On the Distribution of the First-Passage Time for Normal Stationary Random Processes

Vanmarcke, Erik H.

doi:10.1115/1.3423521

Cited by 510 publications

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“…In this equation, f a denotes the mean rate of B-crossings [18], defined as crossings of the barrier level from below [28], and q e is an empirical shape factor of the PSD of the response process [28],…”

Section: Discussionmentioning

confidence: 99%

“…The evaluation of the peak factors p k , p i and p g is based on the common assumption of the first-passage probability for normal stationary random processes X (t) with zero mean as proposed by Vanmarcke [28]. For details it is referred to [4,5,13,27,28].…”

Section: Discussionmentioning

confidence: 99%

“…The ith modal peak factor, p i , and the peak factor of the ground acceleration p g are determined according to [28] …”

Section: Discussionmentioning

confidence: 99%

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Peak floor acceleration demand prediction based on response spectrum analysis of various sophistication

Moschen

Adam

2016

Acta Mech

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This paper addresses the prediction of the median peak floor total acceleration (PFA) demand in spatial elastic structures subjected to seismic excitation. The prediction is based on various response spectrum methods of different degrees of sophistication. Beginning with a recently presented complete-quadraticcombination (CQC) rule for PFA demands, several approximations and simplifications concerning the correlation between modal contributions, peak factors, and cross-spectral moments are discussed, leading to the proposed modified modal combination rules. On several earthquake-excited multi-story spatial generic frame structures, the accuracy of the considered rules is assessed. The outcomes of response history analysis serves as benchmark solution. The results show that the modified CQC rules are simple in practical application and lead to reliable estimations of the median PFA demand of spatial structures with negligible loss of accuracy if peak factors are considered.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Peak floor acceleration demand prediction based on response spectrum analysis of various sophistication

Moschen

Adam

2016

Acta Mech

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“…It is characterized by its probability density function which can be obtained by Monte Carlo simulations [9,29] or by resolution of the Chapman-Kolmogorov equation, via use of numerical [22] or semi-analytical methods such as a numerical path integration [48,21], approximation of the solution by a Galerkin scheme [37,36], a Poisson distribution based assumption [3]. These numerical approaches are important because there are very few problems in which the distribution of the first passage time can be established in closed-form [44,40]. This work seeks to provide an analytical understanding of this problem and therefore focuses on the average value of the first passage time instead of the complete distribution.…”

Section: First Passage Time Of the Parametric And Forced Oscillatorsmentioning

confidence: 99%

Average first-passage time of a quasi-Hamiltonian Mathieu oscillator with parametric and forcing excitations

Vanvinckenroye

Denoёl

2017

Journal of Sound and Vibration

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a b s t r a c tA linear oscillator simultaneously subjected to stochastic forcing and parametric excitation is considered. The time required for this system to evolve from a low initial energy level until a higher energy state for the first time is a random variable. Its expectation satisfies the Pontryagin equation of the problem, which is solved with the asymptotic expansion method developed by Khasminskii. This allowed deriving closed-form expressions for the expected first passage time. A comprehensive parameter analysis of these solutions is performed. Beside identifying the important dimensionless groups governing the problem, it also highlights three important regimes which are called incubation, multiplicative and additive because of their specific features. Those three regimes are discussed with the parameters of the problem.

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“…Particle absorption focuses mainly on random walks, however, a canonical case that does not necessarily extend to more general linear systems [1][2][3][4]. Seminal work by Crandall and others [5][6][7] explored the statistics of first-excursion for a lightly-damped oscillator with Gaussian process noise. Accurate formulas have been vigorously pursued especially for lightly damped oscillators, because a low damping ratio corresponds with long impulse responses, leading to a very long correlation time which complicates the analysis.…”

Section: Introductionmentioning

confidence: 99%

A Single Differential Equation for First-Excursion Time in a Class of Linear Systems

Greytak

Hover

2011

Journal of Dynamic Systems, Measurement, and Control

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First-excursion times have been developed extensively in the literature for oscillators; one major application is structural dynamics of buildings. Using the fact that most closed-loop systems operate with a moderate to high damping ratio, we have derived a new procedure for calculating first-excursion times, for a class of linear continuous, time-varying systems. In several examples we show that the algorithm is both accurate and timeefficient. These are important attributes for real-time path planning in stochastic environments, and hence the work should be useful for autonomous robotic systems involving marine and air vehicles. Nomenclature x(t)State vector. y(t)System output, scalar.A(t), G(t), C System matrices. w(t)Unit Wiener noise process, vector.Lower and upper boundaries, scalar. Σ Σ Σ(t)State covariance matrix.Σ y (t) Output covariance, scalar.P a (t) Probability of no collision, scalar.P hit (t) Collision probability, 1 − P a (t), scalar.

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On the Distribution of the First-Passage Time for Normal Stationary Random Processes

Cited by 510 publications

References 0 publications

Peak floor acceleration demand prediction based on response spectrum analysis of various sophistication

Peak floor acceleration demand prediction based on response spectrum analysis of various sophistication

Average first-passage time of a quasi-Hamiltonian Mathieu oscillator with parametric and forcing excitations

A Single Differential Equation for First-Excursion Time in a Class of Linear Systems

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