Use of metamodels in the multi-objective optimization of mechanical structures with uncertainties

International Journal for Computational Methods in Engineering Science and Mechanics

Volumn 8, Issue 5, 2007, Pages 283-302

  Ghanmi, S ^a   Guedri, M ^a   Bouazizi, M L ^a   Bouhaddi, N ^b  

^a Institut Preparatoire aux Etudes d'Ingenieurs de Nabeul   (Tunisia)

^b FEMTO ST INSTITUTE   (France)

Author keywords

Metamodel; Multi objective optimization; Robustness; Self organizing maps; Stochastic finite element method; Uncertainties

Indexed keywords

FINITE ELEMENT METHOD; GENETIC ALGORITHMS; MATHEMATICAL MODELS; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS); SELF ORGANIZING MAPS;

METAMODELS; MULTI-OBJECTIVE OPTIMIZATION; STOCHASTIC RESPONSE SURFACE METHOD (SRSM);

UNCERTAINTY ANALYSIS;

EID: 34547501775     PISSN: 15502287     EISSN: 15502295     Source Type: Journal    
DOI: 10.1080/15502280701402462     Document Type: Article

References (42)

1. R.A. Ibrahim, Structural Dynamics with Parameter Uncertainties, Applied Mechanics Reviews, vol. 40(3), pp. 309-328, 1987.
2. M. Schinozuka, Monte Carlo Solution of Structural Dynamics, Computers and Structures, vol. 2, pp. 855-874, 1972.
3. M. Papadrakakis, A. Kotsopulos, Parallel Solution Methods for Stochastic Finite Element Analysis using Monte Carlo Simulation, Computer Methods in Applied Mechanics and Engineering, vol. 168, pp. 305-320, 1999.
4. M. Kleiber, T.D. Hien, The Stochastic Finite Element Method, Basic Perturbation Technique and Computer Implementation, John Wiley & Sons, New York, 1992.
5. K.F. Alvin, Efficient Computation of Eigenvector Sensitivities for Structural Dynamics, American Institute of Aeronautics and Astronautics Journal, vol. 35 (11), p. 1760, 1998.
6. M. Schinozuka, G. Deodatis, Response Variability of Stochastic Finite Element Systems, Journal of Engineering Mechanics ASCE, vol. 114(3), pp. 499-519, 1988.
7. F. Yamazaki, M. Schinozuka, G. Dasgupta, Neumann Expansion for Stochastic Finite Element Analysis, Journal of Engineering Mechanics ASCE, vol. 114(8), pp. 1335-1354, 1988.
8. G.I. Schuëller, A. Editor, State-of-the-Art Report on Computational Stochastic Mechanics, Probabilistic Engineering Mechanics, vol. 12(4), pp. 197-321, 1997.
9. K.F. Alvin, Efficient Computation of Eigenvector Sensitivities for Structural Dynamics, American Institute of Aeronautics and Astronautics Journal, vol. 35 (11), p. 1760, 1998.
10. R.G. Ghanem, P.D. Spanos, Stochastic Finite Elements - A Spectral Approach, Springer-Verlag, New York, 1991.
11. P.D. Spanos, A. Zeldin, Galerkin Sampling Method for Stochastic Mechanics Problems, Journal of Engineering Mechanics, vol. 120(5), 1994.
12. R.G. Ghanem, R.M. Kruger, Numerical Solution of Spectral Stochastic Finite Element System, Computer Methods in Applied Mechanics and Engineering, vol. 129, pp. 289-303, 1996.
13. V. Braibant, F. Delcroix, A. Oudshoorn, Méthodes Non-déterministes pour l'Analyse et la Conception Robuste de Produits et de Procédés: Approche par l'Arithmétique des Intervalles, Actes du Colloque IDMME'98, Compiègne, pp. 137-145, 1998.
14. K. H. Lee, I. S. Eom, G. J. Park, W. I. Lee, Robust Design for Unconstrained Optimisation Problems Using Taguchi Method, American Institute of Aeronautics and Astronautics Journal, 1996.
15. K.H. Lee, G.J. Park, Robust Optimization Considering Tolerances of Design Variables, Computers and Structures, vol. 79, pp. 77-86, 2001.
16. I. Doltsinis, Z. Kang, Robust Design of Structures Using Optimization Methods, Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 2221-2237, 2004.
17. I. Doltsinis, Z. Kang, Perturbation-based Stochastic FE Analysis and Robust Design of Inelastic Deformation Processes, Computer Methods in Applied Mechanics and Engineering, 2005.
18. S.S. Isukapalli, Uncertainty Analysis of Transport-transformation Models, PhD dissertation, The State University of New Jersey, New Brunswick, 1999.
