Design of Virtual Sensors for a Pyramidal Weathervaning Floating Wind Turbine

Academic Editors: Kostas Belibassakis and Sarat Chandra Mohapatra Received: 12 June 2025 Revised: 21 July 2025 Accepted: 22 July 2025 Published: 24 July 2025 Citation: del Pozo Gonzalez, H.; Kallinger, M.D.; Yalcin, T.; Rapha, J.I.; Domínguez-García, J.L. Design of Virtual Sensors for a Pyramidal Weathervaning Floating Wind Turbine. J. Mar. Sci. Eng. 2025,13, 1411. https://doi.org/10.3390/ jmse13081411 Copyright: © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/). Article Design of Virtual Sensors for a Pyramidal Weathervaning Floating Wind Turbine Hector del Pozo Gonzalez , Magnus Daniel Kallinger , Tolga Yalcin , José Ignacio Rapha and Jose Luis Domínguez-García * Catalonia Institute for Energy Research (IREC), Jardins de les Dones de Negre, 08930 Barcelona, Spain; [email protected] (H.d.P.G.); [email protected] (M.D.K.); [email protected] (T.Y.); [email protected] (J.I.R.) *Correspondence: [email protected] Abstract This study explores virtual sensing techniques for the Eolink floating offshore wind turbine (FOWT), which features a pyramidal platform and a single-point mooring system that enables weathervaning to maximize power production and reduce structural loads. To address the challenges and costs associated with monitoring submerged components, virtual sensors are investigated as an alternative to physical instrumentation. The main objective is to design a virtual sensor of mooring hawser loads using a reduced set of input features from GPS, anemometer, and inertial measurement unit (IMU) data. A virtual sensor is also proposed to estimate the bending moment at the joint of the pyramid masts. The FOWT is modeled in OrcaFlex, and a range of load cases is simulated for training and testing. Under defined sensor sampling conditions, both supervised and physicsinformed machine learning algorithms are evaluated. The models are tested under aligned and misaligned environmental conditions, as well as across operating regimes belowand above-rated conditions. Results show that mooring tensions can be estimated with high accuracy, while bending moment predictions also perform well, though with lower precision. These findings support the use of virtual sensing to reduce instrumentation requirements in critical areas of the floating wind platform. Keywords: floating wind turbines; virtual sensors; single point mooring; weathervaning; supervised machine learning; physics-informed machine learning 1. Introduction Floating offshore wind turbines (FOWTs) have undergone significant evolution in recent years, with various concepts being applied in industrial settings. To date, commercial floating wind farms include Equinor’s Hywind Tampen and Hywind Scotland, Principle Power’s Kincardine off the Scottish coast, and Ocean Winds’ WindFloat Atlantic off the coast of Portugal [ 1 , 2 ]. During the early stages of floating wind development, cost reduction has been identified as a key requirement for large-scale deployment. Remote monitoring remains a cost challenge in floating wind structures [ 3 , 4 ]. Reducing physical sensors in complex areas lowers procurement and maintenance needs, and virtual sensors offer a viable alternative [3,5]. This article is based on Eolink’s disruptive floating offshore wind turbine (FOWT) concept [ 6 ], which is primarily characterized by a single-point mooring system, distinguishing it from conventional designs that typically use multiple mooring points. Single-point moored systems have been effectively used for years in oil and gas platforms and vessels [7] , J. Mar. Sci. Eng. 2025,13, 1411 https://doi.org/10.3390/jmse13081411 J. Mar. Sci. Eng. 2025,13, 1411 2 of 18 and this concept has now been adapted to wind turbines to enhance power extraction and enable self-alignment. Some earlier works related to this floating wind turbine have been published. Connolly et al. [ 8 ] presented a nonlinear model using Flexcom Wind to validate experimental wave tank tests conducted with a 1:10 scale model of a full-scale 12 MW concept. The models primarily focused on the hydrodynamic behavior of the platform under both moored and non-moored (free-floating body) conditions. The results showed good agreement with various test conditions, including regular waves, random seas, and random seas with steady wind loading, with the exception of the discrepancies in pitch response, where Flexcom tended to overestimate the results. The rest of the founded studies focused on its modeling and development, and documented the configuration and performance of the first wave tank test performed with the structure [ 9 , 10 ]. Finally, the initial concept description can be found in the patent by Guyot [11]. When designing virtual sensors (VSs), approaches can be broadly categorized as either competitive