A multi-region active learning Kriging method for response distribution construction of highly nonlinear problems

Probability distributions of structural responses have been widely used in many engineering applications and their accuracy could significantly affect the performance and credibility of these applications. To obtain accurate distributions, existing methods often need massive calculations of the original response function, especially for highly nonlinear problems. To alleviate the computational burden, this paper proposes a multi-region active learning Kriging method to construct response distributions of highly nonlinear problems. First, a low-precision CDF curve is built based on the one-iteration MPP search and MPP prediction. Multiple regions and response values are then identified to obtain the limit state surfaces for Kriging modeling. To determine the best training points, a multi-region learning strategy including rough and precise selections is developed based on the U learning function and a hybrid index of the reward-based probability and nonlinearity. A two-level stopping criterion is further provided to achieve fast convergence and high accuracy. Finally, the response distributions are constructed using the obtained Kriging model. The effectiveness of the proposed method is verified by four examples.