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Budownictwo i Inżynieria Środowiska

Budownictwo i Inżynieria Środowiska
2017.93, DOI: 10.7862/rb.2017.93

DUAL PROBABILISTIC ANALYSIS OF THE TRANSIENT HEAT TRANSFER BY THE STOCHASTIC FINITE ELEMENT METHOD WITH OPTIMIZED POLYNOMIAL BASIS

Martyna RABENDA, Marcin KAMIŃSKI

DOI: 10.7862/rb.2017.93

Abstract

The main aim of this work is to contrast three various probabilistic computational techniques, namely analytical, simulation and perturbation-based, in a solution of the transient heat transfer problem in specific axisymmetric problem with Gaussian uncertainty in physical parameters. It is done thanks to a common application of the Finite Element Method program ABAQUS (for the deterministic part) and symbolic algebra system MAPLE, where all probabilistic procedures have been programmed. We determine up to the fourth order probabilistic characteristics of the resulting temperatures, i.e. expectations, coefficients of variation, skewness and kurtosis together with the histograms – all as the functions of the input coefficient of variation of random heat conductivity coefficient. Stochastic perturbation technique is implemented here using the tenth order Taylor series expansion and traditional Least Squares Method released with polynomial basis whose final order is a subject of the separate statistical optimization. Probabilistic results computed show almost perfect agreement of all the probabilistic characteristics under consideration, which means that the traditional simulation method may be replaced due to the time and computer scale savings with the stochastic perturbation method.

Full text (pdf)

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About this Article

TITLE:
DUAL PROBABILISTIC ANALYSIS OF THE TRANSIENT HEAT TRANSFER BY THE STOCHASTIC FINITE ELEMENT METHOD WITH OPTIMIZED POLYNOMIAL BASIS

AUTHORS:
Martyna RABENDA (1)
Marcin KAMIŃSKI (2)

AUTHORS AFFILIATIONS:
(1) Politechnika Łódzka
(2) Politechnika Łódzka

JOURNAL:
Budownictwo i Inżynieria Środowiska
2017.93

KEY WORDS AND PHRASES:
heat transfer; Stochastic Finite Element Method; Monte-Carlo simulation; stochastic perturbation technique

FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/biis/807

DOI:
10.7862/rb.2017.93

URL:
http://dx.doi.org/10.7862/rb.2017.93

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