https://ifp.hal.science/hal-03641110Cousin, AlexisAlexisCousinIFPEN - IFP Energies nouvelles - IFPEN - IFP Energies nouvellesGarnier, JosselinJosselinGarnierCMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche ScientifiqueASCII - Analyse d’interactions stochastiques intelligentes et coopératives - CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en AutomatiqueGuiton, MartinMartinGuitonIFPEN - IFP Energies nouvelles - IFPEN - IFP Energies nouvellesMunoz Zuniga, MiguelMiguelMunoz ZunigaIFPEN - IFP Energies nouvelles - IFPEN - IFP Energies nouvellesA Two-Step Procedure for Time-Dependent Reliability-Based Design Optimization Involving Piece-Wise Stationary Gaussian ProcessesHAL CCSD2022Reliability-Based Design Optimization (RBDO)Time-Dependent ReliabilityExtreme Value TheoryAdaptive KrigingActive LearningMonte Carlo[SDE] Environmental Sciences[MATH] Mathematics [math]Belli, Catherine2022-04-14 10:15:432023-06-08 03:26:502022-04-15 09:46:16enJournal articleshttps://ifp.hal.science/hal-03641110/document10.1007/s00158-022-03212-1application/pdf1We 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 time-independent 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.