An effective response domain analysis method for the uncertain structures with multi-responses based on multidimensional parallelepiped model

Abstract

A novel response domain analysis method based on the multidimensional parallelepiped (MP) model is proposed to effectively evaluate the response domains of uncertain structures with multi-responses. The response domain is used to characterize the uncertainty and correlation of responses. Firstly, the rhombus MP model is introduced to describe the uncertainty and correlation of input parameters. Then, to address the large uncertainty of input parameters, an enhanced sub-parallelepiped perturbation analysis method is proposed to calculate the marginal intervals of responses. Next, the first-order perturbation correlation analysis method is developed to calculate the correlation coefficients of responses. The response domains are not limited to being described by the same type of MP model as used in the parameter domain. Instead, the estimated shape matrix analysis method is proposed to determine the best shape matrices of the MP models describing response domains. According to the marginal intervals, correlation coefficients and the best shape matrices of responses, the most reasonable types of MP models are constructed to represent response domains. Finally, several numerical examples are used to verify the effectiveness of the proposed method.