Hybrid uncertain analysis for temperature field prediction with random, fuzzy and interval parameters

• Random, fuzzy and interval parameters are considered simultaneously.
• Fuzzy parameters are decomposed to interval variables based on level-cut method.
• Perturbation theory and random interval moment method are combined.
• Membership functions are reconstructed based on fuzzy decomposition theorem.

This paper presents a hybrid uncertain finite element method (HUFEM) for the uncertain temperature field prediction involving random, fuzzy and interval parameters simultaneously in material properties, external loads and boundary conditions. Random variables are used to quantify the stochastic uncertainty with sufficient experiment data; whereas, fuzzy and interval variables are adopted to model the non-probabilistic uncertainties associated with expert opinions and limited information, respectively. By decomposing fuzzy parameters into interval variables based on level-cut strategy, inversion of the transformed interval random matrix is approximated by the first-order Neumann series first. Then the interval bounds of the probabilistic characteristics of temperature response can be calculated by using the random interval moment method. Their membership functions are eventually derived on the basis of fuzzy decomposition theorem. Numerical results demonstrate the feasibility and effectiveness of HUFEM to solve heat conduction problems with hybrid or pure uncertain parameters.