle swarm optimization to find a global minimum of the objective function shown in Equation (2), used the pitch model in the input variables of the thrust model, with the actuation twist as the independent variables of the function, and wind speed held constant. The results of this optimization are shown in

Table 3. 10 MW turbine model optimization results.

Wind Speed (m/s)		13	14	15	16	17	18
Thrust Force (kN)	Original	1007	903.0	828.8	770.5	722.7	683.3
	Optimized	996.0	893.1	815.5	753.7	703.0	661.8
Improvement (%)		1.09	1.10	1.60	2.18	2.73	3.15

for the 10 MW turbine, and in

Table 4. 15 MW turbine model optimization results.

Wind Speed (m/s)		13	14	15	16	17	18
Thrust Force (kN)	Original	1489	1349	1243	1156	1085	1024
	Optimized	1480	1335	1225	1136	1061	996.8
Improvement (%)		0.60	1.04	1.45	1.73	2.21	2.66

for the 15 MW turbine. The optimization process showed a maximum decrease in thrust load of 3.15% in the 10 MW turbine, and a maximum decrease in thrust load of 2.66% in the 15 MW turbine.

However, closer examination of the twist profiles defined by these optimized points show that some approach the limits of interpolation possible with the models, which is set as a boundary on the optimization process to prevent predictions outside the examined region, which indicates that the global optimum may lay outside the examined region. As such, the methodology, as outlined in Figure 1, then dictates that the process should be repeated for refinement in future work to expand the applicable region in severity of possible twist, and so on until the optimum values lie within the limits of the model. Moreover, the current approach mainly focuses on learning the states of performance variables and does not take changes/evolution into account. In the future, we may use DMD or similar methods to learn the dynamics of the performance variables.

4.2. Future Work

With the results presented showing promising models for general modeling of arbitrary wind turbine parameters, several avenues for future work emerge. Foremost, modeling of larger variety targeted parameters of interest may assist in demonstrating generalizability of the methodology, just as modeling among multiple reference turbines has, with the additional benefit of providing data-driven models for applications that need such models.

When considering the limitations of the presented models, namely, exclusive operation within regions bounded by the data collected, a better understanding of what extents the domain of each input can go to without sacrificing accuracy may help reduce total simulation time by preventing unnecessary repetition of the methodology due to desired information existing outside the model, as in the case of some of the optimization results shown in Table 3 and Table 4. Some future work, therefore, should be spent on developing this understanding of the limitations and boundaries of the models being developed.

Following other work on active morphing blades [82,83], applying optimization of the location and number of actuation points during the first steps of the methodology should improve the ability of the technology to function in desired applications, such as performance optimization, while not improving or modifying the model accuracy directly.

Also of interest for future work are other data types than those used in this paper. The explicit reason for the use of periodic, steady-state data here is due to difficulty in having the OpenFAST simulations incorporate modifications to the overall turbine system architecture during operation. However, with appropriate investigation, inclusion of this should be possible, and is already under preliminary examination. With this change, while the overall methodology will remain unchanged, the variety of usable data-driven methods will increase to include those that operate with consideration to time domain, such as DMD, and the objective function being investigated by the methodology can be updated to include time-varying information such as spatial derivatives of the input variables, to learn the PDE of the underlying performance variables. Such changes are warranted by the ability of data-driven models to capture nonlinear behavior of the system. In this case, the controls applications mentioned throughout the literature show what benefits can also be applied here: a reduction in computational expense and complexity that enables real-time control of a complex system.

5. Conclusions

Through examination of the literature on data-driven models in wind turbine applications, several points are made evident. First, the various purposes of data-driven modeling efforts are generally focused in a handful of narrow topics: reduction in computational expense [46,48,105], improvements in accuracy or other performance over existing methods [63,64,65], and leveraging the unique aspects of data-driven models in novel approaches for existing problems that cannot be solved or are difficult to solve with extant methods, such as fault detection [96,97,98,99].

