Sensitivity analysis of correlated inputs: Application to a riveting process model

Sensitivity analysis evaluates how the variations in the model output can be apportioned to variations in model inputs. After several decades of development, sensitivity analysis of independent inputs has been developed very well, with that of correlated inputs receiving increasing attention in recent years. This paper introduces a new sensitivity analysis technique for model with correlated inputs. The new method allows us to quantitatively distinguish the effects of the correlated and uncorrelated variations of the model inputs on the uncertainty in model output. This is achieved by performing covariance decomposition for the uncertainty contribution of the inputs after decoupling the correlated and uncorrelated parts of the component functions in the high dimension model representation (HDMR) of the output. The proposed method can be implemented conveniently with any existing HDMR technique developed for independent inputs without any change of the original algorithm. It can be applied to nonlinear and non-monotonic models with correlated inputs. An additive model, two non-additive models with analytical sensitivity indices, and a riveting process model are employed to test the proposed method.