19. S.S. Isukapalli, A. Roy, P.G. Georgopoulos, Stochastic Response Surface Methods (SRSMs) for Uncertainty Propagation: Application to Environmental and Biological Systems, Risk Analysis, vol. 18(3), pp. 351-363, 1998.
20. S.S. Isukapalli, P.G. Georgopoulos, Computational Methods for Efficient Sensitivity and Uncertainty Analysis of Models for Environmental and Biological Systems, CCL/EDMAS-03, Piscataway, NJ, 1999.
21. S.S. Isukapalli, A. Roy, P.G. Georgopoulos, Efficient Sensitivity/uncertainty Analysis Using the Combined Stochastic Response Surface Method and Automated Differentiation: Application to Environmental and Biological Systems, Risk Analysis vol. 20(5), pp. 591-602, 2000.
22. K. Deb, Multi-objective Genetic Algorithms: Problem. Difficulties and Construction of Test Problems, Evolutionary Computation, vol. 7, pp. 205-230, 1999.
23. S. Obayashi, D. Sasaki, Y. Takeguchi, and N. Hirose, Multiobjective Evolutionary Computation for Supersonic Wing-Shape Optimization, IEEE Transactions on Evolutionary Computation, vol. 4, pp. 182-187, 2000.
24. J. Vesanto, Data Mining Techniques Based on the Self-organizing Map, Master's thesis, Helsinki University of Technology, 1997.
25. A. Ultsch, F. Morchen, ESOM-MAP: Tools for Clustering, Visualization, and Classification with Emergent SOM, Dep. of Mathematics and Computer Science, University of Marburg, Germany, vol. 46, 2005.
26. T. Kohonen, The Self-organising Map, Proc. IEEE vol. 78(9), pp. 1464-1480, 1990.
27. T. Kohonen, Self-organising Maps, Springer-Verlag, New York, 2001.
28. J. Vesanto, Using SOM in Data Mining, Licentiate Thesis, Helsinki University of Technology, 2000.
29. B.K.L. Fei, J.H.P. Eloff, M.S. Olivier, H.S. Venter, The Use of Self-organising Maps for Anomalous Behaviour Detection in a Digital Investigation, Forensic Science International, vol.162, pp. 33-37, 2006.
30. A. Engelbrecht, Computational Intelligence: An Introduction, Wiley, New York, 2002.
31. J. Vesanto, Data Exploration Process Based on the Self-organising Map, Doctoral Thesis, Acta Polytechnica Scandinavica, Mathematics and Computing Series vol. 15, Helsinki University of Technology, 2002.
32. J. Vesanto, SOM-based Data Visualisation Methods, Intell. Data Anal., vol. 3(2), pp. 111-126, 1999.
33. B. Fei, J. Eloff, H. Venter, M. Olivier, Exploring Forensic Data with Self Organising Maps, Advances in Digital Forensics, Springer, pp. 113-123, 2005.
34. B. Ait Brik, Méthodologies de Conception Robuste et d'Optimisation dans un. Contexte de Conception d'Architectures Mécaniques Nouvelles en Avant Projet, Doctoral Thesis, L'U.F.R des Sciences et Techniques de l'Université de Franche - Comte, 2005.
35. C.C. Li, A. Der Kiureghian, Optimal Discretization of Random Fields, Journal of Engineering Mechanics, vol. 119(6), pp. 1136-1154, 1993.
36. J. Zhang, B. Ellingwood, Orthogonal Series Expansions of Random Fields in Reliability Analysis, Journal of Engineering Mechanics ASCE, vol. 120(12), pp. 2660-2677, 1994.
37. M. Guedri, N. Bouhaddi, R. Majed, Reduction of the Stochastic Finite Element Models using a Robust Dynamic Condensation Method, Journal of Sound and Vibration, vol. 297, pp. 123-145, 2006.
38. H.M. Adelman, R.T. Haftka, Sensitivity Analysis of Discrete Structural Systems, American Institute of Aeronautics and Astronautics Journal, vol. 24(5), pp. 823-832, 1986.
39. R.B. Nelson, Simplified Calculation of Eigenvector Derivatives, American Institute of Aeronautics and Astronautics Journal, vol. 14(9), pp. 1201-1205, 1976.
40. R.L. Fox, M.P. Kapoor, Rates of Change of Eigenvalues and Eigenvectors, American Institute of Aeronautical and Astronautics Journal, vol. 6, pp. 2426-2429, 1968.
41. M. Papadrakakis, N.D. Lagaros, V. Plevris, Design Optimization of Steel Structures Considering Uncertainties, Engineering Structures, vol. 27, pp. 1408-1418, 2005.
42. B. Ait. Brik, S. Ghanmi, N. Bouhaddi, S. Cogan, Robust Design in Structure Mechanics, International Journal for Computational. Methods in Engineering Science and Mechanics, vol. 8 (1), 2007.