A response-surface-based structural reliability analysis method by using non-probability convex model

Due to its weak dependence on the amount of the uncertainty information, the non-probability convex model approach can be used to deal with the problems without sufficient information. In this paper, by integrating the response surface (RS) technique with the convex model approach, a new structural reliability analysis method is developed for many complex engineering problems with black-box limit-state functions. Using the newly developed correlation analysis technique for non-probability convex model, the multi-dimensional ellipsoid is efficiently constructed to characterize the uncertain parameters. A quadratic polynomial without cross terms is adopted to parameterize the black-box limit-state function, based on which the functional values as well as the first-order gradients can be explicitly calculated. At each iteration, the created RS is combined with the iHL-RF algorithm to obtain an approximate reliability index. A sequential procedure is subsequently formulated to update the RS and hence improve the precision of the reliability analysis. Four numerical examples and one engineering application are investigated to demonstrate the effectiveness of the presented method.