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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A Flexible Quasi-Static Mooring Design Optimization Method for Floating Structures

This paper presents a flexible and efficient design method for optimizing the mooring systems of floating structures. Mooring system optimization is challenging because of the strong nonlinearity of mooring system behavior and the many technical constraints that must be satisfied. Furthermore, different mooring configurations can have very different design spaces. While some successful examples of mooring design optimization exist in the literature, developing an optimization approach that can work across various mooring design problems is a larger challenge. We present such a method based on a flexible parameterization that allows a wide variety of mooring designs to be described by a list of variables, a quasi-static mooring model that provides efficient evaluation of a mooring design without directly considering mooring system dynamics, and an optimization framework that generates, evaluates, and adjusts the mooring design while considering user-specified constraints such as offset limits, strength safety factors, and seabed contact limits. We demonstrate the design optimization framework on four mooring design problems, each for a different type of mooring system. We compare the use of different design modes to simplify the optimization problem, showing that they can reduce the computation time by up to 75%. We also compare different optimization algorithms and find that the resulting computational speed can vary by up to 51 times. We perform a sensitivity study on one design and find that the local sensitivity of anchoring radius to water depth has a positive correlation of 0.29, but the global sensitivity shows large nonlinearities. Lastly, we perform a coupled dynamic analysis on one of the optimized designs and find that the predicted mean platform motions and mooring line tensions are within 1% of dynamic results and the extreme motions and tensions are within 14%. Lastly, we show that a DEA-Chain-Polyester mooring configuration is cost-optimal for the given design problem of the demonstrations, which aligns with general industry practice.

16 TIDAL AND WAVE POWER↗
DOE OSTI2024

Shared mooring system designs and cost estimates for wave energy arrays

For floating renewable energy devices to become more cost-efficient and commercially scalable, their mooring system designs must be low-cost and suited for large-scale installations. Large arrays of floating devices, such as wave energy converters (WECs), will likely be designed with an individual mooring system for each device in the array. However, new mooring technology advancements provide options to use shared mooring lines to connect adjacent devices to one another, reducing the total number of anchors in the array, thereby reducing material use and cost. Here, this paper explores the design, modeling, and cost analysis of shared mooring systems for various sizes of arrays consisting of heaving oscillating water column (OWC) WECs. Shared mooring systems for WEC arrays sized in 2 x N and N x N grid layouts are designed to meet the relevant design standards, checking their performance with a nonlinear time-domain dynamic simulation, and the costs of each are calculated and compared. Several assumptions are taken in the design process to produce efficient results, providing a preliminary optimization for guidance on design decisions rather than a full, detailed design analysis. Mooring system costs per WEC were found to decrease as the number of WECs in the array increase, up to certain array sizes. The 2 x 3 array had the lowest mooring system cost per WEC out of all arrays considered, with a 60% cost reduction relative to using individual mooring systems. The 3 x 3 and 4 x 4 arrays achieved a 50% cost per WEC reduction. In addition to these significant cost reductions, the shared mooring system designs can provide advantages through smaller mooring system footprints, lower installation times, and less seabed disturbance.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Frequency-domain modeling of floating wind arrays with shared mooring lines

A frequency-domain model for floating wind turbine dynamics has been extended to model floating wind farms with couplings from shared mooring systems. The model, called RAFT, could previously calculate the mean offsets and wave-induced response spectra for single floating wind turbines. Now, the model supports multiple floating wind turbines, each with their own properties and responses, along with mooring lines that run directly between floating wind turbines in the array, meaning that shared mooring lines or fully suspended dynamic power cables can be included. This capability is achieved by setting up an array-level solution of the system mean offsets and assembling the full system matrices for solving the dynamic response. The quasi-static mooring model MoorPy is used to linearize the mooring system properties. To compute the floating wind turbine relative motions, phase offsets are applied to each turbine's response as a function of wave frequency based on the wavelength and relative positions in the array. These differential motions are then applied to mooring system tension Jacobians to compute the tension loads in the shared mooring lines. Overall, the capability provides a frequency-domain analog to the modeling capabilities of the floating support structure in FAST.Farm. Mean offsets and power spectral density plots of responses are compared between RAFT and FAST.Farm to verify the implementation. The results indicate good agreement within the expectations of a frequency-domain modeling approach and suggest correct implementation of the shared mooring aspects. Additionally, a unique comb-like frequency response in the shared mooring line tensions has been observed. This phenomenon has a clear physical basis and may be an important design consideration for future shared mooring systems.

