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For some applications in structural optimization, it is required to have constraints on the extreme loads that represent long term loading conditions. This usually involves a statistical extrapolation procedure that fits maxima from simulated load time series to short term extreme value distributions and then extrapolates to an n-year return value. Often such situations are highly simplified because of the apparent complexity involved in evaluating the sensitivity of such constraints. However, such simplification is not necessary. In this study, we present a method to evaluate the sensitivities of such extrapolated extreme load constraints in a semi-analytical way. The method uses the implicit function theorem to obtain local derivatives at the points defined by the solution of the maximum likelihood estimate that is used to calculate the parameters of the short term extreme value distributions. Comparing with high accuracy finite difference estimates, the method is shown to give reasonably accurate values. We also demonstrate how the method can be used to estimate the uncertainty of the estimated n-year return value caused by uncertainty in both the maximum likelihood estimate and inherent uncertainties in the data. The method then is applied to a simple optimization example and shown to perform very well compared with using finite difference estimates for the sensitivities. Finally, we note that the method is in principle fairly general and could be applied to similar problems that do not specifically involve statistical extrapolation. [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]

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]

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]