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Strömberg, N. (2019). A Generative Design Optimization Approach for Additive Manufacturing. In: F. Auricchio, E. Rank, P. Steinmann, S.Kollmannsberger and S. Morganti (Ed.), II International Conference on Simulation for Additive Manufacturing: . Paper presented at 2nd International Conference on Simulation for Additive Manufacturing (Sim-AM 2019), Pavie, Italy, September 11-13, 2019 (pp. 130-141). Barcelona, Spain: International Centre for Numerical Methods in Engineering (CIMNE)
Open this publication in new window or tab >>A Generative Design Optimization Approach for Additive Manufacturing
2019 (English)In: II International Conference on Simulation for Additive Manufacturing / [ed] F. Auricchio, E. Rank, P. Steinmann, S.Kollmannsberger and S. Morganti, Barcelona, Spain: International Centre for Numerical Methods in Engineering (CIMNE) , 2019, p. 130-141Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, we present a generative design optimization (GDO) approach for additive manufacturing (AM) by using topology optimization, support vector machines, cellular lattice structures (CLS), design of experiments, morphing and metamodel-based design optimization. By starting from appropriate design domains, a trade-off curve of design concepts is generated by SIMP-based topology optimization (TO). Then, a smooth implicit representation of the TO-solution is established by classifying the discrete density values using soft non-linear support vector machines (SVM). Instead of using the standard soft non-linear SVM of Cortez and Vapnik, we classify the TO solutions by using the 1-norm SVM of Mangasarian. In such manner, the classification is obtained by linear programming instead ofquadratic programming. The implicit SVM-model is further modified by incorporating cellular lattice structures, such as e.g. Gyroid lattice structures, by applying boolean operators. Design of experiments using finite element analysis are then set up by morphing the CLS-modified SVM models for different volume fractions. Finally, metamodel-based design optimization is performed by using optimal ensembles of polynomial regression models, Kriging, radial basis function networks, polynomial chaos expansion and support vector regression. The steps presented above constitute our proposed generative design optimization approach for additive manufacturing and are presented in more detail in the paper.

Place, publisher, year, edition, pages
Barcelona, Spain: International Centre for Numerical Methods in Engineering (CIMNE), 2019
Keywords
Topology optimization, Support vector machines, Lattice Structures, Metamodels
National Category
Applied Mechanics
Identifiers
urn:nbn:se:oru:diva-80213 (URN)978-84-949194-8-0 (ISBN)
Conference
2nd International Conference on Simulation for Additive Manufacturing (Sim-AM 2019), Pavie, Italy, September 11-13, 2019
Available from: 2020-02-26 Created: 2020-02-26 Last updated: 2020-03-17Bibliographically approved
Strömberg, N. (2019). Efficient detailed design optimization of topology optimization concepts by using support vector machines and metamodels. Engineering optimization (Print)
Open this publication in new window or tab >>Efficient detailed design optimization of topology optimization concepts by using support vector machines and metamodels
2019 (English)In: Engineering optimization (Print), ISSN 0305-215X, E-ISSN 1029-0273Article in journal (Refereed) Published
Abstract [en]

In this article, an approach for metamodel-based design optimization (MBDO) of topology optimization (TO) concepts is proposed by using support vector machines (SVMs) as geometric models of the concepts instead of traditional parametric computer aided design (CAD) models. In such a manner, an efficient approach for the MBDO-driven design of TO-based concepts is obtained. An implicit hypersurface representing the TO-based concept is generated by classifying the TO-solutions of zeros and ones by using the 1-norm SVM of Mangasarian. The implicit SVM-based hypersurfaces are then utilized to set up designs of experiments of nonlinear finite element analyses by morphing the TO-based concepts by using Boolean and blending operations. Finally, MBDO is performed by using an ensemble of metamodels consisting of quadratic regression, Kriging, radial basis function networks, polynomial chaos expansion and support vector regression models. The proposed MBDO framework is demonstrated by minimizing the mass of a three-dimensional design domain with a constraint on the plastic limit load. The performance of the approach is most promising.