17 WIND ENERGY↗
DOE OSTI2024

Streamlined Loads Analysis of Floating Wind Turbines With Fiber Rope Mooring Lines: Preprint

This paper presents an approach for more accurate yet relatively streamlined accounting for the nonlinear characteristics of synthetic fiber rope mooring lines for floating wind turbines. First, we select a minimal set of parameters that can efficiently approximate a mooring line material's quasi-static and dynamic stiffness characteristics. We also develop a set of baseline coefficients for different rope materials based on published product information and research papers. We then expand a quasi-static mooring model to include dynamic mooring line stiffness terms in a way that allows the nonlinear stiffness behavior of fiber ropes to be considered even in quasi-static analyses. For dynamic analysis, we have updated the model MoorDyn, coupled with OpenFAST, to work with the new dynamic mooring line stiffness terms. This includes the implementation of a new viscoelastic approach that allows the tension-strain relation of each mooring line segment to vary between two stiffness values depending on the strain rate. After presenting the formulation of the approaches for modeling synthetic ropes, they are demonstrated on a floating wind turbine mooring system with taut polyester rope mooring lines. The results are compared with those of other approaches of similar fidelity including the static-dynamic method and separate simulations with static and dynamic stiffness values. Comparing the results shows the ability of the new method to match the results of the previous methods in a more streamlined manner.

elasticity↗
DOE OSTI2024

Streamlined Loads Analysis of Floating Wind Turbines With Fiber Rope Mooring Lines

This paper presents an approach for more accurate yet relatively streamlined accounting for the nonlinear characteristics of synthetic fiber rope mooring lines for floating wind turbines. First, we select a minimal set of parameters that can efficiently approximate a mooring line material's quasi-static and dynamic stiffness characteristics. We also develop a set of baseline coefficients for different rope materials based on published product information and research papers. We then expand a quasi-static mooring model to include dynamic mooring line stiffness terms in a way that allows the nonlinear stiffness behavior of fiber ropes to be considered even in quasi-static analyses. For dynamic analysis, we have updated the model MoorDyn, coupled with OpenFAST, to work with the new dynamic mooring line stiffness terms. This includes the implementation of a new viscoelastic approach that allows the tension-strain relation of each mooring line segment to vary between two stiffness values, depending on the strain rate. After presenting the formulation of the approaches for modeling synthetic ropes, they are demonstrated on a floating wind turbine mooring system with taut polyester rope mooring lines. The results are compared with those of other approaches of similar fidelity, including the static-dynamic method and separate simulations with static and dynamic stiffness values. Comparing the results shows the ability of the new method to match the results of the previous methods in a more streamlined manner.

elasticity↗
DOE OSTI2024

Floating Wind Farm Layout Optimization Considering Moorings and Seabed Variations

This paper presents a method for optimizing the layout of floating wind farms that accounts for realistic seabed variations and the consequent adjustments to the mooring systems required for different turbine positions. The mooring lines of floating wind farms create large spatial constraints that are depth-dependent, since mooring designs must adapt to variations in seabed conditions over the array area. We develop a layout optimization methodology that addresses this, adjusting mooring system designs based on the local seabed characteristics as the layout changes and using steady-state models for the wake effects and mooring lines. The approach includes design algorithms that adjust the anchor positions and line length to achieve the desired mooring line profile for different water depths, and a layout optimization framework that implements spatial constraints between the turbines, mooring lines, and lease area boundaries. Demonstrating the method on several cases shows the effect of the seabed and spatial-constraint factors, as well as their interactions, on the optimal array layout. This demonstration paves the way for scaling up the method, using more powerful optimization algorithms to handle larger farm sizes and situations with more intensely varied seabed conditions.

17 WIND ENERGY↗
DOE OSTI2023

PacWave Anchoring and Mooring Study

PacWave, with its location in some of the most energetic waters in the nation and a buildout to support grid-connected devices, is poised to become a leader in field testing of wave energy converters (WECs) at high technology readiness levels. As part of the device deployment and testing protocols at PacWave, the client is responsible for providing all mooring system components, since there are currently no mooring system components specified for PacWave. NREL and PNNL have been tasked with conducting a preliminary analysis of permanent or temporary mooring systems at the PacWave South site. Previous work for this task included a global trade study of mooring systems used for WECs, and a site characterization of PacWave South. This current report will use the results of the previous studies to inform the design of various mooring systems to be installed at PacWave, which will allow cost analyses to be performed to compare the costs of acquisition of these mooring systems and the costs of mooring systems designed specifically for clients' devices.

