基于Kriging模型的结构可靠性分析

Analysis of structural reliability based on Kriging model

在结构极限状态方程(LSF)未知的情况下,通常采用响应面法(RSM)模拟结构的极限状态方程,逐步修正求解。由于响应面法对于极限状态方程的多项式假定,使其在计算精度上存在一定的缺陷。本文通过随机选取的部分结构响应,采用K rig ing模型模拟未知状态的结构响应,然后附以最优化的方法求解可靠性指标。该方法突破了极限状态方程的形式对于可靠性计算的制约,避免数学表达式的不同对于可靠性计算的影响。通过数值算例,可以看到本文的方法具有较高的精度和稳定性。

Structural reliability analysis under the condition of limit state function unknown is the important case. Generally, Response Surface Method （RSM） is used to estimate the structural limit state function, then the Moment Methods used to serve. On account of the assumption of polynomial form, the RSM can not solve the problem with high accuracy. That is to say, the polynomial form of RSM restricts the accuracy of reliability analysis. As a semi-parameter interpolation technique, Kriging model, which can avoid the restriction and the influence of different limit state function form, could evaluate the structure response with high accuracy. Combined the Kriging model with the optimization method, the reliability index can be solved. The stability and efficiency of this method are shown in the example.