Excursion probabilities of non-linear systems

International Journal of Non-Linear Mechanics

Volumn 39, Issue 9, 2004, Pages 1447-1452

  Pradlwarter, H J ^a   Schueller G I ^a  

^a UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

First excursion probability; First passage probability; Line sampling; Monte Carlo simulation; Stochastic non linear response; Stochastic system

Indexed keywords

COMPUTER SIMULATION; LINEAR SYSTEMS; MATHEMATICAL MODELS; MONTE CARLO METHODS; OSCILLATORS (ELECTRONIC); PROBABILITY; PROBLEM SOLVING; RANDOM PROCESSES; SAMPLING; WHITE NOISE;

FIRST EXCURSION PROBABILITY; FIRST PASSAGE PROBABILITY; LINE SAMPLING; STOCHASTIC NON-LINEAR RESPONSE; STOCHASTIC SYSTEM;

NONLINEAR SYSTEMS;

EID: 2442549681     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2004.02.006     Document Type: Conference Paper

References (11)

1. Rice O.C. Mathematical analysis of random noise. Bell. Systems Tech. J. 45:1945;46-156.
2. Crandall S.H. Some first passage problems in random vibration. J. Appl. Mech. ASME. 33:1966;624-639.
3. Roberts J.B. First passage probability for nonlinear oscillators. J. Eng. Mech. ASCE. 102:1976;851-866.
4. Bergman L.A., Heinrich J.C. Petrov-Galerkin finite element solution for the first passage probability and moments of first passage time of the randomly free accelerated free particle. Comput. Meth. Appl. Mech. Eng. 27:1981;345-362.
5. Lin Y.K., Cai G.Q. Probabilistic Structural Dynamics: Advanced Theory and Applications. 1995;McGraw-Hill, New York.
6. Pradlwarter H.J., Schuëller G.I., Melnik-Melnikov P.G. Reliability of MDOF-systems. Probab. Eng. Mech. 9:1994;235-243.
7. Pradlwarter H.J., Schuëller G.I. Assessment of low probability events of dynamical systems by controlled Monte Carlo simulation. Probab. Eng. Mech. 14:1999;213-227.
8. S.K. Au, J.L. Beck, Subset simulation: a new approach to calculating small failure probabilities, in: Proceedings of International Conference on Monte Carlo, Monte Carlo, Monaco, 2000, 2000.
9. Au S.K., Beck J.L. First excursion probabilities for linear systems by very efficient importance sampling. Probab. Eng. Mech. 16:2001;193-207.
10. P.S. Koutsourelakis, H.J. Pradlwarter, G.I. Schuëller, Reliability of structures in high dimensions, in: GAMM-Conference Proceedings of the GAMM, Padua, 2003, to appear.
11. G.I. Schuëller, H.J. Pradlwarter, P.S. Koutsourelakis, A comparative study of reliability estimation procedures for high dimensions using FE-analysis, in: G. Turkiyyah (Ed.), Electronic Proceedings of the 16th ASCE Engineering Mechanics Conference, University of Washington, Seattle, USA, 2003.