An exact solution of the first-exit time problem for a class of structural systems

Kovaleva, Agnessa

doi:10.1016/j.probengmech.2009.01.002

Cited by 12 publications

(2 citation statements)

References 8 publications

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Section: Introductionmentioning

confidence: 99%

“…Indicatively, one of the early approaches, restricted to linear systems, relies on the knowledge of the mean up-crossing rates and on Poisson distribution based approximations (e.g., [5] to [7]). Further attempts to address the firstpassage problem range from analytical ones (e.g., [8]) to numerical ones (e.g., [9]). Furthermore, techniques based on the concepts of the numerical path integral (e.g., [10] to [13]), of the probability density evolution (e.g., [3]), or of stochastic averaging/linearization (e.g., [14]) constitute some of the more recent approaches.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear MDOF system Survival Probability Determination Subject to Evolutionary Stochastic Excitation

Mitseas¹,

Kougioumtzoglou²,

Spanos³

et al. 2016

SV-JME

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440 INTRODUCTIONExcitations acting upon dynamical systems such as wind, wave, and seismic loads commonly exhibit evolutionary features. In this setting, not only the intensity of the excitation but also its frequency content exhibit strong variability. This fact necessitates the representation of this class of structural loads by non-stationary stochastic processes. Further, structural systems under severe excitations can exhibit significant nonlinear behavior of the hysteretic kind. Thus, of particular interest to the structural dynamics community is the development of techniques for determining the response and assessing the reliability of nonlinear/hysteretic systems subject to evolutionary stochastic excitations (e.g.,Further, in engineering dynamics, the evaluation of the probability that the system response stays within prescribed limits for a specified time interval is advantageous for reliability based system design applications. In this regard, the first-passage problem, that is, the determination of the above time-variant probability known as survival probability, has been a persistent challenge in the field of stochastic dynamics for many decades.Monte Carlo simulation techniques are among the most potent tools for assessing the reliability of a system (e.g. [4]). Nevertheless, there are cases where the computational cost of these techniques can be prohibitive, especially when large-scale complex systems are considered; thus, rendering the development of alternative efficient approximate analytical/numerical techniques for addressing the first-passage problem necessary. Indicatively, one of the early approaches, restricted to linear systems, relies on the knowledge of the mean up-crossing rates and on Poisson distribution based approximations (e.g., [5] to [7]). Further attempts to address the firstpassage problem range from analytical ones (e.g., [8]) to numerical ones (e.g., [9]

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear MDOF system Survival Probability Determination Subject to Evolutionary Stochastic Excitation

Mitseas¹,

Kougioumtzoglou²,

Spanos³

et al. 2016

SV-JME

View full text Add to dashboard Cite

show abstract

Reliability function determination of nonlinear oscillators under evolutionary stochastic excitation via a Galerkin projection technique

2018

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Efficient path integral approach via analytical asymptotic expansion for nonlinear systems under Gaussian white noise

Di Matteo,

Pirrotta

2024

Nonlinear Dyn

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In this paper an efficient formulation of the Path integral (PI) approach is developed for determining the response probability density functions (PDFs) and first-passage statistics of nonlinear oscillators subject to stationary and time-modulated external Gaussian white noise excitations. Specifically, the evolution of the response PDF is obtained in short time steps, by using a discrete version of the Chapman-Kolmogorov equation and assuming a Gaussian form for the conditional response PDF. Next, the technique involves proceeding to treating the problem via an analytical asymptotic expansion procedure, namely the Laplace’s method of integration. In this manner, the repetitive double integrals involved in the standard implementation of the PI approach are evaluated in a closed form, while the response and first-passage PDFs are obtained by mundane step-by-step application of the derived approximate analytical expression. It is shown that the herein proposed formulation can drastically decrease the associated computational cost by several orders of magnitude, as compared to both the standard PI technique and Monte Carlo solution (MCS) approach. A number of nonlinear oscillators are considered in the numerical examples. Notably, for these systems both response PDFs and first-passage probabilities are presented, whereas comparisons with pertinent MCS data demonstrate the efficiency and accuracy of the technique.

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An exact solution of the first-exit time problem for a class of structural systems

Cited by 12 publications

References 8 publications

Nonlinear MDOF system Survival Probability Determination Subject to Evolutionary Stochastic Excitation

Nonlinear MDOF system Survival Probability Determination Subject to Evolutionary Stochastic Excitation

Reliability function determination of nonlinear oscillators under evolutionary stochastic excitation via a Galerkin projection technique

Efficient path integral approach via analytical asymptotic expansion for nonlinear systems under Gaussian white noise

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