Coupled Dynamic Analysis and Experimental Validation of a 1:15 Scaled Multi-Purpose Offshore Platform Prototype

Abstract

Multi-purpose platforms, which combine renewable energy generation devices and diverse functionalities, are a smart way to expand the applications of offshore platforms. An environmentally friendly multi-purpose offshore platform is proposed by the ‘Blue Growth Farm’ project, which includes a wind turbine, a set of wave energy converters, and an aquaculture system. To assess its feasibility and performance, a field experiment is conducted at an offshore site in Italy using a 1:15 scaled outdoor platform prototype. To provide comprehensive insights into the platform’s behavior, in the present work, aero–hydro–servo–elastic coupled numerical models based on the blade element method and potential flow theory are developed for various experimentally tested configurations of this multi-purpose platform. Time domain analyses are conducted to investigate the performance of the outdoor prototype platform under the recorded realistic environmental loads from the field experiment. The numerical results, including platform motion, mooring line tension forces, and wind turbine responses, agree with the corresponding experimental records. For example, the absolute mean value errors for platform roll and pitch motions are approximately 1 degree, validating the developed numerical model. Meanwhile, the present comparative study demonstrates the feasibility of the proposed multi-purpose concept and can provide a reference for similar projects in the future.

1. Introduction

The utilization of offshore renewable energy provides a sustainable solution to reduce reliance on fossil fuels. However, the deployment of traditional offshore structures has raised environmental concerns due to their potential negative impacts on marine ecosystems. For example, the noise generated during construction and operation can disturb marine mammals and affect their behaviors. To reduce these environmental effects, the adoption of multi-purpose platforms (MPPs), including renewable energy generation devices and other functionalities, emerges as an environmentally friendly and economically viable solution through shared infrastructure and marine space [1]. This promising approach allows for the exploration of offshore energy while reducing its environmental footprint at the same time. Hence, the concept of MPPs has drawn the attention of many stakeholders and has experienced high-level growth since its emergence.

As a main sector of renewable energy, offshore wind energy has achieved rapid growth in recent years, reaching a worldwide capacity of 21 gigawatts in 2021 [2]. Meanwhile, wave energy presents another form of offshore renewable energy, which can be harnessed from the motion of ocean waves. A wave energy converter (WEC) can serve as a supplementary energy provider, ensuring the continuity of energy generation. In parallel with the development of offshore renewable energy, the offshore aquaculture industry has been expanding rapidly to meet the increasing global demand for seafood. Consequently, the integration of offshore energy generation units and aquaculture systems into multi-purpose platforms presents a compelling opportunity. These platforms can enhance power production capacity and stability while simultaneously providing marine products. Over the last two decades, several European Commission projects have investigated multi-purpose platforms [3]. For example, the Mermaid project [4] explored several MPP concepts, such as combined wind and wave platforms in Spain and aquaculture and renewable platforms in the Adriatic Sea. In the Marina project [5], a joint concept was proposed, involving the fusion of Spar-type floating wind turbines and axi-symmetric two-body wave energy converters, aimed at maximizing power production density. Moreover, one of the two concepts in the Tropos project [6] focused on fish aquaculture alongside floating offshore wind and wave technologies, and various support structure forms such as Tension Leg Platforms (TLPs), semisubmersibles, and spar technology were investigated. Additionally, the H₂Ocean project [7] directed its efforts towards the production of hydrogen and seafood by using offshore renewable energies. These European Commission projects have significantly contributed to advancing the understanding and potential of MPPs for offshore renewable energy integration and other functional systems.

Numerical investigations have been conducted into most of the multi-purpose platform concepts mentioned in previous projects. Armesto et al. [8] developed a time domain numerical model to analyze the multi-use platform of the Mermaid project, which comprised a triangular floating platform with four vertical columns, one 5 MW wind turbine, and three semi-annulus-shaped oscillating water columns (OWCs) located at its corners. The motions of the platform within six degrees of freedom (DOFs) were simulated using the boundary element method and linear potential theory. The coupling effects between the platform and the OWCs were considered by calculating the free surface inside each chamber and the friction force due to the viscous losses at the entrance of the OWCs. The numerical study of the Marina project involved two concepts: the Spar Torus Combination (STC) and the Semi-Submersible Flap Combination (SFC). The blade element momentum theory was used for SFC, while a simplified thrust force model was adopted for STC to characterize wind turbine aerodynamics, and the hydrodynamic loads on floaters or WECs were accounted for using potential flow theory or Morison’s formula [9]. Validation of the numerical model was achieved by comparing the numerically predicted responses, including platform motions and power production, against experimental data, demonstrating the numerical model’s ability to simulate the platform responses in most cases. Moreover, based on the FloVAWT design tool developed for the H2Ocean project [10,11], Borg and Collu [12] further discussed the optimal configurations of offshore wind turbines coupled with three generic floating support structures. In their analysis, the 5 MW vertical-axis wind turbine developed by Vita [13] was selected as the reference model. Their study investigated four load cases, i.e., free decay simulations with the turbine in a parked condition, white noise incident wave simulations with no wind, wind-only simulations, and simulations involving realistic met-ocean conditions, in order to assess the platform’s performance. Through the simulation results, it was revealed that the Tension Leg Platform (TLP) configuration is unsuitable for the project design. In addition to potential flow theory, computational fluid dynamics (CFD) methods have been widely employed to analyze the performance of offshore platforms. For example, Li et al. [14] investigated the fluid structure interactions of floating offshore wind turbine (FOWT) platforms under combined wave current conditions. Two configurations, i.e., semi-submersible and barge-type platforms, were studied to reveal the platform geometry’s effect on motion responses. Qin et al. [15] studied the nonlinear motion characteristics of a semi-submersible platform navigating in head waves through CFD simulations and experimental tests. The wave impact distribution was analyzed, and CFD offered advantages over potential flow theory. In recent years, deep learning techniques have been increasingly applied to analyze the characteristics of offshore platforms. Yin et al. [16] presented an intelligent optimization method for semi-submersible platform mooring systems using deep learning techniques combined with Bayesian optimization. They generated a dataset of 2356 design scenarios and successfully validated the method against real operational data, achieving a 29.7% reduction in maximum mooring line tension. Torabbeigi et al. [17] proposed a novel and computationally efficient machine learning-transfer function approach to estimate the total absorbed power of multi-body floating WECs, which was further applied to evaluate the year-round power potential at three locations in the northern Oman Sea.

