Dual interval-and-fuzzy analysis method for temperature prediction with hybrid epistemic uncertainties via polynomial chaos expansion

Abstract

In both mathematical theory and engineering application, the uncertainty propagation problem with incomplete knowledge, especially when different types of epistemic uncertainties exist simultaneously, has been recognized as a challenge issue. By using interval variables and fuzzy variables to characterize the hybrid uncertainties with only boundary information and membership function, this paper proposes a new dual interval-and-fuzzy response analysis method for the thermal engineering system. In the presented dual-stage analysis framework, the temperature response ranges with respect to interval variables are firstly derived, and then the membership functions of response bounds with respect to fuzzy variables are calculated in virtue of level-cut strategy and fuzziness reconstruction. To avoid the huge computational burden caused by repetitive FEM simulations, the Legendre polynomial chaos expansion is adopted as the surrogate model for temperature response. Two Clenshaw–Curtis point-based collocation methods are proposed to calculate the polynomial expansion coefficients, where CCP-CM constructs the collocation points via full tensor product grids, and CCP-MCM employs Smolyak algorithm to reconstruct the sparse grid collocation points. By comparing results with traditional Monte Carlo simulation, a numerical example about a 3D sandwich structure is provided to verify the effectiveness of proposed methodology in practical engineering.