Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods

Publikation: Bog/antologi/afhandling/rapportRapportForskning

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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 outcrossing. 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 hence for the first passage probability density. 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 2 dominating frequencies in the structural response.
OriginalsprogEngelsk
ForlagInstitut for Bygningsteknik, Aalborg Universitetscenter
Antal sider16
StatusUdgivet - 1986
NavnStructural Reliability Theory
NummerR8618
Vol/bind21
ISSN0105-7421

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random vibration
probability density functions
integral equations
intervals
approximation
distribution functions
simulation

Emneord

  • Random Vibration
  • Stochastic Processes
  • First Passage Failure
  • Bimodal Processes
  • Integral Equations

Citer dette

Nielsen, S. R. K., & Sørensen, J. D. (1986). Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods. Institut for Bygningsteknik, Aalborg Universitetscenter. Structural Reliability Theory , Nr. R8618, Bind. 21
Nielsen, Søren R.K. ; Sørensen, John Dalsgaard. / Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods. Institut for Bygningsteknik, Aalborg Universitetscenter, 1986. 16 s. (Structural Reliability Theory ; Nr. R8618, Bind 21).
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title = "Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods",
abstract = "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 outcrossing. 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 hence for the first passage probability density. 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 2 dominating frequencies in the structural response.",
keywords = "Random Vibration, Stochastic Processes, First Passage Failure, Bimodal Processes, Integral Equations, Random Vibration, Stochastic Processes, First Passage Failure, Bimodal Processes, Integral Equations",
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Nielsen, SRK & Sørensen, JD 1986, Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods. Structural Reliability Theory , nr. R8618, bind 21, Institut for Bygningsteknik, Aalborg Universitetscenter.

Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods. / Nielsen, Søren R.K.; Sørensen, John Dalsgaard.

Institut for Bygningsteknik, Aalborg Universitetscenter, 1986. 16 s. (Structural Reliability Theory ; Nr. R8618, Bind 21).

Publikation: Bog/antologi/afhandling/rapportRapportForskning

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AU - Nielsen, Søren R.K.

AU - Sørensen, John Dalsgaard

PY - 1986

Y1 - 1986

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 outcrossing. 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 hence for the first passage probability density. 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 2 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 outcrossing. 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 hence for the first passage probability density. 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 2 dominating frequencies in the structural response.

KW - Random Vibration

KW - Stochastic Processes

KW - First Passage Failure

KW - Bimodal Processes

KW - Integral Equations

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KW - Stochastic Processes

KW - First Passage Failure

KW - Bimodal Processes

KW - Integral Equations

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Nielsen SRK, Sørensen JD. Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods. Institut for Bygningsteknik, Aalborg Universitetscenter, 1986. 16 s. (Structural Reliability Theory ; Nr. R8618, Bind 21).