Non-probabilistic credible set model for structural uncertainty quantification

Abstract

A non-probabilistic credible set model for uncertainty quantification structural parameters is proposed in this paper. The developed method surpasses the probabilistic uncertainty quantification method and traditional non-probabilistic uncertainty quantification method by providing both the distribution range of uncertain structural parameters and the corresponding credibility for scant samples, thereby reducing the computation time and improving the credibility of the uncertainty quantification process. The average inverse-distance information entropy, the expanded uncertainty and credibility are introduced to establish a one-dimensional non-probabilistic credible set uncertainty quantification procedure. The basic theory of non-probabilistic sets and a correlation analysis of multidimensional uncertain parameters are reviewed. This theory and analysis are used to develop a multidimensional non-probabilistic credible set uncertainty quantification method. The optimal non-probabilistic set is searched to determine the local coordinate system. The multidimensional uncertainty quantification is subsequently transformed to a one-dimensional uncertainty quantification. A civil aircraft wing structure case, a stiffened plate case and a dynamic case are utilized to verify the feasibility of applying the developed method to various engineering problems.