An improved interval model updating method via adaptive Kriging models

Interval model updating (IMU) methods have been widely used in uncertain model updating due to their low requirements for sample data. However, the surrogate model in IMU methods mostly adopts the one-time construction method. This makes the accuracy of the surrogate model highly dependent on the experience of users and affects the accuracy of IMU methods. Therefore, an improved IMU method via the adaptive Kriging models is proposed. This method transforms the objective function of the IMU problem into two deterministic global optimization problems about the upper bound and the interval diameter through universal grey numbers. These optimization problems are addressed through the adaptive Kriging models and the particle swarm optimization (PSO) method to quantify the uncertain parameters, and the IMU is accomplished. During the construction of these adaptive Kriging models, the sample space is gridded according to sensitivity information. Local sampling is then performed in key subspaces based on the maximum mean square error (MMSE) criterion. The interval division coefficient and random sampling coefficient are adaptively adjusted without human interference until the model meets accuracy requirements. The effectiveness of the proposed method is demonstrated by a numerical example of a three-degree-of-freedom mass-spring system and an experimental example of a butted cylindrical shell. The results show that the updated results of the interval model are in good agreement with the experimental results.