A Two-Step Procedure for Time-Dependent Reliability-Based Design Optimization Involving Piece-Wise Stationary Gaussian Processes

Alexis Cousin (1) , Josselin Garnier (2, 3) , Martin Guiton (1) , Miguel Munoz Zuniga (1)

1 IFPEN - IFP Energies nouvelles
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 ASCII - Analyse d’interactions stochastiques intelligentes et coopératives

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 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.

Mots clés: Reliability-Based Design Optimization (RBDO); Time-Dependent Reliability; Extreme Value Theory; Adaptive Kriging; Active Learning; Monte Carlo

Domaines: Sciences de l'environnement; Mathématiques [math]

Alexis Cousin, Josselin Garnier, Martin Guiton, Miguel Munoz Zuniga. A Two-Step Procedure for Time-Dependent Reliability-Based Design Optimization Involving Piece-Wise Stationary Gaussian Processes. Structural and Multidisciplinary Optimization, 2022, 65 (4), pp.120. ⟨10.1007/s00158-022-03212-1⟩. ⟨hal-03641110⟩