The Blue Growth Farm (BGF) project [18], launched in 2018, proposed an environmentally friendly, economically viable, and highly efficient multi-purpose platform concept for open sea sites with water depths ranging from 100 m to 200 m. This innovative platform integrated a commercial DTU 10 MW wind turbine, eight oscillating water column WECs, and an automated aquaculture system into a reinforced concrete caisson. Remarkably, the BGF multi-purpose platform was designed to yield 2000 tons/year of fish production through its own energy harvesting capability. To validate the design concept and evaluate the performance of this multi-purpose platform, two model tests were conducted: one involved a 1:40 scale model tested at the Hydrodynamics and Ocean Engineering Tank of Ecole Centrale de Nantes in France [19], while the other examined a 1:15 outdoor prototype tested at the Natural Ocean Engineering Laboratory (NOEL) field site in Italy [20,21]. In addition to the experimental assessments, Li et al. [22,23,24] proposed an aero–hydro–servo–elastic numerical framework to assess the technical feasibility of a BGF multi-purpose platform within the context of a 1:40 scale model test in a water tank. Their framework employed a time domain simulation by coupling SIMO [25] to predict the platform motions and RIFLEX [26] to calculate the structural loads at the interface. The good agreement between the numerical results and the observations from the water tank experiment validated their numerical model, effectively confirming the viability of the BGF multi-purpose platform design concept.

Based on this previous work, the present study develops fully coupled numerical models using the SESAM package to analyze the various configurations tested in the outdoor prototype experiment. A cross-verification of the BGF multi-purpose platform design concept is performed by comparing the dynamic response predicted by numerical simulations with that observed during the field experiment. Therefore, the feasibility of the proposed concept is further validated. The comparison between the present work and Li et al. [22,23,24] is provided in

Table 1. Comparison with previous study (Li et al. [22,23,24]).

Aspect	Li et al. [22,23,24] (1:40 Wave Tank Test)	This Work (1:15 Outdoor Prototype)
Platform scale	1:40	1:15 (configuration updated)
Test environment	Controlled wave tank	Open sea (NOEL, Italy)
Environmental conditions	Idealized (regular/irregular waves)	Realistic met-ocean (measured waves, wind)
Validation data	Tank measurements	Outdoor field measurements
Use of measured environment	No (spectral generation)	Yes (direct input of time series)
Model components	Wind turbine, WECs, mooring	Full system: wind turbine, WECs, mooring, umbilical

. The main contributions of the present work are as follows:

• Advanced numerical modeling: A fully coupled aero–hydro–servo–elastic numerical model of the 1:15 outdoor BGF prototype is developed, updating the previous model from Li et al. [22,23,24] for a 1:40 wave tank test configuration to incorporate an actual outdoor platform configuration, including a wind turbine, WECs, mooring system, and umbilical.
• Comprehensive experimental validation: the numerical model is validated against an outdoor experiment. Notably, the measured environmental time series, including waves and winds, are directly used as input to the simulations, eliminating the uncertainties from spectral parameterization in Li et al. [22,23,24] and enabling a more faithful reproduction of the actual dynamic responses.

This paper is organized as follows. Section 2 describes the outdoor prototype experiments, and Section 3 presents and discusses the results of the frequency domain numerical analysis. The time domain numerical analysis results, and their comparison with the experimental ones, are provided in Section 4. Comprehensive discussion and conclusions are presented in Section 5.

2. Outdoor Prototype Platform

The 1:15 scaled multi-purpose platform outdoor prototype, named ‘Aurora’ and depicted in Figure 1, comprises a steel caissons-based platform, a wind turbine, a series of wave energy converters, an aquaculture system, a four-line mooring system, and an umbilical. It was situated at the Natural Ocean Engineering Laboratory in Reggio Calabria for a comprehensive field experiment campaign conducted from March 2021 to January 2022. The experimental setup was previously described by Ruzzo et al. [20,27], and herein, a brief review of these details is provided. To evaluate the platform’s dynamic responses, the 6 DOF motion responses were measured using two Attitude and Heading Reference System inertial platforms. Mooring loads were measured through four load cells positioned at the four fairleads and an additional load cell installed along a mooring line. Furthermore, the internal pool wave elevations were recorded using several ultrasonic probes positioned at sufficiently high locations determined by both numerical predictions and field observations. For the wind turbine assessment, strain gauges were employed to measure the deformations of the blades and tower, and motion responses such as nacelle accelerations were recorded using encoders. The experimental data underwent initial pre-processing using various in house developed sensor acquisition software, followed by further processing using an internal numerical analysis software.

