Surrogate-assisted reliability-based design optimization: a survey and a unified modular framework

Abstract

Reliability-based design optimization (RBDO) is an active field of research with an ever increasing number of contributions. Numerous methods have been proposed for the solution of RBDO, a complex problem that combines optimization and reliability analysis. Classical approaches are based on approximation methods and have been classified in review papers. In this paper, we first review classical approaches based on approximation methods such as FORM, and also more recent methods that rely upon surrogate modelling and Monte Carlo simulation.We then propose a general framework for the solution of RBDO problems that includes three independent blocks, namely adaptive surrogate modelling, reliability analysis and optimization.These blocks are non-intrusive with respect to each other and can be plugged independently in the framework. After a discussion on numerical considerations that require attention for the framework to yield robust solutions to various types of problems, the latter is applied to three examples (using two analytical functions and a finite element model). Kriging and support vector machines together with their own active learning schemes are considered in the surrogate model block. In terms of reliability analysis, the proposed framework is illustrated using both crude Monte Carlo and subset simulation. Finally, the covariance-matrix adaptation -evolution scheme (CMA-ES), a global search algorithm, or sequential quadratic programming (SQP), a local gradient-based method, are used in the optimization block. The comparison of the results to benchmark studies show the effectiveness and efficiency of the proposed framework. of risk-based or life-cycle cost optimization (Beck and Gomes, 2012;Frangopol and Maute, 2003).Alternative formulations for RBDO have henceforth emerged. One, for instance, consists in maximizing the reliability, or equivalently minimizing the failure probability, under given cost constraints (See for instance Kuschel and Rackwitz (1997); Royset et al. (2001); Taflanidis and Beck (2008)).The approach we consider in this paper, which is also the prevalent in current research, consists in minimizing an initial cost under some probabilistic constraints (Hilton and Feigen, 1960). Let d ∈ R M d be an M d −dimensional vector defining some design parameters of the structure. In the presence of uncertainties, the variability of these parameters can be described by introducing random variables X ∈ X ⊂ R M d ∼ f X|d . These variables are called design parameters with uncertainty, or by slight abuse, random design variables in the sequel. In some cases, design parameters are purely deterministic. To simplify the notation, they are equally considered as X (d) at this stage, where the related random variables would simply have a

Structural System Reliability: Overview of Theories and Applications to Optimization

“…Various surrogate models (Sudret and Der Kiureghian 2002;Papadrakakis and Lagaros 2002;Bichon et al 2008) have been used for the reliability analysis in RBDO. Moustapha and Sudret (2019) surveyed surrogate-based RBDO and benchmark studies on computational efficiency and effectiveness.…”

“…The decoupling-based RBDO generally is more efficient than the double-loop formulation, but more computationally expensive than the single-loop formulation. Furthermore, the computational efficiency of a surrogate-based approach in RBDO and of others was illustrated using numerical examples by Moustapha and Sudret (2019).…”

Chance Constraint Optimization of a Complex System: Application to the Fatigue Design of a Floating Offshore Wind Turbine Mooring System

“…However, it is still time consuming to estimate the reformulated constraints of (9) with a Monte Carlo method. Over the last decades, many approaches have been developed to solve optimization problems with failure constraints among which methods based on an adaptive kriging (AK) strategy [12,13,14]. These methods rely on building a kriging model of the performance functions and enrich this metamodel with a learning criterion.…”

A new method for earthquake-induced damage identification in historic masonry towers combining OMA and IDA

“…The complex geometry and spatial distribution of different masonry materials of most historic buildings coupled with a large number of simulations needed for solving the minimization problem determine an unsustainable computational burden posing major limitations in the real-time SHM practice. Surrogate models (SM) have been recently approached as rapid and computationally efficient tools to reproduce the behavior of a time-demanding numerical model, enabling damage identification through continuous model updating compatible with continuous SHM systems (Moustapha and Sudret 2019;Liu et al 2020;Pepi et al 2020;Micheli et al 2020a, b). Some experiences in the literature can be mentioned about the application of surrogate-based model updating of historic structures (Cabboi et al 2017;Torres et al 2017;García-Macías et al 2021Venanzi et al 2020).…”