A non-probabilistic uncertainty analysis method based on ellipsoid possibility model and its applications in multi-field coupling systems

Abstract

Non-probabilistic methods are usually more appropriate and feasible than probabilistic methods to quantify and propagate uncertainty with small samples in many engineering problems. However, some non-probabilistic methods are easily affected by an outlier in uncertainty quantification and only estimate the bounds of output responses in a feasible region in uncertainty propagation. Moreover, some such methods ignore the situation that its sample points have the characteristic of clustering to the center, which significantly affects the accuracy of uncertainty quantification and propagation. In this study, a novel non-probabilistic uncertainty analysis method is proposed to solve the situation and obtain detailed information within the response interval during the process of uncertainty propagation for some problems with small samples. First, an ellipsoid possibility model (EPM) including multiple ellipsoid domains is established using the estimated covariance matrix and predefined scaling rule, which takes into consideration the distribution characteristic of the sample points. The possibilities of all established ellipsoid domains can be calculated by transforming the oblique ellipsoid space into the standard ellipsoid space. Then, two uncertainty propagation approaches based on the established EPM are presented to obtain the interval of an uncertain response and the possibility on all the possible values of the system response, respectively. Finally, the calculation results based on the proposed uncertainty analysis method are in good agreement with those of the MCS in three numerical examples and two engineering applications. The comparison results with three traditional non-probabilistic methods demonstrate that the proposed non-probabilistic uncertainty analysis method is accurate and practical.