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Robust design: Accounting for uncertainties in engineering
Linköping University, Department of Management and Engineering. Linköping University, The Institute of Technology. (Hållfasthetslära)
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 [en]
Robust optimisation, robust design, robustness, meta model, sensitivity analysis
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:liu:diva-15479Local ID: LIU–TEK–LIC–2008:47ISBN: 978-91-7393-743-6 (print)OAI: oai:DiVA.org:liu-15479DiVA: diva2:117324
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
List of papers
1. Finite element based robustness study of a truck cab subjected to impact loading
Open this publication in new window or tab >>Finite element based robustness study of a truck cab subjected to impact loading
2009 (English)In: International Journal of Crashworthiness, ISSN 1358-8265, Vol. 14, no 2, 111-124 p.Article in journal (Refereed) Published
Abstract [en]

Optimised designs have a tendency of being sensitive to variations. It is therefore of great importance to analyse this sensitivity to assure that a design is robust, i.e. sufficiently insensitive to variations. To analyse robustness, variations are introduced in model parameters and their influences on simulation responses are studied. This is usually achieved using the Monte Carlo method. Though, due to the large number of simulations needed, the Monte Carlo method is very costly for problems requiring a long computing time. Therefore, in this work a meta model-based Monte Carlo method is used to evaluate the robustness of a vehicle structure. That is, the Monte Carlo analysis is performed on a surface approximation of the true response, over the domain of interest. The methodology used is to first identify the variables that influence the response the most, referred to as a screening, using simple linear response surfaces. This is followed by a more detailed sensitivity analysis using only the identified variables and a quadratic response surface, thereby incorporating second order effects. A truck cab model exposed to a pendulum impact load is used as an evaluation of this method, and the important variables and their influence on the response are identified. The effect of including results from forming simulations is also evaluated using the truck cab model. Variations are introduced before forming simulations, thereby taking forming effects into account in the sensitivity analysis. The method was found to be a good tool to identify important dispersion variables and to give an approximate result of the total dispersion, all with a reasonable amount of simulations.

Place, publisher, year, edition, pages
Taylor & Francis, 2009
Keyword
Monte Carlo, meta model, robust design, response surface method, sensitivity analysis, robustness
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-15474 (URN)10.1080/13588260802412992 (DOI)
Projects
ROBDES
Note
On the day of the defence date the status of this article was: Accepted.Available from: 2008-11-11 Created: 2008-11-11 Last updated: 2011-09-19Bibliographically approved
2. An approach to robust optimization of impact problems using random samples and meta-modelling
Open this publication in new window or tab >>An approach to robust optimization of impact problems using random samples and meta-modelling
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.

Keyword
Robust optimisation, geometric imperfections, meta model, robustness
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-15478 (URN)10.1016/j.ijimpeng.2009.07.002 (DOI)
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

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Lönn, David

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