Abstract
Abstract. The need for cost-effective support structure designs for offshore wind turbines has led to continued interest in the development of design optimization methods. So far, almost no studies have considered the effect of uncertainty, and hence probabilistic constraints, on the support structure design optimization problem. In this work, we present a general methodology that implements recent developments in gradient-based design optimization, in particular the use of analytical gradients, within the context of reliability-based design optimization methods. Gradient-based optimization is typically more efficient and has more well-defined convergence properties than gradient-free methods, making this the preferred paradigm for reliability-based optimization where possible. By an assumed factorization of the uncertain response into a design-independent, probabilistic part and a design-dependent but completely deterministic part, it is possible to computationally decouple the reliability analysis from the design optimization. Furthermore, this decoupling makes no further assumption about the functional nature of the stochastic response, meaning that high-fidelity surrogate modeling through Gaussian process regression of the probabilistic part can be performed while using analytical gradient-based methods for the design optimization. We apply this methodology to several different cases based around a uniform cantilever beam and the OC3 Monopile and different loading and constraint scenarios. The results demonstrate the viability of the approach in terms of obtaining reliable, optimal support structure designs and furthermore show that in practice only a limited amount of additional computational effort is required compared to deterministic design optimization. While there are some limitations in the applied cases, and some further refinement might be necessary for applications to high-fidelity design scenarios, the demonstrated capabilities of the proposed methodology show that efficient reliability-based optimization for offshore wind turbine support structures is feasible.
Highlights
Offshore wind energy is becoming an increasingly competitive alternative to the traditional land-based wind farms
By a very particular formulation of the probabilistic constraints used for the support structure design optimization, we demonstrate how these constraints can remain analytically differentiable with respect to the design variables while at the same time using a surrogate model for the stochastic variation of the response
For the reliability-based design optimization (RBDO) formulation based on performance measure approach (PMA), the limit state functions represented by Eqs. (27) and (29) can be directly used, with the understanding that Ftot, f, MKS and fy become probabilistic quantities
Summary
Offshore wind energy is becoming an increasingly competitive alternative to the traditional land-based wind farms. A study founded on gradient-based optimization that does consider a more comprehensive set of loading conditions but does not utilize analytical sensitivities was performed by Häfele et al (2019) They used a Gaussian process surrogate model to simplify the response, making the analysis computationally feasible. In addition to incorporating more advanced optimization methods to the RBDO problem than has been done previously for OWT support structure design, the current approach can be seen as a natural middle ground between, on the one hand, the simplified analytical limit state formulations and, on the other hand, the completely surrogate-model-based limit state formulations, the two most commonly used approaches in reliability analysis and RBDO for OWTs previously. The remaining sections of the paper include a presentation and discussion of the results, in the results section; more detailed treatment of a few points of interest, in the further discussion section; and a summary and final thoughts, in the conclusions
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