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This paper presents the fatigue reliability prediction for welded planar tubular joints of offshore fixed jacket support structures. A coupled model is employed to calculate the dynamic response of the jacket support structure under wind and wave loads. Stress concentration factors (SCFs) are evaluated using Efthymiou parametric equations, and the hot-spot stresses at eight locations on the chord and brace of the tubular joints are derived by summing the stress components from axial, in-plane, and out-of-plane actions. The stress distribution is determined using the rainflow counting method, fatigue damage from an S–N curve, and Miner's rule. Uncertainties associated with the fatigue lifetime evaluation procedure are identified, quantified, and modeled. The focus is specifically given to modeling the uncertainty related to the SCFs, and a framework is proposed to evaluate the fatigue reliability of the joint by incorporating individual uncertainties for each degree of freedom of the SCFs (i.e., axial load crown, axial load saddle, in-plane bending moment, and out-of-plane bending moment). The results reveal that assuming the same uncertainty level (Coefficient of Variation of 0.2) as recommended by DNV-RP-C210 for each degree of freedom of the SCFs and including the uncertainty after obtaining the stress distribution from rainflow counting does not consistently yield conservative reliability index values, as it depends on the critical hot spot. It is essential to note that the simplified assumptions derived from the oil and gas sector may not directly translate to the offshore wind industry due to differences in loading conditions. A reduction of up to approximately 24% in the reliability index is observed for one critical hot spot, while an increase of up to 20% was observed for another. Overall, this paper provides valuable insights into the complex interplay of factors affecting the reliability of joints in offshore fixed jacket support structures, shedding light on the need for tailored approaches to address uncertainties in the specific context of the offshore wind industry. • Fatigue reliability of welded tubular joints in offshore wind turbine (OWT) jacket. • The stress distribution is determined using the rainflow counting method. • Fatigue damage is assessed using an S–N curve and Miner's rule. • Incorporates individual uncertainties for each degree of freedom (DOF) of SCFs. • SCFs uncertainty most impacts hot spot reliability index in OWT jacket joints. • The same uncertainty in each DOF of SCFs does not ensure conservative reliability. [ABSTRACT FROM AUTHOR]

Key performance indicators (KPI) are tools for measuring the progress of a business towards its goals. Although wind energy is now a mature technology, there is a lack of well-defined best practices to asses the performance of a wind farm (WF) during the operation and maintenance (O&M) phase; processes and tools of asset management, such as KPIs, are not yet well-established. This paper presents a review of the major existing indicators used in the O&M of wind farms (WFs), as such information is not available in the literature so far. The different stakeholders involved in the O&M phase are identified and analysed together with their interests, grouped into five categories. A suggestion is made for the properties that KPIs should exhibit. For each category, major indicators that are currently in use are reviewed, discussed and verified against the properties defined. Finally, we propose a list of suitable KPIs that will allow stakeholders to have a better knowledge of an operating asset and make informed decisions. It is concluded that more detailed studies of specific KPIs and the issues of their implementation are probably needed. [ABSTRACT FROM AUTHOR]

Lifetime extension becomes increasingly crucial for industry, since the first offshore wind farms face the end of their design lifetime. The remaining useful lifetime of offshore foundations is driven by fatigue design and loading; both are affected by uncertainty. This paper presents a conditional probability model to link results from inspections with numerical simulations of fatigue cracks. Crack sizes are simulated with a fracture mechanics model applying Paris’ Law. The probability of detection of an existing crack depends on inspection technique and crack size. Results show that uncertainty about remaining useful lifetime significantly reduces after considering inspection outcomes. This decreases risks for the decision-making on lifetime extension of offshore wind turbines. [ABSTRACT FROM AUTHOR]

Fatigue reassessment within the decision process of lifetime extension might be uneconomical when individually performed for each turbine of a large offshore wind farm. This paper analyses the possibilities to extrapolate results from fatigue reassessment of wind turbines at selected design positions to other wind turbines of the wind farm. Five monopile-based turbines placed in a generic offshore wind farm were assessed with integrated aero-hydro-elastic simulations. A fatigue assessment was performed for each out of the five selected turbines using site specific environmental data commonly available during the design process. The results were compared to a fatigue reassessment where environmental data were modified in order to account for changes in environmental conditions during the service lifetime of the wind turbines. Results indicate that an extrapolation is feasible for selected parameters when changes in environmental conditions are small. This is an important step towards an effective and efficient assessment methodology for lifetime extension of offshore wind turbines. [ABSTRACT FROM AUTHOR]