or cooperative [ 12 ]. In wind energy research, most existing methods adopt a cooperative sensing strategy, which integrates data from multiple independent sensors or features to infer quantities that cannot be directly measured or are intended to be virtualized. Applications of virtual sensing have been demonstrated in both onshore and bottom-fixed offshore turbines. Dimitrov and Göçmen [ 13 ] used long short-term memory (LSTM) networks to estimate blade root bending moments, detect wake centers, and forecast blade tip–tower clearance. Hlaing et al. [ 14 ] presented a Bayesian neural network framework for virtual load monitoring across offshore wind farms, using data from a fully instrumented turbine to predict loads and uncertainties on others with limited sensors. Mehlan et al. [ 15 ] developed a digital twin framework combining data-driven and physics-based models for virtual sensing of aerodynamic hub loads and drivetrain bearing fatigue, using SCADA and condition monitoring system (CMS) data. Moreover, Moynihan et al. [16] employed a Gaussian process model to estimate bending moments in offshore wind turbines based on SCADA measurements. When it comes to floating wind turbines, fewer studies are available. Among these, Gräfe et al. [ 17 , 18 ] employed LSTM models to estimate fairlead tensions based on wind speed measurements from a forward-looking, nacelle-mounted LiDAR. Branlard et al. [19] developed and validated a digital twin for the TetraSpar floating wind turbine to estimate aerodynamic loads, wind speed, and tower section loads for fatigue assessment, using virtual sensing and Kalman filtering. Pacheco et al. [20] proposed a digital twin approach to improve monitoring and maintenance of floating wind turbines, using open-source tools to track structural health and predict fatigue. Walker et al. [ 21 ] proposed two data-driven digital twins based on operational data from the Hywind Pilot Park—one to detect long-term drift in mooring line axial tension for structural health monitoring, and another to predict near-future tension for maintenance planning and safety. Although not applied to floating wind turbines, Sauder et al. [ 22 ] introduced a method for estimating top mooring line tensions in semi-submersible platforms using artificial neural networks. Table 1 summarizes the main aspects of existing virtual sensor approaches relevant to floating wind turbines. There are other topics that have contributed to the development of this article. Regarding the supervised machine learning algorithms, in this study, we will focus on random forest and gradient boosting; their basics could be found, respectively, in [ 23 , 24 ]. Works related to the dynamics of floating wind turbines, different levels of accuracy in modeling techniques for floating wind turbine components, and types of mooring lines and their modeling, which served as inspiration, can be found in [25–29]. J. Mar. Sci. Eng. 2025,13, 1411 3 of 18 Table 1. Summary of key virtual sensor approaches in fixed and floating offshore wind turbines. Aspect Key Insights Application Areas Gearbox and drivetrain load estimation, mooring-line tension, tower-base bending moments, converter stress, and structural fatigue monitoring. Techniques Used Kalman filters, linear state-space models, least-squares estimators, physics-informed machine learning, and neural networks integrated with digital twin frameworks. Sensor Inputs SCADA data, accelerometers, condition monitoring systems (CMS), LiDAR, GPS/inclinometers, and motion reference units (MRUs). VS Outputs Bearing forces, mooring tension, tower-base bending moments, remaining useful life, and early detection of anomalies. Reported Benefits Reduces reliance on expensive or hard-to-deploy physical sensors; enables real-time condition monitoring and predictive maintenance for floating offshore wind turbines. The contributions and novelties of this article are the development of virtual sensors for an industrial concept of a pyramidal, weathervaning floating wind turbine to monitor mooring hawser loads and mast top assembly moments using a minimal set of input features. We propose supervised machine learning algorithms and hybrid models that integrate physical constraints, trained on OrcaFlex simulation data under diverse conditions. To the best of our knowledge, this is also one of the first research articles focused on this specific floating wind turbine structure. This paper is organized as follows. Section 2provides a description of the operating concept of the Eolink floating wind turbine, its distinguishing features, and the possible location of physical sensors. Section 3details the methods, including the physics-based and data-driven algorithms employed in developing the virtual sensors. Section 4presents the methods and tools used for sensor development, together with the results obtained. Finally, Section 5concludes the paper. 