Optimized future floating wind turbines (FWTs) are expected to be both larger and relatively lighter than conventional offshore platforms, thus more flexible. The common practice of modeling the platform as a rigid body in coupled dynamic simulations of FWTs can then be questioned. Specifically, natural frequencies of the elastic modes of large flexible platforms can be close to the frequency range of excitation loads. Additionally, platform flexibility can have a significant effect on the natural modes involving significant tower deformation. Considering the platform’s flexibility in coupled simulations of large FWTs requires distributing the hydrodynamic and hydrostatic pressure loads on the flexible model of the platform, instead of the traditional approach of lumping the loads at a single point. This work presents a rational method to evaluate the first-order added mass, radiation damping, and excitation coefficients for a multi-body representation of the platform and develops an energy-conserving distributed formulation for the hydrostatic loads. Assuming small flexible deformations, a decoupled radiation damping matrix is used to model radiation loads for better computational efficiency, while a fully coupled infinite-frequency added mass matrix is used to ensure a stable model. The decoupled radiation coefficients can either be obtained from a single-body or a multi-body diffraction/radiation analysis. A case study of the INO OptiFLEX 22MW semisubmersible FWT is used to illustrate and verify the implementation of the proposed approach. Compared to a baseline model with rigid floater, the results show that introducing platform flexibility significantly affects the high-frequency dynamics of the tower and can also potentially affect mooring line tensions. Moreover, platform flexibility was shown to influence roll and pitch dynamics. These findings highlight the need to model platform flexibility in coupled simulations when analyzing and designing future large FWTs, which can be achieved through the proposed methodology.

In a wind farm with shared mooring, the floating wind turbines (FWTs) are physically coupled through mooring lines. Therefore, motion patterns and mooring line tensions differ from situations where classical (individual) mooring is used. Conventional model testing of such a farm requires physical modelling of all the connected FWTs, which raises practical limitations concerning scaling and cost. In cyber-physical testing, a physical model of a part of the shared mooring farm is coupled with a numerical model of the remaining part of the farm. This paper describes the methodology and results of a cyber-physical test campaign conducted at the basin of NTNU/SINTEF Ocean, Trondheim, on 2- and 9-FWT shared farms. Static excursion tests were conducted to verify the coupling between the physical and numerical FWTs in the cyber-physical tests. Decay tests were performed in which the exact coupled modes of the shared farm were excited. The performance of the farm in irregular waves without wind or current loads was assessed along with mooring line breakage tests. Technical challenges encountered during testing are discussed, and comparisons of experimental results against the closest approximate numerical simulations are presented.

Cyber-physical test and numerical simulation results for two shared mooring farms, consisting of 2 and 9 floating wind turbines, are analysed using a modal basis. Decay tests show a single dominant modal response. In irregular wave tests, comparisons with numerical simulations are limited to 5-9 modes that contribute significantly to line tension. These modes could reproduce the selected line tension standard deviation within 15%. The power spectral density of shared line tension and modal responses in the wave-frequency range exhibits a distinct comb-like frequency response associated with modal excitation from first-order wave loads. To meet the real-time computational requirement of cyber-physical tests, the mooring line model used during the test was a quasi-static model. Numerical comparisons are made between simulations with quasi-static and dynamic mooring line models for the tested shared-mooring farms to assess the impact of this simplification. In irregular wave tests, the quasi-static mooring line model overestimated the horizontal translational motion standard deviation by up to 20% (0.29 m full scale). Although direct application of the quasi-static mooring model underestimated the shared line tension standard deviation by up to approximately 80%, line tensions can be accurately reconstructed during post-processing.

This study presents an optimal experimental design (OED) framework for efficiently identifying low-frequency hydrodynamic loads on floating structures. The proposed method exploits the possibilities offered by cyberphysical (CP) testing, an experimental method allowing real-time control of the boundary conditions applied to the floater. In the present context, the floater is kept in position by a virtual linear mooring system, defined by a stiffness and a damping coefficient. The ease of control of these parameters is leveraged to formulate a rigorous OED approach that maximizes the information gained from the experimental campaign. The method quantifies the information gain and selects the optimal values for the stiffness and damping properties of the active mooring system. The experimental setting identified with the OED approach yields the most reliable estimates of the low-frequency added mass and damping coefficients and wave excitation force. The approach is validated through an experimental campaign conducted at SINTEF Ocean using a scaled model of the INO WINDMOOR 12 MW floating wind turbine. It is concluded that experimental setups with a larger spread in stiffness parameters significantly enhance parameter identifiability, while variations in damping have minimal influence.

