Effective correlation analysis algorithms for uncertain structures based on multidimensional parallelepiped model

Abstract

The correlation analysis of the uncertain structures with multi-responses is carried out based on the multidimensional parallelepiped model in this research. Firstly, the multidimensional parallelepiped model is introduced to quantify the uncertainty and correlation of input parameters. Then, to deal with the large uncertainty of input parameters, the sub-parallelepiped perturbation analysis algorithm is designed to calculate the marginal intervals of output responses. Next, based on the Monte Carlo simulation and the second-order perturbation technique, the Monte Carlo correlation analysis algorithm and the second-order perturbation correlation analysis algorithm are respectively designed to obtain the correlation coefficients of output responses. Subsequently, two uncertainty domain analysis algorithms based on the marginal intervals analysis and the correlation coefficients analysis, are presented to establish the uncertainty domains of output responses. Finally, the effectiveness of proposed algorithms is verified by three numerical examples.