Uncertain temperature field prediction of heat conduction problem with fuzzy parameters

Abstract

This paper proposes a first-order fuzzy perturbation finite element method (FFPFEM) and a modified fuzzy perturbation finite element method (MFPFEM) for the uncertain temperature field prediction with fuzzy parameters in material properties, external loads and boundary conditions. Fuzzy variables are used to represent the subjective uncertainties associated with the expert opinions. Based on the α-cut method, the finite element equilibrium equation is equivalently transformed into groups of interval equations. The interval matrices and vectors in both methods are expanded by the first-order Taylor series. First-order Neumann series is employed in FFPFEM for the inversion of interval matrix, while some high-order terms of the Neumann series are retained in MFPFEM. Based on the fuzzy decomposition theorem, the fuzzy solutions to the original uncertain heat conduction problem are eventually derived. By comparing the results with traditional Monte Carlo simulation and vertex method, two numerical examples evidence the feasibility and effectiveness of the proposed methods at predicting the fuzzy temperature field in engineering.