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Optimal Polynomial Regression Models by using a Genetic Algorithm
Tekniska Högskolan, Högskolan i Jönköping, JTH, Maskinteknik.
Tekniska Högskolan, Högskolan i Jönköping, JTH, Maskinteknik.
Department of Mechanical Engineering Jönköping University P.O. Box 1026, 551 11 Jönköping.
2011 (engelsk)Inngår i: Proceedings of the Second International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering / [ed] Y. Tsompanakis & B.H.V. Topping, Stirlingshire: Civil-Comp Press , 2011, artikkel-id 39Konferansepaper, Publicerat paper (Annet vitenskapelig)
Abstract [en]

Different regression models are commonly used to approximate the behavior of an unknown response in a given design domain. The regression models are usually obtained from a design of experiments, the corresponding responses and the constitution of the regression model. In this work a new approach is proposed, where the constituents of a polynomial regression model are of arbitrary order. A genetic algorithm is used to find the optimal terms to be included in the so-called optimal polynomial regression model. The objective for the genetic algorithm is to minimize the sum of squared errors of the predicted responses. In practice the genetic algorithm generates an optimal set of exponents of the design variables for the specified number of terms in the regression model, where each term is a product of a regression coefficient and the design variables. Several example problems are presented to show the performance and accuracy of the optimal polynomial regression model. Results show an improved performance for optimal polynomial regression models compared to traditional regression models.

sted, utgiver, år, opplag, sider
Stirlingshire: Civil-Comp Press , 2011. artikkel-id 39
Serie
Civil-Comp Proceedings, E-ISSN 1759-3433 ; 97
Emneord [en]
Polynomial regression model, Metamodeling, Design of experiments (DoE)
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-72350DOI: 10.4203/ccp.97.39OAI: oai:DiVA.org:liu-72350DiVA, id: diva2:459271
Konferanse
The Second International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering Conference, 6-9 September, Chania, Crete, Greece
Prosjekter
MERATilgjengelig fra: 2011-11-25 Laget: 2011-11-25 Sist oppdatert: 2019-12-29bibliografisk kontrollert
Inngår i avhandling
1. Robustness Analysis of Residual Stresses in Castings
Åpne denne publikasjonen i ny fane eller vindu >>Robustness Analysis of Residual Stresses in Castings
2012 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
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.

sted, utgiver, år, opplag, sider
Linköping: Linköping University Electronic Press, 2012. s. 44
Serie
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1415
HSV kategori
Identifikatorer
urn:nbn:se:liu:diva-72354 (URN)978-91-7393-002-4 (ISBN)
Disputas
2012-01-20, E1405, Tekniska högskolan, Jönköping, 10:00 (svensk)
Opponent
Veileder
Tilgjengelig fra: 2011-11-25 Laget: 2011-11-25 Sist oppdatert: 2012-04-02bibliografisk kontrollert

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