1. Introduction
Offshore wind energy represents a progressive and eco-friendly approach to electricity production, capitalizing on the consistent winds found offshore. Its adoption is on the rise, as it outperforms conventional onshore wind farms in terms of power generation efficiency [
1]. Initially confined to shallow waters with fixed bottoms, the advent of advanced technology has paved the way for floating wind turbines. These turbines are moored to the ocean floor with adaptable links, making it feasible to venture into deeper waters [
2]. Switching to FOWTs offers several benefits, including access to steadier winds, minimized visual intrusion, and greater compliance flexibility with noise regulations [
3]. The proliferation of offshore wind farms can be attributed to technological progress, supportive policies, and significant financial backing, all contributing to increased power output and a decrease in carbon emissions [
4].
Renewable energy plays a crucial role in global initiatives to address climate change and secure energy supplies. Offshore wind energy, particularly in Europe, has emerged as a front-runner among renewable energy options [
5]. As depicted in
Figure 1, there has been a notable trend in the growth of the average capacity of offshore wind turbines per project from 2000 to 2025. Initially averaging 1.5 MW at the start of the millennium, the capacity of these turbines is expected to reach between 10 and 12 MW by 2025, underscoring the rapid advancements in turbine technology and the expansion of offshore wind projects. This expected growth trend anticipates a focus on larger capacity units in the industry, particularly in markets outside China where the average size is anticipated to be between 7 and 8 MW [
6].
Recent trends in the field include the integration of Wave Energy Converters (WECs) with FOWTs. This hybrid approach, specifically the incorporation of OWCs with FOWTs, has been recognized as a promising strategy for improving renewable energy generation. The combination of FOWTs and OWCs aims to stabilize platforms and improve energy harvest, as shown in
Figure 2. The functioning of an OWC is based on a capture chamber with an opening at the bottom, allowing water to flow in response to incoming waves. The motion of water leads to the compression and expansion of air within the chamber, later driving self-rectifying air turbines at the apex of the chamber. Different models of WECs have been implemented across Europe, exemplified by the NEREIDA Wave Power Plant in Spain and the Limpet facility in Scotland, signifying notable advancements in the field of renewable energy [
7].
The creation of these hybrid offshore structures encompasses complex dynamics [
8]. Noteworthy advancements in modeling and control strategies for FOWTs combined with OWCs have been achieved, with machine learning playing a pivotal role [
9]. These developments have significantly enhanced the efficiency and dependability of such systems [
10]. The design of hybrid offshore structures presents complexities due to their coupled aero-hydro-servo-elastic dynamics [
11]. While bottom-fixed turbines are ideal for shallow waters, floating turbines excel in deeper marine environments. The design of floating wind turbines is categorized into three main types according to their stabilization methods: buoyancy-stabilized (barge platform), mooring-stabilized (tension leg platform), and ballast-stabilized (spar buoy) [
12].
Considerable progress has been realized in the development of modeling and control methodologies for FOWTs coupled with OWCs [
13]. Research efforts are intensively focused on discovering new strategies to enhance both the efficiency and dependability of these sophisticated systems. The application of machine learning, recognized for its prowess in identifying patterns and forecasting based on extensive data collections, has proven to be an instrumental asset in this area [
14]. Utilizing artificial intelligence, machine-learning approaches facilitate the crafting of precise and streamlined models for FOWTs integrated with OWCs.
