Uncertainty analysis for heat convection-diffusion problem with large uncertain-but-bounded parameters

Abstract

To extend the restricted applicability of the traditional perturbation method with small uncertainty level, this paper presents a first-order subinterval parameter perturbation method (FSPPM) and a modified subinterval parameter perturbation method (MSPPM) to solve the heat convection-diffusion problem with large interval parameters in material properties, external loads and boundary conditions. Based on the subinterval theory, the original uncertain-but-bounded parameters with limited information are divided into several small subintervals. The eventual response interval is assembled by the interval union operation. In both methods, the Taylor series is used to approximate the interval matrix and vector. The inversion of interval matrix in FSPPM is evaluated by the first-order Neumann series, while the modified Neumann series with higher-order terms is proposed to calculate the interval matrix inverse in MSPPM. By comparing the results with the traditional Monte Carlo simulation, two numerical examples evidence the remarkable accuracy and effectiveness of the proposed methods at predicting an uncertain temperature field in engineering.