Exact Method of Antithetic Sampling for Higher Dimensionality

Data sampling with Monte Carlo simulation requires enormous computational time and effort to obtain high- accuracy results for cases with significant variables, as large sampling sets are required. Designs based on the Latin hypercube can provide sparse sampling with the desired covariance but optimizing properties such as space-filling is remarkably expensive. To overcome the drawbacks of the current sampling methods, variance reduction technique like Antithetic sampling is proposed. This paper presents a way where Antithetic sampling is extended to higher dimensions using a combination approach such that each combination indicates a sampling location for those dimensions. By summing up all combinations, we can calculate the number of data points for respective dimensions. The objective is to reduce the variances of the estimators with less computational cost by reducing the correlation value. To validate this sampling technique, the proposed method has been applied to two non-linear analytical functions: i) Ishigami function (three-dimensional) and ii) Sobol function (eight-dimensional) and for stochastic natural frequency analysis of a cantilever composite laminate. The obtained results have been compared to the results using conventional sampling methods. The main goal of most of the sampling techniques is to maintain uniformity, reduce the variances and get a correlation equal to zero. The proposed approach generates uniformly distributed samples for three-dimensional and eight eight- dimensional cases where correlation is almost negligible, which cannot be achieved using other sampling techniques. This method gives good correlation results without complex optimization and costly computer simulation for problems with higher dimensions. Therefore, it will be helpful to reduce variances of the estimators by a significant amount for higher dimensions.