基于Kriging代理模型的失效机会测度算法

An Efficient Algorithm for Failure Chance Measure Based on Kriging Model

结构输入变量中同时存在随机输入变量和模糊输入变量情况下,失效机会测度可以很好地衡量结构的安全程度。但是,现有的混合模拟法计算失效可信度是一个双层循环过程,需要调用大量的功能函数。尤其对于大型复杂结构来说,混合模拟法的计算量是难以接受的。因此,本文将混合模拟法和自适应Kriging代理模型相结合,发展了一种失效机会测度的高效算法。通过U学习函数来自适应地选择训练样本点,进而可以自适应地构建功能函数的Kriging代理模型。在备选样本池中自适应训练至收敛的Kriging代理模型可以以要求的精度区分备选样本池中每个样本点的状态是失效还是安全的。因此,可以用收敛的Kriging代理模型代替真实的功能函数,进而通过混合模拟计算失效机会测度,这极大地降低了功能函数调用次数。最后,本文通过两个算例来验证本文发展算法的精确性和高效性。

Failure chance measure can quantify the safety degree of structural system under hybrid uncertainty including random input variable and fuzzy input. However, hybrid simulation is a double-loop process for estimating failure chance measure, and it requires a large number of performance function evaluations. The efficiency of hybrid simulation is unaffordable especially for complex engineering structure. In this paper, an efficient algorithm for estimating failure chance measure is developed by combining hybrid simulation and adaptive Kriging model. U learning function is used to adaptively select the training sample in the candidate sample pool to construct Kriging model of the performance function. The convergent Kriging model can replace the performance function with the presented precision to implement hybrid simulation. The proposed algorithm can significantly reduce the number of the performance function evaluations. Finally, two examples are presented to illustrate the efficiency and accuracy of the proposed algorithm.