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A mixed spectral treatment for the stochastic models with random parameters

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Abstract

In this paper, a mixed spectral technique is suggested for the analysis of stochastic models with parameters having random variations. The proposed mixed technique considers a Volterra-like expansions for all types of randomness. Particularly, the generalized polynomial chaos (gPC) expansion is used for the random parameters and the Wiener–Hermite functionals (WHF) technique is used for the noise. The statistical properties of the functionals enables to derive a deterministic system used to evaluate the solution statistical moments. The new mixed technique is shown to be efficient compared with the classical techniques and analytical solutions could be obtained in many cases. The suggested technique allows to separate the contributions of the different random sources and hence enables to evaluate variance components which are used to estimate the sensitivity indices. The technique is applied successfully to different models with additive and multiplicative noise and compared with the classical sampling techniques. The stochastic nuclear reactor model with random parameters is analyzed with the new technique.

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Authors and Affiliations

  1. Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza, 12613, Egypt

    Mohamed A. El-Beltagy

  2. Mathematics Department, Science Faculty, Tabuk University, Tabuk, Saudi Arabia

    Amnah Al-Juhani

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  1. Mohamed A. El-Beltagy
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  2. Amnah Al-Juhani
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Correspondence to Mohamed A. El-Beltagy.

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El-Beltagy, M.A., Al-Juhani, A. A mixed spectral treatment for the stochastic models with random parameters. J Eng Math 132, 1 (2022). https://doi.org/10.1007/s10665-021-10179-3

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