For condition monitoring, specifically in the case of the prominent fault detection example, the strong representation of data-driven modeling efforts [64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86] is, in part, due to the success of many data-driven modeling techniques in classification tasks, such as NNs, SVM, and decision trees, a feature which is strongly beneficial to the detection of anomalies and faults that differ from standard operating conditions. Condition monitoring, particularly fault detection, is the largest portion of the literature by volume [83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99] and contains a strong foundation of work to build from but may be reaching a point of saturation with some repetitious efforts. Future effort within the topic may become more niche or may instead turn to refinement of accuracy for existing techniques instead of application of novel ones.

In the cases of wake modeling, many data-driven modeling efforts are intended to reduce computational expense [49,50]. Current wake modeling techniques, such as large eddy simulations (LESs), are computationally expensive, and so data-driven methods are employed attempting to reduce this cost through reduced order modeling [45,46], and other techniques. Further data-driven efforts that intersect with wake modeling are also ongoing in the wider realm of aerodynamics [32], contributing to the focus on the topic. Wake modeling is presently a well-founded and growing area of research within this domain [45,46,47,48,49,50], with interdisciplinary efforts to both provide a growing set of tools for flow studies and to opportunities to apply those tools to wind turbine applications.

Unlike the cohesive direction of fault detection and wake modeling, other data-driven applications in the space of performance monitoring lack a clear direction and are generally sparser in the literature [62,63,64,65,66,67]. Efforts such as [65] show promise in allowing predictive, systems-identifying data-driven models to augment performance of turbines through optimizing performance parameters, improving data efficiency to enable real-time applications, and reducing computational expense, yet few sources in the literature focused on tackling this in comparison to the now more well-tread areas of fault detection.

A possible explanation for the discrepancy between volume of work directed toward controls efforts, compared to fault detection, is that fault detection has a wide applicability to many discrete elements in a wind turbine system, while controls, optimization, and performance efforts have application to select elements of the turbine system. Turbine-scale controls efforts have generally focused on pitch control systems and torque control systems [65,66,67,68], or novel methods of controls such as the work by the authors. In contrast, fault detection systems have applicability to any component of the system which sees fatigue, damages, or icing [100,101,102,103,104], including everything from subsystems [86], the drive chain [87,88,89], to the system as a whole [83,84,85]. Similarly, the broader category of performance monitoring takes more advantage of data-driven techniques’ capacity for prediction [67], while fault detection applications are able to take advantage of both classification and prediction [76,91,94], allowing more opportunities for data-driven techniques to permeate.

Original work in this latter area, performance monitoring, is also presented for the modeling and performance optimization of a twist morphing blade with respect to a select performance parameter, aerodynamic thrust load. Several data-driven models are developed, including NN, GPR, decision tree, and SVM. Of these, GPR is found to be the most appropriate model for the system across all cases, in terms of both turbines examined and parameter examined, with a minimum 3.33 times improvement in accuracy over the next best model, and maximum 13.2 times improvement in accuracy over the next best model, in terms of RMSE. From here, an optimization process is run to find the optimal twist configuration for these morphing blades at given wind speeds, resulting in a maximum 3.15% and 2.66% improvement in load reduction for the 10 MW and 15 MW systems, respectively.

This original work therefore highlights the process and development of a data-driven model describing the complex system of a twist morphing turbine blade in a wind turbine. GPR, being highly suited to the modeling of both pitch and thrust load in terms of accuracy, is convenient due to its advantageous computational expense, which becomes a necessary requirement of models in future use cases. Since this technology is a novel axis of control for a turbine, like pitch and torque control before it, the use case for morphing blades involves the real-time operation of the control system. GPR then presents a suitable candidate for this effort, with the models developed here forming a foundation for future work.

6. Patents

The work supports the development of innovation related to United States Patent #WO2019210330A1, titled Flexible wind turbine blade with actively variable twist distribution.