Abstract
We explore the feasibility and performance of a data-driven approach to topology optimization problems involving structural mechanics. Our approach takes as input a set of images representing optimal 2-D topologies, each resulting from a random loading configuration applied to a common boundary support condition. These images represented in a high dimensional feature space are projected into a lower dimensional space using component analysis. Using the resulting components, a mapping between the loading configurations and the optimal topologies is learned. From this mapping, we estimate the optimal topologies for novel loading configurations. The results indicate that when there is an underlying structure in the set of existing solutions, the proposed method can successfully predict the optimal topologies in novel loading configurations. In addition, the topologies predicted by the proposed method can be used as effective initial conditions for conventional topology optimization routines, resulting in substantial performance gains. We discuss the advantages and limitations of the presented approach and show its performance on a number of examples.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bendsoe, M.P., Sigmund, O.: Topology Optimization: Theory, Methods and Applications. Springer (2004)
Schramm, U., Zhou, M.: Recent Developments in the Commercial Implementation of Topology Optimization. In: IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials, pp. 239–248. Springer Netherlands (2006)
Richardson, J.N., Coelho, R.F., Adriaenssens, S.: Robust Topology Optimization of 2D and 3D Continuum and Truss Structures Using a Spectral Stochastic Finite Element Method. In: 10th World Congress on Structural and Multidisciplinary Optimization (2010)
Chapman, C.D., Saitou, K., Jakiela, M.J.: Genetic Algorithms as an Approach to Configuration and Topology Design. Journal of Mechanical Design 116, 1005–1012 (1994)
Jakiela, M.J., Chapman, C.D., Duda, J., Adewuya, A., Saitou, K.: Continuum Structural Topology Design with Genetic Algorithms. Computer Methods in Applied Mechanics and Engineering 186, 339–356 (2000)
Aage, N., Lazarov, B.S.: Parallel Framework for Topology Optimization Using the Method of Moving Asymptotes. Structural and Multidisciplinary Optimization 47, 493–505 (2013)
Dijk, N.P., Maute, K., Langelaar, M., Keulen, F.: Level-Set Methods for Structural Topology Optimization: A Review. Structural and Multidisciplinary Optimization 48, 437–472 (2013)
Norato, J.A., Bendsoe, M.P., Haber, R.B., Tortorelli, D.A.: A Topological Derivative Method for Topology Optimization. Structural and Multidisciplinary Optimization 33, 375–386 (2007)
Bendsoe, M.P., Kikuchi, N.: Generating Optimal Topologies in Structural Design Using a Homogenization Method. Computer Methods in Applied Mechanics and Engineering 71, 197–224 (1988)
Suzuki, K., Kikuchi, N.: A Homogenization Method for Shape and Topology Optimization. Computer Methods in Applied Mechanics and Engineering 93, 291–318 (1991)
Bendsoe, M.P.: Optimal Shape Design as a Material Distribution Problem. Structural Optimization 1, 193–202 (1989)
Rozvany, G.I.N., Zhou, M., Birker, T.: Generalized Shape Optimization without Homogenization. Structural Optimization 4, 250–252 (1992)
Hassani, B., Hinton, E.: A Review of Homogenization and Topology Optimization I–Homogenization Theory for Media with Periodic Structure. Computers and Structures 69, 707–717 (1998)
Rozvany, G.I.N.: Aims, Scope, Methods, History and Unified Terminology of Computer-Aided Topology Optimization in Structural Mechanics. Structural and Multidisciplinary Optimization 21, 90–108 (2001)
Rozvany, G.I.N.: A Critical Review of Established Methods of Structural Topology Optimization. Structural and Multidisciplinary Optimization 37, 217–237 (2009)
Sethian, J.A., Wiegmann, A.: Structural Boundary Design via Level Set and Immersed Interface Methods. Journal of Computational Physics 163, 489–528 (2000)
Wang, M.Y., Wang, X., Guo, D.: A Level Set Method for Structural Topology Optimization. Computer Methods in Applied Mechanics and Engineering 192, 227–246 (2003)
Andreassen, E., Clausen, A., Schevenels, M., Lazarov, B.S., Sigmund, O.: Efficient Topology Optimization in MATLAB Using 88 Lines of Code. Structural and Multidisciplinary Optimization 43, 1–16 (2011)
Sigmund, O.: A 99 Line Topology Optimization Code Written in MATLAB. Structural and Multidisciplinary Optimization 21, 120–127 (2001)
Sirovich, L., Kirby, M.: Low-Dimensional Procedure for the Characterization of Human Faces. Journal of Optical Society of America 4, 519–524 (1987)
Kirby, M., Sirovich, L.: Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces. IEEE Transactions on Pattern Analysis and Machine Intelligence 12, 103–108 (1990)
Turk, M., Pentland, A.: Eigenfaces for Recognition. Journal of Cognitive Neuroscience 3, 71–86 (1991)
Allen, B., Curless, B., Popovic, Z.: The Space of Human Body Shapes: Reconstruction and Parameterization from Range Scans. ACM Transactions on Graphics 22, 587–594 (2003)
Yumer, M.E., Kara, L.B.: Conceptual Design of Freeform Surfaces From Unstructured Point Sets Using Neural Network Regression. In: ASME International Design Engineering Technical Conferences/DAC (2011)
Yumer, M.E., Kara, L.B.: Surface Creation on Unstructured Point Sets Using Neural Networks. Computer-Aided Design 44, 644–656 (2012)
Jolliffe, I.: Principal Component Analysis. Wiley Online Library (2005)
Cox, T., Cox, M.: Multidimensional Scaling. Chapman and Hall, London (1994)
Tenenbaum, J.: Advances in Neural Information Processing, vol. 10, pp. 682–688. MIT Press, Cambridge (1998)
Roweis, S.T., Saul, L.K.: Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science 290, 2323–2326 (2000)
Blanz, V., Vetter, T.: A Morphable Model for the Synthesis of 3D Faces. In: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, pp. 187–194. ACM Press/Addison-Wesley (1999)
Bishop, C.M., Nasrabadi, N.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ulu, E., Zhang, R., Yumer, M.E., Kara, L.B. (2014). A Data-Driven Investigation and Estimation of Optimal Topologies under Variable Loading Configurations. In: Zhang, Y.J., Tavares, J.M.R.S. (eds) Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications. CompIMAGE 2014. Lecture Notes in Computer Science, vol 8641. Springer, Cham. https://doi.org/10.1007/978-3-319-09994-1_38
Download citation
DOI: https://doi.org/10.1007/978-3-319-09994-1_38
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09993-4
Online ISBN: 978-3-319-09994-1
eBook Packages: Computer ScienceComputer Science (R0)