Fully decoupled reliability-based optimization of linear structures subject to Gaussian dynamic loading considering discrete design variables
•Optimal design under uncertainty considering discrete design variables is addressed.•Optimization and reliability analyses are fully decoupled.•Application of standard integer programming algorithms becomes feasible. Reliability-based optimization (RBO) offers the possibility of finding an optimal...
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| Published in | Mechanical systems and signal processing Vol. 156; p. 107616 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin
Elsevier Ltd
01.07.2021
Elsevier BV |
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| Abstract | •Optimal design under uncertainty considering discrete design variables is addressed.•Optimization and reliability analyses are fully decoupled.•Application of standard integer programming algorithms becomes feasible.
Reliability-based optimization (RBO) offers the possibility of finding an optimal design for a system according to a prescribed criterion while explicitly taking into account the effects of uncertainty. However, due to the necessity of solving simultaneously a reliability problem nested in an optimization procedure, the corresponding computational cost is usually high, impeding the applicability of the methods. This computational cost is even further enlarged when one or several design variables must belong to a discrete set, due to the requirement of resorting to integer programming optimization algorithms. To alleviate this issue, this contribution proposes a fully decoupled approach for a specific class of problems, namely minimization of the failure probability of a linear system subjected to an uncertain dynamic load of the Gaussian type, under the additional constraint that the design variables are integer-valued. Specifically, by using the operator norm framework, as developed by the authors in previous work, this paper shows that by reducing the RBO problem with discrete design variables to the solution of a single deterministic optimization problem followed by a single reliability analysis, a large gain in numerical efficiency can be obtained without compromising the accuracy of the resulting optimal design. The application and capabilities of the proposed approach are illustrated by means of three examples. |
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| AbstractList | Reliability-based optimization (RBO) offers the possibility of finding an optimal design for a system according to a prescribed criterion while explicitly taking into account the effects of uncertainty. However, due to the necessity of solving simultaneously a reliability problem nested in an optimization procedure, the corresponding computational cost is usually high, impeding the applicability of the methods. This computational cost is even further enlarged when one or several design variables must belong to a discrete set, due to the requirement of resorting to integer programming optimization algorithms. To alleviate this issue, this contribution proposes a fully decoupled approach for a specific class of problems, namely minimization of the failure probability of a linear system subjected to an uncertain dynamic load of the Gaussian type, under the additional constraint that the design variables are integer-valued. Specifically, by using the operator norm framework, as developed by the authors in previous work, this paper shows that by reducing the RBO problem with discrete design variables to the solution of a single deterministic optimization problem followed by a single reliability analysis, a large gain in numerical efficiency can be obtained without compromising the accuracy of the resulting optimal design. The application and capabilities of the proposed approach are illustrated by means of three examples. •Optimal design under uncertainty considering discrete design variables is addressed.•Optimization and reliability analyses are fully decoupled.•Application of standard integer programming algorithms becomes feasible. Reliability-based optimization (RBO) offers the possibility of finding an optimal design for a system according to a prescribed criterion while explicitly taking into account the effects of uncertainty. However, due to the necessity of solving simultaneously a reliability problem nested in an optimization procedure, the corresponding computational cost is usually high, impeding the applicability of the methods. This computational cost is even further enlarged when one or several design variables must belong to a discrete set, due to the requirement of resorting to integer programming optimization algorithms. To alleviate this issue, this contribution proposes a fully decoupled approach for a specific class of problems, namely minimization of the failure probability of a linear system subjected to an uncertain dynamic load of the Gaussian type, under the additional constraint that the design variables are integer-valued. Specifically, by using the operator norm framework, as developed by the authors in previous work, this paper shows that by reducing the RBO problem with discrete design variables to the solution of a single deterministic optimization problem followed by a single reliability analysis, a large gain in numerical efficiency can be obtained without compromising the accuracy of the resulting optimal design. The application and capabilities of the proposed approach are illustrated by means of three examples. |
| ArticleNumber | 107616 |
| Author | Faes, Matthias G.R. Valdebenito, Marcos A. |
| Author_xml | – sequence: 1 givenname: Matthias G.R. surname: Faes fullname: Faes, Matthias G.R. email: matthias.faes@kuleuven.be organization: KU Leuven, Department of Mechanical Engineering, Technology campus De Nayer, Jan De Nayerlaan 5, St.-Katelijne-Waver, Belgium – sequence: 2 givenname: Marcos A. surname: Valdebenito fullname: Valdebenito, Marcos A. organization: Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, 2562340 Viña del Mar, Chile |
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| Keywords | Gaussian loading Decoupling First excursion probability Linear structure Operator norm |
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| Snippet | •Optimal design under uncertainty considering discrete design variables is addressed.•Optimization and reliability analyses are fully decoupled.•Application of... Reliability-based optimization (RBO) offers the possibility of finding an optimal design for a system according to a prescribed criterion while explicitly... |
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| SubjectTerms | Algorithms Computational efficiency Computing costs Decoupling Design optimization Dynamic loads First excursion probability Gaussian loading Integer programming Linear structure Operator norm Reliability analysis |
| Title | Fully decoupled reliability-based optimization of linear structures subject to Gaussian dynamic loading considering discrete design variables |
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