Interval uncertainty analysis for static response of structures using radial basis functions

By Yisi Liu, Xiaojun Wang, Lei Wang. Applied Mathematical Modelling, 2019

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Abstract This paper proposes a new interval uncertainty analysis method for static response of structures with unknown-but-bounded parameters by using radial basis functions (RBFs). Recently, collocation methods (CM) which apply orthogonal polynomials are proposed to solve interval uncertainty quantification problems with high accuracy. These methods overcome the drawback of Taylor expansion based methods, which are prone to overestimate the response bounds. However, the form of orthogonal basis functions is very complicated in higher dimensions, which may restrict their application when there exist relatively more interval parameters. In contrast to orthogonal basis function, the form of radial basis function (RBF) is simple and stays the same in whatever dimension. This study introduces RBFs into interval analysis of structures and provides a relatively simple approach to solve structural response bounds accurately. A surrogate model of real structural response with respect to interval parameters is constructed with the RBFs. The extrema of the surrogate model can be calculated by some auxiliary methods. The static response bounds can be obtained accordingly. Two numerical examples are used to verify the proposed method. The engineering application of the proposed method is performed by a center wing-box. The results prove the effectiveness of the proposed method.

Subfields: Civil and Structural Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b850d9734aede4e7d4ca43e77f6c0b7ec94fa00d