Subinterval perturbation methods for uncertain temperature field prediction with large fuzzy parameters

Based on the perturbation technology and fuzzy theory, this paper proposes a first-order subinterval perturbation method (FSPM) and a modified subinterval perturbation method (MSPM) to solve the uncertain heat conduction problem with large fuzzy parameters. Using the level-cut strategy and subinterval methodology, the original fuzzy parameters with subjective probability are firstly decomposed into several subinterval variables, while the eventual fuzzy temperature responses are reconstructed by the interval union operation and decomposition theorem. In both perturbation methods, the subinterval matrix and vector are expanded by the Taylor series. The inversion of subinterval matrix in FSPM is approximated by the first-order Neumann series, whereas the modified Neumann series with higher order terms is adopted to calculate the subinterval matrix inverse in MSPM. Comparing the results with traditional Monte Carlo simulations, two numerical examples evidence the remarkable accuracy and effectiveness of the proposed methods to predict uncertain temperature field in engineering.