Structural Engineering and Mechanics

  • 제32권1호
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  • Pages.95-126
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  • 2009
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Parallel processing in structural reliability

  • Pellissetti, M.F. (Institute of Engineering Mechanics, University of Innsbruck)
  • 투고 : 2008.08.21
  • 심사 : 2009.03.03
  • 발행 : 2009.05.10
⟨ 이전 논문 다음 논문 ⟩

초록

The present contribution addresses the parallelization of advanced simulation methods for structural reliability analysis, which have recently been developed for large-scale structures with a high number of uncertain parameters. In particular, the Line Sampling method and the Subset Simulation method are considered. The proposed parallel algorithms exploit the parallelism associated with the possibility to simultaneously perform independent FE analyses. For the Line Sampling method a parallelization scheme is proposed both for the actual sampling process, and for the statistical gradient estimation method used to identify the so-called important direction of the Line Sampling scheme. Two parallelization strategies are investigated for the Subset Simulation method: the first one consists in the embarrassingly parallel advancement of distinct Markov chains; in this case the speedup is bounded by the number of chains advanced simultaneously. The second parallel Subset Simulation algorithm utilizes the concept of speculative computing. Speedup measurements in context with the FE model of a multistory building (24,000 DOFs) show the reduction of the wall-clock time to a very viable amount (<10 minutes for Line Sampling and ${\approx}$ 1 hour for Subset Simulation). The measurements, conducted on clusters of multi-core nodes, also indicate a strong sensitivity of the parallel performance to the load level of the nodes, in terms of the number of simultaneously used cores. This performance degradation is related to memory bottlenecks during the modal analysis required during each FE analysis.