Throughout the field experimental period, a total of seven test configurations were implemented, classified according to whether the WECs were open or closed, the operational state of the wind turbine (i.e., operating or parked), whether fish nets were installed or not, and whether an umbilical was installed or not. As a result, numerical models were developed accordingly, with detailed information, including the dimensions of the sub-components, provided in the subsequent sub-sections.

2.1. Bathymetry

Unlike a flat seabed, the underwater terrain in the outdoor experimental area exhibits a slope. The measured bathymetry data are provided in

Table 2. Measured bathymetry data.

x (m)	Water Depth (m)
−102 m	0 m
−92.11 m	−1 m
−86.89 m	−1.5 m
−80.88 m	−3 m
−76.34 m	−4.5 m
−72.7 m	−6.5 m
−68.19 m	−9 m
−63.98 m	−11 m
−56.06 m	−15 m
−46.71 m	−19.5 m
−33.09 m	−25.5 m
−21.88 m	−30 m
−9.18 m	−35 m
7.17 m	−40 m
30.1 m	−45 m
54.03 m	−50.5 m
74.31 m	−54.5 m
109.06 m	−60.5 m
135.56 m	−65 m
152.96 m	−67.27 m
172.04 m	−70 m

, and their corresponding depiction is presented in Figure 2. It should be clarified that the center of the platform corresponds to the coordinate x = −9.18 m. And according to the survey measurements, the water depth at the platform center is 35 m. This seabed configuration is implemented identically within the time domain numerical analysis.

The exact seabed properties of the outdoor experiment are not available; hence, a conservative assumption is made as in

Table 3. Seabed properties assumed in the numerical simulation.

Properties	Value	Unit
Normal stiffness	50,000	N/m2
Normal damping	500	N/m2
Friction coefficient	1	-

. This assumption can be deemed reasonable based on other offshore structure analyses, but they could be different from the actual properties of the site.

2.2. Platform

The outdoor prototype platform model is illustrated in Figure 3, showing that the wind turbine and WECs are located on the foreside of the platform. Six fish cages are housed in the internal pool of the platform. To ensure stable positioning, the platform is anchored by four mooring lines, connected through four fairleads situated at the corners. The umbilical serves to transport excess unused electricity to the onshore station, with one end of the umbilical located at the middle of the aft side of the platform, while the other end reaches the onshore location. Additionally, in order to maintain the platform’s balance, eight caissons are placed along the right and left sides of the platform. The main geometric dimensions of the steel caisson-based platform outdoor prototype are outlined in

Table 4. Platform dimensions.

Geometry Dimensions	Value
Length overall	14.33 m
Breadth of hull	10.8 m
Hull height	1.6 m
Hull width (outer–inner difference)	0.8 m
Caisson height	0.6 m
Caisson width/length	0.47 m/2.4 m
Draft	1.33 m

.

In both the outdoor experiment and numerical simulation, the local coordinate system of the platform is defined as follows: the origin point is located at the center of the platform (X, Y) and coincides with the mean water level (Z). The positive X axis is directed towards the aft side, while the positive Z axis points upwards.

2.3. Wind Turbine

The wind turbine installed on the platform is a 1:15 scaled model designed by S. Muggiasca et al. [28] based on the DTU 10 MW reference wind turbine [29], as shown in Figure 4. The scaled wind turbine is a traditional horizontal-axis, three-bladed, variable-pitch, variable-speed, upwind wind turbine. Its specifications in terms of dimensions, mass, and operating wind speed are provided in

Table 5. The parameters of the wind turbine installed on the outdoor platform.

Parameter	Value
Rated wind speed	5 m/s
Cut-in wind speed	1.75 m/s
Cut-off wind speed	11 m/s
Blade No.	3
Rotor diameter	6.86 m
Tower length	7.5 m
Tower outer/inner diameter	0.1778 m/0.1678 m
Nacelle mass	174 kg
Tower mass	197 kg

. In line with the experimental setup, the numerical model incorporates control strategies including a variable-speed torque strategy and a blade pitch strategy.

2.4. Wave Energy Converters

The U-Oscillating Water Column (U-OWC) concept, proposed by Boccotti [30], is adopted in the outdoor experiment. The WEC system is physically integrated into the platform structure during its construction, as shown in Figure 5a, with its dimensions provided in Figure 5b. The experiment involves two distinct WEC configurations: WECs closed and WECs open. Initially, the WECs are in a closed configuration and remain so for approximately two months before transitioning to an open configuration, which persists until the end of the experiment. Consequently, two separate numerical models, each corresponding to the two WEC configurations, are developed in the present study.

2.5. Mooring System

The mooring system implemented in the outdoor experiment is composed of 4 mooring lines, each linked to a corner of the platform at one end and at the other end to a dedicated anchor. The spatial arrangement of the mooring system is shown in Figure 6a, while the fairlead in the experiment is shown in Figure 6b. Anchors A1 and A2 are connected, respectively, to the onshore Line 1 and Line 2, whereas anchors A3 and A4 are connected to the offshore Line 3 and Line 4. The mooring system in the outdoor experiment is composed of different line types and lengths, as presented in

Table 6. Mooring line arrangement.

Mooring Line Number	Total Length (m)	Line Arrangement
Onshore line 1	135	55 m of 78 mm stud chain 80 m of 32 mm stud chain
Onshore line 2	135	55 m of 78 mm stud chain 80 m of 32 mm stud chain
Offshore line 3	145	55 m of 78 mm stud chain 90 m of 32 mm stud chain
Offshore line 4	145	55 m of 78 mm stud chain 90 m of 32 mm stud chain

.

The properties of these stud chain mooring lines, characterized by their nominal diameters, are provided in

Table 7. Mooring line properties.

