Probability of Failure in Random Vibration

Søren R.K. Nielsen, John Dalsgaard Sørensen

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

3 Citationer (Scopus)

Resumé

Close approximations to the first-passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first-passage probability density function and the distribution function for the time interval spent below a barrier before out-crossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval and thus for the first-passage
probability density. As a result of the theory, an exact inclusion-exclusion series for the first passage density function in terms of unconditional joint crossing rates is obtained. The results of the theory agree well with simulation results for narrow-banded processes dominated by a single frequency, as well as for bimodal processes with two dominating frequencies in the structural response.
OriginalsprogEngelsk
TidsskriftJournal of Engineering Mechanics
Vol/bind114
Udgave nummer7
Sider (fra-til)1218-1230
Antal sider13
ISSN0733-9399
DOI
StatusUdgivet - 1988

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Probability density function
Integral equations
Distribution functions

Emneord

  • Vibration
  • Failures
  • Probability Density Functions
  • Time Series Analysis

Citer dette

Nielsen, Søren R.K. ; Sørensen, John Dalsgaard. / Probability of Failure in Random Vibration. I: Journal of Engineering Mechanics. 1988 ; Bind 114, Nr. 7. s. 1218-1230.
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Probability of Failure in Random Vibration. / Nielsen, Søren R.K.; Sørensen, John Dalsgaard.

I: Journal of Engineering Mechanics, Bind 114, Nr. 7, 1988, s. 1218-1230.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Probability of Failure in Random Vibration

AU - Nielsen, Søren R.K.

AU - Sørensen, John Dalsgaard

PY - 1988

Y1 - 1988

N2 - Close approximations to the first-passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first-passage probability density function and the distribution function for the time interval spent below a barrier before out-crossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval and thus for the first-passageprobability density. As a result of the theory, an exact inclusion-exclusion series for the first passage density function in terms of unconditional joint crossing rates is obtained. The results of the theory agree well with simulation results for narrow-banded processes dominated by a single frequency, as well as for bimodal processes with two dominating frequencies in the structural response.

AB - Close approximations to the first-passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first-passage probability density function and the distribution function for the time interval spent below a barrier before out-crossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval and thus for the first-passageprobability density. As a result of the theory, an exact inclusion-exclusion series for the first passage density function in terms of unconditional joint crossing rates is obtained. The results of the theory agree well with simulation results for narrow-banded processes dominated by a single frequency, as well as for bimodal processes with two dominating frequencies in the structural response.

KW - Vibration

KW - Failures

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KW - Time Series Analysis

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KW - Failures

KW - Probability Density Functions

KW - Time Series Analysis

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