키워드

참고문헌

  1. Alonso, J., de Alfonso, C., García, G. and Hernández, V. (2007), "Grid technology for structural analysis", Adv. Eng. Software, 38(11-12), 738-749 https://doi.org/10.1016/j.advengsoft.2006.08.029
  2. Au, S.K. and Beck, J. (2001), "Estimation of small failure probabilities in high dimensions by subset simulation", Probabilist. Eng. Mech., 16(4), 263-277 https://doi.org/10.1016/S0266-8920(01)00019-4
  3. Bitzarakis, S., Papadrakakis, M. and Kotsopulos, A. (1997), "Parallel solution techniques in computational structural mechanics", Comput. Meth. Appl. Mech. Eng., 148(1-2), 75-104 https://doi.org/10.1016/S0045-7825(97)00028-5
  4. Charmpis, D. and Papadrakakis, M. (2005), "Improving the computational efficiency in finite element analysis of shells with uncertain properties", Comput. Meth. Appl. Mech. Eng., 194(12-16), 1447-1478 https://doi.org/10.1016/j.cma.2003.12.075
  5. Coutinho, A., Martins, M., Sydenstricker, R. and Elias, R. (2006), "Performance comparison of data-reordering algorithms for sparse matrix-vector multiplication in edge-based unstructured grid computations", Int. J. Numer. Meth. Eng., 66, 431-460 https://doi.org/10.1002/nme.1557
  6. Ditlevsen, O. and Madsen, H.O. (1996), Structural Reliability Methods, John Wiley & Sons, Chichester
  7. Farhat, C., Cortial, J., Dastillung, C. and Bavestrello, H. (2006), "Time-parallel implicit integrators for the nearreal-time prediction of linear structural dynamic responses", Int. J. Numer. Meth. Eng., 67, 697-724 https://doi.org/10.1002/nme.1653
  8. Farhat, C. and Lesoinne, M. (1993), "Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics", Int. J. Numer. Meth. Eng., 36(5), 745-764 https://doi.org/10.1002/nme.1620360503
  9. Ghanem, R. and Kruger, R. (1996), "Numerical solution of spectral stochastic finite element systems", Comput. Meth. Appl. Mech. Eng., 129, 289-303 https://doi.org/10.1016/0045-7825(95)00909-4
  10. Hartmann, J., Krahnke, A. and Zenger, C. (2008), "Cache efficient data structures and algorithms for adaptive multidimensional multilevel finite element solvers", Appl. Numer. Math., 58, 435-448 https://doi.org/10.1016/j.apnum.2007.01.024
  11. Johnson, E.A., Wojtkiewicz, S.F., Bergman, L.A. and Jr., B.F.S. (1997), "Observations with regard to massively parallel computation for monte carlo simulation of stochastic dynamical systems", Int. J. Non-linear Mech., 32(4), 721-734 https://doi.org/10.1016/S0020-7462(96)00097-2
  12. Johnson, E., Proppe, C., Spencer Jr, B., Bergman, L., Sz$\acute{e}$kely, G. and Schu$\ddot{e}$ller, G.I. (2003), "Parallel processing in computational stochastic dynamics", Probabilist. Eng. Mech., 18(1), 37-60 https://doi.org/10.1016/S0266-8920(02)00041-3
  13. Keese, A. and Matthies, H. (2005), "Hierarchical parallelisation for the solution of stochastic finite element equations", Comput. Struct., 83, 1033-1047 https://doi.org/10.1016/j.compstruc.2004.11.014
  14. Koutsourelakis, P., Pradlwarter, H.J. and Schu$\ddot{e}$ller, G.I. (2004), "Reliability of structures in high dimensions, part I: Algorithms and applications", Probabilist. Eng. Mech., 19(4), 409-417 https://doi.org/10.1016/j.probengmech.2004.05.001
  15. Krysl, P. and Bittnar, Z. (2001), "Parallel explicit finite element solid dynamics with domain decomposition and message passing: Dual partitioning scalability", Comput. Struct., 79(3), 345-360 https://doi.org/10.1016/S0045-7949(00)00130-9
  16. Lehoucq, R., Sorensen, D. and Yang, C. (1998), ARPACK Users Guide: Solution of Large-Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods, SIAM: Philadelphia, PA
  17. Leite, J.P.B. and Topping, B.H.V. (1999), "Parallel simulated annealing for structural optimization", Comput. Struct., 73, 545-564 https://doi.org/10.1016/S0045-7949(98)00255-7
  18. Mackay, D. and Law, K. (1996), "A parallel implementation of a generalized lanczos procedure for structural dynamic analysis", Int. J. High Speed Comput., 8(2), 171-204 https://doi.org/10.1142/S0129053396000124
  19. Metropolis, N. and Ulam, S. (1949), "The monte carlo method", J. Am. Stat. Assoc., 44, 335-341 https://doi.org/10.2307/2280232