In harsh sea conditions, it is possible for offshore wind turbines (OWTs) to be exposed to slamming loads due to breaking waves, especially plunging breaking waves. These slamming loads lead to significant structural responses and can affect the ultimate limit state (ULS) design and the fatigue limit state (FLS) design of OWTs. However, detailed consideration of slamming loads is not a common practice in the design of primary structures in offshore wind industry. Studies on integrated dynamic analysis of OWTs with consideration of slamming loads are very limited. When applying slamming loads on OWTs, several aspects should be considered, such as the detection of breaking waves, the calculation of slamming loads, and the approaches to integrate the slamming loads in fully coupled analysis, etc. This paper provides an extensive review of key issues concerning these aspects, which can benefit the application of slamming loads on OWTs. [ABSTRACT FROM AUTHOR]

Wind turbine jacket structures are complex structures, whose joints design is generally driven by fatigue. These joints, along with their complex welds, are of special interest in terms of cost reduction. Therefore, a thorough analysis and understanding of the background behind the assessment proposed in guidelines is motivated. The paper presents a study of the influence of meshing for the assessment of tubular K-joints following the hot-spot approach using numerical methods. The accuracy of the results is discussed for several mesh layouts. The influence of the mesh density, element shape and element type are investigated. Furthermore, a parametric study is performed in order to see the variation of the results for several diameters, thicknesses and brace inclination combinations. The hot-spot method is proved to be robust regarding mesh regularity. However, the efficiency of irregular mesh models is very low and a high number of elements is needed in order to find an asymptotic behaviour that tends to a constant solution for increasing mesh refinement. Conclusions can be drawn for which cases it is worth to invest time in semiautomatic meshing. A discussion is done regarding which element size and type is better regarding accuracy and computational time. [ABSTRACT FROM AUTHOR]

One increasingly popular type of foundations for offshore wind turbines in shallow water are truss structures. These are exposed to wave slamming forces from breaking wave events. These forces depend, among other parameters, on the slamming factor C s that typically takes values between π -2π. So far, several studies about slamming forces have been done for monopile structures, but not much work has been done regarding truss structures such as offshore jackets. This paper is based on the WaveSlam project in which an instrumented multi-membered truss model has been subjected to regular and irregular waves in the large wave flume at FZK Hannover in 2013. The structure was built at scale 1:8 and equipped with force transducers along the bracings and columns that measured the structural response from the breaking waves. The goal of this study was to characterize the breaking wave forces acting on the front bracings of the structure, in order to estimate the respective slamming factors. The tested structure has been modelled and validated with a finite element model in ANSYS and a wave run test is analyzed. The wave loads have been defined as uniform loads with a triangular force time history acting along the bracings. Through a fitting procedure, the initial responses from ANSYS and from the data were matched with a relative error of 3% for one single wave test. From this, a slamming factor of 4.78 is found in the highest part of the front bracings. The characterization of more breaking wave loads is recommended in order to get an estimate of the largest slamming factor, which is relevant for design purposes. [ABSTRACT FROM AUTHOR]

Time domain analyses of Offshore Wind Turbines involve a lot of computational effort. In this paper, we present a method for reducing this effort by using results from analyses with shorter simulation lengths to predict the results of the longer simulations lengths required by the standards. This involves using simple statistical treatment of the first 10 minutes of simulation data, and a subsequent linear regression, to predict the damage equivalent load of the full 60 minutes simulation. With some reservations about the general applicability of the method, the results are promising. Some suggestions for further investigations and developments of the presented methods are discussed. [ABSTRACT FROM AUTHOR]

Considerable variations in environmental site conditions can exist within large offshore wind farms leading to divergent fatigue loads on support structures. An efficient frequency-domain method to calculate wave-induced fatigue loads on offshore wind turbine monopile foundations was developed. A verification study with time-domain simulations for a 4MW offshore wind turbine showed result accuracies of more than 90% for equivalent bending moments at mudline and interface level. This accuracy and computation times in the order of seconds make the frequency-domain method ideal for preliminary design and support structure optimization. The model is applied in sensitivity analysis of fatigue loads using Monte-Carlo simulations. Local and global sensitivity studies and a probabilistic assessment give insight into the importance of site parameters like water depth, soil stiffness, wave height, and wave period on fatigue loads. Results show a significant influence of water depth and wave period. This provides a basis for design optimization, load interpolation and uncertainty analysis in large wind farms. [ABSTRACT FROM AUTHOR]

