A sequential radial basis function method for interval uncertainty analysis of multidisciplinary systems based on trust region updating scheme

Uncertainty analysis is an essential procedure to evaluate reliability or robustness in uncertainty-based multidisciplinary optimization. Considering non-probabilistic interval uncertainties, this paper proposes a trust region-based sequential radial basis function (TR-SRBF) method for interval uncertainty analysis of multidisciplinary systems. First, the radial basis function neural network (RBFNN) is introduced to establish the correlation model between uncertain parameters and multidisciplinary outputs. After training a crude RBFNN via a small number of initial sample points, the proposed method sequentially collects sample points and updates the surrogate model according to the current accuracy. A trust region-based updating scheme is established to determine the sampling areas and guide the collection of new sample points. After successively updating, a satisfactory surrogate model will be obtained, based on which the extrema of multidisciplinary outputs can be obtained conveniently with some auxiliary algorithms. Further, to reduce the sample size, an alternant scheme is then presented to calculate the lower and upper bounds of the multidisciplinary outputs simultaneously. Finally, numerical examples are provided to demonstrate the effectiveness and applicability of TR-SRBF. By contrast with the static surrogate-based method, the results show that the proposed method can achieve better efficiency as well as high accuracy. The main contribution of this paper is to provide a novel dynamic surrogate-based interval uncertainty analysis method called TR-SRBF to calculate the upper and lower bounds of multidisciplinary outputs, in which the RBFNN is sequentially updated with the proposed trust region-based sampling scheme while the bounds are alternately calculated.