  20. Papadrakakis, M. and Kotsopulos, A. (1999), "Parallel solution methods for stochastic finite element analysis using monte carlo simulation", Comput. Meth. Appl. Mech. Eng., 168(1-4), 305-320 https://doi.org/10.1016/S0045-7825(98)00147-9
  21. Papadrakakis, M., Lagaros, N. and Fragakis, Y. (2003), "Parallel computational strategies for structural optimization", Int. J. Numer. Meth. Eng., 58(9), 1347-1380 https://doi.org/10.1002/nme.821
  22. Pellissetti, M.F., Pradlwarter, H.J. and Schuëller, G.I. (2007), "Relative importance of uncertain structural parameters, Part II: Applications", Comput. Mech., 40(4), 637-649 https://doi.org/10.1007/s00466-006-0128-8
  23. Pradlwarter, H.J. (2007), "Relative importance of uncertain structural parameters, Part I: Algorithm", Comput. Mech., 40(4), 627-635 https://doi.org/10.1007/s00466-006-0127-9
  24. Pradlwarter, H. and Schu$\ddot{e}$ller, G. (2008, submitted), "Uncertain linear systems in dynamics, Part 2: Efficient reliability assessment", Comput. Struct
  25. Rubinstein, R. (1981), Simulation and the Monte Carlo Method, John Wiley & Sons, New York, Chichester, Brisbane, Toronto
  26. Saleh, A. and Adeli, H. (1996), "Parallel eigenvalue algorithms for large-scale control-optimization problems", J. Aerospace Eng., 9(3), 70-79 https://doi.org/10.1061/(ASCE)0893-1321(1996)9:3(70)
  27. Schu$\ddot{e}$ller (Ed.), G.I. (1997), "A state-of-the-art report on computational stochastic mechanics", Probabilist. Eng. Mech., 12(4), 197-321 https://doi.org/10.1016/S0266-8920(97)00003-9
  28. Schu$\ddot{e}$ller, G.I. (2007), "On the Treatment of Uncertainties in Structural Mechanics and Analysis (based on a Plenary Keynote Lecture Presented at the Third M.I.T. Conference on Computational Fluids and Solids Mechanics), Boston, USA", Comput. Struct., 85(5-6), 235-243 https://doi.org/10.1016/j.compstruc.2006.10.009
  29. Schu$\ddot{e}$ller, G.I. and Pradlwarter, H.J. (2007), "Benchmark study on reliability estimation in higher dimensions of structural systems - an overview", Struct. Safety, 29(3), 167-182 https://doi.org/10.1016/j.strusafe.2006.07.010
  30. Schu$\ddot{e}$ller, G.I., Pradlwarter, H.J. and Koutsourelakis, P. (2004), "A critical appraisal of reliability estimation procedures for high dimensions", Probabilist. Eng. Mech., 19(4), 463-474 https://doi.org/10.1016/j.probengmech.2004.05.004
  31. Shinozuka, M. and Deodatis, G. (1997), "Parallel implementation of mcs - synthesis of seismic ground motion using a stochastic barrier model", Probabilist. Eng. Mech., Special Issue on Computational Stochastic Mechanics, 12(4), 213-216
  32. Sotelino, E. (2003), "Parallel processing techniques in structural engineering applications", Struct. Eng., ASCE, 129(12), 1698-1706 https://doi.org/10.1061/(ASCE)0733-9445(2003)129:12(1698)
  33. Sz$\acute{e}$kely, G., Pradlwarter, H.J. and Schu$\ddot{e}$ller, G.I. (1998), Computational Stochastic Structural Analysis - Software Development, in S. Lydersen et al., ed., Proceedings of the ESREL'98 -Safety and Reliability, Vol. 2, A.A. Balkema, Rotterdam, Trondheim, Norway, 1013-1020
  34. Sz$\acute{e}$kely, G. and Schu$\ddot{e}$ller, G.I. (2001), "Computational procedure for a fast calculation of eigenvectors and eigenvalues of structures with random properties", Comput. Meth. Appl. Mech. Eng., 191(8-10), 799-816 https://doi.org/10.1016/S0045-7825(01)00290-0
  35. Umesha, P.K., Venuraju, M.T., Hartmann, D. and Leimbach, K.R. (2005), "Parallel computing techniques for sensitivity analysis in optimum structural design", J. Comput. Civil Eng., 21(6), 463-477 https://doi.org/10.1061/(ASCE)0887-3801(2007)21:6(463)
  36. Valdebenito, M. and Schu$\ddot{e}$ller, G. (2008), Quality Assurance of Uncertain Mechanical Systems Considering the effects of Fatigue and Fracture, in '8th World Congress on Computational Mechanics, (WCCM8)', Venice, Italy, EU
  37. Wriggers, P. and Boersma, A. (1998), "A parallel algebraic multigrid solver for problems in solid mechanics discretisized by finite elements", Comput. Struct., 69(1), 129-137 https://doi.org/10.1016/S0045-7949(98)00053-4
  38. Zienkiewicz, O. and Taylor, R. (2000), The Finite Element Method, 5th edn, Butterworth-Heinemann, Oxford, UK

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