Variance-based sensitivity analysis for models with correlated inputs and its state dependent parameter solution

Sensitivity analysis is indispensable to structural design and optimization. This paper focuses on sensitivity analysis for models with correlated inputs. To explore the contributions of correlated inputs to the uncertainty in a model output, the universal expressions of the variance contributions of the correlated inputs are first derived in the paper based on the high dimensional model representation (HDMR) of the model function. Then by analyzing the composition of these variance contributions, the variance contributions by an individual correlated input to the model output are further decomposed into independent contribution by the individual input itself, independent contribution by interaction between the individual input and the others, contribution purely by correlation between the individual input and the others, and contribution by interaction associated with correlation between the individual input and the others. The general expressions of these components are also derived. Based on the characteristics of these general expressions, a universal framework for estimating the various variance contributions of the correlated inputs is developed by taking the efficient state dependent parameter (SDP) method as an illustration. Numerical and engineering tests show that this decomposition of the variance contributions of the correlated inputs can provide useful information for exploring the sources of the output uncertainty and identifying the structure of the model function for the complicated models with correlated inputs. The efficiency and accuracy of the SDP-based method for estimating the various variance contributions of the correlated inputs are also demonstrated by the examples.