Calculating sensitivities of thermal systems with uncertain properties using the stochastic finite element method and finite differencing

摘要

A very effective way of determining the statistical characteristics of a system's response to random parameters or boundary conditions is to compute the sensitivities using the Stochastic Finite Element method or by finite differencing the finite element solutions of the response. For constant properties, the two approaches are comparable in accuracy and efficiency. For temperature dependent properties, most finite element methods represent the temperature dependency by piecewise continuous linear segments and there is a question about the effect of imprecisions in specifying the endpoints of the segments on the accuracy of the computed sensitivity in both approaches. This paper examines a one-dimensional steady state problem which is very sensitive to a temperature varying conductivity to study the effect of the endpoints and the accuracy and efficiency of the two methods.