Structural reliability with credibility based on the non-probabilistic set-theoretic analysis

A structural reliability analysis method based on the non-probabilistic credible set model is proposed in this paper. Compared with the probabilistic method, the developed method overcomes the high requirement for the sample size of structural uncertain parameters. Moreover, it surpasses the traditional non-probabilistic reliability analysis method by relating the reliability index to its corresponding credibility. Via introducing the non-probabilistic credible set uncertainty quantification, the distribution range of the required credibility for structural uncertain parameters can be determined by scant samples. Accordingly, the improved uncertainty propagation analysis methods based on the non-probabilistic credible set uncertainty quantification are established to obtain the bounds of structural response by transforming into local coordinate system. The non-probabilistic credible reliability index is constructed and three advanced efficient approaches are developed to calculate that. Moreover, the procedure of structural non-probabilistic credible reliability analysis method is built by combining the above content. Besides, the influence of credibility on non-probabilistic credible reliability is discussed. A cantilever beam example, an aeroengine turbine disk case and a pressure vessel case are utilized to verify the feasibility of applying the proposed approach to various engineering problems.