2. Eolink Floating Wind Turbine Concept Figure 1a presents the front view of the design of Eolink’s floating wind turbine, and more detailed figures can be found in [ 6 ]. In contrast to conventional configurations that use a single tower, this design employs four distinct pillars that connect the turbine structure to the corners of the floating platform, as described in Figure 1b. As described in [8] , this configuration yields a more uniform stress distribution, reduced dynamic vibration, a smaller platform footprint, and lower initial investment costs. The pyramid-shaped support base distributes the rotor’s mass evenly between bearings at both ends, enabling a lighter nacelle and the use of four slender supports instead of a single monolithic pole. At a 5-MW scale, the platform measures approximately 50 m in length and 50 m in width, with a hub height of about 100 m supporting a rotor diameter of 140 m. Furthermore, the platform’s structural robustness and hydrodynamic stability allow it to accommodate turbines exceeding 10 MW at full scale. The turbine is engineered to naturally align with the wind via a front-mounted tether, as depicted in Figure 1c. Although wind direction and ocean currents are generally aligned in deep-water conditions, the design incorporates a dynamic ballast system capable of adjusting the turbine orientation by up to 120° to manage any misalignment. The floating platform is attached to the seabed using three anchor lines (red dots in Figure 1c), all of them connected to the rotating buoy (green dot in Figure 1c). The buoy contains all the mechanical rotating equipment necessary to achieve effective weathervaning. This system also enables load mitigation by decoupling the platform’s motion from its mooring system. In a simplified top-view representation, when the platform weathervanes to align with the wind force ( Fwind ) coming from a direction βwind , it experiences resulting J. Mar. Sci. Eng. 2025,13, 1411 4 of 18 forces in the surge ( Fx ) and sway ( Fy ) directions. These forces displace the turbine from its initial position, while the mooring system provides a restoring force ( Fm ) to maintain platform stability. The available power output of the floating offshore wind turbine (FOWT) depends on its alignment with the wind direction, expressed as Pav =f(βplatform , βwind) . When misaligned (i.e., βplatform =βwind ), the turbine produces less power than in the aligned condition (i.e., βplatform =βwind ). This effect is discussed in more detail in the following sections. Nacelle MRU Turbine GPS Anemometer Mast MRU (a) h L L (b) x y platform wind (c) Figure 1. (a) Front view of the Eolink pyramidal single-point moored platform, showing the locations of the possible physical sensors. (b) Description of the moments in the pyramidal mast’s structure, and (c) top view of the angles formed by the system to align the direction of the wind force (F wind ). The zoom resumes the force in surge (Fx) and sway (Fy), while (Fm) denotes the mooring force. 3. Methods and Design of the Virtual Sensors 3.1. Methodology The development of virtual sensors for floating offshore wind platforms follows a structured pipeline, as illustrated in Figure 2. The process begins with the definition of the platform configuration and physical sensor layout, which provides the basis for subsequent simulation and modeling. High-fidelity dynamic responses are then generated using OrcaFlex 11.5 simulations, incorporating the relevant environmental and operational conditions. To ensure compatibility with real-world measurement systems, the synthetic data is adapted to match the sampling characteristics of the onboard physical sensors. The processed data is used to develop two parallel models—a physics-based model in Simulink and machine learning models trained with scikit-learn and xgboost . These two models are later integrated into a PIML (physics-informed machine learning) framework during the training and model selection phase, where optimal configurations are selected based on accuracy and generalization performance. Finally, the trained virtual sensor is validated against reference data, and its performance is visualized. Visualization Model selection and validation Machine learning training Platform and physical sensor definition Physics-based model Sensor sampling adaptation Figure 2. Workflow for virtual sensor development. J. Mar. Sci. Eng. 2025,13, 1411 5 of 18 3.2. Assumptions of Physical Sensors Installed In the initial phase of developing virtual sensors, the first step is to identify which physical sensor measurements can serve as effective input features. Although detailed guidelines on sensor placement for floating wind turbine designs are limited, several sensor technologies are generally assumed to