A unified propagation approach of stochastic-fuzzy uncertainties in nonlinear structural dynamic responses

This paper proposes a unified analysis method to address the dynamic response analysis of nonlinear structures under hybrid stochastic-fuzzy uncertainties. The method constructs two types of hybrid uncertainty models to handle different uncertainty scenarios: (1) the Stochastic-fuzzy model, in which stochastic variables and fuzzy variables follow independent distributions, and (2) the Fuzzy-stochastic model, where uncertain parameters are treated as stochastic variables with fuzzy distribution parameters. By employing α-cut set technology, the fuzziness is discretized, transforming the hybrid models into a stochastic-interval form. The Polynomial-Chaos-Chebyshev-Interval Method (PCCIM) is then developed by integrating Polynomial Chaos theory and the Chebyshev interval method, enabling efficient dynamic response analysis of structures with hybrid uncertainties under external excitation. The method solves system responses for different α-level sets, reconstructs the fuzzy membership distribution of response indicators, and completes structural performance evaluation. Numerical experiments have systematically validated the efficacy of the proposed method in addressing dual types of stochastic-fuzzy hybrid uncertainties, with significant improvements in computational efficiency compared with traditional methods like the Hybrid Monte Carlo Method (HMCM). The established universal analysis framework is suitable for various nonlinear structures, providing an innovative solution for multi-domain structural uncertainty quantification research. The results also reveal the complex dynamic behaviors of typical nonlinear structures, such as the two-degree-of-freedom wing structure, under hybrid uncertainties, highlighting the importance of considering both stochastic and fuzzy uncertainties in structural design and performance evaluation.