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Design of Experiments - A- D- I- S-optimality
Tekniska Högskolan, Högskolan i Jönköping, JTH. Forskningsområde Simulering och optimering. (Simulering och optimering)
2010 (English)In: Proceedings of the 2nd International Conference on Engineering Optimization, 2010Conference paper, Published paper (Refereed)
Abstract [en]

A metamodel approximates an original model with a model that is more efficient and yields information about the response. Response surfaces and Kriging approximations are such metamodels. A metamodel is based on evaluations of the original function at some design points, where the choice of design points is crucial. The design points constitute the design of experiments (DoE). There are many methodologies of how to chose the DoE. In this work A-, D-, I- and S-optimal DoEs are generated and evaluated. The optimal DoEs are obtained by solving the following mathematical optimization problems:

  • A-otimality. Minimize the average variance of the model coefficient estimates.
  • D-otimality. Minimize the generalized variance of the model coefficient estimates.
  • I-otimality. Minimize the average of the expected variance (taken as an integral)over the region of prediction.
  • S-otimality. Maximize the geometric mean of the distances between nearest neighborsof the design points.

The optimization problems are solved by a hybrid method which consists of a genetic algorithm and sequential linear programming. The different optimality criteria are evaluated for a number of test cases in order to show the characteristics of each criteria. Regular as well as non-regular design spaces are considered. Furthermore, Kriging approximations of the well known Rosenbrock’s banana function are generated to evaluate the accuracy of a resulting metamodel based on the different DoEs. Results from the test cases show that D-optimal DoEs tend to place more design points close to the boundary of the design space compared to A- and I-optimality. It is also shown that A- D- and I-optimal DoEs often include duplicate design points which is not beneficial for a deterministic response, but might be beneficial for non-deterministic responses. Concerning S-optimal DoEs the design points are evenly distributed over the entire design space and no duplicates occur. Furthermore, the S-optimal DoE generates the best fitted Kriging approximation of the Rosenbrock’s banana function.

Place, publisher, year, edition, pages
2010.
Keyword [en]
A- D- I- S-optimality, Design of experiments (DoE), Response surface, Kriging, Genetic algorithm, Sequential linear programming
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-72346OAI: oai:DiVA.org:liu-72346DiVA: diva2:459262
Conference
2nd International Conference on Engineering Optimization. September 6 - 9, Lisbon, Portugal
Available from: 2011-01-17 Created: 2011-11-25 Last updated: 2011-11-25Bibliographically approved
In thesis
1. Robustness Analysis of Residual Stresses in Castings
Open this publication in new window or tab >>Robustness Analysis of Residual Stresses in Castings
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is about robustness analysis of residual stresses in castings. This topic includes the analysis of residual stresses in castings and the robustness analysis itself, both covered in the thesis.

Residual stresses are important when designing casted components. For instance, the residual stress state after casting might affect the fatigue life, facilitate crack propagation and cause spring-back related problems when a casted component is machined or used. Examples of components where such problems are recognized are stamping dies and brake discs, both considered in the thesis. Residual stresses in castings are simulated by finite element analysis in this thesis. A sequential un-coupled approach is used where a thermal analysis of the solidification and cooling generates a temperature history. Then a quasi-static structural analysis is performed, driven by the temperature history. During the structural analysis residual stresses are developed due to different cooling rates in combination with plasticity. For comparison, measurements of residual stresses in castings have also been performed. The agreement between analyses and measurements is satisfactory.

In a residual stress analysis there are several random variables such as process, geometrical and material parameters. Usually those random variables are assumed to be deterministic and their nominal values are used. It can be beneficial to include the variation of the random variables in analysis of residual stresses. For that purpose robustness analysis of the residual stresses are performed in this thesis. In some of the appended papers the robustness is evaluated with respect to variation in e.g. Young’s modulus, yield strength and hardening, thermal expansion coefficient, geometric dimensions and time in mould of the casting. The robustness analyses are performed by using metamodels as surrogates to the finite element model, due to the computational expensiveness of the residual stress analyses. Conventional regression models, Kriging approximations and an optimal polynomial regression model, proposed in one of the appended papers, are metamodels used in the thesis. When a metamodel is established the choice of the design of experiments can be crucial. The generation of the design of experiments is also investigated in the thesis. For instance, a hybrid method constituted by a genetic algorithm and sequential linear programming is proposed for the generation of optimal design of experiments. A-, D-, I- and S-optimal design of experiments are generated by the developed  hybrid method. Those design of experiments as well as Latin  Hypercube sampled design of experiments are used throughout the thesis. Since residual stress analysis, robustness analysis and metamodeling are considered in the thesis, more or less all parts required to perform robustness analysis of residual stresses in castings are covered.

Results in the thesis show that the level of residual stresses in castings can be high due to the casting process. Thus, crack development and spring-back related problems might be influenced by those stresses. Results also show that the level of residual stresses can be very dependent on the variation in certain random variables such as the thickness of the casting, hardening and Young’s modulus. Therefore, it can be of importance to include the variations of the random variables in order to accurately predict the residual stresses when designing castings.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. 44 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1415
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-72354 (URN)978-91-7393-002-4 (ISBN)
Public defence
2012-01-20, E1405, Tekniska högskolan, Jönköping, 10:00 (Swedish)
Opponent
Supervisors
Available from: 2011-11-25 Created: 2011-11-25 Last updated: 2012-04-02Bibliographically approved

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