An efficient meta-model-based method for uncertainty propagation problems involving non-parameterized probability-boxes

To capture inevitable aleatory and epistemic uncertainties in engineering problems, the probability box (P-box) model is usually an effective quantification tool. The non-parameterized P-box is more general and more flexible than parameterized P-box. While the efficiency of uncertainty propagation methods for non-parameterized P-box is crucial and demands urgently to improve. This paper proposes an efficient meta-model-based method for uncertainty propagation problems involving non-parameterized probability-boxes. In which, the typical Kriging meta-model is first utilized to build the mapping relationship between the non-parameterized P-box variables with the system response. Then, the constructed Kriging model is applied for interval analysis, and the cumulative distribution function of the response function can be obtained using interval Monte Carlo. During building the meta-model, an active learning strategy is proposed and applied to reduce the amount of training data needed from the perspective of exploration and exploitation. Since the prediction variance of Kriging model is not used, the proposed active learning method is not limited to Kriging model and can be applied in any existing meta-models. The numerical examples demonstrate that the proposed method has high accuracy and efficiency in handling nonlinearity, high-dimensional and complex engineering problems.