In this paper it is investigated if, by coupling the catenary mooring systems of a number of turbines, the number of lines and anchors needed and subsequently the costs could be reduced and what kind of dynamic phenomena such a mooring system will exhibit. A row, triangular and rectangular arrangement of floating wind turbines is analyzed in terms of their cost saving potential and their dynamic properties in the frequency domain. The row arrangement is further investigated in the time domain, with a one dimensional simplified model. The most important forces to evaluate the station keeping performance, except current, are applied. These consist of irregular wave forces, employing the Morison equation, estimated wave drift and wind forces. Diffraction effects have been estimated by employing the McCamy-Fuchs theory. Four operational and a 50-year extreme load case have been applied. The results are showing that significant cost reductions of up to 60% in mooring system and 8% in total system costs could be achieved. The dynamic analysis shows the general feasibility of integrated mooring systems. No resonance problems seem to exist. However displacements are increasing with the number of floaters, and cost savings diminish for larger numbers of turbines, as the required diameters, lengths and costs of mooring chains increase. [ABSTRACT FROM AUTHOR]

Design optimization of offshore wind turbine support structures is an expensive task; due to the highly-constrained, non-convex and non-linear nature of the design problem. This paper presents an analytical gradient-based method to solve this problem in an efficient and effective way. The design sensitivities of the objective and constraint functions are evaluated analytically while the optimization of the structure is performed, subject to sizing, eigenfrequency, extreme load and fatigue load constraints. A case study was carried out for the OC4 jacket substructure to evaluate the method. Results show that an optimal jacket design with 52 percent structural mass reduction was attained in 27 iterations, while satisfying all design constraints under the simplified load cases used. Besides, it is shown that the analytical sensitivity analysis was more accurate and efficient than the often used finite difference approximations. It could avoid numerical artifacts that typically occur in the analysis of extreme load constraint sensitivities. [ABSTRACT FROM AUTHOR]

Abstract: Jacket substructures for offshore wind turbines show strong potentials in water depths from 25 up to 70m. A review of state-of-practice and enhanced state-of-the-art modeling of offshore wind turbine jackets is conducted regarding detailed joint properties. The state-of-the-art approach takes advantage of an accurate description of the local joint behavior by use of superelements, enabling more accurate load simulations. Studies conducted in the past highlighted both strong benefits as well as shortcomings of this approach, whereas the drawbacks were mainly related to the size of superelements and the application of local wave loading. This work develops a smart sizing for detailed joint models taking into account the loading and location of the jacket joints. A concept of local wave loading is presented as well. Advice on recommendable parameters is given and enables an optimized superelement application for jacket substructures. As an example the potential for fatigue load reduction is shown using the NREL offshore 5-MW baseline wind turbine and the OC4 reference jacket. The predicted fatigue lifetime was increased by about 15%. [Copyright &y& Elsevier]

Abstract: A multivariate Markov chain model is presented for generating sea state time series based on observed time series. The sea state is represented by the wave height, wind speed, wave period, wind direction and wave direction. Two ways of capturing the seasonal variation in the sea state parameters resulted in two distinct models. Their quality was assessed by comparing their statistical properties to what was obtained from observed time series. In one of the models (Model 1) transition probabilities were estimated separately for each month, while in the other (Model 2) a monthly transformation of the data were performed. Two different sea state data sets were considered in the validation, and it was found that both models compared favorably to the empirical data. It was concluded that Model 1 worked best for the longest data set considered, but was challenged by the shorter time series, where Model 2 worked best. Model 2 uses the observed data more efficiently, but relies on stationarity after removing the monthly variability. This seems to be a reasonable approximation for the data considered. The effect of changing the wave height resolution in the modeled time series was also investigated. [Copyright &y& Elsevier]

Abstract: Performing a dynamic analysis of an offshore wind turbine with an aero-elastic solver relies on the inclusion of a model to represent the behavior of the piled foundations. The most commonly used solution is the p-y method, which was developed for offshore oil and gas applications and has been extended to the offshore wind energy industry. There are several shortcomings with this method, however, which can affect the accuracy of wind turbine simulations. These shortcomings are identified and explained in this work. More advanced pile foundations models which account for many nonlinear behaviors ignored by the traditional p-y method have been developed in the past for applications unrelated to offshore wind turbines. These models can nevertheless be applied to offshore wind turbine simulations and are discussed herein. A proposed method for incorporating these so called ‘dynamic p-y’ models into wind turbine simulations is laid out and discussed. [Copyright &y& Elsevier]

