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2014 | 24 | 4 | 865-886

Tytuł artykułu

A hybrid algorithm for solving inverse problems in elasticity

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
The paper offers a new approach to handling difficult parametric inverse problems in elasticity and thermo-elasticity, formulated as global optimization ones. The proposed strategy is composed of two phases. In the first, global phase, the stochastic hp-HGS algorithm recognizes the basins of attraction of various objective minima. In the second phase, the local objective minimizers are closer approached by steepest descent processes executed singly in each basin of attraction. The proposed complex strategy is especially dedicated to ill-posed problems with multimodal objective functionals. The strategy offers comparatively low computational and memory costs resulting from a double-adaptive technique in both forward and inverse problem domains. We provide a result on the Lipschitz continuity of the objective functional composed of the elastic energy and the boundary displacement misfits with respect to the unknown constitutive parameters. It allows common scaling of the accuracy of solving forward and inverse problems, which is the core of the introduced double-adaptive technique. The capability of the proposed method of finding multiple solutions is illustrated by a computational example which consists in restoring all feasible Young modulus distributions minimizing an objective functional in a 3D domain of a photo polymer template obtained during step and flash imprint lithography.

Rocznik

Tom

24

Numer

4

Strony

865-886

Opis fizyczny

Daty

wydano
2014
otrzymano
2013-08-21
poprawiono
2014-03-29
poprawiono
2014-05-29

Twórcy

  • Department of Computer Science, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland
  • Department of Computer Science, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland
  • Chair of Optimization and Control Theory, Jagiellonian University, Kraków, Poland
  • Department of Computer Science, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland
  • Department of Computer Science, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland
  • Department of Computer Science, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