Place, publisher, year, edition, pages
Taylor & Francis, 2019
Keywords
Support vector machines, topology optimization, metamodels
National Category
Applied Mechanics
Identifiers
urn:nbn:se:oru:diva-75953 (URN)10.1080/0305215X.2019.1646258 (DOI)000481217300001 ()
Available from: 2019-08-30 Created: 2019-08-30 Last updated: 2019-08-30Bibliographically approved
Strömberg, N. (2019). Reliability-based Design Optimization by using Ensemble of Metamodels. In: Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering: . Paper presented at 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019), Crete, Greece, June 24-26, 2019. ECCOMAS
Open this publication in new window or tab >>Reliability-based Design Optimization by using Ensemble of Metamodels
2019 (English)In: Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, ECCOMAS , 2019Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
ECCOMAS, 2019
National Category
Applied Mechanics
Identifiers
urn:nbn:se:oru:diva-80212 (URN)
Conference
3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2019), Crete, Greece, June 24-26, 2019
Available from: 2020-02-26 Created: 2020-02-26 Last updated: 2020-03-17Bibliographically approved
Strömberg, N. (2018). Automatic Postprocessing of Topology Optimization Solutions by Using Support Vector Machines. In: Proceedings of the ASME Design Engineering Technical Conference: Volume 2B. Paper presented at ASME International Design Engineering Technical Conferences (IDETC) / Computers and Information in Engineering Conference (CIE), Quebec, Canada, August 26–29, 2018. American Society of Mechanical Engineers (ASME)
Open this publication in new window or tab >>Automatic Postprocessing of Topology Optimization Solutions by Using Support Vector Machines
2018 (English)In: Proceedings of the ASME Design Engineering Technical Conference: Volume 2B, American Society of Mechanical Engineers (ASME) , 2018Conference paper, Published paper (Refereed)
Abstract [en]

The postprocessing step from the density result in topology optimization to a parametric CAD model is typically most time consuming and usually involves several hands on maneuvers by an engineer. In this paper we propose an approach in order to automate this step by using soft non-linear support vector machines (SVM). Our idea is to generate the boundaries separating regions of material (elements with densities equal to one) and no material (elements with densities equal zero) obtained from topology optimization automatically by using SVM. The hypersurface of the SVM can then in the long run be explicitly implemented in any CAD software. In this work we generate these hypersurfaces by solving the dual formulation of the SVM with soft penalization and nonlinear kernel functions using quadratic programming or the sequential minimal optimization approach. The proposed SVM-based postprocessing approach is studied on topology optimization results of orthotropic elastic design domains with mortar contact conditions studied most recently in a previous work. The potential energy of several bodies with non matching meshes is maximized. In such manner no extra adjoint equation is needed. Intermediate density values are penalized using SIMP or RAMP, and the regularization is obtained by applying sensitivity or density filters following the approaches of Sigmund and Bourdin. The study demonstrates that the SVM-based postprocessing approach automatically generates proper hypersurfaces which can be used efficiently in the CAD modelling.

Place, publisher, year, edition, pages
American Society of Mechanical Engineers (ASME), 2018
National Category
Applied Mechanics
Identifiers
urn:nbn:se:oru:diva-73412 (URN)10.1115/DETC2018-85051 (DOI)000461130700001 ()2-s2.0-85057014507 (Scopus ID)
Conference
ASME International Design Engineering Technical Conferences (IDETC) / Computers and Information in Engineering Conference (CIE), Quebec, Canada, August 26–29, 2018
Funder
Vinnova
Available from: 2019-03-29 Created: 2019-03-29 Last updated: 2019-03-29Bibliographically approved
Amouzgar, K. & Strömberg, N. (2017). Radial Basis Functions as Surrogate Models with A Priori Bias in Comparison with a Posteriori Bias. Structural and multidisciplinary optimization (Print), 55(4), 1453-1469
Open this publication in new window or tab >>Radial Basis Functions as Surrogate Models with A Priori Bias in Comparison with a Posteriori Bias
2017 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 55, no 4, p. 1453-1469Article in journal (Refereed) Published
Abstract [en]

In order to obtain a robust performance, the established approach when using radial basis function networks (RBF) as metamodels is to add a posteriori bias which is defined by extra orthogonality constraints. We mean that this is not needed, instead the bias can simply be set a priori by using the normal equation, i.e. the bias becomes the corresponding regression model. In this paper we demonstrate that the performance of our suggested approach with a priori bias is in general as good as, or even for many test examples better than, the performance of RBF with a posteriori bias. Using our approach, it is clear that the global response is modelled with the bias and that the details are captured with radial basis functions. The accuracy of the two approaches are investigated by using multiple test functions with different degrees of dimensionality. Furthermore, several modeling criteria, such as the type of radial basis functions used in the RBFs, dimension of the test functions, sampling techniques and size of samples, are considered to study their affect on the performance of the approaches. The power of RBF with a priori bias for surrogate based design optimization is also demonstrated by solving an established engineering benchmark of a welded beam and another benchmark for different sampling sets generated by successive screening, random, Latin hypercube and Hammersley sampling, respectively. The results obtained by evaluation of the performance metrics, the modeling criteria and the presented optimal solutions, demonstrate promising potentials of our RBF with a priori bias, in addition to the simplicity and straight-forward use of the approach.

