基于代理模型的工程结构可靠性分析

摘要

In the reliability analysis of practical engineering structures,performance functions are generally complex and implicit functions with high nonlinearity,which makes the traditional methods of reliability analysis,such as the first-order second-moment,inefficient and inconvenient.Surrogate model can be a good alternative method to solve this problem.The computational efficiency and accuracy of the reliability analysis based on the quadratic polynomial response surface method (RSM) and Kriging method are compared by several numerical examples.Meanwhile,the strategies of accumulating all samples and selectively accumulating samples in the iteration of fitting surrogate model are studied.The examples show that RSM has difficulty in fitting the limit state surface with high degree of nonlinearity,while Kriging method performs well.Kriging method has advantage over RSM on both computational efficiency and accuracy.Therefore,Kriging method is used to carry out the reliability analysis of three structural examples.The results show that the iterative process may oscillate and cannot converge if samples are not accumulated.Sample accumulation can accelerate and stabilize the iteration,and accumulating samples selectively is better than accumulating all samples in terms of computational efficiency and accuracy.%在实际工程结构的可靠性分析中,功能函数一般是复杂的非线性程度较高的隐式函数,给常用的一次二阶矩等传统可靠性分析方法带来效率低、求解难度大等困难,针对这一问题,可以使用代理模型代替原隐式功能函数进行可靠性分析.通过多个数值算例对比了基于二次多项式响应面法(RSM)和Kriging方法进行可靠性分析时的计算效率和精度,同时研究了多次拟合近似代理模型过程中的样本全部累积和选择累积策略.算例表明,RSM难以对非线性程度高的极限状态曲面作出较好的拟合,Kriging方法有良好的预测能力,无论是在计算效率还是精度上都要优于 RSM.因此继续基于 Kriging 方法对3个工程结构进行可靠度分析,算例结果表明若未进行样本累积,有可能迭代过程振荡不能收敛到最终的可靠指标值;迭代过程中采用样本累积能显著改善收敛性能,通常样本选择累积在计算效率和精度上都要优于样本全部累积.