Authors: Dongwei Huang, Feng Wu, Sheng Zhang, Biaosong Chen, Hongwu Zhang
In order to accurately and efficiently solve the statistical moments of stochastic dynamic problems, a method combining adaptive weights quasi-Monte Carlo method (AWQMCM) and Galerkin projection method (GPM) is proposed. Based on the sample set of quasi-Monte Carlo method (QMCM), the adaptive weights are obtained by combining the generalized polynomial chaos expansion and the least square method. The proposal of adaptive weights can effectively reflect the discrepancy of the sample set, so that the samples collocated with adaptive weights can perform more uniformly. Subsequently, the stochastic dynamic model is projected into the deterministic basis vector space based on GPM and matrix perturbation theory. The implementation of the reduced-order model dependent on deterministic basis vector (ROMDDBV) considerably improves the computational efficiency of random responses. Numerical examples show that the calculation accuracy of statistical moments based on AWQMCM is superior to the QMCM, and compared with the full-order model, the calculation efficiency of random responses obtained by ROMDDBV is significantly improved. What’s more, the adaptive weights are associated with the sample set and the distribution of random variables, which makes it universal and applicable to the calculation of statistical moments of other stochastic problems.