Properties	32 mm Chain	78 mm Chain
Nominal diameter	32 mm	78 mm
Mass per unit length	22 kg/m	133 kg/m
Breaking load	83 t	450 t
Axial stiffness	1.03 × 108 N	6.14 × 108 N
Transversal added mass coefficient	1	1
Longitudinal added mass coefficient	0.5	0.5
Transversal drag coefficient	2.4	2.4

. It should be noted that the axial stiffness for both stud chains, as presented in the table, is estimated according to the empirical formula $K_{axial}=1.01\times {10}^8{d}^2 \mathrm{kN}$ where d is the mooring line diameter in meters. The precise anchor positions are obtained through an on-site survey, with the initial data originally provided in the global axis system (Universal Transverse Mercator zone 33, UTM 33). Consequently, these positions are converted into the local coordinate system of the platform and listed in

Table 8. Anchor positions in global axis system (E,N) and local axis system (X, Y, Z).

Anchor	E	N	X (m)	Y (m)	Z (m)
Anchor1	556,166	4,218,096	77	−85	−4.2819
Anchor2	556,305.03	4,218,199.69	80.89	88.4	−3
Anchor3	556,060.48	4,218,222.94	−88	90	−56.864
Anchor4	556,202.32	4,218,333.76	−88	−90	−56.864

.

2.6. Umbilical

The umbilical is also implemented into the numerical model, in accordance with the outdoor experiment. The umbilical consists of a cable and 14 floaters, extending from its initiation at the midpoint of the platform’s aft side to its termination at the onshore station. Detailed specifications, including the length of each segment, line materials, and floater properties, are summarized in

Table 9. Umbilical length and properties.

Properties	Value	Properties	Value
Umbilical (Upper) length	33.81 m	Torsional stiffness	3.428 kN·m2
Floats length	8.32 m	Bending stiffness	0.124 kN·m2
Umbilical (Lower) length	12.97 m	Float diameter	0.206 m
Total length (from platform to touchdown point)	55.1 m	Float section linear mass	15.26 kg/m
Linear mass	6.53 kg/m	Float section linear gross buoyancy	−315 N/m
Linear wet weight	44 N/m	Float section linear dry weight	150 N/m
Minimum Breaking Load	380 kN	Length of a single float	0.308 m
Outer diameter	50 mm	Distance between floats	0.308 m
Axial stiffness	50 MN	Number of floats	14

.

The layout of the umbilical and its static configuration are illustrated in Figure 7. For the numerical simulation, the section extending from the platform connection point to the touchdown point is modeled, as the portion from the touchdown point to the onshore station is not expected to notably impact the response of the coupled system.

3. Numerical Model Development

In this section, both frequency domain and time domain analyses are conducted for the multi-purpose platform model, using the SESAM software 2023. The frequency domain analysis is performed using the module HydroD/Wadam, and the time domain analysis is conducted using Sima, which is an interface-coupled software combining Simo and Riflex [31].

3.1. Frequency Domain Hydrodynamic Model

In light of the WECs’ attachment to the platform, this study entails the development of two distinct models reflecting varying configurations of the steel platform: closed WEC chambers and open WEC chambers, with the intent of conducting a comprehensive frequency domain analysis. In the closed WEC chamber configuration, the WECs are fully enclosed by steel plates, leading to a change in the center of gravity position compared to the open WEC chamber configuration. Both panel models and Finite Element Method (FEM) models for the two configurations are presented in Figure 8 and Figure 9. Notably, only the submerged section of the platform is modeled for the open WEC chamber configuration, emphasizing the difference.

The frequency domain hydrodynamic analysis is conducted using linear potential flow theory. The water depth is set at 35 m to replicate the conditions of the outdoor experiment. The hydrostatic restoring stiffness matrices are provided in Equation (1) for the closed WEC chambers configuration and Equation (2) for the open configuration. The diagonal elements of the added mass matrices for both configurations are presented in Figure 10 and Figure 11.

$$K=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 3.510\mathrm{E}+05 \mathrm{N}/\mathrm{m}& 0& 2.412\mathrm{E}+05 \mathrm{N}/\mathrm{rad}& 0\\ 0& 0& 0& 4.000\mathrm{E}+06 \mathrm{N}\cdot \mathrm{m}/\mathrm{rad}& 0& 6.607\mathrm{E}+05 \mathrm{N}\cdot \mathrm{m}/\mathrm{rad}\\ 0& 0& 2.412\mathrm{E}+05 \mathrm{N}\cdot \mathrm{m}/\mathrm{m}& 0& 7.381\mathrm{E}+06 \mathrm{N}\cdot \mathrm{m}/\mathrm{rad}& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]$$

(1)

$$K=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 3.310\mathrm{E}+05 \mathrm{N}/\mathrm{m}& 0& 1.077\mathrm{E}+05 \mathrm{N}/\mathrm{rad}& 0\\ 0& 0& 0& 3.968\mathrm{E}+06 \mathrm{N}\cdot \mathrm{m}/\mathrm{rad}& 0& 6.24\mathrm{E}+03 \mathrm{N}\cdot \mathrm{m}/\mathrm{rad}\\ 0& 0& 1.077\mathrm{E}+05 \mathrm{N}\cdot \mathrm{m}/\mathrm{m}& 0& 6.537\mathrm{E}+06 \mathrm{N}\cdot \mathrm{m}/\mathrm{rad}& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]$$

(2)

Figure 12 and Figure 13 present the wave force transfer functions for the closed WEC chamber configuration and open WEC chamber configuration, respectively. The angles in the figures indicate the wave directions.

