A probability-interval hybrid uncertainty analysis method based on the arbitrary polynomial chaos-Chebyshev interval expansion

This paper proposes hybrid uncertainty propagation analysis method for the problems involving both random and interval variables by synergistically integrating arbitrary Polynomial Chaos (aPC) with Chebyshev polynomials. In this method, the aPC method is adopted to handle random uncertainties, and an interval method based on Chebyshev is proposed to deal with interval uncertainties. The principal advantages of the proposed method are: (1) It characterizes random variables using aPC, requiring only statistical moments from sample data and eliminating the reliance on pre-assumed precise probability distributions. (2) It seamlessly integrates this with a Chebyshev-based treatment of interval variables, providing a robust and efficient analysis tool. The validity and advantages of the proposed method are demonstrated through numerical examples and representative engineering case studies.