Estimation of failure probabilities of linear dynamic systems by importance sampling

Sadhana - Academy Proceedings in Engineering Sciences

Volumn 31, Issue 4, 2006, Pages 429-443

  Olsen, Anna Ivanova ^a   Naess, Arvid ^a  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

Importance sampling; Linear dynamic systems; Time variant reliability

Indexed keywords

DISPLACEMENT RESPONSE; FAILURE PROBABILITY; TIME DISCRETIZATION; TIME VARIANT RELIABILITY PROBLEMS;

FAILURE ANALYSIS; ITERATIVE METHODS; MONTE CARLO METHODS; PROBABILITY DENSITY FUNCTION; RELIABILITY; WHITE NOISE;

TIME VARYING SYSTEMS;

EID: 33749318539     PISSN: 02562499     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02716785     Document Type: Article

References (16)

1. Au S K, Beck J L 2001 First excursion probabilities for linear systems by very efficient importance sampling. Probab. Eng. Mech. 16: 193-207
2. Chung K L, Williams R J 1990 Introduction to stochastic integration 2nd edn (Boston: Birkhäuser)
3. Girsanov I V 1960 On transforming a certain class of stochastic processes by absolutely continuous substitution of measures. Theor. Probab. Appl. 5: 285-301
4. Ivanova A, Naess A 2004 Importance sampling for dynamic systems by approximate calculation of the optimal control function. Proc. 4th Int. Conf. on Mathematical Methods in Reliability, Sante Fe, NM, USA (Singapore: World Scientific)
5. Lin Y K, Cai G Q 1995 Probabilistic structural dynamics, advanced theory and applications. (MCGraw-Hill)
6. Macke M, Bucher C 2003 Importance sampling for randomly excited dynamical systems. J. Sound Vibr. 268: 269-290
7. Milstein G N 1995 Numerical integration of stochastic differential equations (Dordrecht: Kluwer Academic)
8. Naess A 1999 Comments on importance sampling for time variant reliability problems. Stochastic Struct. Dyn. 4: 197-202
9. Naess A, Skaug C 2000 Importance sampling for dynamical systems. In Proc. ICASP 8 Conference (eds) R E Melchers, M G Stewart (Rotterdam: A A Balkema) pp 749-755
10. Newton N J 1994 Variance reduction for simulated diffusions. SIAM J. Appl. Math. 54: 1780-1805
11. Øksendal B 1998 Stochastic differential equations: An introduction with application (5th edn) (Berlin: Springer)
12. Olsen A I, Naess A 2004 Importance sampling for dynamic systems by approximate calculation of the optimal control function. In Modern statistical and mathematical methods in reliability of series on quality, reliability and engineering statistics (eds) A Wilson, N Limnios, S Keller-McNulty, Y Armijo (Singapore: World Scientific) 10: 339-352
13. Rudin W 1987 Real and complex analysis (New York: McGraw-Hill)
14. Soong T T, Grigoriu M 1997 Random vibration of mechanical and structural systems (Englewood Cliffs, NJ: Prentice-Hall)
15. Tanaka H 1998 Application of an importance sampling method to time-dependent system reliability analyses using the girsanov transformation. Proceedings of ICOSSAR'97 - The 7th International Conference on Structural Safety and Reliability (eds) N Shiraishi, M Shinozuka, Y K Wen (Rotterdam: A A Balkema) 1: 411-418
16. Tanaka H 1999 Importance sampling simulation for a stochastic fatigue crack growth model. In Proc. ICASP 8 Conference (eds) R E Melchers, M G Stewart (Rotterdam: A A Balkema) pp 749-755