Abstract
The paper develops the idea of [8], i.e., the application of Artificial Neural Networks (ANNs) in probabilistic reliability analysis of structures achieved by means of Monte Carlo (MC) simulation. In this method, a feed-forward neural network is used for generating samples in the MC simulation. The patterns for network training and testing are computed by a Finite Element Method (FEM) program. A high numerical efficiency of this Hybrid Monte Carlo Method (HMC) is illustrated by two examples of the reliability analysis that refer to a steel girder [4] and a cylindrical steel shell [2].
Keywords:
reliability, Artificial Neural Networks (ANNs), Finite Element Method (FEM), Hybrid Monte Carlo Method (HMC), steel girder, cylindrical steel shellReferences
[1] J. Kaliszuk. Reliability analysis of construction and construction elements using artificial neural networks (in Polish). Ph.D. Thesis, University of Zielona Góra, 2005.
[2] J. Kaliszuk. Updating of FEM Models for laboratory tests on cylindrical panels and their reliability analysis by the hybrid FEM/ANN Monte Carlo method. In: A. Borkowski, T. Lewiński, [Eds.],19th International Conference on Computer Methods in Mechanics. Short Papers, 235-236, Publishing House of the Warsaw University of Technology, Warszawa, 2011.
[3] J. Kaliszuk, J. Marcinowski, Z. Waszczyszyn. Experimental Investigation and Numerical Modelling of Large Displacements of Elasto-plastic Cylindrical Shell. In: W. Pietraszkiewicz, C. Szymczak, [Eds.], SSTA 8: Shell Structures: Theory and Applications, Proceedings of the 8th SSTA Conference, 477–480. Taylor & Francis, London, 2005.
[4] J. Kaliszuk, Z. Waszczyszyn. Reliability analysis of a steel girder by the hybrid FEM/BPNN Monte Carlo method. In: M.A. Giżejowski, A. Kozłowski et al., [Eds.], Progress in Steel, Composite and Aluminium Structures: Proc. XIth Intern. Conf. on Metal Structures, 346–347. Taylor& Francis Group, London, 2006.
[5] M. Królak. Postcritical behaviour and load carrying capacity of thin-walled girders (in Polish). PWN, Warszawa, 1990.
[6] P. Marek, M. Guštar, Th. Anagnos. Probabilistic Assessment of Structures using Monte Carlo Simulation. TeReCo, 2001.
[7] E. Pabisek, J. Kaliszuk, Z. Waszczyszyn. Neural and finite element analysis of a plane steel frame reliability by the Classical Monte Carlo method. In: L. Rutkowski, J. Siekmann, R. Tadeusiewicz, L.A. Zadeh, [Eds.], Artificial Intelligence and Soft Computing, Proc. 7th Intern. Conf., Zakopane, 2004, 1081–1086. Springer, Heidelberg, 2004.
[8] M. Papadrakakis, V. Papadopoulos, N.D. Lagaros. Structural reliability analysis of elastic-plastic structures using neural networks and Monte Carlo simulation. Computer Methods in Applied Mechanics and Engineering, 136: 145–163, 1996.
[9] Z. Waszczyszyn, L. Ziemiański. Neural networks in the identification analysis of structural mechanics problems. In: Z. Mróz, G.E. Stavroulakis, [Eds.], Parameter identification of materials and structures. CISM Courses and Lectures, 469: 265–340. Springer, Wien-New York, 2005.
[10] COSMOS/M, Finite element analysis system. Version 2.5. Structural Research and Analysis Corp., California: Los Angeles, 1999.
[11] Neural Network Toolbox for Use with MATLAB, User’s Guide, Version 3. The Math Works, Inc., Natick, MA, 1998.
[12] PN-B-06200. Building steel structures. Requirements for production and control. Basic requirements. PKN, Warszawa, 2002.
[13] PN-EN 1990. Eurocode: Basis of structural design. PKN, Warszawa, 2004.
[14] PN-EN 1993. Eurocode 3: Design of steel structures. PKN, Warszawa, 2006.
[2] J. Kaliszuk. Updating of FEM Models for laboratory tests on cylindrical panels and their reliability analysis by the hybrid FEM/ANN Monte Carlo method. In: A. Borkowski, T. Lewiński, [Eds.],19th International Conference on Computer Methods in Mechanics. Short Papers, 235-236, Publishing House of the Warsaw University of Technology, Warszawa, 2011.
[3] J. Kaliszuk, J. Marcinowski, Z. Waszczyszyn. Experimental Investigation and Numerical Modelling of Large Displacements of Elasto-plastic Cylindrical Shell. In: W. Pietraszkiewicz, C. Szymczak, [Eds.], SSTA 8: Shell Structures: Theory and Applications, Proceedings of the 8th SSTA Conference, 477–480. Taylor & Francis, London, 2005.
[4] J. Kaliszuk, Z. Waszczyszyn. Reliability analysis of a steel girder by the hybrid FEM/BPNN Monte Carlo method. In: M.A. Giżejowski, A. Kozłowski et al., [Eds.], Progress in Steel, Composite and Aluminium Structures: Proc. XIth Intern. Conf. on Metal Structures, 346–347. Taylor& Francis Group, London, 2006.
[5] M. Królak. Postcritical behaviour and load carrying capacity of thin-walled girders (in Polish). PWN, Warszawa, 1990.
[6] P. Marek, M. Guštar, Th. Anagnos. Probabilistic Assessment of Structures using Monte Carlo Simulation. TeReCo, 2001.
[7] E. Pabisek, J. Kaliszuk, Z. Waszczyszyn. Neural and finite element analysis of a plane steel frame reliability by the Classical Monte Carlo method. In: L. Rutkowski, J. Siekmann, R. Tadeusiewicz, L.A. Zadeh, [Eds.], Artificial Intelligence and Soft Computing, Proc. 7th Intern. Conf., Zakopane, 2004, 1081–1086. Springer, Heidelberg, 2004.
[8] M. Papadrakakis, V. Papadopoulos, N.D. Lagaros. Structural reliability analysis of elastic-plastic structures using neural networks and Monte Carlo simulation. Computer Methods in Applied Mechanics and Engineering, 136: 145–163, 1996.
[9] Z. Waszczyszyn, L. Ziemiański. Neural networks in the identification analysis of structural mechanics problems. In: Z. Mróz, G.E. Stavroulakis, [Eds.], Parameter identification of materials and structures. CISM Courses and Lectures, 469: 265–340. Springer, Wien-New York, 2005.
[10] COSMOS/M, Finite element analysis system. Version 2.5. Structural Research and Analysis Corp., California: Los Angeles, 1999.
[11] Neural Network Toolbox for Use with MATLAB, User’s Guide, Version 3. The Math Works, Inc., Natick, MA, 1998.
[12] PN-B-06200. Building steel structures. Requirements for production and control. Basic requirements. PKN, Warszawa, 2002.
[13] PN-EN 1990. Eurocode: Basis of structural design. PKN, Warszawa, 2004.
[14] PN-EN 1993. Eurocode 3: Design of steel structures. PKN, Warszawa, 2006.
