An iterative interval analysis method based on Kriging-HDMR for uncertainty problems

In recent years, growing attention has been paid to the interval investigation of uncertainty problems. However, the contradiction between accuracy and efficiency always exists. In this paper, an iterative interval analysis method based on Kriging-HDMR (IIAMKH) is proposed to obtain the lower and upper bounds of uncertainty problems considering interval variables. Firstly, Kriging-HDMR method is adopted to establish the meta-model of the response function. Then, the Genetic Algorithm & Sequential Quadratic Programing (GA&SQP) hybrid optimization method is applied to search for the minimum/maximum values of the meta-model, and thus the corresponding uncertain parameters can be obtained. By substituting them into the response function, we can acquire the predicted interval. Finally, an iterative process is developed to improve the accuracy and stability of the proposed method. Several numerical examples are investigated to demonstrate the effectiveness of the proposed method. Simulation results indicate that the presented IIAMKH can obtain more accurate results with fewer samples.