be integrated into these systems. Wind speed and direction are typically measured using anemometers and/or wind LiDAR systems, while variables related to wave elevation, wave direction, current velocity, and direction can be captured by wave buoys or radar-based instruments. Structural health monitoring can be obtained by installing accelerometers to record dynamic motions and strain gauges to detect elastic deformations in key structural components. Global Positioning System (GPS) sensors are installed to precisely track the platform’s location and movement, together with inertial measurement units (IMUs) for assessing orientation and tilt. Apart from that, it is assumed that all rotor nacelle assembly (RNA) components of the wind turbine, generator, and related systems are equipped with standard sensor placements (e.g., accelerometers for vibration monitoring, temperature sensors for thermal regulation, etc.). The used system and its associated sampling frequencies are presented in Table 2. Table 2. Sampling frequencies of the sensors used in the study. Physical Sensor Sample Frequency Unit Anemometer 1 Hz GPS 1 Hz Mooring Tension 5 Hz Mast/Nacelle MRU 10 Hz Wave-Current Data Constant – 3.3. Load Cases in OrcaFlex and Data Analysis Table 3summarizes the load cases defined for the dynamic analysis performed with OrcaFlex at full scale. These cases include different turbine states, such as operational, idling, and parked (survival), under varying environmental conditions. Wind inputs include steady, turbulent, directional-change, and step-gust conditions, with mean speeds ranging from below-rated conditions up to extreme 50-year return values. Wave conditions are described by significant wave height ( Hs ) and peak period ( Tp ), covering realistic mild to severe sea states consistent with wind intensity. Currents are modeled as steady and unidirectional, with magnitudes ranging from 0.1 m/s to 0.9 m/s, aligned with each case’s severity. Selected cases include wind–wave–current misalignment to evaluate its influence on the system’s dynamic response. Table 3. Summary of simulated load cases used in the dynamic analysis with OrcaFlex. Case Turbine Condition Wind Model Wave Model Current Model Misalignment 1 Operational Turbulent 7 m/s Hs= 1.0 m, Tp= 5 s Constant 0.1 m/s No 2 Operational Turbulent 11 m/s Hs= 2.5 m, Tp= 6 s Constant 0.2 m/s Yes 3 Operational Turbulent 15 m/s Hs= 3.5 m, Tp= 7.5 s Constant 0.2 m/s No 4 Operational Turbulent 9 m/s Hs= 1.8 m, Tp= 5.5 s Constant 0.1 m/s No 5 Operational Turbulent 13 m/s Hs= 3.0 m, Tp= 7 s Constant 0.2 m/s Yes 6 Operational Dir. change at 9 m/s Hs= 2.0 m, Tp= 5.5 s Constant 0.1 m/s Yes 7 Operational Dir. change at 13 m/s Hs= 3.0 m, Tp= 7 s Constant 0.2 m/s Yes 8 Operational Step gust to 25 m/s Hs= 4.0 m, Tp= 8 s Constant 0.3 m/s No 9 Idling (Storm) Steady 25 m/s Hs= 6.0 m, Tp= 10 s Constant 0.6 m/s Yes 10 Parked (Survival) Extreme wind (50-year) Hs= 8.0 m, Tp= 12 s Constant 0.9 m/s Yes 11 Parked (Survival) No wind Hs= 10.0 m, Tp= 15 s Constant 0.9 m/s No J. Mar. Sci. Eng. 2025,13, 1411 6 of 18 First, to determine which measurements can serve as inputs for the design of the virtual sensors, we need to identify the correlated variables. The correlations were calculated using the Spearman correlation method. Figure 3shows the five most correlated features for each desired target. Note that the strongest correlation coefficients are those closest to 1 or −1. Fhawser2 windSpeed Surge Sway windDir -1 -0.5 0 0.5 1 Correlation Coefficient thrust torque MastForePortSideF bladePitch Pitch -1 -0.5 0 0.5 1 Correlation Coefficient Figure 3. Front view of the Eolink pyramidal single-point moored platform, showing the locations of the desired virtual sensors and statistics of the five most correlated variables obtained using Spearman correlation. The virtual sensor for the forces in one of the hawsers (violet upper-side box) and the statistics of the five most correlated variables related to the force in the mast fore port side, assembled at the top point (green lower-side box). As can be seen in the green lower side box, the force in the right hawser exposes the highest correlation with the forces in the other hawser, as can be easily understood. However, this variable will not be taken into account, since we are neglecting the installation of a physical sensor there. Next, we can see correlations with wind speed and direction, as these factors directly influence the aerodynamic loads on the wind turbine. As wind speed increases, so does the magnitude of the force transmitted through the turbine through the floater into the mooring system, giving a reaction. Similarly, changes in wind direction alter the distribution of these forces along the hawsers. Additionally, surging exhibits a high correlation, followed by the swaying of the structure. The