The first tower bending frequency of a floating wind turbine (FWT) can be significantly higher in water than if the substructure were clamped on land. The paper presents a simplified two-degree-of-freedom analytical model of the coupled floater-tower motions describing this phenomenon. In spite of its simplicity, the model conveniently explains coupling effects, the relationship between wet and dry eigenfrequencies and mode shapes, and highlights the driving parameters for such couplings. For common semi-submersible wind turbine designs, the coupling between tower deflection and rigid floater motions has little effect on the near-rigid-body modes of motion, but a significant effect on the modes involving tower deflection. The corresponding wet mode shape typically involves an out-of-phase motion between the floater and the tower, and the natural frequency predicted by the model increases compared to a floater resting on land. Another important finding for the prediction of fatigue damage is that the damping of tower vibrations can be significantly increased due to the coupling. Energy is transferred from the tower vibration mode to the near-rigid-body mode and dissipated by hydrodynamic damping. The main driving parameter for coupled vibrations is the ratio between the inertia of the turbine compared to the inertia and added mass of the floater. Coupling effects are stronger for heavy turbines mounted on light floaters and must therefore be considered carefully in future floating wind turbine concepts with increasing power ratings and optimized floaters. The limitations of the simplified model are discussed by comparing its predictions against a linear finite element analysis that captures deformation of the tower and against experimental results.

Cyber–physical testing has been applied for a decade in hydrodynamic laboratories to assess the dynamic performance of floating wind turbines (FWTs) in realistic wind and wave conditions. Aerodynamic loads, computed by a numerical simulator fed with model test measurements, are applied in real time on the physical model using actuators. The present paper proposes a set of short and targeted benchmark tests that aim to quantify the performance of actuators used in cyber–physical FWT testing. They aim at ensuring good load tracking over all frequencies of interest and satisfactory disturbance rejection for large motions to provide a realistic test setup. These benchmark tests are exemplified on two radically different 15 MW FWT models tested at SINTEF Ocean using a cable-driven robot.

Hydrodynamic model-scale experiments are an intrinsic part of the design of marine structures, as they enable validating and calibrating the involved hydrodynamic numerical models. Such seakeeping experiments are generally conducted using a simple spring-based mooring system, with fixed properties throughout the tests. In the context of cyber-physical testing, the marine structure is kept in position in the laboratory by a virtual mooring system, the properties of which can be adjusted on the fly. This paper provides an algorithmic approach for maximizing the information gain from the test by optimizing the mooring stiffness and damping parameters that define the experiment. The method is verified with synthetic data generated for the INO Windmoor 12MW floater, and is shown to be robust to noise and unmodeled effects.

This paper presents a data-driven approach for estimating the linear and quadratic transfer functions relating incoming waves to hydrodynamic loads on floaters. The procedure relies on constructing a nonlinear auto-regressive (NARX) surrogate model for forecasting the hydrodynamic loads and a harmonic probing algorithm for extracting the transfer functions of the system. The implemented harmonic probing method is of numerical nature and avoids the use of computationally expensive symbolic coding tools. The method was verified against synthetic data generated from a potential-flow-based numerical model of the INO WINDMOOR 12 MW floater. The main advantage of NARX models is the flexibility of their structure, meaning that they do not presuppose that the nonlinearity of the hydrodynamic load is quadratic, as it is commonly done.

Wave loads on lattices of marine structures, such as wind parks with shared mooring systems, are considered. Modal excitation induced by second-order low-frequency wave loads is derived, leading to modal quadratic transfer functions. The consequence for the modal loads, of applying Newman’s approximation is investigated.

