Response probability density functions of strongly non-linear systems by the path integration method

Iourtchenko, D. V.; Mo, Eirik; Næss, Arvid

doi:10.1016/j.ijnonlinmec.2006.04.002

Cited by 57 publications

(16 citation statements)

References 17 publications

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“…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%

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%

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

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“…It can be handled by conventional methods such as cell mapping technique [6] or Path Integration (PI) approach. Despite some advantage of one method over another, finding a joint response PDF of a generally nonlinear multi-degree-of-freedom (MDOF) system is computationally challenging and expensive, therefore mostly low dimensional 1 − 2 DOF systems resulted in 2 − 4D FPK equation (not counting time) have been analyzed, although the amount of real time required was tremendous [7][8][9][10]. The fact that the higher the order of a system the heavier the computational costs generated a term the curse of dimensionality.…”

Section: Introductionmentioning

confidence: 99%

GPU computing for accelerating the numerical Path Integration approach

Alevras

Yurchenko

2016

Computers & Structures

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The paper discusses a novel approach of accelerating the numerical Path Integration method, used for generating a stationary joint response probability density function of a dynamic system subjected to a random excitation, by the GPU computing. The paper proposes the parallelization of nested loops technique and demonstrates the advantages of GPU computing. Two, three and four dimensional in space problems are investigated as a part of the pilot project and the achieved maximum accelerations are reported. Three degree-of-freedom system (6D) is approached by the Path Integration technique for the first time. The application of the proposed GPU methodology for problems of stochastic dynamics and reliability are discussed.

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“…In this context, the so-called Path Integral (PI) technique, developed for the PDF determination of systems under normal and Poissonian white noise [10][11][12][13], has been modified and adapted for the solution of the first-passage problem of nonlinear systems [5,14,15].…”

Section: Introductionmentioning

confidence: 99%

Path Integral Method for First-Passage Probability Determination of Nonlinear Systems Under Levy White Noise

Bucher¹,

Matteo²,

Paola³

et al. 2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. In this paper the problem of the first-passage probabilities determination of nonlinear systems under alpha-stable Lévy white noises is addressed. Based on the properties of alpha-stable random variables and processes, the Path Integral method is extended to deal with nonlinear systems driven by Lévy white noises with a generic value of the stability index alpha. Furthermore, the determination of reliability functions and first-passage time probability density functions is handled step-by-step through a modification of the Path

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Response probability density functions of strongly non-linear systems by the path integration method

Cited by 57 publications

References 17 publications

Nonlinear MDOF system Survival Probability Determination Subject to Evolutionary Stochastic Excitation

Nonlinear MDOF system Survival Probability Determination Subject to Evolutionary Stochastic Excitation

GPU computing for accelerating the numerical Path Integration approach

Path Integral Method for First-Passage Probability Determination of Nonlinear Systems Under Levy White Noise

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