Uncertainty Propagation Using Possibility Theory and Function Approximations

Based on the nature and extent of uncertainty existing in an engineering system, different approaches can be used for uncertainty propagation. If the uncertainty of the system is due to imprecise information, and lack of statistical data, the Possibilistic theory can be used. During preliminary design, uncertainties need to be accounted for and due to lack of sufficient information, assigning a probability distribution may not be possible. Moreover, the flight conditions (loads, control surface settings, etc.) during a mission could take values within certain bounds, which do not follow any pattern. The uncertain information in these cases is available as intervals with lower and upper limits. In this case, the fuzzy-arithmetic-based method is suitable to estimate the possibility of failure. The use of surrogate models to improve the efficiency of prediction is presented in this article. Various numerical examples are presented to demonstrate the applicability of the method to practical problems.