Probability of First-Passage Failure for Nonstationary Random Vibration

1975 ◽  
Vol 42 (3) ◽  
pp. 716-720 ◽  
Author(s):  
J. B. Roberts
Keyword(s):  
White Noise ◽  
Barrier Height ◽  
Random Vibration ◽  
Series Solution ◽  
Short Pulse ◽  
Random Excitation ◽  
Numerical Results ◽  
Linear Oscillator ◽  
First Passage ◽  
First Passage Failure

The problem of calculating the probability of first-passage failure, Pf, is considered, for systems responding to a short pulse of nonstationary random excitation. It is shown, by an analysis based on the “in and exclusion” series, that, under certain conditions, Pf tends to Pf*, the probability calculated by assuming Poisson distributed barrier crossings, as the barrier height, b, tends to infinity. The first three terms in the series solution provide bounds to Pf which converge when b is large. Methods of estimating Pf from these terms are presented which are useful even when the series is divergent. The theory is illustrated by numerical results relating to a linear oscillator excited by modulated white noise.

First-passage failure of preisach hysteretic systems

2014 ◽  
Vol 27 (5) ◽  
pp. 477-485 ◽  
Author(s):  
Ming Xu ◽  
Xiaoling Jin ◽  
Yong Wang ◽  
Zhilong Huang
Keyword(s):  
First Passage ◽  
Hysteretic Systems ◽  
First Passage Failure

Break-out of dynamic balance of nonlinear ecosystems using first passage failure theory

2015 ◽  
Vol 80 (3) ◽  
pp. 1403-1411 ◽  
Author(s):  
S. L. Wang ◽  
X. L. Jin ◽  
Z. L. Huang ◽  
G. Q. Cai
Keyword(s):  
Dynamic Balance ◽  
First Passage ◽  
Failure Theory ◽  
First Passage Failure

An Integral Equation Method for the First-Passage Problem in Random Vibration

1984 ◽  
Vol 51 (3) ◽  
pp. 674-679 ◽  
Author(s):  
P. H. Madsen ◽  
S. Krenk
Keyword(s):  
Integral Equation ◽  
Random Vibration ◽  
Integral Equation Method ◽  
Nonstationary Process ◽  
Alternative Methods ◽  
Approximation Formula ◽  
First Passage ◽  
Special Cases ◽  
Nonstationary Stochastic Process ◽  
First Passage Problem

The first-passage problem for a nonstationary stochastic process is formulated as an integral identity, which produces known bounds and series expansions as special cases, while approximation of the kernel leads to an integral equation for the first-passage probability density function. An accurate, explicit approximation formula for the kernel is derived, and the influence of uni or multi modal frequency content of the process is investigated. Numerical results provide comparisons with simulation results and alternative methods for narrow band processes, and also the case of a multimodal, nonstationary process is dealt with.

Sign in / Sign up

Export Citation Format

Share Document