Hybrid uncertainty propagation of coupled structural acoustic system with large fuzzy and interval parameters
Abstract Based on the finite element framework and uncertainty analysis theory, this paper proposes a first order subinterval perturbation finite element method (FSPFEM) and a modified subinterval perturbation finite element method (MSPFEM) to solve the uncertain structural acoustic problem with large fuzzy and interval parameters. Fuzzy variables are used to represent the subjective uncertainties associated with the expert opinions; whereas, interval variables are adopted to quantify the objective uncertainties with limited information. By using the level cut strategy and subinterval methodology, the original large fuzzy and interval parameters are decomposed into several subintervals with small uncertainty level. In both FSPFEM and MSPFEM, the subinterval matrix and vector are expanded by the Taylor series. The inversion of subinterval matrix in FSPFEM is approximated by the first order Neumann series, while the modified Neumann series with higher order terms is adopted in MSPFEM. The eventual fuzzy interval frequency responses are reconstructed by the interval union operation and fuzzy decomposition theorem. A numerical example evidences the remarkable accuracy and effectiveness of the proposed methods to solve engineering structural acoustic problems with hybrid uncertain parameters.