Place, publisher, year, edition, pages
Springer Publishing Company, 2017
Keywords
metamodeling, radial basis function, design optimization, design of experiment
National Category
Applied Mechanics Computer Sciences
Research subject
Mechanical Engineering
Identifiers
urn:nbn:se:oru:diva-56960 (URN)10.1007/s00158-016-1569-0 (DOI)000398951100020 ()2-s2.0-84989170510 (Scopus ID)
Available from: 2017-04-05 Created: 2017-04-05 Last updated: 2018-01-13Bibliographically approved
Strömberg, N. (2017). Reliability-based design optimization using SORM and SQP. Structural and multidisciplinary optimization (Print), 56(3), 631-645
Open this publication in new window or tab >>Reliability-based design optimization using SORM and SQP
2017 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 56, no 3, p. 631-645Article in journal (Refereed) Published
Abstract [en]

In this work a second order approach for reliability-based design optimization (RBDO) with mixtures of uncorrelated non-Gaussian variables is derived by applying second order reliability methods (SORM) and sequential quadratic programming (SQP). The derivation is performed by introducing intermediate variables defined by the incremental iso-probabilistic transformation at the most probable point (MPP). By using these variables in the Taylor expansions of the constraints, a corresponding general first order reliability method (FORM) based quadratic programming (QP) problem is formulated and solved in the standard normal space. The MPP is found in the physical space in the metric of Hasofer-Lind by using a Newton algorithm, where the efficiency of the Newton method is obtained by introducing an inexact Jacobian and a line-search of Armijo type. The FORM-based SQP approach is then corrected by applying four SORM approaches: Breitung, Hohenbichler, Tvedt and a recent suggested formula. The proposed SORM-based SQP approach for RBDO is accurate, efficient and robust. This is demonstrated by solving several established benchmarks, with values on the target of reliability that are considerable higher than what is commonly used, for mixtures of five different distributions (normal, lognormal, Gumbel, gamma and Weibull). Established benchmarks are also generalized in order to study problems with large number of variables and several constraints. For instance, it is shown that the proposed approach efficiently solves a problem with 300 variables and 240 constraints within less than 20 CPU minutes on a laptop. Finally, a most well-know deterministic benchmark of a welded beam is treated as a RBDO problem using the proposed SORM-based SQP approach.

Place, publisher, year, edition, pages
Springer, 2017
Keywords
RBDO, FORM, SORM, SQP
National Category
Computer Sciences
Identifiers
urn:nbn:se:oru:diva-59289 (URN)10.1007/s00158-017-1679-3 (DOI)000406604700009 ()2-s2.0-85015679938 (Scopus ID)
Available from: 2017-08-29 Created: 2017-08-29 Last updated: 2018-01-13Bibliographically approved
Amouzgar, K. & Strömberg, N. (2014). An approach towards generating surrogate models by using RBFN with a priori bias. In: Proceedings of the ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, 2014, Vol. 2B: . Paper presented at ASME, International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE, Buffalo, NY, USA, August 17-20, 2014. New York, USA: ASME Press, Article ID V02BT03A024.
Open this publication in new window or tab >>An approach towards generating surrogate models by using RBFN with a priori bias
2014 (English)In: Proceedings of the ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, 2014, Vol. 2B, New York, USA: ASME Press, 2014, article id V02BT03A024Conference 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

Place, publisher, year, edition, pages
New York, USA: ASME Press, 2014
Keywords
Optimization, Response Surface, Surrogate Modelling, RBF, RBFN, Approximation Function
National Category
Applied Mechanics Mechanical Engineering
Research subject
Mechanical Engineering
Identifiers
urn:nbn:se:oru:diva-48247 (URN)000379987300024 ()2-s2.0-84961312861 (Scopus ID)978-0-7918-4632-2 (ISBN)
Conference
ASME, International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE, Buffalo, NY, USA, August 17-20, 2014
Available from: 2016-02-18 Created: 2016-02-15 Last updated: 2019-12-13Bibliographically approved
Amouzgar, K., Rashid, A. & Strömberg, N. (2013). Multi-objective optimization of a disc brake system by using SPEA2 and RBFN. In: ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference: Volume 3B: 39th Design Automation Conference. Paper presented at ASME 2013 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE), Portland, Oregon, USA, August 4-7, 2013. New York: ASME Press
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 Conference, New York: ASME Press, 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: ASME Press, 2013
Keywords
Multi-objective Optimization, Disc Brake, RBF, RBFN, Surrogate Modelling, Response Surface, Pareto-front
National Category
Applied Mechanics Mechanical Engineering
Research subject
Mechanical Engineering
Identifiers
urn:nbn:se:oru:diva-48246 (URN)10.1115/DETC2013-12809 (DOI)000362380400029 ()2-s2.0-84896968665 (Scopus ID)978-0-7918-5589-8 (ISBN)
Conference
ASME 2013 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE), Portland, Oregon, USA, August 4-7, 2013
Available from: 2013-06-25 Created: 2016-02-15 Last updated: 2019-12-13Bibliographically approved
Rashid, A. & Strömberg, N. (2013). Sequential simulation of thermal stresses in disc brakes for repeated braking. Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, 227(8), 919-929
Open this publication in new window or tab >>Sequential simulation of thermal stresses in disc brakes for repeated braking
2013 (English)In: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 227, no 8, p. 919-929Article in journal (Refereed) Published
Abstract [en]