16 TIDAL AND WAVE POWER↗
DOE OSTI2026

Evaluation of 1/100-Scale Mooring Systems for Wave Energy Converters

This study evaluates the feasibility, accuracy, and limitations of using 1/100th scale physical mooring systems to represent full-scale mooring behavior for wave energy converters (WECs) during small-scale tank testing. The work focuses on an RM3-style point absorber deployed in conditions representative of the PacWave South test site and examines whether small-scale physical testing can reliably inform numerical modeling, design decisions, and future prototype development. Overall, this study concludes that small-scale (1/100th) physical mooring models can provide valuable qualitative insights, including relative comparisons between mooring types and trends in device behavior, but cannot reliably replicate full-scale mooring loads or dynamic response without significant scaling distortion. Physical tests at this scale are most appropriate for motion characterization and model validation within known limitations, not for deriving absolute mooring loads or final engineering design values. Key lessons learned emphasize the importance of improved instrumentation strategies, iterative wave tank tuning, more precisely manufactured scaled mooring components, and enhanced anchoring systems to reduce experimental uncertainty.

16 TIDAL AND WAVE POWER↗
DOE OSTI2024

Generalized Quasi-Static Mooring System Modeling with Analytic Jacobians

This paper presents a generalized and efficient method for quasi-static analysis of mooring systems, including complex scenarios such as when shared mooring lines interconnect multiple floating wind or wave energy devices. While quasi-static mooring models are well established, most published formulations are focused on specific applications, and no publicly available implementations provide efficient handling of large mooring system networks. The present formulation addresses these gaps by: (1) formulating solutions for edge cases not typically supported by quasi-static models; (2) creating a fully generalized model structure such that any combination of mooring lines, point masses, and floating bodies can be assembled; and (3) deriving analytic expressions for the system Jacobians (stiffness matrices) so that systems with many degrees of freedom can be solved efficiently. These techniques form the theory basis of MoorPy, an open-source mooring analysis library. The model is demonstrated on nine scenarios of increasing complexity with features of interest for offshore renewable energy applications. When compared with steady-state results from a lumped-mass dynamic model, the results show that the quasi-static formulation accurately calculates profiles and tensions and that its analytic approach provides more efficient and reliable computation of system stiffness matrices than finite-differencing methods. These results verify the accuracy of the MoorPy model.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

The OCEAN ICE mooring compilation: a standardised, pan-Antarctic database of ocean hydrography and current time series

Continuous moored time series of temperature, salinity, pressure and current speed and direction are of great importance for understanding the continental shelf and under-ice-shelf dynamics and thermodynamics that govern water mass transformations and ice melting in and around Antarctic marginal seas. In these regions, icebergs and sea ice make ship-based mooring deployment and recovery challenging. Nevertheless, over decades, expeditions around the fringe of Antarctica sporadically deployed and recovered hundreds of moored instruments, including those facilitated through ice shelves boreholes. These datasets tend to be archived in a wide range of data centres, with, to our knowledge, no clear format standardisation. As a result, systematic analysis of historical mooring time series in the marginal seas is often challenging. Here we present the first version of a standardised pan-Antarctic moored hydrography and current time series compilation, with broad international contributions from data centres, research institutes and individual data owners. The mooring records in this compilation span over five decades, from the 1970s to the 2020s, providing an opportunity for a systematic study of the pan-Antarctic water mass transport and shelf connectivity. As a demonstration of the utility of this compilation, we present spectral analysis of the compiled current velocity time series, which unsurprisingly shows the dominating presence of tidal variability within most records. This component of the variability is fitted using multi-linear regression to tidal frequencies, and the tidal fit is removed from the original time series to leave de-tided variability. Given the limited record durations to months to years, de-tided variability is dominated by synoptic (3–10 d period), intraseasonal (10–80 d) and seasonal (∼6 months–1 year) signals. The spatial distribution of the kinetic energy integrated within frequency bands is presented and discussed within respective regional contexts, and future avenues of research are proposed. This data compilation is assembled under the endorsement of Ocean-Cryosphere Exchanges in ANtarctica: Impacts on Climate and the Earth System (OCEAN ICE) project (https://ocean-ice.eu/, last access: 23 October 2025) funded by the European Commission and UK Research and Innovation. It is available and regularly updated in NetCDF format with the SEANOE database at https://doi.org/10.17882/99922 (Zhou et al., 2024a).

