Dual Probabilistic Analysis of the Transient Heat Transfer by the Stochastic Finite Element Method With Optimized Polynomial Basis

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.

On Selecting Composite Functions Based on Polynomials for Responses Describing Extreme Magnitudes of Structures

“…The weighed one is only auxiliary. When considering many approximations fa(b), the selection of the final response function in the initial stage of RFM development was made arbitrarily [30,66], while now it is the subject of additional optimization [57,65,67,68] related to curve fitting error measures (see Section 2.3): correlation maximization, minimization of the root-meansquare error (RMSE) or the residues variance. In addition to or interchangeably with the criteria calculated between the discrete data and the approximation, analogous magnitudes calculated in-between the LSM and the WLSM solutions are used [28,42]the weights change in calculations does not affect how the structure behaves in reality.…”