Optimizing floating wind turbines and their mooring systems requires validated computational models that predict wave-frequency and low-frequency hydrodynamic loads. Low-frequency loads are crucial for determining extreme offsets and tension in mooring lines and are generally described by a quadratic transfer function. The quadratic transfer function, obtained with numerical tools, accurately predicts low-frequency loads in mild sea states. However, since the existing numerical methods are based on potential and perturbation theory, they generally fail to accurately predict low-frequency loads in moderate-to-extreme sea states where current, viscous, and beyond-second-order potential effects become significant. Developing a procedure for empirical transfer function estimation is, therefore, necessary to overcome these limitations. This paper describes an existing framework for estimating any higher-order transfer functions from experimental data. The framework employs a nonlinear auto-regressive model based on Kriging to establish a causal input/output relationship between the wave-elevation and hydrodynamic force histories exerted on the floater. Then, higher-order transfer functions are extracted using harmonic probing. The procedure was validated by estimating the linear surge transfer function of the INO WINDMOOR 12 MW floater using synthetic data. The data-driven results showed an excellent agreement with the theoretically computed transfer function.

Results from full scale fatigue tests of offshore mooring chains are analyzed. The data set includes new and used chains, tested at a variety of mean load levels. The used chains have been retrieved after operation offshore and include samples with varying surface conditions, ranging from as-new to heavily corroded. Based on a parameterized S–N curve intercept parameter, the effects of mean load and chain condition are estimated empirically by regression analysis. A hierarchical linear model is used, to account for and quantify correlations within subsets of the data. The choice of grouping criterion for the hierarchical model is discussed, and assessed based on the current data. Results show that the mean load and corrosion effects are both significant. Differences in the fatigue performance of new versus used chains are quantified and discussed.

A reliability formulation for mooring chain fatigue is developed, including the effects of mean load and degradation due to corrosion. They are included by starting from a S-N model with parameterized dependence to the mean load and a customized corrosion condition scale. The paper includes a thorough case study, based on a realistic case. A global sensitivity analysis is used to justify a reduction of the model dimension. A reliability analysis is then performed, and the effect on failure probability from variation of a range of parameters and model assumptions is studied.

A probabilistic model for mooring chain fatigue damage is developed based on the S–N approach. The effects of mean load and corrosion condition on the fatigue capacity of the chains are included by adopting a parameterized S–N curve intercept parameter, and the model allows for the uncertainties and time dependencies of these to be addressed. Uncertainties in fatigue loads are also accounted for, including the annual variability which may be of importance in certain cases. Furthermore, the resulting model distinguishes between damage due to prior known loads and future unknown loads, to allow for reduced uncertainties in case that the load history is available from measurements or calculations. Measures are taken to ensure that the correlation between mean and cyclic loads is handled implicitly. A case study based on extensive hindcast-based simulations for a realistic mooring system is performed, and the respective effects of uncertainties in fatigue capacity, corrosion development and fatigue loads are presented and discussed.

The paper describes a sensor fusion method that provides reliable, uninterrupted and bias-free estimates of the top tension in a mooring line. The method exploits the geometric nonlinearity of mooring systems installed in shallow to moderate water depths: a change of line length (due to winching) affects the local dynamic stiffness of the mooring line. Based on measurements of fairlead displacements and of the dynamic part of the top tension, the line length and true (unbiased) mean tension can be inferred. The method combines the use of (1) a classical kinematic observer to derive fairlead motions, (2) the compression of the recent history of fairlead motions to a few parameters, (3) a bank of neural networks, each network modelling the response corresponding to a given line length/static tension, and (4) a heuristic approach to selecting the most promising model among the candidates. One major advantage of the method is its sparsity, making it computationally efficient so it can be applied both offline, on large sets of recorded historical data, and online running on lightweight embedded hardware. The paper presents in detail each component listed above, and the method as a whole is verified on a realistic case. Given that enough excitation is present, the estimator was found to converge towards the true value of the tension, and to cope well with transient conditions such as winching operations, and with the presence of oceanic current.

A novel empirical method to study wind-assisted cargo ships is presented. The physical ship model, including propulsion units, interacts in real-time with a numerical sail model during free-running tests. Loads from the (virtual) sails are applied on the physical model using a cable-driven robot. All loads components except heave are applied with high accuracy and repeatability. The method is described thoroughly, and applied to investigate the benefits of wind assistance on a 190m bulk-carrier, equipped with four rotor sails. Key performance indicators for wind assistance are established when sailing in steady wind profiles of various directions and velocities, and a propulsion analysis is performed. An important conclusion is that the increase of hydrodynamic resistance due to heel, leeway and rudder (that balance transverse sail loads) is rather limited for this ship, except when sailing close-hauled in strong winds. It is also demonstrated that experiments in a unsteady (virtual) wind environment can be successfully conducted. The effect of turbulence on the motions of this ship are found to be very limited. The conclusion discusses the other types of studies that can be enabled by this novel cyber-physical empirical method.

