The importance measure on the non-probabilistic reliability index of uncertain structures

In the non-probabilistic uncertainty structural analysis, the input uncertain variables of it, such as loads and material properties, will be propagated to the output responses, which include the displacement, stress and compliance, etc. To measure the effect of these non-probabilistic input variables on the output response, two new uncertainty importance measures on the non-probabilistic reliability index are discussed. For the linear limit state function, the analytical solutions of the importance measures are derived. To reduce computational effort, the discretization method and the surrogate model method are presented to calculate the two importance measures in case of the non-linear limit state. Finally, four examples demonstrate that the proposed importance measures can effectively describe the effect of the input variables on the reliability of the structure system, and the established methods can effectively obtain the two importance measures.