Figure 14 and Figure 15 present the second-order wave force drift force experienced by the platform for the closed WEC chamber configuration and open WEC chamber configuration, respectively. Both waves are in a zero direction.

In addition to the platform response parameters, the free surface elevations within the inner pool are also computed in the form of response amplitude operators (RAOs), i.e., the amplitude of oscillations of the inner pool’s surface, measured in meters, in response to a 1 m incident wave amplitude.

The coordinates corresponding to the six points designated for fish cage sensor locations in the outdoor experiment are provided in

Table 10. Points locations under fish cage central sensors to estimate inner pool wave elevation.

	X (m)	Y (m)	Z (m)
Point 1	3.3 m	−1.7 m	0
Point 2	3.3 m	1.7 m	0
Point 3	0	−1.7 m	0
Point 4	0	1.7 m	0
Point 5	−3.3 m	−1.7 m	0
Point 6	−3.3 m	1.7 m	0

. The free surface wave elevations at the center points of these six fish cages are provided in Figure 16 and Figure 17, respectively, for both the closed WEC chamber and open WEC chamber configurations. It can be observed from these figures that the wave elevation within the inner pool does not consistently reduce, as the potential flow theory overestimates the resonance of a constrained water volume [32].

3.2. Time Domain Aero–Hydro–Servo–Elastic Coupled Model

An aero–hydro–servo–elastic coupled model consisting of the platform, wind turbine, WECs, mooring system, and umbilical is developed using the commercial simulation tool Sima (module of SESAM 2023), as shown in Figure 18.

The hydrodynamic loads on the supporting platform and WECs are estimated using the potential flow theory, and the hydrodynamic properties, including the hydrostatic restoring stiffness matrix, added mass, 1st-order wave force transfer functions, and 2nd-order drift force transfer functions, are obtained in the frequency domain using the panel model code Wadam. Then they are applied in the time domain simulation, in which the equation of motion is

$$\left(M_{ij}+m_{ij}\right){\ddot{x}}_j(t)+{\displaystyle \underset{0}{\overset{t}{\int }}{K}_{ij}(t-\mathsf{\tau })}{\dot{x}}_j(\mathsf{\tau })d\mathsf{\tau }+C_{ij}{x}_j(t)+F_m(t)=F(t), i,j=1,2,\dots ,6$$

(3)

where M_ij and m_ij are the mass matrix and added mass matrix at infinite frequency, respectively. $K_{ij}(t-\mathsf{\tau })$ is the retardation function, C_ij is the hydrostatic restoring stiffness matrix, and F_m is the mooring load. x, $\dot{x}$ and $\ddot{x}$ are the displacement, the velocity, and the acceleration vectors. F_iw is the environmental force, including both 1st-order and 2nd-order wave excitation force, wind drag force, current drag force, and any other forces.

The same methodology for calculating aerodynamics applied in the BGF project’s previous work [22,25] is utilized in the present work, i.e., the blade element momentum (BEM) method [33] with engineering corrections from the dynamic inflow model [34], Glauert correction [35], Prandtl factor [36], as well as a dynamic stall model [33]. In addition to the aerodynamic loads, the reference control system for blade pitch and electrical torque for power extraction [37] are applied in the numerical wind turbine model. The variable-speed generator torque works at below-rated wind speeds to maximize the power capture, and the blade-pitch controller uses the feedback of the generator speed at over-rated wind speeds to feather the blades to regulate the generator power.

The wind turbine blades, the wind turbine tower, the mooring lines, and the umbilical are all modeled using the FEM as nonlinear beam elements [38]. Structural damping is also included by applying global Rayleigh damping for all flexible finite elements. Regarding the WEC model, the simplified model developed in the project’s previous work [22,39] is still employed in the present work to enable a balance between simulation accuracy and efficiency. In the simplified model, a linear damping coefficient is used to represent the force transferred from the WEC to the platform.

In addition, it should be clarified that despite conducting extensive field surveys and measurements to determine the parameters for the outdoor experimental setup, there are still some uncertainties in the numerical data that cannot be avoided. For example, due to the large size of the platform, the exact position of the center of gravity and the inertial moment cannot be measured directly, and the actual value may not be consistent with that listed in Table 2. Similarly, the exact seabed properties are not available and have to be estimated. Therefore, these uncertainties will lead to discrepancies in the comparison between the numerical and experimental results.

4. Numerical Model Validation

The outdoor experiment campaign lasted over six months, and the data were stored in 10 min samples, generating a large volume of measured data. Various environmental conditions were recorded over the six-month period, and it would be cumbersome to validate the developed model with all the recorded data.

The numerical simulation results and comparisons against the experimental observations for two out of the total seven configurations are provided in this study, in which there were no fish nets and the wind turbine was inoperative. These configurations were selected based on the status of each component. The basic configuration, referred to as configuration A, i.e., no aquaculture cages, WEC chambers closed, no umbilical, and wind turbine operating, is chosen to validate the coupled numerical model. And a more complex configuration, including no aquaculture cages, WEC chambers open, an umbilical, and an operating wind turbine, is named configuration B.

A critical environmental condition, namely, the most frequently occurring condition, is selected for subsequent numerical analysis and comparison. For each configuration grouping, each 10 min time history is classified in terms of maximum wave height (using 10 or 15 bins depending on the range) and its zero crossing period, identifying the most frequently occurring 10 min conditions as well as the 10 min with the highest wave height, as shown in Figure 19. Similarly, the 10 min wind velocity time histories have been classified in terms of wind direction and wind velocity (bins of 20), shown in Figure 20, identifying the most frequently occurring wind velocity as well as the extreme wind velocity.