2. Technical Literature Review
Machine learning is revolutionizing the domain of wind turbine regulation, marking a pivotal shift in research related to wind turbine control and surveillance through the integration of advanced machine learning and deep learning algorithms [
15]. A key focus area is the stabilization of FOWTs for marine energy uses, in which deep reinforcement learning (DRL) techniques, including actor-critic networks in conjunction with a globally asymptotically stable observer, are employed to dynamically manage FOWTs across diverse environmental settings [
16]. This simulation-driven analysis illustrates the advantage of such methodologies over conventional linear quadratic regulator (LQR) techniques in stabilizing FOWTs. Innovative, model-independent controllers utilizing reinforcement learning (RL) and Bayesian optimization (BO) offer adjustments without dependency on traditional mathematical models, aiming to boost energy production and minimize turbine stress [
17]. Additionally, data-oriented predictive control tactics employing deep learning alongside multi-objective optimization tackle the model complexity and the dilemma of conflicting control aims in FOWTs [
18]. These approaches enable accurate individual blade adjustment, optimizing the energy yield and ensuring platform steadiness in variable wind scenarios [
19]. In the field of FOWT monitoring and safety, deep learning significantly contributes to the analysis of mooring line tension. Through simulations under assorted environmental conditions, it has been discerned that surge movements primarily affect mooring line tension, regardless of the mooring configuration, whereas the elasticity of blades and towers plays a minor role in tension predictions [
20].
Gaussian process metamodels have recently been utilized as an innovative approach for encapsulating the hydrodynamic and structural dynamics of FOWTs [
21]. These metamodels process inputs such as wave height, forces, and moments at the tower-platform junction to forecast platform movements and rotations. The investigation assesses three varieties of Gaussian process metamodels, showcasing their capability in accurately simulating platform behaviors. Additionally, a multi-criteria decision-making (MCDM) framework for the development of offshore wind farms in Ireland has been introduced, incorporating technical, financial, environmental, and societal factors to evaluate the sustainability of offshore wind locations [
22]. Utilizing interval type-2 fuzzy sets and energy economic metrics such as the levelized cost of electricity (LCoC), this framework offers a refined decision-support system [
23].
Table 1 summarizes various soft computing techniques employed in FOWT applications, detailing their specific areas of application and the resulting benefits or outcomes. These methods enhance the performance, stability, and efficiency of FOWTs by addressing complex dynamic and control challenges.
For the modeling of FOWTs, several innovative methodologies and technologies have been developed to advance their performance. J. Jonkman and collaborators [
32] have been at the forefront with the introduction of OpenFAST for wind turbine behavior, a comprehensive tool that integrates fatigue, aerodynamics, structures, and turbulence aspects with a gain-scheduled proportional-integral approach. This simulator is instrumental in deciphering FOWT dynamics and facilitates the creation of robust control algorithms, including a standard collective blade pitch control mechanism [
33]. Addressing the critical issue of vibrations in FOWTs, the TORA concept has been developed [
34]. TORA is designed to enhance the structural stability of FOWTs, contributing to their smoother and more dependable functioning. Furthermore, M.A. Lackner and his team have introduced FAST-SC, a customized structural control system tailored for FOWTs [
35]. This system allows for the meticulous management of the turbine’s structural elements, optimizing its performance comprehensively.
OpenFAST [
36] is a pivotal tool in the development of diverse control strategies for FOWTs. It facilitates the exploration of active and passive control methods, including strategies focused on blade, torque, and rotational speed adjustments, and the application of the Tuned Mass Damper (TMD) for enhanced stability. In the pursuit of augmenting platform stability, a novel PID complementary airflow control method has been integrated into Offshore Wind Converters [
37]. This technique guarantees consistent performance amidst variable weather conditions. Furthermore, collective torque control is identified as a key factor in the operational efficiency of FOWTs, with PID control systems widely implemented to reduce discrepancies between target and actual values, thus ensuring adequate control over FOWT operations [
38].
There are various modeling techniques for FOWT-OWCs with semi-submersible configurations, which examine their dynamics within both time and frequency analytical domains. However, there is a need for intelligent machine learning models and control mechanisms for hybrid system stability. Therefore, this article has two primary novel objectives. The first is to develop novel control-oriented regressive intelligent modeling specifically for the hybrid design of FOWTs and OWCs. The second objective involves utilizing estimated models to implement gain scheduling PID feedback control. This control, aided by numerical tools and air valve control strategies, aims to ensure overall system control and stability. OWCs are utilized in this study primarily for platform stabilization. Consequently, their power output is generally lower compared to that of wind turbines. For instance, the OWC plant at the Mutriku Wave Power Plant in Spain has an installed capacity of 296 kW, while the wind turbines have a capacity of 5 MW [
39].
