An efficient hybrid uncertainty analysis method dealing with random and interval uncertainties

In performing reliability analysis of complex structural systems, the simultaneous presence of random and interval parameters significantly increases the complexity of structural reliability assessment. In this paper, an efficient probability-interval hybrid uncertainty analysis method based on chaos control and multiplicative dimensional reduction techniques is proposed. In the proposed method, the modified chaos control method is introduced to solve the iterative non-convergence problem in Hasofer-Lind-Rackwitz-Fiessler (HL-RF) algorithm, and the multiplicative dimensional reduction method is used to transform the interval analysis as the function extremum problem, which effectively improves the solving efficiency. The effectiveness of the proposed method is validated through benchmark numerical examples, and its practical applicability is exemplified by fatigue fracture analysis of the flexspline in harmonic drives and stiffness failure analysis of a 10-bar aluminum truss. The results demonstrate that the presented method can significantly reduce the time required for hybrid uncertainty analysis while maintaining the accuracy.