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http://dx.doi.org/10.12989/sem.2009.32.1.001

Efficient Monte Carlo simulation procedures in structural uncertainty and reliability analysis - recent advances  

Schueller, G.I. (Institute of Engineering Mechanics, University of Innsbruck)
Publication Information
Structural Engineering and Mechanics / v.32, no.1, 2009 , pp. 1-20 More about this Journal
Abstract
The present contribution addresses uncertainty quantification and uncertainty propagation in structural mechanics using stochastic analysis. Presently available procedures to describe uncertainties in load and resistance within a suitable mathematical framework are shortly addressed. Monte Carlo methods are proposed for studying the variability in the structural properties and for their propagation to the response. The general applicability and versatility of Monte Carlo Simulation is demonstrated in the context with computational models that have been developed for deterministic structural analysis. After discussing Direct Monte Carlo Simulation for the assessment of the response variability, some recently developed advanced Monte Carlo methods applied for reliability assessment are described, such as Importance Sampling for linear uncertain structures subjected to Gaussian loading, Line Sampling in linear dynamics and Subset simulation. The numerical example demonstrates the applicability of Line Sampling to general linear uncertain FE systems under Gaussian distributed excitation.
Keywords
uncertainty propagation; stochastic; Monte Carlo Simulation; dynamics; reliability;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 7  (Related Records In Web of Science)
Times Cited By SCOPUS : 7
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1 Au, S. and Beck, J. (2001a), "First excursion probabilities for linear systems by very efficient importance sampling", Probabilist. Eng. Mech., 16, 193-207   DOI   ScienceOn
2 Au, S., Ching, J. and Beck, J. (2007), "Application of subset simulation methods to reliability benchmark problems", Struct. Safety, 29, 183-193   DOI   ScienceOn
3 Au, S.-K. and Beck, J.L. (2001b), "Estimation of small failure probabilities in high dimensions by subset simulation", Probabilist. Eng. Mech., 16(4), 263-277   DOI   ScienceOn
4 Au, S.K. and Beck, J.L. (2003), "Important sampling in high dimensions", Struct. Safety, 25(2), 139-163   DOI   ScienceOn
5 Cai, G. and Lin, Y. (1996), "Generation of non-gaussian stationary processes", Phys. Rev. E, 54(1), 299-303   DOI   ScienceOn
6 Cameron, R. and Martin, W. (1947), "The orthogonal development of nonlinear functionals in series of fourierhermite functionals", Ann. Math., 48, 385-392   DOI   ScienceOn
7 Ching, J., Beck, J. and Au, S. (2005), "Hybrid subset simulation method for reliability estimation of dynamical systems subject to stochastic excitation", Probabilist. Eng. Mech., 20, 199-214   DOI   ScienceOn
8 Deodatis, G. and Shinozuka, M. (1989), "Simulation of seismic ground motion using stochastic waves", J. Eng. Mech., ASCE, 115(12), 2723-2737   DOI
9 Ding, C., Hsieh, C., Wu, Q. and Pedram, M. (1996), "Stratified random sampling for power estimation", Iccad 00, 576
10 Ding, C., Wu, Q., Hsieh, C. and Pedram, M. (1998), "Stratified random sampling for power estimation", IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems, 17(6), 465-471   DOI   ScienceOn
11 Ditlevsen, O. and Madsen, H.O. (2005), Structural Reliability Methods. (First edition published by John Wiley & Sons Ltd., Chichester, 1996, ISBN 0 471 96086 1), Internet edition 2.2.5
12 Fishman, G. (1996), Monte Carlo: Concepts, Algorithms, Applications, Springer, New York
13 Grigoriu, M. (1995), Non-Gaussian Processes. Examples, Theory, Simulation, Linear Random Vibration, and MATLAB Solutions, Prentice Hall, Englewood Cliffs, New Jersey
14 Geman, S. and Geman, D. (1988), "Stochastic relaxation, gibbs distributions, and the bayesian restoration of images", 611-634   DOI   ScienceOn
15 Ghanem, R. and Kruger, R. (1996), "Numerical solution of spectral stochastic finite element systems", Comput. Meth. Appl. Mech. Eng., 129   DOI   ScienceOn
16 Ghanem, R. and Spanos, P. (1991), Stochastic Finite Elements: A Spectral Approach, Springer Verlag, Berlin
17 Hammersley, J. and Handscomb, D. (1964), Monte Carlo Methods, Chapman and Hall, London
18 Hastings, W. (1970), "Monte carlo sampling methods using markov chains and their applications", Biometrika 82, 711-732   DOI   ScienceOn
19 Helton, J. and Davis, F. (2003), "Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems", Reliab. Eng. Syst. Safety, 81(1), 23-69   DOI   ScienceOn
20 Huntington, D. and Lyrintzis, C. (1998), "Improvements to and limitations of latin hypercube sampling", Probabilist. Eng. Mech., 13(9), 245-253   DOI   ScienceOn
21 Kahn, H. (1956), "Use of different monte carlo sampling techniques", in H.A. Meyer, ed., Symposium on Monte Carlo Methods, John Wiley & Sons