The paper’s structure has been outlined as follows:
Section 3 gives a detailed explanation of the subsystems within the FOWT-OWC system, along with their mathematical modeling.
Section 4 delves into the proposed designs for the hybrid platform’s geometry and the associated hydrodynamic calculations.
Section 5 discusses the proposed PID control for managing platform pitch and mitigating unwanted vibrations. Experimental findings, corroborated through cross-validation, are detailed in
Section 6. The paper ends with the final section, offering conclusions and suggestions for future research directions.
5. Model Validation and Control Results
This section details the simulations conducted to assess the effectiveness of the proposed modeling and control method for the hybrid FOWT-OWC system.
The comprehensive validation process is outlined in
Figure 16, and reveals a robust predictive model with exceptional performance metrics. The first figure sets a remarkable precedent, with near-perfect correlation coefficients exceeding 0.9997 across all datasets, showcasing the model’s high correlation with the datasets and the effectiveness of the underlying algorithm. Subsequent figures illustrate a commendable level of generalizability, with correlations consistently around or above 0.90. Such results are indicative of a well-tuned model that has been meticulously trained to translate the complexities of the data while maintaining commendable performance consistency when exposed to new, unseen datasets.
Moreover, the moderate performance depicted in the third figure, with correlations stabilizing between 0.76 to 0.78, underscores the model’s reliability in providing stable predictions despite varying data conditions. The fourth figure reinforces these findings, demonstrating the model’s resilience with high training and overall data correlation coefficients of 0.97, while a slight reduction in the test set correlation suggests a balanced approach to model fitting, avoiding overfitting while still capturing essential data patterns. These results collectively signal a promising direction for future deployment, offering a strong foundation for confident, data-driven decision-making and further affirming the model’s potential for practical application across diverse scenarios.
The series of validation graphs shown in
Figure 17 demonstrates the robust training model efficiency and predictive accuracy. The blue, green, and red lines represent training, validation, and testing, respectively. The model achieved optimal validation performance, with the best validation MSE remarkably low at 0.001169 by epoch 96, 0.68048 by epoch 34, 2.1952 by epoch 7, and 0.16825 by epoch 23, indicating rapid convergence and a strong learning capability. The MSE on a logarithmic scale swiftly declined from the initial epochs, underscoring the model’s ability to generalize without overfitting, as the test errors closely followed the validation errors. This consistency in low error rates across all phases highlights the model’s well-tuned balance between bias and variance, emphasizing its readiness for real-world application with a high degree of confidence in its predictive stability.
The set of error histograms from the predictive model evaluation provides insightful data on the distribution of prediction errors across training, validation, and test datasets. The histograms are plotted (see
Figure 18) with errors calculated as the difference between targets and model outputs, and they are segmented into 20 discrete bins, offering a clear visual representation of the error magnitude and frequency. In each histogram, most errors cluster around the zero-error bin, which is a positive indication of the model’s accuracy. Notably, the concentration of errors in bins close to zero across all datasets suggests that the model predictions are well-aligned with the actual values. The similar error distributions in the training, validation, and test sets imply that the model is not overfitted to the training data and has a consistent error profile when applied to unseen data. The distribution tails are thin, indicating fewer instances of large errors, which enhances the model’s credibility for practical applications.
The graphs illustrated in
Figure 19 are the errors of four distinct models across a 600-s horizon, with a particular focus on fore-aft and platform pitch errors. Models N1, N2, N3, and N4 exhibit an impressive level of accuracy, as evidenced by their error metrics closely reaching the zero line, indicating predictions that consistently align with the actual values. These models demonstrate exceptional reliability, maintaining a steady course even when faced with the complexities of dynamic forecasting. In general, the collective performance of these models paints a promising picture of predictive accuracy and offers a robust foundation for complex forecasting in dynamic environments.
