New global sensitivity indices for structure system with multivariate outputs and their effective solutions

Global sensitivity analysis for input random variables is an important component of safety evaluation and optimal design in engineering structure. For many mathematical models encountered in engineering structure system involving multivariate outputs, this paper defines a set of new variance-based global sensitivity indices based on dimensionless model. These indices can synthetically measure the uncertainty effect on the multivariate outputs induced by the corresponding input random variable expediently and can effectively keep global sensitivity analysis information of each output. Simultaneously, to solve the costly computation problem in the Monte Carlo simulation, we calculate the new index by using a surrogate model which is based on a multiplicative version of the dimensional reduction method. The algorithm can greatly reduce model calls and save the calculation cost without decreasing its accuracy. Lastly, a numerical example and an engineering example are presented to show the reasonableness of the proposed index and the efficiency of the algorithm.