Parameter vertex method and its parallel solution for evaluating the dynamic response bounds of structures with interval parameters

In this article, we propose a parameter vertex method to determine the upper and lower bounds of the dynamic response of structures with interval parameters, which can be regarded as an extension of the matrix vertex method proposed by Qiu and Wang. The matrix vertex method requires considerable computation time and encounters the dependency problem in practice, thereby limiting its application in engineering. The proposed parameter vertex method can avoid the dependency problem, and the number of possible vertex combinations in the proposed method is significantly less than that in the matrix vertex method. The parameter vertex method requires that each matrix element in the dynamic differential equation is monotonic with respect to the uncertain parameter, and that the dynamic response reaches its extreme value when the uncertain parameter is at its endpoint. To further reduce the runtime, both vertical and transversal parallel algorithms are introduced and integrated into the parameter vertex method to improve its computational efficiency. Two numerical examples are presented to demonstrate the proposed method combined with both parallel algorithms. The performances of the two parallel algorithms are thoroughly studied. The parameter vertex method combined with parallel algorithm can be used for large-scale computing.