For the top-tower fore-aft displacement (
), a set of graphical analyses is presented in
Figure 20. A detailed overview of the neural network’s training performance is rigorously compared against FAST simulations across a spectrum of wave periods. For the shortest wave period of 5 s, the trained network demonstrates excellent synchronization with the simulation data, capturing the rapid oscillatory patterns with minimal deviation. As the wave period increases to 10 and 14 s, the network maintains this high level of reliability, despite the longer periods introducing more complex dynamics to the training task. The graphs show that the network adeptly adjusts to these changes, with the error between the simulation and the trained network remaining consistently low. The longest wave period of 20 s tests the limits of the network’s predictive capacity. The corresponding graph indicates that while the overall trend and periodicity are captured, there is a slight increase in the deviation from the FAST simulation data. This is due to the inherent challenges in modeling such extended patterns, or could reflect a need for further training or refinement of the network for these conditions. Across all periods, however, the consistent performance of the trained network, especially in lower frequency waves, is indicative of a robust training regime that has prepared the network to handle a diverse range of scenarios with varying wind speeds. These results are encouraging for the application of the trained network in real-world situations in which adaptability to different environmental conditions has been considered carefully.
Figure 21 presents the training results of the Trained Model, set against FAST Data Network outputs, and using varying wave periods for the platform pitch. Each graph reveals the model’s performance over extended time frames, capturing the dynamics of platform pitch in response to simulated maritime conditions. The first graph, depicting the scenario with a 5-s wave period, shows an exceptional alignment between the Trained Model and the FAST Data Network, suggesting that the model has effectively internalized the system dynamics within this range. As the wave period increases to 10, 14, and 20 s in subsequent graphs, the Trained Model consistently mirrors the FAST Data Network’s pitch response, albeit with minor variations that become more pronounced with longer wave periods. These discrepancies are due to the increased complexity and potential non-linearities introduced at extended intervals. However, even at a 20-s wave period, the Trained Model demonstrates an impressive ability to replicate the complex patterns of the FAST simulations, exhibiting its robustness and adaptability.
Overall, the Trained Model’s performance across these varying conditions highlights its refined learning capabilities and potential for real-world application. Despite the challenges posed by longer wave periods and the intricate behaviors they induce, the model shows it can predict with high accuracy, making it a valuable tool for navigating the complexities of maritime environments.
The series of control implementation graphs in
Figure 22, demonstrates the performance of a PID-controlled system, in which the green lines represent the control actions and their resulting system stability, indicated by the reduced oscillations. The first graph reveals that the control actions closely follow the predicted model values with minimal oscillations, suggesting that the PID controller is well-tuned for the system’s dynamics within this specific scenario. The small oscillation amplitude indicates a finely adjusted control response that quickly stabilizes the platform pitch. Moving to the second graph, as the system is subjected to what may be a different set of conditions or a longer wave period, there is a slight increase in the oscillation magnitude. Despite this, the control action remains effective, keeping the platform pitch oscillations within a narrow band, indicative of a robust control system that compensates for the increased complexity of the input signal.
The third graph shows the response of the system to yet another set of conditions, potentially with even longer wave periods. Here, the control action successfully dampens oscillations, although there is a noticeable transient deviation after each significant change in the platform pitch. The transient peaks suggest the system may be approaching the limits of its design parameters, yet it still manages to return to a stable state quickly without prolonged or escalating oscillations. In the fourth graph, despite further complexity due to extended intervals or increased environmental challenges, the PID controller, improved by gain scheduling, demonstrates a commendable job of maintaining stability. The control actions result in bounded oscillations, indicating that the system has a good transient response and can settle within an acceptable range after being subjected to disturbances.
The effectiveness of the PID control system in reducing oscillations across different wave periods is presented in
Table 5. The data reveal that the mean oscillation amplitude is significantly reduced when the control system is applied, demonstrating significant reductions in oscillation amplitudes across different conditions. For instance, at a wave period of 20 s and a wind speed of 5 m/s, the fore-aft displacement is reduced by 35%, indicating the control system’s robustness. The consistent reduction in oscillation percentage, ranging from 5% to 35%, underscores the PID system’s capability to enhance stability and control in FOWT-OWC integrated systems under diverse operational scenarios. These findings highlight the potential of the PID control system in practical applications requiring precise oscillation control.