In this paper, an efficient sequential approach for simulating thermal stresses in brake discs for repeated braking is presented. First, a frictional heat analysis is performed by using an Eulerian formulation of the disc. Then, by using the temperature history from the first step of the sequence, a plasticity analysis with temperature dependent material data is performed in order to determine the corresponding thermal stresses. Three-dimensional geometries of a disc and a pad to a heavy truck are considered in the numerical simulations. The contact forces are computed at each time step taking the thermal deformations of the disc and pad into account. In such manner, the frictional heat power distribution will also be updated in each time step, which in turn will influence the development of heat bands. The plasticity model is taken to be the von Mises yield criterion with linear kinematic hardening, where both the hardening and the yield limit are temperature dependent. The results show that during hard braking, high compressive stresses are generated on the disc surface in the circumferential direction which cause yielding. But when the disc cools down, these compressive stresses transform to tensile residual stresses. For repeated hard braking when this kind of stress history is repeated, we also show that stress cycles with high amplitudes are developed which might generate low cycle fatigue cracks after a few braking cycles.

Place, publisher, year, edition, pages
London, United Kingdom: Sage Publications, 2013
Keywords
Eulerian framework, frictional heat, thermal stresses, disc brake, repeated braking
National Category
Applied Mechanics Mechanical Engineering
Research subject
Mechanical Engineering
Identifiers
urn:nbn:se:oru:diva-48271 (URN)10.1177/1350650113481701 (DOI)000321702800014 ()2-s2.0-84884572691 (Scopus ID)
Available from: 2016-02-18 Created: 2016-02-15 Last updated: 2018-05-26Bibliographically approved
Strömberg, N. (2013). The Influence of Sliding Friction on Optimal Topologies. In: Recent Advances in Contact Mechanics: Papers Collected at the 5th Contact Mechanics International Symposium (CMIS2009). Paper presented at 5th Contact Mechanics International Symposium (CMIS2009), Chania, Greece, April 28-30, 2009 (pp. 327-336). Springer Berlin/Heidelberg, 56
Open this publication in new window or tab >>The Influence of Sliding Friction on Optimal Topologies
2013 (English)In: Recent Advances in Contact Mechanics: Papers Collected at the 5th Contact Mechanics International Symposium (CMIS2009), Springer Berlin/Heidelberg, 2013, Vol. 56, p. 327-336Conference paper, Published paper (Refereed)
Abstract [en]

In this paper the influence of sliding friction on optimal topologies is investigated and some preliminary results are presented. A design domain unilaterally constrained by a spinning support is considered. Most recently, Stromberg and Klarbring have developed methods for performing topology optimization of linear elastic structures with unilateral contact conditions. In this works sliding friction is also included in the contact model. In such manner it is possible to study how the spinning of the support will influence the optimal design. This was not possible before. The support is modeled by Signorini's contact conditions and Coulomb's law of friction. Signorini's contact conditions are regularized by a smooth approximation, which must not be confused with the well-known penalty approach. The state of the system, which is defined by the equilibrium equations and the smooth approximation, is solved by a Newton method. The design parametrization is obtained by using the SIMP-model. The minimization of compliance for a limited value of volume is considered. The optimization problem is solved by a nested approach where the equilibrium equations are linearized and sensitivities are calculated by the adjoint method. The problem is then solved by SLP, where the LP-problem is solved by an interior point method that is available in the package of Mat lab. In order to avoid mesh-dependency and patterns of checker-boards the sensitivities are filtered by Sigmund's filter. The method is implemented by using Mat lab and Visual Fortran, where the Fortran code is linked to Mat lab as mex-files. The implementation is done for a general design domain in 2D by using fully integrated isoparametric elements. The implementation seems to be very efficient and robust.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2013
Series
Lecture Notes in Applied and Computational Mechanics, ISSN 1613-7736 ; 56
National Category
Mechanical Engineering Applied Mechanics
Research subject
Mechanical Engineering
Identifiers
urn:nbn:se:oru:diva-48284 (URN)10.1007/978-3-642-33968-4_20 (DOI)000315535300020 ()2-s2.0-84870737711 (Scopus ID)978-3-642-33967-7 (ISBN)
Conference
5th Contact Mechanics International Symposium (CMIS2009), Chania, Greece, April 28-30, 2009
Available from: 2007-12-17 Created: 2016-02-15 Last updated: 2017-10-17Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-6821-5727

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