The PHI2 method: A way to compute time-variant reliability

Reliability Engineering and System Safety

Volumn 84, Issue 1, 2004, Pages 75-86

  Andrieu Renaud, C ^a   Sudret, B ^b   Lemaire, M ^a  

^a LaRAMA IFMA and UBP   (France)

^b EDF R AND D   (France)

Author keywords

Asymptotic approach; FORM SORM; Outcrossing rate; PHI2 method; Time invariant reliability; Time variant reliability

Indexed keywords

CRACKS; FINITE ELEMENT METHOD; POISSON DISTRIBUTION; PROBLEM SOLVING; RANDOM PROCESSES; STEEL CORROSION; TIME VARYING SYSTEMS; VECTORS;

ASYMPTOTIC APPROACH; FORM/SORM; OUTCROSSING RATE; PH12 METHODS; TIME-INVARIANT RELIABILITY; TIME-VARIANT RELIABILITY;

RELIABILITY;

EID: 1642633036     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2003.10.005     Document Type: Conference Paper

References (31)

1. Breitung K. Asymptotic approximations for the outcrossing rates of stationary vector processes. Stochast Process Appl. 13:1988;195-207.
2. Schall G., Faber M.H., Rackwitz R. The ergodicity assumption for sea states in the reliability estimation of offshore structures. J Offshore Mech Arctic Engng. 113:1991;241-246.
3. Engelung S., Rackwitz R., Lange C. Approximations of first passage times for differentiable processes based on higher order threshold crossings. Probab Engng Mech. 10:(1):1995;53-60.
4. Rackwitz R. Computational techniques in stationary and non-stationary load combination - a review and some extensions. J Struct Engng. 25:(1):1998;1-20.
5. Hagen O., Tvedt L. Vector process out-crossing as parallel system sensitivity measure. J Engng Mech, ASCE. 121:(10):1991;2201-2220.
6. Li C.C., Der Kiureghian A. Lemaire M., Favre J.L., Mébarki A. Mean out-crossing rate of nonlinear response to stochastic input. Proceedings of the Seventh International Conference on Applications of Statistics and Probability (ICASP) in Civil Engineering and Risk Analysis, Paris, France. 1995;295-302.
7. Li C.C., Der Kiureghian A. Cooke R., Mendel M., Vrijling H. Mean out crossing of nonlinear response to stochastic input. Engineering probabilistic design and maintenance for flood protection. 1997;173-176 Kluwer Academic Publishers, Dordrecht, The Netherland.
8. Der Kiureghian A., Li C.C. Frangopol D., Corotis R., Rackwitz R. Nonlinear random vibration analysis through optimization. Reliability and optimization of structural systems. Proceedings of the Seventh IFIP WG 7.5 Working Conference on Reliability and Optimization of Structural Systems. 1996;197-206 Pergamon Press, UK.
9. Der Kiureghian A. The geometry of random vibrations and solutions by FORM and SORM. Probab Engng Mech. 15:(1):2000;81-90.
10. Vijalapura P., Conte J., Meghella M. Melchers R., Stewart M. Time-variant reliability analysis of hysteretics SDOF systems with uncertain parameters and subjected to stochastic loading, ICASP8. vol. 1:2000;827-834 Balkema, Amsterdam.
11. Andrieu C., Rachad A., Mitteau J.-C., Lemaire M. Evaluation d'une structure au cours de sa dégradation dans le temps. Revue Française de Génie Civil. vol. 6:2002;Hermès, Paris. p. 469-77.
12. Andrieu C., Lemaire M., Sudret B. The PHI2 method: a way to assess time-variant reliability using time-invariant reliability tools. Proceedings of the European Safety and Reliability Conference ESREL'02, March. 2002;ISdF, Lyon. p. 472-9.
13. Andrieu-Renaud C. Fiabilité mécanique des structures soumises à des phénomènes physiques dépendant du temps, PhD Thesis, Université Blaise Pascal, Clermont-Ferrand, France; 2002.
14. Sudret B., Defaux G., Andrieu C., Lemaire M. Comparison of methods for computing the probability of failure in time-variant reliability using the outcrossing approach. Spanos P.D., Deodatis G. Proceedings of the Fourth International Conference on Computational Stochastic Mechanics (CSM4). 2003;609-618 Millpress, Rotterdam.
15. RCP Gmbh, COMREL and SYSREL user's manual, Munich; 1998.
16. Bolotin V.V. Wahrscheinlichkeitsmethoden zur Berechnung von Konstruktionen. 1981;VEB Verlag für Bauwesen, Berlin.
17. Shinozuka M. Probability of failure under random loading. J Engng Mech Div, ASCE. 90:(EM5):1964;147-171.
18. Rice S.O. Mathematical analysis of random noise. Bell Syst Technol J. 32:1944;282-332.
19. Rice S.O. Mathematical analysis of random noise. Bell Syst Technol J. 33:1945;46-156.
20. Belayev Y.K. On the number of exits across the boundary of a region by a vector stochastic process. Theor Probab Appl. 13:1968;320-324.
21. Cramer H., Leadbetter M.R. Stationary and related processes. 1967;Wiley, New York.
22. Breitung K., Rackwitz R. Nonlinear combinaison of load processes. J Struct Mech. 10:(2):1982;145-166.
23. Abdo T., Rackwitz R. A new β-point algorithm for large time invariant and time-variant reliability problems. Reliability and optimization of structures. Proceedings of the Third WG 7.5 IFIP Conference, Berkeley. 1990.
24. Bryla P., Faber M.H., Rackwitz R. Second order methods in time-variant reliability. Proceedings of the OMAE'91. vol. II:1991;. p. 143-50.
25. Hagen O. Threshold up-crossing by second order methods. Probab Engng Mech. 7:1992;235-241.
26. Ditlevsen O., Madsen H.O. Structural reliability methods. 1996;Wiley, New York.
27. Schuëller G. A state-of-the-art report on computational stochastic mechanics. Probab Engng Mech. 12:(4):1997.
28. Sudret B, Der Kiureghian A. Stochastic finite element methods and reliability. A state-of-the-art report, Report No. UCB/SEMM-2000/08, University of California Berkeley; 2000.
29. Li C.C., Der Kiureghian A. Optimal discretization of random fields. J Engng Mech. 119:(6):1993;1136-1154.
30. Andrieu C., Lemaire M., Sudret B. Time-variant reliability using the PHI2 method: principles and validation by Monte Carlo simulation. Der Kiureghian A., Madanat S., Pestana J.M. Proceedings of the Ninth International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP9). 2003;27-34 Millpress, Rotterdam.
31. BPEL. Règles techniques de conception et de calcul des ouvrages et constructions en béton précontraint suivant la méthode des états limites, Eyrolles. 1991.