presence of these mooring-related features is expected, especially in surging, as observed in other floating wind substructures. On the other hand, the variables most correlated to the bending moment at the top of the pyramidal wind structure are depicted in the purple upper-side box. Aerodynamic thrust tends to appear since it directly generates bending and torsional forces, while the load transmitted through the masts adds to these moments. The forces in the upwind masts appear, as expected, to be linked to the forces at the connection between the substructure and the nacelle. The platform pitch probably appears due to altering the effective load distribution, affecting the lever arm of these forces. Additionally, the appearance of control parameters such as blade pitch and rotor speed is believed to be related to the need to adjust aerodynamic loads and regulate power, thereby influencing the overall moment at the top. Following these two findings, a simplified scheme of the virtual sensors is introduced in Figure 4. We propose the following objectives: The first objective is to design a virtual J. Mar. Sci. Eng. 2025,13, 1411 7 of 18 sensor (VS1) for one of the hawsers in the mooring system, aiming to avoid the installation of sensors underwater. The input features for this sensor include wind speed, wind direction, and, if needed, surge, as elements of X3 . Since the forces are highly correlated, the output of the first virtual sensor ( Fhawser1 ) is later used to calculate the tension in the other hawser ( Fhawser2 ). In this way, the sensor estimates the force in both of the mooring hawsers. The last objective is to develop another virtual sensor (VS3) to estimate the top masts’ bending moment ( BMmasts ) based on aerodynamic thrust forces, platform pitch dynamics, and the torque. Additionally, the inclusion of control parameters such as pitch angle and rotor angular velocity will be evaluated in a subsequent phase. VS1 VS2 Fhawser1 Fhawser2 X1 VS3BMmasts X3 Figure 4. A simplified scheme of the input–output of the developed virtual sensors. Although the virtual sensors presented here are designed using supervised machine learning models trained on a wide range of the floating platform’s behaviors, it is important to note that a method for integrating physics-based constraints into the supervised machine learning models will be introduced later in this paper, to avoid relying just on data-driven algorithms and to enable comparisons. Therefore, let us firstly introduce the main equations defining the dynamics of the platform, and later, the supervised machine learning algorithms used. 3.4. Physics Relations for PIML Integration The simplified model used in the physics-informed algorithms includes key environmental loads and mooring constraints acting on the floating offshore wind turbine (FOWT). As previously discussed and depicted in Figure 1, the platform exhibits weathervaning behavior and must be modeled with six degrees of freedom (6DOF): surge, sway, heave, roll, pitch, and yaw. Two hawsers connect selected columns of the platform to a buoy, which is anchored to the seabed using three mooring lines. The environmental loads considered include aerodynamic forces from wind, hydrodynamic forces from waves and steady currents, and hydrostatic restoring forces resulting from buoyancy and gravity. The platform dynamics are governed by the Newton–Euler equations, incorporating added mass and hydrodynamic damping from OrcaWave, along with restoring forces derived from hydrostatics and the mooring system. The equations can be expressed in a generalized coordinate system, where q =hx;ηi is the generalized position vector, including translational ( x ) and rotational ( η ) coordinates, and ˙ q=h˙x;ωi is the generalized velocity vector. The system’s dynamics are governed by a generalized mass-inertia matrix, added mass, damping, and restoring forces. The equation of motion is as follows: (M+A)¨ q+B˙ q+Cq +"0 ω×((I+Aθ)ω)#=τ(1) J. Mar. Sci. Eng. 2025,13, 1411 8 of 18 where Mis the global mass-inertia matrix, Ais the added mass and added inertia matrix, B represents hydrodynamic and rotational damping, and Cis the restoring force and moment matrix. The nonlinear gyroscopic term ω×((I+Aθ)ω) appears only in the rotational part of the equation. The generalized external force vector is given by the aerodynamic, hydrodynamic, and mooring forces and moments: τ="Faero +Fhydro +Fm Maero +Mhydro +Mm.