Optimal design of offshore wind turbine support structures under uncertainty - Towards a framework for practical reliability-based design optimization
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As part of efforts to reduce the costs of offshore wind energy, optimization methods for the design of support structures are an important contribution. In order to account for the uncertainties in the design process without using conservative safety factors, detailed probabilistic modeling needs to be integrated into design optimization. The present project seeks to develop methodology for optimal design under uncertainty that can negotiate the demands for accurate design with the requirements for use in a practical setting. This problem is multi-faceted: Efficient and accurate optimization and probabilistic methods are both required and even with these in place, a method for making the basic safety assessments of the support structure designs more efficient is also needed. Ideally, all of these elements should fit together as part of a larger framework. An overarching theme for the work is to build on state-of-the-art deterministic optimization methods for offshore wind turbine support structures. These methods use gradient-based procedures with analytical sensitivities in order to make the optimization both more accurate and efficient than relevant alternatives. The first study in the present work proposes an extension of the state-of-the-art methods by showing how the same idea can be formulated for extreme load constraints based on statistical extrapolation to n-year return values. Analytical sensitivities for these constraints can be formulated by using the implicit function theorem. It is shown that this leads to accurate predictions for the gradients. To address the computational issue induced by the large number of environmental states that have to be simulated for lifetime fatigue assessment, two different methods are proposed. These are based on the idea that, since the intended use is within optimization, it makes sense to perform one full assessment for the initial support structure design and to then use this information to derive reduced sets of states for estimating the lifetime damage. The first method is based on simply sorting the states by how much they contribute to the total fatigue sum and then assuming that the error in using only these states is invariant under changes to the design. The second method is based on deriving a fatigue damage distribution and using this as a sampling distribution, assumed invariant, for an importance sampling Monte Carlo method. Both methods give large reductions in the required number of simulations while giving estimation errors of no more than a few percent. Finally, a method for reliability-based design optimization of offshore wind turbine support structures is proposed. This method facilitates the use of analytical sensitivities and an overall efficient probabilistic assessment by factoring the stochastic response into a design-dependent, deterministic part and a design-independent, probabilistic part. Surrogate modeling for the design-independent part then ensures that (after fitting) no additional simulations are required for the probabilistic assessment. The method is tested on several cases and it is shown that very little computational effort is added compared to the equivalent deterministic optimization procedure. It is also shown how all the work in this thesis fits together and could be unified into a practical framework for optimal design under uncertainty.