Multilevel sampling based sparse polynomial expansion for efficient uncertainty analysis of mechanical system

The polynomial chaos is widely used in uncertainty analysis of the mechanical system, in which, the samplings hugely affect the efficiency and accuracy. In this paper, a multilevel sampling based sparse polynomial chaos approach is presented for efficient uncertain analysis of the mechanical system, in which, 1) the dynamic responses are approximated with sparse polynomial chaos expansion which enables the sampling number to be much less than that of the polynomial terms, and the number of deterministic systems would be reduced, 2) the multilevel sampling based resampling strategy is applied to weaken the Restricted Isometry Property condition for sparse polynomial chaos expansion based equations solving, and in addition, 3) such multilevel sampling based on evaluating system coherence with generalized coordinates acceleration is used to reduce the motion equations with deterministic parameters for obtaining the dynamic responses accu-rately and efficiently. Finally, the presented approach is validated with three examples. The re-sults are shown that the sparse polynomial chaos can be utilized to calculate the mean and standard deviation with 1E-5 and 1E-2 accuracy. The sparse polynomial chaos based on multi-level sampling can be used to reduce the sampling size by 25% compared with the Latin Hy-percube sampling. Compared with coherence optimal sampling, the convergence of the proposed sampling method is more stable as the sampling size is increased. Lastly, multilevel sampling also can be used to reduce the deterministic motion equations by 20% to obtain 1E-5 accuracy dy-namic responses compared with the Latin Hypercube sampling.