Global sensitivity analysis based on distance correlation for structural systems with multivariate output

Models with multivariate output are often used in practical structural systems. Multivariate global sensitivity analysis (GSA) plays an important role in quantifying the contribution of uncertainty in the model input to the output, which is quite useful for simplifying the models and improving the model performance. Many traditional global sensitivity indices can be considered as dependence measures of model input and output. However, these dependence measures can only measure the dependence between two scalar random variables. In this paper, the distance correlation, which can measure the dependence between random vectors, is utilized for multivariate GSA for structural systems with multivariate output. The distance correlation based sensitivity index not only considers the whole probability distribution of multivariate output but also can be easily estimated with only a single set of input-output samples. A numerical example is adopted at first. Then the distance correlation based sensitivity index is applied to a vibration problem in structural dynamics, a truss structure model and a wing box structure model. The results show that the distance correlation based sensitivity index has a higher robustness compared to the covariance-decomposition based sensitivity index.