Using random set theory to calculate reliability bounds for a wing structure

Abstract

This paper shows how uncertainty can be propagated through a computer model when the input data consists of uncertainty affected by imprecision and randomness. The proper orthogonal decomposition (POD) is used to determine the dominant air pressure distributions on a wing, and the uncertainty in the POD modal amplitude variables is propagated through a finite element (FEM) structural model to calculate the reliability bounds for the wing. It is shown that: (i) when working with imprecise input, the traditional probabilistic approach is inadequate because it would force the designer to add unavailable information; (ii) the proposed mathematical model of uncertainty is capable of capturing the incomplete knowledge upon which important conceptual and preliminary decisions must be made; (iii) this approach indicates if and where resources should be invested to acquire more information; (iv) the proposed techniques can be easily implemented using existing numerical codes; (v) a limited number of model runs is necessary to calculate bounds on the output distributions.