Sensitivity analysis method for model with correlated inputs and multivariate output and its application to aircraft structure

Traditional sensitivity analysis methods for the model with correlated inputs and univariate output fail to provide satisfactory results for multivariate output. In this work, we first establish a reasonable contribution classification for the univariate output with the correlated input. Then the covariance decomposition method is extended to the case of correlated inputs as a reference, and the vector projection sensitivity index is extended to aggregate the correlated and uncorrelated contributions of the input to multiple outputs. The definition of the new sensitivity index is based on the vector projection, which can take into account both uncertainties and correlations among multiple outputs by projecting the conditional variance vector (built by the full marginal variance contributions) on the unconditional variance vector (built by unconditional variance magnitudes and correlation of the multiple outputs). The mathematical properties of the extended vector projection sensitivity index are discussed and its relations with other existing sensitivity indices are highlighted. Two numerical examples and two engineering examples about an aircraft structure are employed to illustrate the validity and potential benefits of the extended vector projection sensitivity index.