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

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 approxim...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization Vol. 60; no. 5; pp. 2157 - 2176
Main Authors: Moustapha, Maliki, Sudret, Bruno
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2019
Springer Nature B.V
Subjects:
Approximation
Computational Mathematics and Numerical Analysis
Computer simulation
Covariance matrix
Design optimization
Engineering
Engineering Design
Evolutionary algorithms
Finite element method
Kriging interpolation
Mathematical models
Modular design
Monte Carlo simulation
Quadratic programming
Regression analysis
Reliability analysis
Review Article
Robustness (mathematics)
Search algorithms
Support vector machines
Theoretical and Applied Mechanics
Reliability-based design optimization
Surrogate modelling
Active learning
RBDO
Simulation methods
ISSN:1615-147X, 1615-1488
Online Access:Get full text
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Summary: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 generalization of the existing surrogate-assisted and simulation-based RBDO techniques using a unified framework 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 regression 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, is used in the optimization block. The comparison of the results to benchmark studies shows the effectiveness and efficiency of the proposed framework.
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ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-019-02290-y