A two-step procedure for time-dependent reliability-based design optimization involving piece-wise stationary Gaussian processes

Abstract

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.

Quantifying and clustering the wake-induced perturbations within a wind farm for load analysis

“…Wake models allow us to simulate the wind conditions' distribution at each turbine, however, the RBD step is too costly to be performed for each turbine. For further details regarding the RBD, one may refer to the work of [7,8,9,10,11], proposing several approaches to reduce the computational cost of this step. In order to speed up the RBD at the scale of a wind farm, the present work aims at building clusters of WT similarly affected by the wake.…”