In real-time hybrid model testing, complex ocean structures are emulated by fusing numerical modelling with traditional hydrodynamic model testing. This is done by partitioning the ocean structure under consideration into a numerical and a physical substructure, coupled in real time via a measurement and control interface. The numerically computed load vector is applied to the physical substructure by means of multiple actuated winches so that the resulting experimental platform becomes a type of cable-driven parallel robot. In this context, the placement of the actuated winches is important to ensure that the loads can be accurately and robustly transferred to the physical substructure. This paper addresses this problem by proposing a performance measure and an associated actuator placement procedure that enables accurate force tracking and ensures that the numerically calculated loads can be actuated throughout the testing campaign. To clarify the application of the proposed procedure, it is applied to the design of a test setup for a moored barge. Overall, the paper represents a guideline for robust and beneficial actuator placement for real-time hybrid model testing using cable-driven parallel robots for load-actuation.

It is well known that flap wavemakers behave in a nonlinear way when either the flap angle or the flap velocity becomes large. Moreover, the hinge depth should be adapted to the period of the generated waves in order to minimize linear evanescent modes, which may contribute to the formation of nonlinear spurious waves. For example, imposing a sinusoidal motion with a relatively long period and a large amplitude to a short flap will result in a surface elevation composed of a regular wave with the same period as the flap motion, but also of a variety of harmonics with higher frequencies. Second-order harmonics can be predicted theoretically for regular and irregular waves, and they can be corrected by modifying the control signal of the wavemaker. However, there is no theory that can describe nor mitigate effects of orders higher than two. The design of the wavemaker is then essential to generate extreme sea states with good quality and predictability in a laboratory. In this paper, the nonlinearities of flap wavemakers are investigated experimentally for regular and irregular waves generated in SINTEF Ocean’s laboratories. Nonlinearities of order two and three are estimated from times series of the surface elevation measured at different locations by an array of wave probes. Particular focus is put on identifying the effects of the classical second-order correction on the second- and third-order harmonics.

An application of cyber-physical testing to the empirical estimation of difference-frequency quadratic transfer functions is presented. As an alternative to today's procedure based on hydrodynamic tests with broad-banded or realistic (e.g., JONSWAP) wave spectra, tests in bichromatic waves are considered. The laboratory setup is the one developed by Sauder & Tahchiev (2020) that enables magnifying the sensitivity of the floater response to the low-frequency wave loading by adjusting the stiffness and damping parameters of a virtual soft mooring system. Bayesian experimental design is proposed to optimize the selection of the control variables (frequencies in the bichromatic wave and properties of the virtual mooring system) for a batch of cyber-physical tests. The experimental design algorithm is based on the recent work of Huan & Marzouk (2013). In a virtual yet realistic case study using an uncertain parametric quadratic transfer function, we demonstrate how the uncertainty of its describing parameters and other calibration parameters (low-frequency added mass and hydrodynamic damping) can be reduced. Results indicate that the proposed procedure has the potential for reducing experimental cost for calibration of hydrodynamic models.

In this article, we present a novel method for force allocation for overconstrained cable-driven parallel robot setups that guarantees continuously differentiable cable forces and allows for small penalized errors in the resulting wrench. For the latter, we also provide a bound on the error under some assumptions. We study real-time feasibility by performing numerical simulations on a large set of configurations.

Low-frequency (LF) motions of floating structures are commonly modeled as the response of an oscillator to a second-order wave excitation. We present here an empirical method that reliably estimates the oscillators parameters and quadratic transfer function (QTF) used in such models. The method is based on an active stationkeeping system that enables to accurately control external boundary conditions applied on the floating structure in a wave basin. The resulting system can be successively tuned to different frequency ranges of interest. Then, by deconvolution and optimization, LF damping and added-mass loads, as well as a response-independent wave excitation load, can be evaluated. From the wave elevation, and estimated load time series, the difference-frequency QTF is finally estimated by a cross-bi-spectral analysis, including a new treatment of statistical noise. The paper describes the proposed method in details, and illustrates it with the study of a ship-shaped floating unit in a sea-state of relevance for the fatigue design of mooring systems (steep waves, low return period).