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D-optimality of non-regular design spaces by using a Bayesian modification and a hybrid method
Tekniska Högskolan, Högskolan i Jönköping, JTH, Maskinteknik.
Tekniska Högskolan, Högskolan i Jönköping, JTH, Maskinteknik. (Teknisk mekanik)
2010 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 42, no 1, 73-88 p.Article in journal (Refereed) Published
Abstract [en]

In this work a hybrid method of a genetic algorithm  and sequential linear programming is suggested to obtain a D-optimal design of experiments. Regular as well as non-regular design spaces are considered. A D-optimal design of experiments maximizes the determinant of the information matrix, which appears in the normal equation. It is known that D-optimal design of experiments sometimes include duplicate design points. This is, of course, not preferable since duplicates do not add any new information to the response surface approximation and the computational effort is therefore wasted. In this work a Bayesian modification, where higher order terms are added to the response surface approximation, is used in case of duplicates in the design of experiments. In such manner, the draw-back with duplicates might be eliminated. The D-optimal problem, which is obtained by using the Bayesian modification, is then solved by a hybrid method. A hybrid method of a genetic algorithm that generates a starting point for sequential linear programming is developed. The genetic algorithm performs genetic operators such as cross-over and mutation on a binary version of the design of experiments, while the real valued version is used to evaluate the fitness. Next, by taking the gradient of the objective, a LP-problem is formulated which is solved by an interior point method that is available in Matlab. This is repeated in a sequence until convergence is reached. The hybrid method is tested for four numerical examples. Results from the numerical examples show a very robust convergence to a global optimum. Furthermore, the results show that the problem with duplicates is eliminated by using the Bayesian modification.

Place, publisher, year, edition, pages
2010. Vol. 42, no 1, 73-88 p.
Keyword [en]
D-optimality, Design of experiments (DoE), Sequential linear programming (SLP), Genetic algorithms (GA), Response surface methodology (RSM), Bayesian modification (BM)
National Category
Mechanical Engineering
URN: urn:nbn:se:liu:diva-72347DOI: 10.1007/s00158-009-0464-3OAI: diva2:459249
Available from: 2009-06-15 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.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1415
National Category
Engineering and Technology
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)
Available from: 2011-11-25 Created: 2011-11-25 Last updated: 2012-04-02Bibliographically approved

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