A mixed spectral treatment for the stochastic models with random parameters

El-Beltagy, Mohamed A.; Al-Juhani, Amnah

doi:10.1007/s10665-021-10179-3

Cited by 2 publications

(1 citation statement)

References 31 publications

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“…[10]), or coupled approaches (e.g. [11,12]). We focus solely on polynomial chaos, even though all of the content presented below can be easily transposed to other surrogates.…”

Section: Introductionmentioning

confidence: 99%

Verification of polynomial chaos surrogates in the framework of structural vibrations with uncertainties

Serra,

Florentin

2023

Mechanics & Industry

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Surface response models, such as polynomial chaos Expansion, are commonly used to deal with the case of uncertain input parameters. Such models are only surrogates, so it is necessary to develop tools to assess the level of error between the reference solution (unknown in general), and the value provided by the surrogate. This is called a posteriori model verification. In most works, people usually search for the mean quadratic error between the reference problem and the surrogate. They use statistical approaches such as resampling or cross-fold validation, residual based approaches, or properties of the surrogate such as variance decay. Here, we propose a new approach for the specific framework of structural vibrations. Our proposition consists of a residual-based approach combined with a polynomial chaos expansion to evaluate the error as a full random variable, not only its mean square. We propose different variants for evaluating the error. Simple polynomial interpolation gives good results, but introducing a modal basis makes it possible to obtain the error with good accuracy and very low cost.

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“…[10]), or coupled approaches (e.g. [11,12]). We focus solely on polynomial chaos, even though all of the content presented below can be easily transposed to other surrogates.…”

Section: Introductionmentioning

confidence: 99%

Verification of polynomial chaos surrogates in the framework of structural vibrations with uncertainties

Serra,

Florentin

2023

Mechanics & Industry

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Dual Solutions and Stability Analysis for Buongiorno Model of Magnetohydrodynamics Nanofluid Flow Past a Heated Shrinking Slippery Surface

Tshivhi

Makinde

2023

j nanofluids

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This study investigates the combined effects of magnetic field, Joule heating, viscous dissipation, thermophoresis, and Brownian motion towards a convectively heated shrinking and slippery surface on a stagnation point flow of nanofluid is theoretically examined. The modified Buongiorno model for nanofluid flow is employed and numerically solved using a shooting technique together with the Runge-Kutta-Fehlberg integration scheme. It is found that dual solutions appear in certain range of shrinking surface parameter. The temporal stability analysis of the dual solutions to small disturbances was performed and the upper solution branch is found to be a stable and physically realistic solution to the problem. Appropriate results showing the influence of magnetic field, Surface slipperiness, Eckert number, Biot number, Brownian motion, and thermophoresis parameters on the nanofluid temperature, velocity, nanoparticles concentration, Nusselt number, skin friction, and Sherwood number are quantitatively discussed, and depicted graphically and in tables.

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A mixed spectral treatment for the stochastic models with random parameters

Cited by 2 publications

References 31 publications

Verification of polynomial chaos surrogates in the framework of structural vibrations with uncertainties

Verification of polynomial chaos surrogates in the framework of structural vibrations with uncertainties

Dual Solutions and Stability Analysis for Buongiorno Model of Magnetohydrodynamics Nanofluid Flow Past a Heated Shrinking Slippery Surface

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