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The computational advantage of this approach is realized for uncertainty quantification tasks where a large number of realizations has to be evaluated.
A number of realizations, covered in the Tech article, discuss how this quality can be leveraged.
The effective properties can be determined for large volumes and a small number of realizations.
Conversely, smaller volumes can be used providing that a sufficient number of realizations are considered.
The number of realizations has to be sufficiently large to accurately represent the distribution of the input variables.
Sensitivity analysis shows that the procedure is stable and is not sensitive to the number of realizations.
A straightforward calculation of such averages converges slowly and therefore requires a large number of realizations of the system.
The MCSGA approach yields one optimal design each for a large number of realizations generated to represent the uncertain K-field.
A set of exploratory design cases is completed using the orthogonal array concept based on the Taguchi method, hence reducing the number of realizations.
Utilizing a few random collocation points, the method indicates also a very good agreement compared to the sampling-based Monte Carlo simulations with large number of realizations.
In the first approach, statistical analysis with number of realizations is performed with increasing RVE size of randomly generated CNT within polymer.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com