  • Ahopelto J. and Haatainen T. (2002). Step and flash imprint lithography, in C.M. Sotomayor Torres (Ed.), Alternative Lithography. Unleashing the Potentials of Nanotechnology, Kluwer Academic Publisher, Boston, MA/Dortrecht/London, Chapter 6, pp. 127-142.
  • Alvarez-Aramberri, J., Pardo, D. and Barucq, H. (2013). Inversion of magnetotelluric measurements using multigoal oriented hp-adaptivity, Procedia Computer Science 18(8): 1564-1573.
  • Babuška, I. and Guo, B. (1986a). The hp-version of the finite element method, Part I: The basic approximation results, Computational Mechanics 1(1): 21-41.
  • Babuška, I. and Guo, B. (1986b). The hp-version of the finite element method, Part II: General results and applications, Computational Mechanics 1(3): 203-220.
  • Banks, H.T. and Kunisch, K. (1989). Estimation Techniques for Distributed Parameter Systems, Birkhäuser, Boston, MA.
  • Barabasz, B., Gajda, E., Migórski, S., Paszyński, M. and Schaefer, R. (2011a). Studying inverse problems in elasticity by hierarchic genetic search, IPM'2011 Conference Proceedings, Sieniawa, Poland, pp. 9-10.
  • Barabasz, B., Migórski, S., Schaefer, R. and Paszyński, M. (2011b). Multi-deme, twin adaptive strategy hp-HGS, Inverse Problems in Science and Engineering 19(1): 3-16.
  • Barabasz, B., Schaefer, R. and Paszyński, M. (2009). Handling ambiguous inverse problems by the adaptive genetic strategy hp-HGS, in G. Allen, J. Nabrzyski, E. Seidel, G.D. van Albada, J. Dongarra and P.M.A. Sloot (Eds.) Computational Science-ICCS 2009, 9th International Conference, Baton Rouge, LA, USA, May 25-27, 2009, Proceedings, Part II, Lecture Notes in Computer Sience, Vol. 5545, Springer-Verlag, Berlin/Heidelberg, pp. 904-913.
  • Burczyński, T. and Beluch, W. (2001). The identification of cracks using boundary elements and evolutionary algorithms, Engineering Analysis with Boundary Elements 25(4-5): 313-322.
  • Burczyński, T., Kuś, W., Długosz, A. and Orantek, P. (2004). Optimization and defect identification using distributed evolutionary algorithms, Engineering Applications of Artificial Intelligence 17(4): 337-344.
  • Burns, R., Johnson, S., Schmid, G., Kim, E., Dickey, D., Meiring, J., Burns, S., Stacey, N., Willson, C., Convey, D., Wei, Y., Fejes, P., Gehoski, K., Mancini, D. Nordquist, K., Dauksher, W.J and Resnick, D.J. (2004). Mesoscale modeling for SFIL simulating polymerization kinetics and densification, Proceedings of SPIE 2004, Santa Clara, CA, USA, Vol. 5374, pp. 348-360.
  • Cabib, E., Davini, C. and Chong-Quing, R. (1990). A problem in the optimal design of networks under transverse loading, Quarterly of Applied Mathematics 48(2): 251-263.
  • Cabib, E., Schaefer, R. and Telega, H. (1998). A parallel genetic clustering for inverse problems, in B. Kagström, J. Dongarra, E. Elmroth and J. Wasniewski (Eds.), Applied Parallel Computing. Large Scale Scientific and Industrial Problems. 4th International Workshop, PARA'98, Umea, Sweden, June 14-17, Proceedings, Lecture Notes in Computer Science, Vol. 1541, Springer, Berlin/Heidelberg, pp. 551-556.
  • Caicedo, J.M. and Yun, G. (2011). A novel evolutionary algorithm for identifying multiple alternative solutions in model updating, Structural Health Monitoring 10(5): 491-501.
  • Cantú-Paz, E. (2000). Efficient and Accurate Parallel Genetic Algorithms, Kluwer Academic Publishers, Norwell, MA.
  • Chase Geoffrey, J., Barroso, Luciana, R. and Hwank, K.-S. (2004). LMS-based structural health monitoring methods for the ASCE benchmark problem, Proceedings of the 2004 American Control Conference, Boston, MA, USA, Vol. 5, pp. 4201-4206.
  • Ciarlet, G. (1978). The Finite Element Method for Elliptic Problems, North Holland, Amsterdam.
  • Colburn, M. (1978). Step and Flash Imprint Lithography: A Low Pressure, Room Temperature Nonoimprint Lithography, Ph.D. thesis, University of Texas, Austin, TX.
  • Colburn, M., Suez, I., Choi, B., Meissi, M., Bailey, T., Sreeni-vasan, S., Ekerdt, J. and Willson, C. (2001). Characterization and modeling of volumetric and mechanical properties for SFIL photopoly-mers, Journal of Vacuum Science and Technology 19(6): 2685-2689.
  • Demkowicz, L. (2006). Computing with hp-Adaptive Finite Elements, Vol. I: One and Two Dimensional Elliptic and Maxwell Problems, Chapman and Hall/CRC Applied Mathematics and Nonlinear Science, London.
  • Demkowicz, L., Kurtz, J., Pardo, P., Paszyński, M., Rachowicz, W. and Zdunek, A. (2007). Computing with hpAdaptive Finite Elements, Vol. II: Frontiers: ThreeDimensional Elliptic and Maxwell Problems with Applications, Chapman and Hall/CRC Applied Mathematics and Nonlinear Science, London.
  • Denkowski, Z., Migórski, S. and Papageorgiou, N. (2003a). An Introduction to Nonlinear Analysis: Applications, Kluwer Academic/Plenum, New York, NY.
