基于Armijo准则的自适应稳定转换法

结构可靠度分析是结构不确定性设计的关键环节，计算效率和鲁棒性是评估可靠度分析算法性能的两个重要指标。首先针对两个已有的一次二阶矩算法（iHL-RF算法和方向性稳定转化法）进行分析，发现iHL-RF算法根据Armijo准则可以自适应调整迭代步长，但计算效率低；方向性稳定转化法根据振荡的方向性可以提高计算效率，但自适应性差。结合两种算法的优点，将Armijo准则用于自适应调整方向性稳定转化法的混沌控制因子，提出了基于Armijo准则的自适应稳定转换法。通过四个非线性算例将本文提出的算法与HL-RF、iHL-RF、混沌控制法以及方向性稳定转换法等四种算法的收敛性和计算效率进行比较。结果表明，相比其他四种可靠度分析算法，本文算法在求解二维和多维非线性极限状态函数时均具有更好的收敛性和更高的计算效率。

Armijo-based adaptive stability transformation method

Structural reliability analysis is the key part of structural uncertainty design,and efficiency and robustness are two important indexes used to evaluate the performance of reliability analysis methods.At the beginning of this paper,two existing first-order-second-moment methods,named as the iHL-RF method and the directional stability transformation method respectively,are analyzed.It is found that the step length could be adaptively adjusted by the Armijo rule in the iHL-RF method,but the computational efficiency is low.Moreover,the directional stability transformation method could enhance the efficiency based on the direction property of oscillation,but the adaptability is poor.Combining the advantages of the two algorithms,the Armijo rule could be used to adaptively adjust the chaos control factor of the directional stability transformation method,and then the Armijo-based adaptive stability transformation method is proposed.Finally,based on four nonlinear examples,the convergence and efficiency are compared among five methods including HL-RF,iHL-RF,chaos control method,directional stability transformation method and our proposed method.Numerical results show that the proposed method has better convergence and higher efficiency than the other four reliability analysis methods when solving two-dimensional and multi-dimensional nonlinear limit state functions.