Abstract: An alternative support structure for offshore wind turbines is presented that removes the need for an expensive transition piece and allows for significant savings in steel weight. The concept is based on replacing both the traditional wind turbine tower and the usual support structure with a single lattice tower that extends from the sea bottom to the rotornacelle- assembly. An overview is given of studies performed and results obtained for this design so far, of its advantages and disadvantages, and of future plans for improved automatic optimization of the design. Although it is diffcult to show the economic viability of the full-height lattice tower concept, due to the general problem of reliably quantifying fabrication and installation costs, the major reduction in steel weight makes this an attractive concept that should be given further consideration, especially for future offshore projects in deep waters. [Copyright &y& Elsevier]

Abstract: Among several possible support structure types for offshore wind turbines, a full-height lattice tower is one design option. Advantages of this design are the smaller amount of steel used for the structure compared to other concepts, and the possibility to install the whole structure in one operation. Based on the complexity of dynamic loadings on the support structure by wind and wave as well as operational loads, an initial lattice tower design with constant member dimensions over the tower height shows a large optimization potential and can be optimized section by section. This paper presents basic considerations for an iterative optimization approach and identifies sensitivities for the optimization process of a full-height lattice tower. It was found that an analysis with constant member dimensions over the tower height gives an indication about the required dimensions for an optimized design. [Copyright &y& Elsevier]

Abstract: This paper describes a new tool for the optimization of catenary mooring systems for floating wind turbines with a semi-submersible support structure. Each source of environmental loading -wind, current and waves -is spread over a range of compass directions, based upon probability distributions determined by meteorological and oceanographic measurements. Frequency domain analysis is applied to determine the linear response of the platform. Mean forces due to wind and current are determined to find the mean position of the platform and thereby the linearized mooring stiffness matrix. Subsequently, the stochastic loads from wind sea, ocean swell and turbulent wind are applied in the form of spectral loading matrices. The resulting mooring system design is site-specific, accounting for the directionality of environmental loads. A large number of different scenarios can be evaluated quickly and approximately. Hence the tool is useful for preliminary design of floating wind turbines.As an example application, a symmetric semi-submersible design with three columns is analyzed. Results for two sites in the North Sea, with different water depths and distinct directionality of environmental loads, are compared and indicate that spectral wind loads should be considered when designing mooring systems for floating wind turbines. [Copyright &y& Elsevier]

Abstract: Up to one third of the total cost of energy from offshore wind generation is contributed by operation and maintenance (O&M). Compared to its onshore counterpart, this fraction is significantly higher. Costs are not only caused by spare-parts and repair actions, but also by production losses due to downtime. The accessibility of a turbine in case of a failure is one main aspect affecting downtime. Therefore, a tool has been developed and implemented in MATLAB to simulate the operating phase of a wind farm with special emphasis toward the modeling of failures and repair. As an example application, a site at the UK east coast was chosen, and a few distinct scenarios were considered. Results include how sensitive availability changes with respect to changes in maintenance fleet and maintenance scheduling strategy. A quantification of potential cost savings due to an increase in availability is also stated. [Copyright &y& Elsevier]

Abstract: This paper investigates two different approaches for individual pitch control for wind turbines. The first one is a gain scheduled decentralised control design and the second one is a robust H∞ loop shaping control design. Both controllers work well in the region above rated wind speed, exhibiting a response that is mostly independent of wind speed. The investigation is conducted based on the NREL 5MW benchmark wind turbine. Turbine modeling and control is conducted in FAST and Simulink. [Copyright &y& Elsevier]

Abstract: The analysis of functional and effective brain connectivity forms an important tool for unraveling structure–function relationships from neurophysiological data. It has clinical applications, supports the formulation of hypotheses regarding the role and localization of functional processes, and is often an initial step in modeling. However, only a few of the commonly applied connectivity measures respect metric properties: reflexivity, symmetry, and the triangle inequality. This may hamper interpretation of findings and subsequent analysis. Connectivity indices obtained by metric measures can be seen as functional distances, and may be represented in Euclidean space by the methods of multidimensional scaling. We sketch some classes of measures that do allow for such a reconstruction, in particular the class of Wasserstein distances, and discuss their merits for interpreting cortical activity assessed by magnetoencephalography. In an application to magnetoencephalographic recordings during the execution of a bimanual task, the Wasserstein distances between relative circular variances indicated cortico-muscular synchrony as well as cross-talk between bilateral primary motor areas in the -band. [Copyright &y& Elsevier]