#(2) The aerodynamic loads depend on the exposed surfaces of the structure and the relative alignment between the platform and the wind. For each of the j structural components, the aerodynamic force and moment contributions are modeled as follows: Faero,j=0.5 ρaCD,jAe,jU2nj, (3) Maero,j=0.5 ρaCM,jAe,jU2ra,j, (4) where ρa is the air density, CD,j and CM,j are the drag and moment coefficients for component j , Ae,j is its effective projected area (which is a function of the platform’s orientation relative to the wind), n j is the unit vector in the effective wind direction for component j , and r a,j is the lever arm from the center of gravity (CG) to the center of force application on component j . The aerodynamic coefficients CD,j and CM,j vary depending on the flow regime and angle of attack αj . For the different components (e.g., rotor, masts, etc.), these coefficients are functions of different Reynolds numbers, Rej=f(ρa , U , Lj , µa) , where Lj is a characteristic length of the component and µa is the air’s dynamic viscosity. The angle of attack αj is the angle between the wind direction and the reference axis of the component. Changes in αj alter the pressure distribution over the surface, influencing both drag and lift forces. The mast’s structure has been modeled as a pyramidal truss subjected to a horizontal wind load (relative to the prevailing wind direction) applied by the turbine at the top node. The equilibrium of the structure is determined by decomposing the forces into components along the coordinate axes, using unit vectors to represent the direction of each mast and its corresponding force. These forces are balanced at the top node, where the turbine’s thrust force is applied. The internal forces along the masts are treated as axial forces, and the structure is assumed to be in a state of static equilibrium with no external moments except for the applied wind force. Following the scheme introduced in Figure 1b, each mast connects the top node, given by P= ( 0, 0, h) , to a base node of the square-shaped floater. Given a side length Lm=∥ ri∥=√2a2+h2 , let a=Lm/ 2 and define the base nodes as A= (a , a , 0 ) , B= (−a , a , 0 ) , C= (−a , −a , 0 ) , D= (a , −a , 0 ) , so the vectors from the top node Pto the base nodes are  rA=   a a −h   , rB=   −a a −h   , rC=   −a −a −h   , rD=   a −a −h   . (5) while the unit vectors along the masts are defined by u i= ri/Lm being i=A , B , C , D . Following the scheme in Figure 1b, and assuming that the thrust force of the wind turbine, given by Equation (9) is applied at P and acts in the positive x -direction, the wind load vector becomes F w= (FT , 0, 0 ) . Next, let Ti be the internal force in the mast joining P to node i (with positive values indicating tension). Then, the equilibrium at the top node P is given by J. Mar. Sci. Eng. 2025,13, 1411 9 of 18 Fw+ D ∑ i=A Tiui=0. (6) Since at each base node i , the reaction is given by the force transmitted through the corresponding mast, Ri=Tiui, structure is given by Fw+ D ∑ i=A Ri=0. (7) Moreover, taking moments about the origin into account yields rP×Fw+ D ∑ i=A ri×Ri=0, (8) where rPis the position vector of the top node P. Finally, for the rotor, we considered that the thrust force, determined at the height of the top of the masts h as depicted in Figure 1, is influenced by the platform’s pitching rate, ˙ θp. This yields FT=0.5ρaπR2CTωrR Ur,β(U−h˙ θp)2, (9) where ρ is the air density, R denotes the rotor diameter, CT denotes the thrust coefficient, which is a function of the tip speed ratio (characterized by the rotor speed ωr ) and the blade pitch angle β . Since the floating platform does not apply active yaw control, yawing is achieved exclusively through adjustments in blade pitch. Note that the same strategy is also employed in the OrcaFlex model. Generator torque control is employed to regulate the turbine’s rotational speed, ensuring a stable power output, which in fact depends on both wind speed and platform misalignment as Pav =0.5ρaCp(α)AU3cos(∆β). (10) where ∆β=βplatform −βwind, as depicted in Figure 1c. The hydromechanics analysis was carried out to evaluate the forces and moments applied to the floating platform in all six degrees of freedom (surge, sway, heave, pitch, roll, and heave). In general, hydromechanics can be split into hydrostatics and hydrodynamics. Hydrostatics, such as buoyancy forces, contribute to restoring forces that let the structure float upright. On the other hand, hydrodynamics are mainly influenced by the dynamic wave environment and are used to calculate the forces impacting the structure. As this is a reduced-order model, the submerged and surface-piercing parts are simplified as cylindrical slender columns, enabling the use of Morison’s equation. Considering the columns’ geometry, directional effects of waves and their relative local velocity, the hydrodynamic force on the arc length sof a submerged part was calculated as follows: dFhydro(s) = 0.5ρwCD(s)D(s)|u(s)|u(s)ds +ρwCM(s)πD(s)2 4 du(s) dt ds, (11) where ρw is the water density, CD(s) and CM(s) are local drag and inertia coefficients, D(s) is the local diameter of the element, and u (s) is the local velocity due to waves with its associated direction. Integrating Equation (11) over the wet surface gives the total waveinduced force. The hydromechanics analysis was conducted in OrcaFlex, and the results were extracted using look-up tables for the development of the virtual sensors. Finally, each mooring line, whether a hawser from the platform to the buoy or an anchor line from J. Mar. Sci. Eng. 2025,13, 1411 16 of 18 (a) Random Forest (b) Gradient Boosting (c) PIML Figure 9. Regression scores of virtual sensor 3 (VS3) for top mast joint bending moment. (a) Wind speed and direction. (b) VS3 response from different models Figure 10. Virtual sensor 3 (VS3) results for the top masts bending moment. 