Non-probabilistic Integrated Reliability Analysis of Structures with Fuzzy Interval Uncertainties using the Adaptive GPR-RS Method

Abstract

Due to its weak dependence on the quantity of variable samples, the non-probabilistic reliability analysis method based on the convex set model is applicable to practical problems in structural engineering with inherent uncertainties. However, when dealing with the black-box limit-state function issues in practical complex structural engineering, the traditional quadratic polynomial response surface (QP-RS) method has the problem of insufficient precision in approximating a highly nonlinear function. Meanwhile, fixing the limits of interval variables is trickier in case of scant samples and meager statistical information. To remedy the above deficiencies, this paper introduces a reasonable integrated reliability analysis approach. First, an adaptive Gaussian process regression response surface (GPR-RS) method that dynamically improves the fitted accuracy near the design point of the black-box limit-state function is formulated. Furthermore, the integrated reliability index with consideration of fuzzy interval uncertainties is presented. Three validation and two application examples are employed, which have justified the approach as a more reasonable assessor of practical complex structural reliability with safer results.