Statistically, the lower oscillation amplitudes across all four scenarios suggest that the PID gain scheduling is effectively calibrated. The control system appears to possess both a high degree of precision and an ability to quickly adapt to varying conditions, maintaining the platform pitch within tightly controlled limits. This is consistent with a well-designed control system that can mitigate the risk of instability even when dealing with complex, dynamic environmental inputs.
Figure 23 shows the PID controller’s voltage output over time for various wave periods and wind speeds. Specifically, it includes wave periods of 5 s, 10 s, 14 s, and 20 s, each plotted with their respective time scales: 600 s, 1200 s, 1800 s, and 2400 s. These time scales correspond to the selected wave periods, ensuring a comprehensive representation of the controller’s performance. The stepwise increase in voltage across all graphs indicates a controlled and adaptive approach to system regulation, with the gain scheduling effectively modulating the PID gains to manage the dynamic environment.
In the first graph, the voltage response is moderate, reflecting proportional and deliberate action to minor disturbances. The second graph shows a stronger response, suggesting the controller’s compensation for more significant disturbances. The third and fourth graphs extend this pattern, with the controller addressing sustained or evolving disturbances, maintaining system stability throughout. The consistent valve voltage increase without abrupt fluctuations highlights the PID controller’s effectiveness in ensuring smooth and stable system control over time.
The PID control tuning process was conducted using Simulink MATLAB to ensure precise optimization of the PID parameters. The control design of the FOWT-OWC system was modeled in Simulink, and initial PID parameters were estimated through theoretical and empirical methods. Simulations were run to observe system responses, with iterative adjustments made using Simulink PID Tuner for optimal performance. The tuning process ensured the control system could handle various environmental conditions, maintain stability, and minimize overshoot and settling time. The final PID parameters were validated through extensive testing, demonstrating the control strategy’s effectiveness and reliability in practical applications, as shown in
Table 6. These configurations are reflective of strategic adjustments made to ensure optimal system performance across varying maritime conditions. For N1, which operates within a 5-m wave environment, the proportional gain is set at 0.65, indicating a strong responsive action is favored in this scenario. This is complemented by a derivative gain of 0.02, which moderates the rate of change in the system’s response, providing a dampening effect to potential oscillations. N2, adapting to a 10-m wave period, utilizes a slightly lower proportional gain of 0.565, demonstrating a controlled and less aggressive approach to system error correction. The derivative gain here is adjusted to 0.0164, fine-tuning the system’s responsiveness to changes over time. In the case of N3, contending with a 14-m wave period, the proportional gain is increased to 0.89, reflecting a robust control strategy to swiftly address system deviations. The corresponding derivative gain of 0.084 is indicative of a strategy designed to provide stability and counteract the inertia that comes with larger wave impacts. Finally, parameters for N4, a 20-m wave period, show a proportional gain of 0.73, balancing prompt corrective action with the need for stability in more substantial wave conditions. The derivative gain is set at 0.072, suggesting a tailored approach to maintain control without over-dampening the response of system. The integral gains for all networks are notably negative; instead of accumulating positive corrections, they accumulate negative corrections.
This unique adjustment offers advantages in these specialized applications, as it implies a reduction of the integral response, which could potentially be beneficial in systems where over-integration of the error could lead to instability or performance issues. Overall, the selection of PID parameters demonstrates a thoughtful approach to achieving a balance between responsiveness and stability, ensuring that each network can effectively cope with the dynamic challenges presented by its specific operational wave period.
The reliance on simulation data poses a challenge, as it may not capture all real-world variabilities. Additionally, assumptions regarding environmental conditions and system parameters can affect the generalizability of the findings. Consequently, there is a necessity for field tests to validate the effectiveness of the proposed ANN models and PID control strategies in practical applications. The authors plan to incorporate Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) in future comparative analyses to leverage their advanced spatial and temporal processing capabilities. This strategic expansion is intended to enhance the modeling accuracy and increase the predictive precision of their simulations, thereby broadening the scope and depth of their methodology.