Abstract: Uncertainty factors are usually contained in the mathematical proxy model of complex physical system. In practical engineering problems such as mechanical system reliability optimization design, the key parameters of the model can be calibrated and the model structure can be modified to improve the fidelity of the proxy model. However, for imprecise probabilistic models with mixed uncertainties, the traditional model updating method based on the Euclidean distance is not applicable. To solve this problem, a new model updating method based on the Wasserstein distance measure is proposed, which builds the kernel function based on the Wasserstein distance measure, and uses the geometric properties of Wasserstein distance in P-dimensional parameter space to quantify the differences between different probability distributions. Compared with the existing model updating methods, high-order hyper-parameters of the model can be calibrated to significantly reduce the uncertainty of model structure and parameters. In order to reduce the calculation cost, the approximate Bayesian inference and sliced segmentation technology is further adopted to meet the engineering requirements. The validity of this method for practical engineering problems, such as statics and dynamics, is verified by the constitutive parameter checking problem of forced vibration steel plate and the multidisciplinary uncertainty quantification problem of NASA Langley.

Key words: Wasserstein distance, Bayesian methods, imprecise probability, model updating, approximate reasoning