Non-probabilistic polygonal convex set model for structural uncertainty quantification

Abstract

In this paper, a general polygonal convex set model and clustering polygonal convex set model are proposed for more reasonably quantifying non-probabilistic uncertainties. Firstly, through the principal component analysis of uncertain samples, a new interval model based on principal component analysis is constructed to characterize the correlation of uncertain parameters. Then, the polygonal convex set model is further constructed by combining the traditional interval model and the interval model based on principal component analysis. Because the polygonal convex set model more compactly and adaptively envelopes all the uncertain samples using the irregular boundaries, it is very suitable for quantification analysis of high-dimensional uncertain problems. In addition, as the polygonal convex set model has the linear boundaries, the classical simplex optimization method is properly adopted to effectively solve the corresponding uncertainty propagation problems. In order to handle the complex problems with large uncertainties, the clustering polygonal convex set model is further established by combing a several sub polygonal convex set models based on cluster analysis. Because the linear approximation of performance function is suitable in the local range of each sub polygonal convex set model, the simplex optimization method can still provide an effective propagation results by solving each sub model. Finally, three numerical examples are investigated to illustrate the feasibility and effectiveness of the proposed two non-probabilistic models on structural uncertainty quantification.