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An approach to robust optimization of impact problems using random samples and meta-modelling
Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
Norwegian University of Science and Technology, Trondheim.
Linköping University, Department of Management and Engineering, Solid Mechanics . Linköping University, The Institute of Technology.
2010 (English)In: International Journal of Impact Engineering, ISSN 0734-743X, Vol. 37, no 6, 723-734 p.Article in journal (Refereed) Published
Abstract [en]

Conventionally optimized structures may show a tendency to be sensitive to variations, for instance in geometry and loading conditions. To avoid this, research has been carried out in the field of robust optimization where variations are taken into account in the optimization process. The overall objective is to create solutions that are optimal both in the sense of mean performance and minimum variability. This work presents an alternative approach to robust optimization, where the robustness of each design is assessed through multiple sampling of the stochastic variables at each design point. Meta-models for the robust optimization are created for both the mean value and the standard deviation of the response. Furthermore, the method is demonstrated on an analytical example and an example of an aluminium extrusion with quadratic cross-section subjected to axial crushing. It works well for the chosen examples and it is concluded that the method is especially well suited for problems with a large number of random variables, since the computational cost is essentially independent of the number of random variables. In addition, the presented approach makes it possible to take into consideration variations that cannot be described with a variable. This is demonstrated in this work by random geometrical perturbations described with the use of Gaussian random fields.

Place, publisher, year, edition, pages
2010. Vol. 37, no 6, 723-734 p.
Keyword [en]
Robust optimisation, geometric imperfections, meta model, robustness
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:liu:diva-15478DOI: 10.1016/j.ijimpeng.2009.07.002OAI: oai:DiVA.org:liu-15478DiVA: diva2:117169
Projects
ROBDES
Note
Tidigare titel: Robust optimisation methodology using random samples and meta modelling Available from: 2008-11-11 Created: 2008-11-11 Last updated: 2011-08-24Bibliographically approved
In thesis
1. Robust design: Accounting for uncertainties in engineering
Open this publication in new window or tab >>Robust design: Accounting for uncertainties in engineering
2008 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns optimization of structures considering various uncertainties. The overall objective is to find methods to create solutions that are optimal both in the sense of handling the typical load case and minimising the variability of the response, i.e. robust optimal designs.

Traditionally optimized structures may show a tendency of being sensitive to small perturbations in the design or loading conditions, which of course are inevitable. To create robust designs, it is necessary to account for all conceivable variations (or at least the influencing ones) in the design process.

The thesis is divided in two parts. The first part serves as a theoretical background to the second part, the two appended articles. This first part includes the concept of robust design, basic statistics, optimization theory and meta modelling.

The first appended paper is an application of existing methods on a large industrial example problem. A sensitivity analysis is performed on a Scania truck cab subjected to impact loading in order to identify the most influencing variables on the crash responses.

The second paper presents a new method that may be used in robust optimizations, that is, optimizations that account for variations and uncertainties. The method is demonstrated on both an analytical example and a Finite Element example of an aluminium extrusion subjected to axial crushing.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2008. 34 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1389
Keyword
Robust optimisation, robust design, robustness, meta model, sensitivity analysis
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-15479 (URN)LIU–TEK–LIC–2008:47 (Local ID)978-91-7393-743-6 (ISBN)LIU–TEK–LIC–2008:47 (Archive number)LIU–TEK–LIC–2008:47 (OAI)
Presentation
ACAS, Campus Valla, Linköpings Universitet, Linköping (Swedish)
Opponent
Supervisors
Projects
ROBDES
Available from: 2009-04-03 Created: 2008-11-11 Last updated: 2009-05-07Bibliographically approved
2. Robust optimisation of structures: Evaluation and incorporation of variations in simulation based design
Open this publication in new window or tab >>Robust optimisation of structures: Evaluation and incorporation of variations in simulation based design
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns the robustness of structures considering various uncertainties. The overall objective is to evaluate and develop simulation based design methods in order to find solutions that are optimal both in the sense of handling typical load cases and minimising the variability of the response, i.e. robust optimal designs. Conventionally optimised structures may show a tendency of being sensitive to small perturbations in the design or loading conditions. These variations are of course inevitable. To create robust designs, it is necessary to account for all conceivable variations (or at least the influencing ones) in the design process. The thesis is divided into two parts. The first part serves as a theoretical background for this work. It includes introductions to the concept of robust design, basic statistics, optimisation theory and metamodelling. The second part consists of five appended papers on the topic.

The first and third papers focuse on the evaluation of robustness, given some dispersions in the input data. Established existing methods are applied, and for paper three, comparisons with experimentally evaluated dispersions on a larger system are made.

The second and fourth paper introduce two new approaches to perform robust optimisation, i.e. optimisations where the mean performance and the robustness in the objectives are simultaneously optimised. These methods are demonstrated both on an analytical example and on a Finite Element model design example. The fifth paper studies the variations in mechanical properties between several different batches of the same steel grade. A material model is fitted to each batch of material, whereby dispersions seen in test specimens are transferred to material model parameter variations. The correlations between both test and material model parameters are studied.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2011. 39 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1382
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-70199 (URN)978-91-7393-129-8 (ISBN)
Public defence
2011-09-23, C3, Hus C, Campus Valla, Linköpings universitet, Linköping, 10:15 (Swedish)
Opponent
Supervisors
Available from: 2011-08-24 Created: 2011-08-24 Last updated: 2011-09-07Bibliographically approved

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Lönn, DavidNilsson, Larsgunnar

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