一种自适应PC-Kriging模型的结构可靠性分析方法

为提高小失效概率及耗时的复杂结构可靠性评估精度和效率，提出了一种基于PC-Kriging(polynomial-chaos-based Kriging)模型与自适应k-means聚类分析相结合的结构可靠性分析方法.PC-Kriging的回归基函数采用稀疏多项式最优截断集合来近似数值模型全局行为，并用Kriging来处理模型输出的局部变化.在基函数的建立上，PC-Kriging采用最小角回归(LAR)计算功能函数可能的多项式基函数集的数量，同时用Akaike信息准则(AIC)来确定最优多项式形式.自适应k-means聚类分析确保每次迭代添加若干个对失效概率贡献较大的样本点.通过两个数值算例分析，结果表明所提出方法在能够保证失效概率估计值的有效性和准确性的同时减小结构功能函数的评估次数.

A Structural Reliability Analysis Method Based on Adaptive PC-Kriging Model

To improve the accuracy and efficiency of reliability assessment for complex structures with small failure probability and time-consuming model， a structural reliability analytical method based on PC-Kriging (polynomial-chaos-based Kriging) model and adaptive k-means clustering analysis was proposed. PC-Kriging’s regression basis function approximated the global behavior of the numerical model by using the sparse polynomial optimal truncation set， and Kriging was used to deal with the local variation of the output of the model. PC-Kriging used least angle regression (LAR) to calculate the number of possible polynomial basis function sets of performance function， and adopted Akaike information criterion (AIC) to determine the optimal polynomial form. The adaptive k-means clustering analysis ensured that some of the significant contribution sample points toward the failure probability can be added as the new training samples in each iteration. The results of two numerical examples indicated that the proposed method can not only guarantee the validity and accuracy of the estimation of failure probability but also reduce structural performance function evaluation times.