Uncertainty Quantification of a 1-D Beam Deflection Due to Stochastic Parameters

El-Beltagy, Mohamed A.; Galal, Osama H.; Wafa, Mohamed I.

doi:10.1063/1.3637007

“…The obtained results showed that the uncertainty associated with load is very small, whereas the dimension uncertainty has a significant effect on the uncertainty of estimation of beam deflection [10]. The effect of the uncertain system parameters on the deflection of a simply supported beam are studied by using stochastic finite volume method considering stochastic modulus of elasticity and stochastic load [11]. A bayessian finite element approach is adapted to update system parameters [12].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Regression Based Approach for Beam Deflection Estimation

Batbooti,

Mohammed,

Jabbar

et al. 2023

Adv. Sci. Technol. Res. J.

1

0

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Deflection of a beam is the movement of the beam from its initial position to another position depending on the applied load. Beam deflection estimation gives an indication about the possible deformation of the beam. A parametric Bayesian linear based model is introduced to mimic the experimentally collected data to estimate the stochastic deflection of a simply supported beam. A Gaussian noise is assumed to understand the stochastic behavior of the beam deflection as well as a Gaussian prior. The model mapping function used in this work is known as radial basis function, which can be linear or nonlinear. Three basis functions are compared, namely are linear, Gaussian and modified Gaussian function proposed in this work. The modified Gaussian function is a simple function introduced in this work. The performance of the functions is analyzed for three central concentrated loads. The best model can describe the observed data is found to be the modified Gaussian model with regularization factor of 0.9 for three loading cases. The prediction based linear basis function is better than the use of the Gaussian basis function prediction according to error of estimation. The maximum RMS error obtained for modified Gaussian radial basis function corresponding to central load of 4 kg is smaller than that of a theoretical based model for the same loading conditions.

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“…Later, El-Beltagy et al [11] developed this method to include the effect of random load and random modulus of elasticity using both of RBF neural network and polynomial chaos expansion (PCE).…”

Section: Introductionmentioning

confidence: 99%

Upwind Finite-Volume Solution of Stochastic Burgers’ Equation

El-Beltagy¹

2012

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In this paper, a stochastic finite-volume solver based on polynomial chaos expansion is developed. The upwind scheme is used to avoid the numerical instabilities. The Burgers' equation subjected to deterministic boundary conditions and random viscosity is solved. The solution uncertainty is quantified for different values of viscosity. Monte-Carlo simulations are used to validate and compare the developed solver. The mean, standard deviation and the probability distribution function (p.d.f) of the stochastic Burgers' solution is quantified and the effect of some parameters is investigated. The large sparse linear system resulting from the stochastic solver is solved in parallel to enhance the performance. Also, Monte-Carlo simulations are done in parallel and the execution times are compared in both cases.

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Upwind Finite-Volume Solution of Stochastic Burgers’ Equation

El-Beltagy¹,

Wafa²,

Galal³

2012

AM

4

0

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In this paper, a stochastic finite-volume solver based on polynomial chaos expansion is developed. The upwind scheme is used to avoid the numerical instabilities. The Burgers' equation subjected to deterministic boundary conditions and random viscosity is solved. The solution uncertainty is quantified for different values of viscosity. Monte-Carlo simulations are used to validate and compare the developed solver. The mean, standard deviation and the probability distribution function (p.d.f) of the stochastic Burgers' solution is quantified and the effect of some parameters is investigated. The large sparse linear system resulting from the stochastic solver is solved in parallel to enhance the performance. Also, Monte-Carlo simulations are done in parallel and the execution times are compared in both cases.

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Uncertainty Quantification of a 1-D Beam Deflection Due to Stochastic Parameters

Cited by 3 publications

References 4 publications

Bayesian Regression Based Approach for Beam Deflection Estimation

Bayesian Regression Based Approach for Beam Deflection Estimation

Upwind Finite-Volume Solution of Stochastic Burgers’ Equation

Upwind Finite-Volume Solution of Stochastic Burgers’ Equation

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