4.1. Time Domain Analysis for Basic Configuration A

To validate the developed numerical model, a time domain analysis is conducted for the outdoor prototype’s basic configuration. The wave direction is −55.02° after being converted into the numerical coordinate system, and the measured time histories of the wave elevation and wind data are depicted in Figure 21 and Figure 22. In order to accurately reproduce the oceanic condition, the time histories of the wave and wind loads are directly input into the numerical simulation. The wave height and wave period are estimated as H_s = 0.145 m, T_p = 4 s according to the measured wave elevation. It should be noted that the wave measurement point coordinate in the numerical coordinate system is x = 78.472 m, y = −33.507 m, z = −1.9 m, so that the measured wave data is pre-processed before being imported. Furthermore, there is a phase difference between the wave surface elevation in Figure 21 and that of the prototype.

4.1.1. Platform Motion for Configuration A

The time histories and power spectrum densities of the 6 DOF platform motions are compared with the field measurement in Figure 23 and Figure 24, respectively. Additionally, the initial 500 s of numerical results are excluded to eliminate transient response effects. For the translational mode, the motion velocity was only measured when the motion displacement of the rotational mode was available. It can be observed from these figures that, apart from the yaw motion, the numerically predicted motion responses generally match the field measurement. One reason that accounts for the discrepancies between the numerical results and the experimental records in the roll direction is that the platform, while at rest, is slightly inclined in the roll direction [20].

The statistical values, including the mean, minimum and maximum values, along with the standard deviations, are compared with the experimental data in

Table 11. Statistical comparison of platform motions between numerical simulation results and experimental data.

Platform Motions		vx (m/s)	vy (m/s)	vz (m/s)	Roll (deg)	Pitch (deg)	Yaw (deg)
Experiment record	Mean	−0.002	0.002	0.011	1.124	0.255	−33.015
	Max	0.125	0.141	0.165	1.765	2.291	−30.779
	Min	−0.122	−0.106	−0.117	0.409	−1.704	−34.458
	SD	0.029	0.027	0.030	0.188	0.343	0.701
Numerical results	Mean	0.000	0.000	0.000	0.049	0.352	0.331
	Max	0.077	0.140	0.185	2.592	2.043	0.784
	Min	−0.071	−0.153	−0.176	−2.656	−1.340	−0.033
	SD	0.014	0.026	0.038	0.409	0.311	0.093

. Regarding the standard deviation of the platform velocities, a slight change in wave direction during the compared period of the outdoor experiment contrasts with the consistent direction maintained in the numerical simulation, potentially contributing to the disparity in standard deviation values. Upon comparing the standard deviation of the rotational displacements of the platform in response, the numerical results appear to overestimate these values. This could be attributed to uncertainties associated with the moment of inertia in the outdoor model. In terms of yaw motion, the absolute difference between the numerical and experimental data is approximately 1.8 degrees—a negligible value, especially considering that this parameter remains the same for both the scaled and full-scale configurations. Nonetheless, the lower numerical yaw standard deviation indicates a potential overestimation of the catenary mooring system’s yaw stiffness in the numerical model compared to the experimental one, and this stiffness is the primary driver of the response value. In addition, unmodeled asymmetric drag sources, e.g., fish cages and local current, may contribute to the higher yaw motions observed experimentally. In the numerical model, the current is assumed to be uniform and aligned with the platform’s centerline, which represents an idealized condition that may not fully capture the complex, locally varying currents present at the experimental site.

4.1.2. Mooring Line Tension Force for Configuration A

The comparison between the experimentally recorded data and the numerically simulated results of mooring loads at the fairlead positions is presented in Figure 25 for time histories, Figure 26 for spectral analyses, and summarized in

Table 12. Statistical comparison of mooring line loads between numerical simulation results and experimental data for Configuration A.

Mooring Line Loads		Line 1	Line 2	Line 3
Experiment record	Mean Values (t)	1.178 t	1.253 t	1.504 t
	Standard deviation (t)	0.017 t	0.012 t	0.032 t
Numerical results	Mean Values (t)	1.524 t	1.624 t	1.705 t
	Standard deviation (t)	0.015 t	0.010 t	0.017 t

for key statistical parameters. The load cell for line 4 was malfunctioning during this period; hence, the data for the mooring load on line 4 is not presented.

Overall, the agreement is deemed acceptable, despite certain discrepancies in mean values and standard deviations. Concerning the mean values, lines 1 and 2 exhibit an overestimation of around 29%, while line 3 demonstrates a significantly improved agreement, with an overestimation of mooring line tension by approximately 13%. The discrepancies in the standard deviations of mooring line tensions are, in absolute terms, very small with respect to the average values. Good agreements are observed for lines 1 and 2, while for line 3, the standard deviation of the numerical result is underestimated. This discrepancy can be explained by the uncertainties relating to the actual mooring line characteristics and seabed properties. To shed light on these discrepancies, several seabed properties are explored to assess their impacts on mooring loads. The results indicate that variations in seabed stiffness, ranging from maximum to minimum, can induce changes in mooring loads of up to 100%. In the numerical simulation, a relatively conservative choice of seabed properties is adopted, leading to an overestimation of loads. This cautious approach ensures a safety-margin assessment of mooring line tension loads, which aligns with the current stage of design considerations.

4.1.3. Wind Turbine Tower and Nacelle-Related Data Comparison for Configuration A

This section involves a comprehensive comparison between the predicted tower base structural loads, nacelle accelerations, and output power obtained through numerical simulations and the corresponding experimental data to validate the wind turbine model within the framework of the coupled numerical dynamics model. It is noteworthy that a temporal gap exists in the experimental data due to the wind turbine being parked in the field test, while in the numerical simulation, the wind turbine is assumed to be operating continuously.

