Analytical variance based global sensitivity analysis for models with correlated variables

In order to quantitatively analyze the variance contributions by correlated input variables to the model output, variance based global sensitivity analysis (GSA) is analytically derived for models with correlated variables. The derivation is based on the input-output relationship of tensor product basis functions and the orthogonal decorrelation of the correlated variables. Since the tensor product basis function based simulator is widely used to approximate the input-output relationship of complicated structure, the analytical solution of the variance based global sensitivity is especially applicable to engineering practice problems. The polynomial regression model is employed as an example to derive the analytical GSA in detail. The accuracy and efficiency of the analytical solution of GSA are validated by three numerical examples, and engineering application of the derived solution is demonstrated by carrying out the GSA of the riveting and two dimension fracture problem.