Active Learning Kriging Integrated Method for Reliability Analysis of One-Dimensional Structures with Spatially Variable Parameters

The spatial variability of structural parameters has a significant impact on the stochastic response and reliability analysis of engineering structures. In traditional methods, structural parameters are often simplified into random variables, and the spatial correlations among them are frequently neglected. Representing the spatial variability of structural parameters using random fields provides a more realistic and effective alternative. Although the traditional Monte Carlo simulation method can still maintain high accuracy in handling the reliability problems of structures with spatial variability, it becomes a great impediment when the computational cost of obtaining structural responses is expensive. In this paper, an integrated structural reliability analysis method that is easy to implement, efficient, and accurate is proposed by integrating a general random field simulation approach and an improved reliability analysis method. First, using the random field simulation method based on active learning kriging, 1D random field simulation of spatially variable parameters is realized with a small number of random variables. Correspondingly, the reliability problem of a 1D structure with spatially variable parameters can be transformed into a reliability problem that only contains random variables. Subsequently, within the active learning kriging Monte Carlo simulation framework, a new learning function that fully accounts for the impact of sample point signs, the error of the predicted failure probability, the probability density function values, and the U-values is proposed, and it is named SEFU. Finally, the accuracy and effectiveness of the proposed method were verified through three engineering examples, which analyzed the effects of the number of meshed elements, the scales of fluctuation, and the coefficient of variation on the structural reliability index. The results indicate that the novel proposed method significantly improves the computational efficiency of reliability analysis with high estimating accuracy of the failure probability. Further, the new learning function exhibits higher computational efficiency compared with the classical U and expected feasibility functions.