基于LCF-Kriging模型的结构多失效模式可靠度计算

针对多失效模式下结构体系可靠度计算中的代理模型构建成本与计算精度如何权衡的问题,论文以减小体系失效概率预测方差为出发点,推导出最大贡献函数(LCF-Largest Contribution Function)来识别对体系失效概率方差影响较大的样本.LCF函数可减少对体系失效概率方差影响较小区域内样本数量,进而提高代理模型的计算效率;通过置信水平和允许相对误差建立LCF函数的学习停止条件,能够保证已有样本信息不浪费.论文选取能够对多个功能函数联合构建的多输出Kriging模型作为代理模型,基于LCF-Kriging模型并结合MCS对体系可靠度进行计算,功能函数的相关性可通过各失效模式的逻辑关系予以考虑.数值算例表明,在适当的学习停止条件下,对于串联、并联和串并混联的结构体系可靠度评估,论文方法均能在计算精度和计算效率之间达到满意平衡.

Structural Reliability Calculation With Multiple Failure Modes Using LCF-Kriging Model

In order to balance the construction cost and the prediction accuracy of the surrogate model used to estimate structural system reliability with multi-failure modes, the Largest Contribution Function (LCF) is proposed. The LCF is used to identify the best samples from candidate samples in the construction process of surrogate model. Since the best samples have great influence on the variance of system failure probability, the prediction accuracy of system failure probability can be improved. Mathematical formulas of LCFs for the series system, parallel system and series-parallel system are derived based on the structural reliability theory. The learning stopping condition of LCF is established by using confidence level and allowable relative error, it can ensure that the information about existing samples is not wasted. A multi-output Kriging model is selected as surrogate model, it can approximate multiple performance functions at the same time. The structural system reliability is calculated by using the LCF-Kriging model and MCS, the correlation between performance functions can be considered by the logical relationship of failure modes. Some examples are introduced to demonstrate the efficiency and the accuracy of the proposed method. It is found that the proposed method can achieve the satisfactory balance between the construction cost and the accuracy for structural reliability estimations of series system, parallel system and series-parallel system under the appropriate learning stopping condition.