Under certain harsh environmental conditions, jacket structures supporting offshore wind turbines might be exposed to plunging breaking waves, causing slamming forces that affect the structural integrity and fatigue life. The slamming forces should thus be properly considered during the design, but a suitable force model specifically for jacket structures is currently in absence. In this study, a five-parameter force model is developed for estimating global slamming forces due to plunging breaking waves on jacket structures, based on statistical analyses of experimental data from the WaveSlam project. The force model is developed by considering a total of 176 individual breaking waves, under six wave conditions. For each individual breaking wave, the time history of the slamming force is calculated based on hammer test data in addition to wave test data, and the wave parameters are acquired from a wave elevation measurement. The acquired time histories and wave parameters are then used to determine the parameters involved in the force model, including two exponential parameters (i.e. α 1 and α 2 ) and three dimensionless coefficients for the expressions of wave-dependent parameters (i.e. duration coefficient ζ 1 , rising time coefficient ζ 2 , and peak force coefficient ζ 3 ). It is found that α 1 , α 2 , ζ 1 and ζ 2 are approximately constant, and ζ 3 follows a lognormal distribution. The quantile that determines ζ 3 should be carefully selected so as to provide a conservative prediction. A quantile of 95% is suggested in this paper, and it is found to be conservative based on the verification of the developed force model. Therefore, for a given sea state, this force model can give a deterministic and conservative prediction of the slamming force time history, regardless of the randomness of slamming forces. Challenges for the application of the force model are also addressed. [ABSTRACT FROM AUTHOR]

This study investigates the global slamming forces due to plunging breaking waves on a jacket structure, based on the statistical analysis of the experimental data from the WaveSlam project. Hammer tests and wave tests were conducted in the project, and the data are used to reconstruct the time series of the global slamming force by employing a method based on linear regression. The used wave test data were acquired under one wave condition. A total of 3910 force time series are reconstructed and analyzed statistically to reveal the characteristics of the slamming force. For each force time series, six parameters are introduced to describe it, including the peak force, duration, impulse and rising time, etc. The variability and correlation of these parameters are investigated. The distribution of these parameters is modeled with various probability distributions. The results show the high variability of the slamming force and the importance of statistical analyses. Based on these statistical analyses, the slamming coefficient is estimated from the peak force. For a curling factor of 0.4, the mean slamming coefficient is about 1.29. When considering one standard deviation around the mean, the slamming coefficient varies from 0.70 to 6.78 for a curling factor ranging from 0.1 to 0.5. A representative time series of wave slamming force is obtained by averaging the individual force time series. Accordingly, a 3-parameter triangular force model and a 5-parameter exponential force model are proposed to describe the development of the slamming force in time. [ABSTRACT FROM AUTHOR]

Abstract: Traditionally wind turbines are built in the upwind configuration, but the alternative of a downwind rotor has distinct advantages. A main issue with such a configuration is the tower shadow effect. The presence of the tower generates a complex wind field, consisting of an averaged velocity deficit, unsteady fluctuations from vortex shedding processes and turbulence. Since this tower shadow is commonly implemented using parametric steady wake models, the dynamic behaviour of the wake is not directly accounted for. The present paper introduces a general method for calibrating the parametric steady wake models and an effective turbulence intensity (accounting both for the velocity profile and the unsteady effects) from computational fluid dynamic simulations of the unsteady structural shadow. To demonstrate its potential the method is used in a blade fatigue comparison study. A 15 percent more flexible and lighter blade for the downwind mounted rotors showed a decrease in blade fatigue loads of three, four, and two percent compared to the conventional upwind mounted rotor on a monopile tower for the monopile tower and truss towers at 0 and 22.5 degrees, respectively. This example shows that the truss tower at 0 degree angle seems to result in the lowest blade fatigue loads. The proposed calibration method is completely general and can be used to obtain efficient, effective engineering models for the aerodynamic flow behind complex, multi-membered structures. [Copyright &y& Elsevier]

Abstract: The concept of breakpoint graph, known from the theory of sorting by reversal, has been successfully applied in the theory of gene assembly in ciliates. We further investigate its usage for gene assembly, and show that the graph allows for an efficient characterization of the possible orders of loop recombination operations (one of the three types of molecular operations that accomplish gene assembly) for a given gene during gene assembly. The characterization is based on spanning trees within a graph built upon the connected components in the breakpoint graph. We work in the abstract and more general setting of so-called legal strings. [Copyright &y& Elsevier]

