First Excursion Probabilities for Low Threshold Levels by Differentiable Processes

  • C. Lange
Part of the Lecture Notes in Engineering book series (LNENG, volume 76)

Abstract

A general method for the calculation of first excursion probabilities of stochastic processes, vector processes or fields is presented with particular reference to applications to reliability problems in mechanics. Based on a discrete random variable representation of excursion events different approximations of first excursion probabilities are studied. A Gram-Charlierseries expansion for the case of low levels as well as results about convergence are derived. Some examples illustrate the results.

Keywords

Fatigue 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. /1/.
    ADLER, R.J. The geometry of random fiels. Wiley, London 1981Google Scholar
  2. /2/.
    BOLOTIN, V.V. ahrscheinlichkeitsmethoden zur Berechnung von Konstruktionen. Verlag für Bauwesen, Berlin 1981Google Scholar
  3. /3/.
    BREITUNG, K. Asymptotic crossing rates for stationary Gaussion vector processes. Stoch. Pr. and their Appl. 29, 1988, 195–207CrossRefMATHMathSciNetGoogle Scholar
  4. /4/.
    CRAMER, H.; LEADBETTER, M.R. Stationary and related processes. Wiley, New York 1969MATHGoogle Scholar
  5. /5/.
    FISZ, M. Wahrscheinlichkeitsrechnung und mathematische Statistik. Deutscher Verlag der Wissenschaften, Berlin 1973Google Scholar
  6. /6/.
    FRIEDRICH, H.; LANGE, C. Stochastisch beanspruchte mechanische Systeme. Fachbuchverlag, Leipzig (in print)Google Scholar
  7. /7/.
    GAGANOV, V.A. Ob ozenkach momentov tschisla peresetscheni nulevo urovnja Gaussovskim stationarym prozessom. Vestnik LGU, 1973, 1, 136–138MathSciNetGoogle Scholar
  8. /8/.
    HOHENBICHLER, M.; RACKWITZ, R. Asymptotic crossing rate of Gaussian vector processes into intersections of failure domains. Prob. Eng. Mech. 1, 3, 1986, 177–179CrossRefGoogle Scholar
  9. /9/.
    KAISER, W.; KNÖFEL, L., FRIEDRICH H., LANGE, C. Erdbebenerregte Rundlaufkrane. Forschungsbericht, AdW, IMech, Berlin 1985, 104 pp.Google Scholar
  10. /10/.
    KENDALL, M.G. The advanced theory of statistics. Vol. I, II, Griffin, London 1948Google Scholar
  11. /11/.
    LANGE, C.; FRIEDRICH, H. Zuverlässigkeitsuntersuchungen für mechanische Systeme auf der Grundlage zufälliger Felder. FMC-Series No. 43, AdW, IMech, Chemnitz 1989, 90 pp.Google Scholar
  12. /12/.
    LEADBETTER, M.R.; LINDGREN, G.; ROOTZEN, H. Extremes and related properties of random sequences and. processes. Springer, New York 1983CrossRefMATHGoogle Scholar
  13. /13/.
    LEVENBACH, H. The zero-crossing problems. Queen’s Univ., Kingston, Ont. Res. Rep. 63–4, 1963Google Scholar
  14. /14/.
    MIROSHIN, P.N. Dostatotschnoje ulsowie konetschnosti momentov tschisla nulej dlja differenzirujemovo Gaussovskovo stationarnovo processa. Teor. verojatn. i ee primen., 1973, 3, 481–490Google Scholar
  15. /15/.
    MIROSHIN, P.N. Asymptotika vtorovo momenta tschisla peresetscheni prjamoi kt+a Gaussovskim stationarnym processom. Vestnik LGU, 1972, 19, 106–112Google Scholar
  16. /16/.
    MIROSHIN, P.N.; ZVETKOV, V.I. Asymptotika tretjevo momenta tschisla peresetscheni prjamoi kt+a Gaussovskim stationarnym prozessom. Vestnik LGU, 1977, 1, 90–97Google Scholar
  17. /17/.
    RICE, S.O. Mathematical analysis of random noise. Bell. System Tech. J. 23, 145, 282–232; 24, 1945, 46–156Google Scholar
  18. /18/.
    STRATONOVICH, R.L. Topics in the theory random noise. Vol. I., Gordon and Breach, New York 1963Google Scholar
  19. /19/.
    VOLKONSKI, V.A.; ROSANOV, J.A. Einige Grenzwertsätze für Zufallsfunktionen. I, II, Teor. veroj. i ee primen. 1959, 4, 1986–207; 1961, 6, 203–215Google Scholar

Copyright information

© International Federation for Information Processing, Geneva, Switzerland 1992

Authors and Affiliations

  • C. Lange
    • 1
  1. 1.Institut für MechanikChemnitzGermany

Personalised recommendations