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2001

High Frequency, Long Time Series Measurements from the Bermuda Testbed Mooring in Support of SIMBIOS

It has been recognized that optical moorings are important platforms for the validation of Sea-Viewing Wide Field-of-view Sensor (SeaWiFS). It was recommended that optical moorings be maintained in order to: (1) provide long-term time series comparisons between in situ and SeaWIFS measurements of normalized water-leaving radiance; (2) develop and test algorithms for pigment biomass and phytoplankton primary productivity; and (3) provide long-term, virtually continuous in situ observations which can be used to determine and optimize the accuracy of derived satellite products. These applications require the use of in situ radiometers for long periods of time to evaluate and correct for inherent satellite undersampling (aliasing and biasing) and degradation of satellite color sensors (e.g., drifts as experienced by the Coastal Zone Color Scanner). The Bermuda Testbed Mooring (BTM) program was initiated in 1994 at a site located about 80km southeast of Bermuda in waters of about 4530 m depth. In August 1997, with NASA's support, we started to provide the Sensor Intercomparison and Merger for Biological and Interdisciplinary Oceanic Studies (SIMBIOS) program with large volumes of high frequency, long-term time-series bio-optical data from the BTM for SeaWiFS satellite ocean color groundtruthing and algorithm development. This NASA supported portion of the BTM activity spanned three years and covered five BTM deployments. During these three years, the quality of radiometric data has improved dramatically. Excellent agreement between BTM moored data and both SeaWiFS and nearby ship profile radiometric data demonstrate that technical advances in the moored optical observations have reduced the major difficulties that moored platforms face: biofouling and less frequent calibration.

Dickey, Tommy↗
DOE OSTI2024

Deformed Fredkin model for the ν = 5 / 2 Moore-Read state on thin cylinders

We propose a frustration-free model for the Moore-Read quantum Hall state on sufficiently thin cylinders with circumferences ≲ 7 magnetic lengths. While the Moore-Read Hamiltonian involves complicated long-range interactions between triplets of electrons in a Landau level, our effective model is a simpler one-dimensional chain of qubits with deformed Fredkin gates. We show that the ground state of the Fredkin model has high overlap with the Moore-Read wave function and accurately reproduces the latter's entanglement properties. Moreover, we demonstrate that the model captures the dynamical response of the Moore-Read state to a geometric quench, induced by suddenly changing the anisotropy of the system. We elucidate the underlying mechanism of the quench dynamics and show that it coincides with the linearized bimetric field theory. The minimal model introduced here can be directly implemented as a first step towards quantum simulation of the Moore-Read state, as we demonstrate by deriving an efficient circuit approximation to the ground state and implementing it on an IBM quantum processor. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Moore Machine Motion Controls Refurbishment Statement of Work and Specification

Diamond Turning Machines known as “Moore” machines are used in the production of Potassium diHydrogen Phosphate (KDP) optics required for the National Ignition Facility (NIF). These machines are owned by the Department of Energy, as provided by Lawrence Livermore National Security LLC (LLNS). Moore Machines 1 and 2 are located at the Gooch & Housego (G&H) facility in Highland Heights, OH. The existing Aerotech motion controllers, motor drivers/amplifiers, input/output (I/O) hardware, control computer, software user interface, human machine interface (HMI), cabling, and encoders are beyond service life and require replacement. This Statement of Work (SoW) defines the motion control system refurbishment requirements for the Moore diamond turning machines designated Moore 1 and Moore 2. The motion controls system design shall include a motion control computer, control software, motor drive amplifiers and controllers, linear scale encoders, rotary encoders, HMI, power distribution, emergency stop (E-Stop) and interlocks, cabling, switches, solenoids, transducers, sensors, actuators, ancillary system interfaces, and related components necessary for a complete machine tool control system. The Subcontractor shall include effort to standardize systems between the two machines if reasonably possible.

