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

• Published in: Structural and multidisciplinary optimization Vol. 65; no. 4
• Main Authors: Cousin, Alexis, Garnier, Josselin, Guiton, Martin, Munoz Zuniga, Miguel
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2022; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Design optimization; Engineering; Engineering Design; Environmental Sciences; Extreme value theory; Extreme values; Gaussian process; Harmonic oscillators; Mathematics; Random processes; Reliability; Research Paper; Theoretical and Applied Mechanics; Time dependence; Wind turbines; Adaptive kriging; Extreme value theory; Reliability-based design optimization (RBDO); Monte Carlo; Active learning; Time-dependent reliability; Adaptive Kriging; Reliability-Based Design Optimization (RBDO); Extreme Value Theory; Time-Dependent Reliability; Active Learning
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-022-03212-1

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.