**ROCEWEA. low-discrepancy sequence**
# Title of paper:
*
***Application of Adaptive Weights Quasi Monte Carlo Method by Combination of Uncertainty Reduced-order
Model Based on Deterministic Projection Basis Vector in Stochastic Dynamic Problems**

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. Whatâ€™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.
## Sequences

**Type: **m,n.txt

**File: **gauss.rar

**File: **uniform.rar

**Contents: **

The theory of sample: optimized Halton sequences.

The number of samples: m = 100, 200, 400, 600 and 800.

The distribution of random variables: gauss & uniform.

The number of random variables: n = 2, 3, 4, 5, 6, 7, 8, 9, and 10.

Based on any combination of random variables and the number of sample points, the *sample points *and
the *weights* are provided.

**Tips:** If you find any bug in our files, please contact us: Feng Wu: Email:
vonwu@dlut.edu.cn