The numerically predicted bending moment at the tower base is compared against the experimental record, as shown in Figure 27. It should be mentioned that the axial and torsion stiffness of the wind turbine tower utilized in the numerical simulation is derived based on the distributed average fore–aft and side–side stiffness measured in the experiment. The fluctuation of the numerically predicted results is greater than that of the experimental ones. This discrepancy implies that the tower stiffness is underestimated within the numerical model, resulting in a conservative design choice. Future calibration will be achieved through remeasurement of tower rigidity or model order reduction techniques.

The comparison of nacelle accelerations is presented in Figure 28. The mean values are zero across all three directions, and the corresponding standard deviations are detailed in

Table 13. Comparison of standard deviations in nacelle accelerations between numerical simulation results and experimental data for Configuration A.

Standard Deviation (m/s2)	Acceleration in x	Acceleration in y	Acceleration in z
Experimental record	0.021 m/s2	0.023 m/s2	0.021 m/s2
Numerical result	0.058 m/s2	0.086 m/s2	0.066 m/s2

. The standard deviations of the numerical results are larger than those of the experimental findings, mainly due to an overestimation during the period from 1200 s to 1500 s. This overestimation is deemed to be attributed to an underestimation of tower bending stiffness. Regarding the nacelle accelerations in the x and y directions, the numerical model overestimates them in the time record (i.e., on the safe side) after 1200 s, while there is a good correspondence or slight overestimation in the time period before 1200 s. As evidenced in Figure 22, the wind direction remains relatively stable at approximately 275 degrees from 0 s to around 100 s, subsequently shifting and increasing to values around 325 degrees after 1200 s. The employed scaled wind turbine is capable of adjusting its yaw angle to align the wind rotor area perpendicularly with the primary wind direction. However, this flexibility is absent in the numerical model, where the yaw angle is predefined at the simulation’s commencement and remains fixed throughout. This discrepancy in yaw angle adjustment leads to differences in the orientation of aerodynamic loads between the numerical model and the experiment, eventually leading to the distinctions in the x and y nacelle accelerations.

The comparison of output power is presented in Figure 29 for the entire simulation time. During the initial operational phase of the wind turbine, the output power remains at zero for both the experimental record and the numerical simulation results. In the subsequent operational phase, the maximum output power values reach 0.447 W for the experimental record and 0.455 W for the numerical simulation.

4.2. Time Domain Analysis for Configuration B

The time period selected for numerical model simulation for configuration B spans from 10:43:51 to 10:52:33 (GMT + 1, i.e., Italian Daylight Saving Time, DST) on 19 July 2021. The wave elevation over this period is plotted in Figure 30. The wave direction is set at −65.65° after being converted into the numerical coordinate system. The wind velocity and direction are illustrated in Figure 31.

4.2.1. Platform Motion for Configuration B

As it is different from the first case, the experimental record of platform translation motion is stored as acceleration in this scenario. Hence, differential operations are conducted to derive the corresponding numerical predicted results. The comparisons of the 6 DOF platform motions are presented in Figure 32 for time histories and Figure 33 for power spectrum densities. The statistical parameters covering the mean, minimum, and maximum values and standard deviations are compared with their experimental counterparts in

Table 14. Statistical comparison of platform motions between numerical simulation results and experimental data for configuration B.

Platform Motions		ax (m/s)	ay (m/s)	az (m/s)	Roll (deg)	Pitch (deg)	Yaw (deg)
Experimental record	Mean	−0.001	−0.003	0.027	−0.412	0.841	−80.891
	Max	0.103	0.156	0.104	0.053	1.347	−80.498
	Min	−0.120	−0.152	−0.064	−0.857	0.460	−81.591
	SD	0.030	0.046	0.021	0.159	0.164	0.182
Numerical results	Mean	0.000	0.000	0.000	0.041	0.443	0.266
	Max	0.062	0.041	0.085	0.332	0.726	0.437
	Min	−0.062	−0.048	−0.074	−0.292	0.169	0.011
	SD	0.018	0.012	0.028	0.115	0.087	0.063

. The discussion of the discrepancies observed between the numerical results and the experimental records is similar to the one in Section 4.1.1.

4.2.2. Mooring Line Tension Force for Configuration B

The comparisons between the experimental and numerical mooring loads are provided in Figure 34 for time history, Figure 35 for spectral analysis, and

Table 15. Statistical comparison of mooring line loads between numerical simulation results and experimental data for Configuration B.

Mooring Lines Loads		Line 1	Line 2	Line 3	Line 4_1	Line 4_2
Experiment record	Mean Values (t)	1.174 t	1.329 t	1.492 t	1.743 t	1.055 t
	Standard deviation (t)	0.016 t	0.008 t	0.020 t	0.024 t	0.017 t
Numerical results	Mean Values (t)	1.490 t	1.593 t	1.728 t	1.399 t	1.164 t
	Standard deviation (t)	0.008 t	0.007 t	0.008 t	0.008 t	0.007 t

for the main statistical parameters. During this period, the load cells positioned at distances of 12.5 m and 25 m from the fairlead position for line 4 were functioning. Thus, the comparison for the mooring load on line 4 is provided using the load cells named line 4_1 and line 4_2, respectively.