42 ENGINEERING↗
DOE OSTI2025

2024 Incubator Final Report: Active Hybrid Mooring

This Incubator project has defined and developed a representation of an active hybrid mooring (AHM) system in Simulink to assess whether the speed and accuracy of AHM is sufficient to warrant further investigation in a larger project. We first built a representative mooring system for the VolturnUS-S 15MW floating offshore wind turbine (FOWT) in 1,000-meter water depth to provide baseline loads and displacements needed in the AHM system, with the results showing off-the-shelf actuators would be practical. We then defined model configurations for the numerical and physical substructures, using standalone MoorDyn v2 with a novel input strategy and chained hydraulic actuators represented in Simulink Simscape, respectively. The remainder of the project has focused on verifying the existing models for speed and accuracy against OpenFAST simulations, increasing their complexity to enable six degree of freedom (6DOF) operation, and connecting the numerical and physical substructures into a single holistic model. The verification phase of the project has shown promising results, though further refinement is needed to resolve accuracy discrepancies and for robust performance across a wider range of metocean conditions. The numerical model we developed is computationally stable and operates faster than real time using a time step of 0.01 seconds or shorter, indicating the model is likely fast enough for our AHM design to operate successfully. Additionally, the Simscape model of a hydraulic actuator operates with less than 0.3% relative error when actuating mooring loads from an OpenFAST simulation of the VolturnUS-S 1,000-meter mooring system. The aforementined refinements will be performed in the next year as a Continuing Incubator, with key remaining tasks include programming the predictor-corrector loop to minimize movement error, testing against more complex nonlinear wave cases, and expanding to enable loads from connected shared mooring lines.

17 WIND ENERGY↗
DOE OSTI2024

Integrated floating wind farm layout design and mooring system optimization to increase annual energy production

As we cluster wind turbines in wind farms to gain energy from sites with high wind speeds, wake losses occur within the wind farm. Wake loss is a term used to describe the lower energy production of a downwind turbine that is totally or partially in the wake of an upwind turbine. To decrease wake losses inside the wind farm, the wind farm’s layout is optimized. However, a variety of factors constrain the wind farm layout optimization, such as the size of the lease area relative to the number of turbines to be placed, or the shape of the lease area. Therefore, many wind farms end up with a regular grid layout, such as the Horns Rev 1 wind farm in the North Sea. The ability of a floating offshore wind turbine (FOWT) to change its position based on the wind direction and its mooring system design presents an opportunity to further decrease wake losses in floating wind farms. In this work, we integrate the design of the FOWT mooring systems with the floating wind farm layout design with the goal of increasing the farm’s annual energy production. We use the Horns Rev 1 wind farm as a case study to demonstrate our method. The results show that allowing the FOWT to relocate can decrease wake losses up to 18%. Moreover, the newly developed mooring systems are less stiff and therefore allow larger motion of the FOWT; hence, the material cost of the mooring system decreases by an estimated 17%.

17 WIND ENERGY↗
DOE OSTI2025

2025 Continuing Incubator Final Report: Active Hybrid Mooring

This project advanced the development of an active hybrid mooring system integrating experimental testing with numerical simulation to capture complex mooring dynamics not feasible in existing wave basins, including deep-water and shared mooring interactions. Verification testing of the complete hybrid system yielded good agreement in mooring tension and platform translation responses, though discrepancies in platform pitch response indicate that further refinement may be needed in future work.

16 TIDAL AND WAVE POWER↗
DOE OSTI2026

Advanced Mooring Lines for Marine Energy Workshop – Summary Report

This report summarizes the outcomes of the virtual Advanced Mooring Lines for Marine Energy Workshop. The workshop convened experts from industry, academia, and national laboratories to identify key challenges associated with the deployment of synthetic mooring lines for marine energy applications. Discussions focused on four technical areas—materials, failure and degradation, testing, and modeling. Despite the significant promise of leveraging synthetic mooring systems for marine energy applications, discussion highlighted broader research and development needed to address the lack of validated long-term performance data, insufficient structural health monitoring frameworks, limited large-scale testing capabilities, and gaps in predictive modeling. Overall, the workshop emphasized the importance of coordinated research and development efforts to advance reliable, durable, and cost-effective synthetic mooring solutions for marine energy applications.

16 TIDAL AND WAVE POWER↗
NASA NTRS1994

Update on TAO moored ORG array

During the Coupled Ocean Atmosphere Response Experiment (COARE) six TAO moorings were equipped with optical rain gauges (ORG's). In late 1993 moorings deployed on the equator at 154E and 157.5E were recovered and not redeployed as they were augmentations to the TAO array for COARE only. In December 1993, four TAO moorings were equipped with ORG's: one each at 2N, 156E and 2S, 156E and ORG doublets on the equator at 0, 156E and 0, 165E. The 2N, 156E mooring has been lost. By the end of April all sites will have been serviced and six refurbished sensors will again be deployed in the same locations.

Freitag, H. Paul↗