In this paper, we seek to minimize the cost of the anchoring system of a floating offshore wind turbine under reliability constraints. Taking into account the uncertainties on the model, on the resistance threshold and on the environmental conditions implies constraints expressed as probabilities depending on random vectors and a piecewise stationary Gaussian process. The main difficulty of the studied problem is to compute these probabilities since reliability methods require many calls to the simulator of the system. We propose in this paper a two-step methodology allowing to solve the optimization problem with a reasonable number of calls to the simulator. First, we exploit the properties of the problem to reformulate the constraints into easier to compute ones. Then we propose a new approach based on adaptive kriging well suited to the reformulated problem: AK-ECO.
We consider in this paper a time-dependent reliability-based design optimization (RBDO) problem with constraints involving the maximum and/or the integral of a random process over a time interval. We focus especially on problems where the process is a stationary or a piece-wise stationary Gaussian process. A two-step procedure is proposed to solve the problem. First, we use ergodic theory and extreme value theory to reformulate the original constraints into timeindependent ones. We obtain an equivalent RBDO problem for which classical algorithms perform poorly. The second step of the procedure is to solve the reformulated problem with a new method introduced in this paper and based on an adaptive kriging strategy well suited to the reformulated constraints called AK-ECO for Adaptive Kriging for Expectation Constraints Optimization. The procedure is applied to two toy examples involving a harmonic oscillator subjected to random forces. It is then applied to an optimal design problem for a floating offshore wind turbine.
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