Uncertainties Quantification and Propagation of Multiple Correlated Variables with Limited Samples

In order to estimate the reliability of an engineering structure based on limited test data, it is distinctly important to address both the epistemic uncertainty from lacking in samples and correlations between input uncertain variables. Both the probability boxes theory and copula function theory are utilized in proposed method to represent uncertainty and correlation of input variables respectively. Moreover, the uncertainty of response of interest is obtained by uncertainty propagation of correlated input variables. Nested sampling technique is adopted here to insure the propagation is always feasible and the response's uncertainty is characterized by a probability box. Finally, a numerical example illustrates the validity and effectiveness of our method. The results indicate that the epistemic uncertainty cannot be conveniently ignored when available samples are very limited and correlations among input variables may significantly affect the uncertainty of responses.