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Metamodel based multi-objective optimization
Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.ORCID iD: 0000-0001-7534-0382
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

As a result of the increase in accessibility of computational resources and the increase in the power of the computers during the last two decades, designers are able to create computer models to simulate the behavior of a complex products. To address global competitiveness, companies are forced to optimize their designs and products. Optimizing the design needs several runs of computationally expensive simulation models. Therefore, using metamodels as an efficient and sufficiently accurate approximate of the simulation model is necessary. Radial basis functions (RBF) is one of the several metamodeling methods that can be found in the literature.

The established approach is to add a bias to RBF in order to obtain a robust performance. The a posteriori bias is considered to be unknown at the beginning and it is defined by imposing extra orthogonality constraints. In this thesis, a new approach in constructing RBF with the bias to be set a priori by using the normal equation is proposed. The performance of the suggested approach is compared to the classic RBF with a posteriori bias. Another comprehensive comparison study by including several modeling criteria, such as problem dimension, sampling technique and size of samples is conducted. The studies demonstrate that the suggested approach with a priori bias is in general as good as the performance of RBF with a posteriori bias. Using the a priori RBF, it is clear that the global response is modeled with the bias and that the details are captured with radial basis functions.

Multi-objective optimization and the approaches used in solving such problems are briefly described in this thesis. One of the methods that proved to be efficient in solving multi-objective optimization problems (MOOP) is the strength Pareto evolutionary algorithm (SPEA2). Multi-objective optimization of a disc brake system of a heavy truck by using SPEA2 and RBF with a priori bias is performed. As a result, the possibility to reduce the weight of the system without extensive compromise in other objectives is found.

Multi-objective optimization of material model parameters of an adhesive layer with the aim of improving the results of a previous study is implemented. The result of the original study is improved and a clear insight into the nature of the problem is revealed.

Place, publisher, year, edition, pages
Jönköping: Jönköping University, School of Engineering , 2015. , 25 p.
Series
JTH Dissertation Series, 13
Keyword [en]
Multi-objective optimization, strength Pareto evolutionary algorithm, SPEA2, metamodel, surrogate model, response surface, radial basis functions, RBF
National Category
Computer Engineering Mechanical Engineering
Identifiers
URN: urn:nbn:se:hj:diva-28432ISBN: 978-91-87289-14-9 (print)OAI: oai:DiVA.org:hj-28432DiVA: diva2:875865
Presentation
2015-12-11, E1405, School of Engineering, Gjuterigatan 5, Jönköping, 14:00
Opponent
Supervisors
Available from: 2015-12-02 Created: 2015-12-02 Last updated: 2015-12-02Bibliographically approved
List of papers
1. Multi-Objective Optimization of a Disc Brake System by using SPEA2 and RBFN
Open this publication in new window or tab >>Multi-Objective Optimization of a Disc Brake System by using SPEA2 and RBFN
2013 (English)In: ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference: Volume 3B: 39th Design Automation ConferencePortland, Oregon, USA, August 4–7, 2013, New York: American Society of Mechanical Engineers , 2013Conference paper, Published paper (Other academic)
Abstract [en]

Many engineering design optimization problems involve multiple conflicting objectives, which today often are obtained by computational expensive finite element simulations. Evolutionary multi-objective optimization (EMO) methods based on surrogate modeling is one approach of solving this class of problems. In this paper, multi-objective optimization of a disc brake system to a heavy truck by using EMO and radial basis function networks (RBFN) is presented. Three conflicting objectives are considered. These are: 1) minimizing the maximum temperature of the disc brake, 2) maximizing the brake energy of the system and 3) minimizing the mass of the back plate of the brake pad. An iterative Latin hypercube sampling method is used to construct the design of experiments (DoE) for the design variables. Next, thermo-mechanical finite element analysis of the disc brake, including frictional heating between the pad and the disc, is performed in order to determine the values of the first two objectives for the DoE. Surrogate models for the maximum temperature and the brake energy are created using RBFN with polynomial biases. Different radial basis functions are compared using statistical errors and cross validation errors (PRESS) to evaluate the accuracy of the surrogate models and to select the most accurate radial basis function. The multi-objective optimization problem is then solved by employing EMO using the strength Pareto evolutionary algorithm (SPEA2). Finally, the Pareto fronts generated by the proposed methodology are presented and discussed.

