Steady-state response analysis of cracked rotors with uncertain‑but‑bounded parameters using a polynomial surrogate method

Uncertain‑but‑bounded (UBB) parameters are used to describe the non-probabilistic uncertainties in rotor systems. A general non-intrusive polynomial surrogate is constructed to quantify the uncertain effects of the UBB quantities on the dynamic responses. The surrogate is convenient to establish and able to deal with a large number of uncertain variables. The zeros of the Chebyshev series are used as sample points and the least square method (LSM) is employed to evaluate the coefficients. At the sample points of the polynomial surrogate, the harmonic balance method is applied to obtain the sample responses (PS-HBM). During the surrogate modeling, the deterministic rotor system with a breathing crack is treated as a black box and no modifications should be made to the deterministic finite element (FE) analysis process. It needs no distribution laws and is especially helpful in small sample sized problems. Numerical simulations of the rotor system with various UBB parameters are carried out to demonstrate the effectiveness of the surrogate. Moreover, its accuracy and efficiency are verified by comparisons with other classic sampling methods.