22 Kameda, H. and Morikawa, H. (1991), "Simulation of conditional random fields - a basis for regional seismic monitoring for urban earthquake hazards mitigation-", in Y. Wen, ed., Intelligent Structures-2, Monitoring and Control, Proceeding of the International Workshop on Intelligent Systems, Elsevier Science Publishers, England, Perugia, Italy, 13-27
23 Katafygiotis, L. and Zuev, K. (2007), "Estimation of small failure probabilities in high dimensions by adaptive linked importance sampling", in Conference on Computational Methods in Structural Dynamic and Earthquake Engineering, Grete, Greece
24 Kameda, H. and Morikawa, H. (1992), "An interpolating stochastic process for simulation of conditional random fields", Probabilist. Eng. Mech., ASCE, 7(4), 242-254   DOI   ScienceOn
25 Kameda, H. and Morikawa, H. (1993), "Conditioned stochastic processes for conditional random fields", J. Eng. Mech., 120(4), 855-875   DOI   ScienceOn
26 Katafygiotis, L. and Cheung, S. (2007), "Application of spherical subset simulation methodand auxiliary domain method on a benchmark reliability study", Struct. Safety, 29, 194-207   DOI   ScienceOn
27 Katafygiotis, L. and Zuev, K. (2008), "Geometric insight into the challenges of solving high-dimensional reliability problems", Probabilist. Eng. Mech., 23, 208-218   DOI   ScienceOn
28 Katafygiotis, L., Moan, T. and Cheung, S. (2007), "Auxiliary domain method for solving multi objective dynamic reliability problems for nonlinear structures", Struct. Eng. Mech., 25(3), 347-363   ScienceOn
29 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   DOI   ScienceOn
30 Liu, J. (2001), Monte Carlo Strategies in Scientific Computing, Springer Series in Statistics, Springer
31 Liu, P.L. and Der Kiureghian, A. (1986), "Multivariate distribution models with prescribed marginals and covariances", Probabilist. Eng. Mech., 1(2), 105-112   DOI   ScienceOn
32 Neal, R.M. (2001), "Annealed importance sampling", Statist. Comput., 11(2), 125-139   DOI   ScienceOn
33 Lo$\grave{e}$ve, M. (1977), Probability Theory, 4th edition edn, Springer-Verlag, New York
34 Metropolis, N. and Ulam, S. (1949), "The monte carlo method", J. Am. Statist. Assoc., 44, 335-341   DOI   ScienceOn
35 Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller E. (1953), "Equation of state calculation by fast computing machines", J. Chem. Phys., 21, 1087-1092   DOI
36 Olsen, A.I. and Naess, A. (2006), "Estimation of failure probabilities of linear dynamic systems by importance sampling", Sadhana, 31-4, 429-443   DOI   ScienceOn
37 Olsson, A., Sandberg, G. and Dahlblom, O. (2003), "On latin hypercube sampling for structural reliability analysis", Struct. Safety, 25, 47-68(22)   DOI   ScienceOn
38 Pradlwarter, H. and Schu$\ddot{e}$ller, G. (2008, submitted), "Reliability assessment of uncertain dynamical linear systems - Recent advances", Struct. Safety
39 Pradlwarter, H.J. and Schu$\ddot{e}$ller, G.I. (2004), "Excursion probability of non-linear systems", Int. J. Non-linear Mech., 39(9), 1447-1452   DOI   ScienceOn
40 Pradlwarter, H.J., Schu$\ddot{e}$ller, G.I., Koutsourelakis, P.S. and Charmpis, D.C. (2007), "Application of line sampling simulation method to reliability benchmark problems", Struct. Safety, 29(3), 208-221   DOI   ScienceOn
41 Rice, S. (1954), "Mathematical analysis of random noise", in N. Wax, ed., Selected Papers on Noise and Stochastic Processes, Dover, pp. 133-294. originally appeared in two parts in the Bell System Technical Journ. in Vol. 23, July 1944 and in Vol. 24, January 1945
42 Shinozuka, M. (1972), "Monte carlo solution of structural dynamics", Comput. Struct., 2(5+6), 855-874   ScienceOn
43 Schu$\ddot{e}$ller, G.I. and Stix, R. (1987), "A critical appraisal of methods to determine failure probabilities", Journal of Struct. Safety, 4, 293-309   DOI   ScienceOn
44 Schu$\ddot{e}$ller, G.I., Bucher, C., Bourgund, U. and Ouypornprasert, W. (1989), "On efficient computational schemes to calculate structural failure probabilities", J. Probabilist. Eng. Mech., 4(1), 10-18   DOI   ScienceOn
45 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   DOI   ScienceOn
46 Shinozuka, M. and Jan, C.M. (1972), "Digital simulation of random processes and its applications", J. Sound Vib., 25(1), 111-128   DOI   ScienceOn
47 Yamazaki, F. and Shinozuka, M. (1988), "Digital generation of non-gaussian stochastic fields", J. Eng. Mech., ASCE, 114(7), 1183-1197   DOI   ScienceOn
48 Yang, J.N. (1972), "Simulation of random envelope processes", J. Sound Vib., 25(1), 73-85
49 Yang, J.N. (1973), "On the normality and accuracy of simulated random processes", J. Sound Vib., 26(3), 417-428   DOI   ScienceOn
50 Yang, W.N. and Liou, W.W. (1996), "Combining antithetic variates and control variates in simulation experiments", ACM Trans. Model. Comput. Simul., 6(4), 243-260   DOI   ScienceOn