Place, publisher, year, edition, pages
New York: American Society of Mechanical Engineers, 2013
Keyword
Multi-objective Optimization, Disc Brake, RBF, RBFN, Surrogate Modelling, Response Surface, Pareto-front
National Category
Applied Mechanics
Identifiers
urn:nbn:se:hj:diva-21587 (URN)10.1115/DETC2013-12809 (DOI)978-0-7918-5589-8 (ISBN)
Conference
ASME 2013 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2013 August 4-7, 2013, Portland, OR, USA
Available from: 2013-06-25 Created: 2013-06-25 Last updated: 2015-12-02Bibliographically approved
2. An approach towards generating surrogate models by using RBFN with a apriori bias
Open this publication in new window or tab >>An approach towards generating surrogate models by using RBFN with a apriori bias
2014 (English)In: Proceedings of the ASME 2014 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2014 August 17-20, 2014, Buffalo, NY, USA, 2014Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, an approach to generate surrogate modelsconstructed by radial basis function networks (RBFN) with a prioribias is presented. RBFN as a weighted combination of radialbasis functions only, might become singular and no interpolationis found. The standard approach to avoid this is to add a polynomialbias, where the bias is defined by imposing orthogonalityconditions between the weights of the radial basis functionsand the polynomial basis functions. Here, in the proposed a prioriapproach, the regression coefficients of the polynomial biasare simply calculated by using the normal equation without anyneed of the extra orthogonality prerequisite. In addition to thesimplicity of this approach, the method has also proven to predictthe actual functions more accurately compared to the RBFNwith a posteriori bias. Several test functions, including Rosenbrock,Branin-Hoo, Goldstein-Price functions and two mathematicalfunctions (one large scale), are used to evaluate the performanceof the proposed method by conducting a comparisonstudy and error analysis between the RBFN with a priori and aposteriori known biases. Furthermore, the aforementioned approachesare applied to an engineering design problem, that ismodeling of the material properties of a three phase sphericalgraphite iron (SGI) . The corresponding surrogate models arepresented and compared

Keyword
Optimization, Response Surface, Surrogate Modelling, RBF, RBFN, Approximation Function
National Category
Applied Mechanics
Identifiers
urn:nbn:se:hj:diva-24673 (URN)
Conference
ASME, International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE, Buffalo, NY, August 17-20, 2014
Available from: 2014-09-08 Created: 2014-09-08 Last updated: 2015-12-02Bibliographically approved
3. Multi-objective optimization of material model parameters of an adhesive layer by using SPEA2
Open this publication in new window or tab >>Multi-objective optimization of material model parameters of an adhesive layer by using SPEA2
2015 (English)In: Advances in structural and multidisciplinary optimization: Proceedings of the 11th World Congress of Structural and Multidisciplinary Optimization (WCSMO-11) / [ed] Qing Li, Grant P Steven, Zhongpu (Leo) Zhang, 2015, 249-254 p.Conference paper, Published paper (Refereed)
Abstract [en]

The usage of multi material structures in industry, especially in the automotive industry are increasing. To overcome the difficulties in joining these structures, adhesives have several benefits over traditional joining methods. Therefore, accurate simulations of the entire process of fracture including the adhesive layer is crucial. In this paper, material parameters of a previously developed meso mechanical finite element (FE) model of a thin adhesive layer are optimized using the Strength Pareto Evolutionary Algorithm (SPEA2). Objective functions are defined as the error between experimental data and simulation data. The experimental data is provided by previously performed experiments where an adhesive layer was loaded in monotonically increasing peel and shear. Two objective functions are dependent on 9 model parameters (decision variables) in total and are evaluated by running two FEsimulations, one is loading the adhesive layer in peel and the other in shear. The original study converted the two objective functions into one function that resulted in one optimal solution. In this study, however, a Pareto frontis obtained by employing the SPEA2 algorithm. Thus, more insight into the material model, objective functions, optimal solutions and decision space is acquired using the Pareto front. We compare the results and show good agreement with the experimental data.

Keyword
Multi-objective optimization, parameter identification, micro mechanical model, adhesive, CZM
National Category
Computer Engineering Mechanical Engineering
Identifiers
urn:nbn:se:hj:diva-28422 (URN)978-0-646-94394-7 (ISBN)
Conference
11th World Congress of Structural and Multidisciplinary Optimization (WCSMO-11)
Available from: 2015-12-01 Created: 2015-12-01 Last updated: 2016-11-10Bibliographically approved
4. Radial basis functions with a priori bias in comparisonwith a posteriori bias under multiple modeling criteria
Open this publication in new window or tab >>Radial basis functions with a priori bias in comparisonwith a posteriori bias under multiple modeling criteria
(English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488Article in journal (Other academic) Submitted
National Category
Computer Engineering Mechanical Engineering
Identifiers
urn:nbn:se:hj:diva-28431 (URN)
Available from: 2015-12-02 Created: 2015-12-02 Last updated: 2017-12-01

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Amouzgar, Kaveh

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