  • Denkowski, Z., Migórski, S. and Papageorgiou, N. (2003b). An Introduction to Nonlinear Analysis: Theory, Kluwer Academic/Plenum, New York, NY.
  • Descloux, J. (1973). Méthode Des Éléments Finis, Ecole Polytechnique Fédérale de Lausanne, Lausanne.
  • Engl, H.W., Hanke, M. and Neubauer, A. (2000). Regularization of Inverse Problems, Kluwer, Dordrecht.
  • Figueiredo, E., Park, G., Farrar, C.R., Worden, K. and Figueiras, J. (2011). Machine learning algorithms for damage detection under operational and environmental variability, Structural Health Monitoring 10(6): 559-572.
  • Friswell, M.I. and Mottershead, J.E. (2001). Inverse methods in structural health monitoring, Key Engineering Materials 204-205: 201-210.
  • Garibaldi, L., Surace, C., Holford, K. and Ostachowicz, W.M. (1999). Damage Assessment of Structures, Trans Tech Publications, Zürich.
  • Glover, F. and Kochenberger, G. (2002). Handbook of Metaheuristics, Kluwer Academic Publishers, Dordrecht.
  • Horst, R. and Pardalos, P. (1995). Handbook of Global Optimization, Kluwer, Dordrecht.
  • Hughes, T. (2000). The Finite Element Method. Linear Statics and Dynamic Finite Element Analysis, Dover Publications, Mineola, NY.
  • Huhtala, A. and Sven, B. (2011). A Bayesian approach to vibration based structural health monitoring with experimental verification, Rakenteiden Mekaniikka (Journal of Structural Mechanics) 44(4): 330-344.
  • Isakov, V. (2006). Inverse Problems for Partial Differential Equations, Springer, New York, NY.
  • Kirikera, Goutham, R., Shinde, V., Schulz, Mark, J., Ghoshal, A., Sundaresan, Mannur, J., Allemang, Randall, J. and Won Lee, J. (2008). A structural neural system for real-time health monitoring of composite materials, Structural Health Monitoring 7(1): 65-83.
  • Koper, K., Wysession, M. and Wiens, D. (1999). Multimodal function optimization with a niching genetic algorithm: A seismological example, Bulletin of the Seismological Society of America 89(4): 978-988.
  • Lashin, S. and Likoshvai, V. (2004). Evolutionary algorithms for mathematical models of gene regulatory networks, Proceedings of the 4th International Conference on Bioinformatics of Genome Regulation and Structure, BGRS 2004, Novosibirsk, Russia, Vol. 2, pp. 81-84.
  • Mahfoud, S. (1997). Niching methods, in T. Back, D.B. Fogel and Z. Michalewicz (Eds.), Handbook of Evolutionary Computations, Oxford University Press, Oxford, Chapter C.6.1, pp. C6.1:1-C6.1:4.
  • Meruane, V. and Heylen, W. (2009). Damage detection with parallel genetic algorithms and operational modes, Structural Health Monitoring 9(6): 481-496.
  • Oden, J.T. and Prudhomme, S. (2001). Goal-oriented error estimation and adaptivity for the finite element method, Computers and Mathematics with Applications 41(5): 735-756.
  • Osman, I. and Kelly, J. (1996). Meta-Heuristics: Theory and Applications, Kluwer Academic Publishers, Norwell, MA.
  • Osman, I.H. and Laporte, G. (1996). Metaheuristics: A bibliography, Annals of Operations Research 63(5): 511-623.
  • Paszyńska, A., Grabska, E. and Paszyński, M. (2012a). A graph grammar model of the hp adaptive three dimensional finite element method, Part I, Fundamenta Informaticae 114(2): 149-182.
  • Paszyńska, A., Grabska, E. and Paszyński, M. (2012b). A graph grammar model of the hp adaptive three dimensional finite element method, Part II, Fundamenta Informaticae 114(2): 183-201.
  • Paszyńska, A., Paszyński, M. and Grabska, E. (2008). Graph transformations for modeling hp-adaptive finite element method with triangular elements, in M. Bubak, G.D. van Albada, J. Dongarra and P.M.A. Sloot (Eds.) Computational Science-ICCS 2008, 8th International Conference, Kraków, Poland, June 23-25, Proceedings, Part III, Lecture Notes in Computer Science, Vol. 5103, Springer, Berlin, pp. 604-613.
  • Paszyńska, A., Paszyński, M. and Grabska, E. (2009). Graph transformations for modeling hp-adaptive finite element method with mixed triangular and rectangular elements, in G. Allen, J. Nabrzyski, E. Seidel, G.D. van Albada, J. Dongarra and P.M.A. Sloot (Eds.), Computational Science-ICCS 2009, 9th International Conference, Baton Rouge, LA, USA, Proceedings, Part II, Lecture Notes in Computer Science, Vol. 5545, Springer, Berlin, pp. 875-884.
  • Paszyński, M. (2009a). On the parallelization of self-adaptive hp-finite element methods, Part I: Composite programmable graph grammar model, Fundamenta Informaticae 93(4): 411-434.
  • Paszyński, M. (2009b). On the parallelization of self-adaptive hp-finite element methods, Part II: Partitioning communication agglomeration mapping (PCAM) analysis, Fundamenta Informaticae 93(4): 435-457.
  • Paszyński, M., Barabasz, B. and Schaefer, R. (2007). Efficient adaptive strategy for solving inverse problems, in Y. Shi, G.D. van Albada, J. Dongarra and P.M.A. Sloot (Eds.), Computational Science-ICCS 2007. 7th International Conference, Beijing China, May 27-30, 2007, Proceedings, Part I, Lecture Notes in Computer Science, Vol. 4487, Springer, Berlin, pp. 342-349.
