On the consideration of uncertainty in design: optimization - reliability - robustness

Lelièvre, Nicolas; Beaurepaire, Pierre; Mattrand, Cécile; Gayton, Nicolas; Otsmane, Abdelkader

doi:10.1007/s00158-016-1556-5

Cited by 35 publications

(15 citation statements)

References 74 publications

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“…The design variables are based on problems to be solved, e.g., diameter or the number of coils in a string design as reported in the paper. Lelièvre et al (2016) investigated the possible robustness and reliability formulations with multiple educational codes provided in Scilab (a free and open-source software for numerical computations, ESI Group 2021) to deal with uncertainties in structural sizing optimization. The design variables depend on specific problems, e.g., member length and angle of the bracket structure.…”

Section: Sizing and Ground Structure Approachesmentioning

confidence: 99%

A comprehensive review of educational articles on structural and multidisciplinary optimization

Wang

Zhao

Zhou

et al. 2021

Struct Multidisc Optim

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Ever since the publication of the 99-line topology optimization MATLAB code (top99) by Sigmund in 2001, educational articles have emerged as a popular category of contributions within the structural and multidisciplinary optimization (SMO) community. The number of educational papers in the field of SMO has been growing rapidly in recent years. Some educational contributions have made a tremendous impact on both research and education. For example, top99 (Sigmund in Struct Multidisc Optim 21(2):120-127, 2001) has been downloaded over 13,000 times and cited over 2000 times in Google Scholar. In this paper, we attempt to provide a systematic and comprehensive review of educational articles and codes in SMO, including topology, sizing, and shape optimization and building blocks. We first assess the papers according to the adopted methods, which include density-based, level-set, ground structure, and more. We then provide comparisons and evaluations on the codes from several key aspects, including techniques, efficiency, usability, readability, environment, and compatibility. In addition, we conduct numerical experiments on the reviewed codes using the benchmark cantilever beam example to provide feedback on the overall user experience. With a systematic review and comparison, this paper aims to offer insights on the educational values and practicality for employing these codes. We try to provide not only guidance for beginners to approach various optimization methods, but also a dictionary to direct readers to effectively target the relevant codes and building blocks based on their demands. Finally, based on the findings in this review paper, we provide some perspectives and recommendations for future educational contributions.

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Section: Sizing and Ground Structure Approachesmentioning

confidence: 99%

A comprehensive review of educational articles on structural and multidisciplinary optimization

Wang

Zhao

Zhou

et al. 2021

Struct Multidisc Optim

View full text Add to dashboard Cite

show abstract

“…The main advantage of this formulation is its low computational cost, however, the obtained solution depends on the associated weights for the mean and the standard deviation. An example of this formulation can be found in [41,42].…”

Section: Optimization Under Uncertaintymentioning

confidence: 99%

Robustness and reliability investigations on a nonlinear energy sink device concept

Braydi

Gogu

Paredes

2020

Mechanics & Industry

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In this work, the reliability and robustness of a nonlinear energy sink device concept are investigated. The system is studied and optimized in deterministic and probabilistic cases. It is also studied under various types of uncertainty modelings with different reliability based robust design optimization formulations. The obtained results reveal the sensitivity of the device to the input uncertainties. The optimal designs obtained with the formulation under uncertainties are very different from the deterministic optimal design. New system configurations are obtained which ensure robust, highly reliable designs. In addition, a comparison is made between the different formulations and a conclusion is drawn about the suitable formulations for such a problem.

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“…It is then crucial to be able to take into account aleatoric uncertainties in optimisation problems. This consideration is called robust optimisation, or also robust design in [11], or optimisation under uncertainties [12,13,14]. Furthermore, the distinction is 2 sometimes made between stochastic optimisation and robust optimisation, depending on the knowledge available on the aleatoric uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Robust calibration of numerical models based on relative regret

Trappler¹,

Arnaud²,

Vidard³

et al. 2021

Journal of Computational Physics

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Classical methods of calibration usually imply the minimisation of an objective function with respect to some control parameters. This function measures the error between some observations and the results obtained by a numerical model. In the presence of uncontrollable additional parameters that we model as random inputs, the objective function becomes a random variable, and notions of robustness have to be introduced for such an optimisation problem. In this paper, we are going to present how to take into account those uncertainties by defining the relative-regret. This quantity allow us to compare the value of the objective function to its best performance achievable given a realisation of the random additional parameters. By controlling this relative-regret using a probabilistic constraint, we can then define a new family of estimators, whose robustness with respect to the random inputs can be adjusted.

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On the consideration of uncertainty in design: optimization - reliability - robustness

Cited by 35 publications

References 74 publications

A comprehensive review of educational articles on structural and multidisciplinary optimization

A comprehensive review of educational articles on structural and multidisciplinary optimization

Robustness and reliability investigations on a nonlinear energy sink device concept

Robust calibration of numerical models based on relative regret

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