5. Conclusions This study investigated virtual sensor development for the Eolink weathervaning floating wind turbine relying on a single-point mooring system. Virtual sensors were proposed as a means to reduce reliance on physical sensors in cases where direct measurement is expected to be difficult or costly. Three virtual sensors were developed using supervised machine learning (random forest and XGBoost) and a physics-informed machine learning (PIML) approach, trained on OrcaFlex simulation data under varying conditions. The first virtual sensor estimated the force in one mooring hawser using environmental and motion inputs, demonstrating strong performance across algorithms. The second virtual sensor, estimating force in the other hawser based only on the output of the first, demonstrated improved accuracy using the PIML model compared to purely data-driven methods. The third sensor, targeting bending moments at the top joint assembly, showed lower accuracy, likely due to missing inputs related to mast accelerations or vibrations and the limitations of the simplified physics model. Overall, the results obtained using synthetic OrcaFlex data suggest that virtual sensing could be a viable approach to reduce the need for physical instrumentation in complex areas of the studied floating wind turbine, thereby providing a foundation for real-world applications. J. Mar. Sci. Eng. 2025,13, 1411 17 of 18 Author Contributions: Conceptualization, H.d.P.G. and M.D.K.; methodology, H.d.P.G. and J.I.R.; software, H.d.P.G. and T.Y.; validation, M.D.K., formal analysis, H.d.P.G.; investigation, H.d.P.G.; resources, H.d.P.G. and M.D.K.; data curation, H.d.P.G. and T.Y.; writing—original draft preparation, H.d.P.G. and M.D.K.; writing—review and editing, J.I.R. and T.Y.; visualization, H.d.P.G.; supervision, J.I.R. and J.L.D.-G.; project administration, J.I.R. and J.L.D.-G.; funding acquisition, J.L.D.-G. All authors have read and agreed to the published version of the manuscript. Funding: The research leading to these results has received financial support from the European Union as part of the Horizon Europe HORIZON-CL5-2021-D3-03 under the BLOW (BLack sea Offshore Wind) project (grant agreement number 101084323), and from the Research and Universities Department of the Catalonia Government under the FI2024 program (grant agreement 2024-FI_B-00930). Data Availability Statement: The data related to the platform design is confidential. Since IREC authors do not have permission to disseminate sensitive data or parameters protected by a US Patent [11], these have not been disclosed to uphold confidentiality rights. Acknowledgments: IREC authors would like to express their gratitude to the Eolink team for their collaboration and for enabling the publication of this research, with a special thanks to Benjamin Decurey and Xavier Piot for all their assistance during the development of the models. Conflicts of Interest: The authors declare no conflicts of interest and have no financial, personal, or professional ties that could influence the results of this study. The authors state that the methodologies and procedures used to develop the models and synthesize the data for this study of the floating platform under the BLOW project have been fully detailed for research purposes. This article does not reflect any commercial purposes or interests associated with Eolink. Abbreviations The following abbreviations are used in this manuscript: FOWT Floating Offshore Wind Turbine VS Virtual Sensor GPS Global Positioning System IMU Inertial Measurement Unit MRU Motion Reference Unit SCADA Supervisory Control and Data Acquisition RF Random Forest PIML Physics-Informed Machine Learning RMSE Root Mean Square Error MSE Mean Square Error MAE Mean Absolute Error BLOW Black Sea Offshore Wind References 1. Edwards, E.C.; Holcombe, A.; Brown, S.; Ransley, E.; Hann, M.; Greaves, D. Evolution of floating offshore wind platforms: A review of at-sea devices. Renew. Sustain. Energy Rev. 2023,183, 113416. [CrossRef] 2. del Pozo Gonzalez, H.; Kallinger, M.D.; Rapha, J.I.; Domínguez-García, J.L. Modern Floating Wind Energy Technologies. 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