  • Paszyński, M. and Demkowicz, L. (2006). Parallel fully automatic hp-adaptive 3D finite element package, Engineering with Computers 22(3-4): 255-276.
  • Paszyński, M., Kurtz, J. and Demkowicz, L. (2006). Parallel fully automatic hp-adaptive 2D finite element package, Computer Methods in Applied Mechanics and Engineering 195(7-8): 711-741.
  • Paszyński, M., Gurgul, P., Sieniek, M. and Pardo, D. (2010a). Unified modeling language description of the object-oriented multi-scale adaptive finite element method for step-and-flash imprint lithography, IOP Conference Series: Materials Science and Engineering 10(1): 012247.
  • Paszyński, M., Pardo, D. and Paszyńska, A. (2010b). Parallel multi-frontal solver for p adaptive finite element modeling of multi-physics computational problems, Journal of Computational Science 1(1): 48-54.
  • Paszyński, M., Romkes, A., Collister, E., Meiring, J., Demkowicz, L. and Willson, C. (2005). On the modeling of step-and-flash imprint lithography using molecular statics models, Technical Report 05-38, ICES, Austin, TX.
  • Paszyński, M. and Schaefer, R. (2010). Graph grammar-driven parallel partial differential equation solver, Concurrency and Computation: Practice and Experience 22(9): 1063-1097.
  • Rachowicz, W., Pardo, D. and Demkowicz, L. (2006). Fully automatic hp-adaptivity in three dimensions, Computer Methods in Applied Mechanics and Engineering 195(37-40): 4816-4842.
  • Rocca, P., Benedetti, M., Donelli, M., Franceschini, D. and Massa, A. (2009). Evolutionary optimization as applied to inverse scattering problems, Inverse Problems 25(12): 123003.
  • Ryszka, I., Paszyńska, A., Grabska, E. and Paszyński, M. (2013). Graph grammar systems for modeling three dimensional finite element method, Fundamenta Informaticae, (submitted).
  • Samarski, A.A. and Vabishchevich, P.N. (2007). Numerical Methods for Solving Inverse Problems of Mathematical Physics, Walter de Gruyter, Berlin.
  • Schaefer, R. and Barabasz, B. (2008). Asymptotic behavior of hp-HGS (hp-adaptive finite element method coupled with the hierarchic genetic strategy) by solving inverse problems, in M. Bubak, G.D. van Albada, J. Dongarra, and P.M.A. Sloot (Eds.), Computational Science-ICCS 2008. 8th International Conference, Kraków, Poland, June 23-25, 2008, Proceedings, Part III, Lecture Notes in Computer Science, Vol. 5103, Springer, Berlin/Heidelberg, pp. 682-692.
  • Schaefer, R. and Kołodziej, J. (2003). Genetic search reinforced by the population hierarchy, in K. DeJong, R. Poli and J. Rowe (Eds.), Foundations of Genetic Algorithms 7, Morgan Kaufman, Burlington, MA, pp. 383-399.
  • Schwab, C. (1998). p and hp Finite Element Methods, Oxford University Press, Oxford.
  • Singh, A., Minsker, B. and Takagi, H. (2006). Interactive genetic algorithms for inverse groundwater modeling: Issues with human fatigue and prediction models, in R. Walton (Ed.), Proceedings of the 2005 World Water and Environmental Resources Congress: Impacts of Global Climate Change, May 15-19, 2005, Anchorage, AK, Vol. 5, American Society of Civil Engineers, Reston, VA, pp. 3081-3092.
  • Strug, B., Paszyńska, A., Paszyński, M. and Grabska, E. (2013). Using a graph grammar system in the finite element method, International Journal of Applied Mathematics and Computer Science 23(4): 839-853, DOI:10.2478/amcs-2013-0063.
  • Tanaka, M. (Ed.) (2003). Inverse Problems in Engineering Mechanics IV. Proceedings of the International Symposium on Inverse Problems in Engineering Mechanics 2003 (ISP 2003), Nagano, Japan, Elsevier, Amsterdam.
  • Tarantola, A. (2005). Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, Philadelphia, PA.
  • Tikhonov, A.N., Goncharskii, A., Stepanov, V.V. and Yagola, A.G. (1995). Numerical Methods for the Solution of IllPosed Problems, Mathematics and Its Applications, Vol. 328, Springer-Verlag, Berlin/Heidelberg.
  • Vose, M. (1999). The Simple Genetic Algorithm, MIT Press, Boston, MA.
  • Wierzba, B., Semczuk, A., Kołodziej, J. and Schaefer, R. (2003). Hierarchical genetic strategy with real number encoding, Proceedings of the 6th Conference on Evolutionary Algorithms and Global Optimization, Łagów Lubuski, Poland, pp. 231-237.
  • Xavier, C., Vieira, V., Martins, D. and Dos Santos, R. (2006). Comparing two parallel genetic algorithms for the inverse problem associated to the cardiac bidomain equations, Workshop on High Performance Computing in the Life Sciences, HPC LIFE, Ouru Preto, Brazil.
  • Zhu, C., Byrd, R. H., Lu, P. and Nocedal, J. (1997). Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization, ACM Transactions on Mathematical Software 23(4): 550-560.

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