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在结构可靠度指标的求解中,HL-RF迭代算法由于其格式简单,效率高被广泛应用到一次二阶矩计算中。然而该方法仅适用于功能函数非线性程度低的情况,当功能函数非线性程度较高时,HL-RF算法常会出现混沌、振荡和周期解的现象,甚至导致不收敛。该文在混沌控制理论的基础上提出了一种新的修正的混沌控制算法来控制迭代过程中产生的振荡。该方法在保留基于混沌控制方法稳健性的同时提高了计算效率,并对迭代过程中振荡现象引入了一种新的判据。当迭代过程逐渐收敛到最可能失效点时,采用经典的HL-RF算法;当检测到振荡时,采用基于修正混沌控制的迭代算法。算例结果表明:基于修正混沌控制的迭代算法能有效解决迭代中的振荡问题,与经典的HL-RF算法相比,该算法具备效率和稳健性方面的优势。
In solving the structural reliability index, the HL-RF iterative algorithm is widely used in the second-order moment calculation due to its simple format and high efficiency. However, this method is only suitable for cases where the nonlinearity of the function is low. When the degree of nonlinearity of the function is high, the HL-RF algorithm often has the phenomenon of chaos, oscillation and periodic solution, even leading to non-convergence. Based on the theory of chaos control, a new modified chaos control algorithm is proposed to control the oscillation in iterative process. This method improves the computational efficiency while preserving the robustness based on the chaotic control method and introduces a new criterion for the oscillation in the iterative process. When the iterative process converges to the most probable failure point, the classical HL-RF algorithm is adopted. When oscillation is detected, an iterative algorithm based on modified chaos control is adopted. The experimental results show that the iterative algorithm based on modified chaos control can effectively solve the oscillation problem in iteration. Compared with the classical HL-RF algorithm, this algorithm has the advantages of efficiency and robustness.