Lifetime extension needs low-cost assessments that can identify the remaining useful life of offshore wind monopiles. A novel concept for load monitoring was developed that only needs strain gauges installed at one level of the support structure. Damage equivalent loads were calculated from strain measurements and extrapolated along a monopile using a regression algorithm. In this paper, the assumptions behind the load extrapolation algorithm were verified with two consecutive months of measurement data from an offshore wind park. The verification was performed separately for two offshore wind turbines. Both turbines had strain gauges installed at a distance of approximately 15 m and 25 m. Results show that monthly damage equivalent loads can be predicted with errors smaller than 4% based on measurement data only. Prediction using linear regression resulted in similar results for the total fatigue damage as a nonlinear k-nearest neighbor approach, but individual 10-min damage equivalent loads showed larger differences than for the more robust k-nearest neighbor algorithm, especially for small loads. These results are very promising and should motivate further research. • Strain gauges installed at one level of the transition piece can be used to monitor loads of the monopile also. • Measured loads can be extrapolated along a monopiles using aero-hydro-elastic simulations and a regression algorithm. • Verification with data from two offshore wind turbines confirms good performance of the load extrapolation algorithm. • Results are similar for two offshore wind turbines located in the same wind farm. • Results are insensitive to the distance between measurement and extrapolation location. [ABSTRACT FROM AUTHOR]

The two-phase flow CFD model REEF3D has been used for modeling waves breaking over a sloping seabed for a spilling and a plunging breaker. This model is based on Reynolds-averaged Navier–Stokes (RANS) equations with the level set method (LSM) for the free surface and k – ω model for turbulence. First, the characteristics and geometric properties of plunging breaking waves with different offshore wave steepnesses over slopes are examined and discussed. The study further explores the hydrodynamic characteristics of spilling and plunging breakers in terms of the wave height evolution and attenuation, horizontal and vertical velocity, free surface profile evolution, and the geometric properties during the development of the breaking process. The numerical results show a good agreement with experimental data in terms of free surface elevation, horizontal and vertical velocity, wave envelope and turbulent intensity for the spilling and plunging breakers. Results of numerical simulations describing the physical flow characteristics such as the formation of the forward overturning water jet, air pocket, splash-up, and the secondary wave during the breaking process are presented for both cases. For both cases, the physical flow process is found to have similar flow features, but the breaking process occurs at significantly different scales. [ABSTRACT FROM AUTHOR]

In large offshore wind farms fatigue loads on support structures can vary significantly due to differences and uncertainties in site conditions, making it necessary to optimize design clustering. An efficient probabilistic fatigue load estimation method for monopile foundations was implemented using Monte-Carlo simulations. Verification of frequency domain analysis for wave loads and scaling approaches for wind loads with time domain aero-elastic simulations lead to 95% accuracy on equivalent bending moments at mudline and tower bottom. The computational speed is in the order of 100 times faster than typical time domain tools. The model is applied to calculate location specific fatigue loads that can be used in deterministic and probabilistic design clustering. Results for an example wind farm with 150 turbines in 30–40 m water depth show a maximum load difference of 25%. Smart clustering using discrete optimization algorithms leads to a design load reduction of up to 13% compared to designs based on only the highest loaded turbine position. The proposed tool improves industry-standard clustering and provides a basis for design optimization and uncertainty analysis in large wind farms. [ABSTRACT FROM AUTHOR]

Design optimization of offshore wind turbine support structures is an expensive task due to the highly-constrained, non-convex and non-linear nature of the design problem. A good depth of detail in the problem formulation can give useful insights in the practical design process, but may also compromise the efficiency. This paper presents an analytical gradient-based method to solve the problem in an effective and efficient way. The design sensitivities of the objective and constraint functions are evaluated analytically, while the optimization procedure is performed in the time domain, subjected to sizing, eigenfrequency, extreme load and fatigue load constraints. A case study on the OC4 and UpWind jacket substructures show that the method was reliable and consistent in delivering superior efficiency and accuracy in the optimization study, as compared with the conventional finite difference approach. The global optimum was probably achieved in the design optimization process, where the large number of design constraints implemented can possibly be the blessing in disguise, as they seem to enable the optimizer to find the global optimum. Both the buckling and fatigue load constraints had significant influence over the design of tubular members and joints, while each component is oriented to maximize the utilization against the prescribed limit state functions. [ABSTRACT FROM AUTHOR]