In general, the agreement is acceptable, except for some discrepancies in terms of mean values and standard deviations. With respect to the mean values, there is an overestimation of approximately 26.9% and 19.9% for line 1 and line 2, respectively, while for line 3, the agreement is improved with an overestimation of around 15.8%. In addition, the differences between the predicted values for line 4_1 and line 4_2, when compared to the experimental records, are −19.7% and 10.3%, respectively. Preliminary observation of standard deviations indicates that, in absolute terms, the standard deviation of mooring line tensions remains notably small compared to the average value. The comparison results are similar to those of the previous case, and the reasons for the discrepancies are discussed in Section 4.1.

4.2.3. Umbilical Force for Configuration B

Although there is no experimental force record for the umbilical fairlead position, this force is still calculated in the present numerical simulation, provided in Figure 36. It can be concluded that within the realm of numerical simulation, the force exerted on the umbilical fairlead position is comparatively small when compared with the forces acting on the mooring lines, suggesting that the influence of the umbilical on the platform’s motion response is negligible.

4.2.4. Wind Turbine Tower- and Nacelle-Related Data Comparison for Configuration B

The numerically predicted bending moment at the tower base is compared against the experimental record, as shown in Figure 37. In the outdoor prototype experiment, the measured tower base strain has a constant offset, which should be subtracted because the signals were not at zero during installation. Considering that the value of the constant offset is unknown, the measured strain data are adjusted by subtracting the mean value of the data in the initial period. Due to the underestimation of tower stiffness described previously, the numerical results lean towards a more conservative outlook than the experimental record, which is suitable for the current design stage.

The nacelle accelerations comparison is plotted in Figure 38. The standard deviations of nacelle accelerations for both the numerical results and experimental records are provided in

Table 16. Comparison of standard deviations in nacelle accelerations between numerical simulation results and experimental data for Configuration B.

Standard Deviation (m/s2)	Acceleration in x	Acceleration in y	Acceleration in z
Experimental record	0.044 m/s2	0.044 m/s2	0.060 m/s2
Numerical result	0.036 m/s2	0.041 m/s2	0.027 m/s2

, and the mean values are zero for all three directions.

The comparison of output power is presented in Figure 39 for the entire validation duration. It should be clarified that in the experiment, the wind turbine started to operate at 0 s. However, in the numerical simulation, the wind turbine was already operating, resulting in divergent output power values during the initial stage.

5. Discussion and Conclusions

The aero–hydro–servo–elastic coupled model of dynamics for the BGF multi-purpose platform at a 1:15 outdoor prototype scale developed in the present work is based on the model in the 1:40 model described in [22]. Modifications have been introduced to align with the configuration of the field experiment platform. In each simulation, rather than deriving the wind speed and turbulence from an average wind speed and turbulence spectrum, and rather than deriving the water surface elevation from a given wave spectrum, the exact environmental conditions recorded during the experimental time window are directly incorporated into the time domain numerical analyses. Additionally, drawing from observations during experiments with the 1:40 model, the inclusion of second-order wave loads, particularly low-frequency wave-difference loads, has been recognized as pivotal for accurately capturing platform motion. Therefore, these factors have been taken into account in the present numerical model to avoid underestimations of surge and sway displacement.

In general, the numerical results are in line with the experimental findings, demonstrating the appropriateness of the developed numerical tool to support the design and analysis of the multi-purpose platform. However, in order to achieve a trade-off between model accuracy and computational cost needs, some simplifications are made in the current numerical model, which should be clarified here.

Regarding the open configuration of the wave energy converter modeling, the local fluid dynamics within WECs are not considered, which may lead to an overestimation of the platform motions and internal pool responses. By comparing the discrepancies between the numerical predictions and experimental records for the WEC closed and WEC open configurations, this simplification can be treated as acceptable, which is due to the mild environment of the outdoor experiments.

The yaw angle of the wind turbine cannot be changed during the simulation, nor can the wind direction; i.e., a given wind direction and wind turbine rotor angle with respect to the wind direction have to be set as a starting condition and cannot be changed during the simulation, which differs from the real experiment. Furthermore, the overestimated stiffness of the catenary mooring system also contributes to the discrepancies in yaw angle.

In addition to the above simplifications, there are some uncertainties due to the size of the prototype model and outdoor conditions:

• The exact position of the center of gravity affects the average values of the roll and pitch position.
• The exact value of the moments of inertia affects the standard deviation of the rotational motions.
• The exact length and stiffness of the mooring lines. The stiffness is estimated by using the empirical formulation.
• The exact stiffness of the wind turbine tower affects the wind turbine tower bending loads. The current numerical model underestimates the tower rigidity.
• The exact seabed properties affect the mooring line loads by up to 100%.

These discrepancies have been identified, and an interpretation of their source has been provided, offering insights into potential areas for future investigation, both in terms of refinements of the numerical modeling approaches and in terms of experimental measurement techniques. However, some improvements can still be made for future work. For a relatively large-scale model tested within an uncontrolled environment, it is necessary to undertake a comprehensive re-measurement campaign, covering all key parameters that could potentially influence the variables of interest. Formal uncertainty quantification would further strengthen the validation. In particular, for the current model, the mooring system characteristics, as installed, present some uncertainties that may have significant impacts on the overall system response to wind, wave, and current loads. This re-measurement campaign is also necessary because, since the environmental loads cannot be controlled, it is not possible to conduct the conventional system-identification experiments that are used to confirm the main characteristics of dynamic systems. On the other hand, the current numerical model is based on a potential flow approach to estimating wave loads. It is therefore suggested, as future work, to complement this approach with a higher fidelity approach; for example, a CFD approach, capable of modeling the inner pool dynamics and other non-linear phenomena such as slamming/impact loads and green water with higher accuracy.