Temat: generalized polynomial chaos - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Numerical modeling of uncertainty in acoustic propagation via generalized Polynomial Chaos
Autorzy:: Dammak, Khalil
Koubaa, Sana
Elhami, Abdelkhalak
Walha, Lassaad
Haddar, Mohamed
Powiązania:: https://bibliotekanauki.pl/articles/280126.pdf
Data publikacji:: 2019
Wydawca:: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:: finite element simulation
uncertainty quantification
acoustic propagation
generalized Polynomial Chaos
Opis:: This work aims at increasing the performance prediction for acoustic propagation systems that will operate in the presence of the inevitable parameters uncertainty. In the present contribution, the finite element method is applied to solve an acoustic problem described by the Helmholz equation when the geometric and material properties present uncertainty. The influence of the uncertainty of physical parameters on the pressure field is discussed. The results using the polynomial chaos expansion method are compared with Monte Carlo simulations. It is show that uncertainty levels in the input data could result in large variability in the calculated pressure field in the domain.
Źródło:: Journal of Theoretical and Applied Mechanics; 2019, 57, 1; 3-15
1429-2955
Pojawia się w:: Journal of Theoretical and Applied Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: A dynamic bi-orthogonal field equation approach to efficient Bayesian inversion
Autorzy:: Tagade, P. M.
Choi, H. L.
Powiązania:: https://bibliotekanauki.pl/articles/330516.pdf
Data publikacji:: 2017
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:: Bayesian framework
stochastic partial differential equation
Karhunen–Loève expansion
generalized polynomial chaos
dynamically biorthogonal field equations
ramy Bayesa
stochastyczne równanie różniczkowe
przekształcenie Karhunena-Loeve'a
chaos wielomianowy
Opis:: This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen–Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE) that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs) define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.
Źródło:: International Journal of Applied Mathematics and Computer Science; 2017, 27, 2; 229-243
1641-876X
2083-8492
Pojawia się w:: International Journal of Applied Mathematics and Computer Science
Dostawca treści:: Biblioteka Nauki

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