基于混沌控制的结构可靠度算法

The Structural Reliability Algorithm Based on Chaos Control

摘要: 如果功能函数或极限状态函数有着较高的非线性程度，采取HL-RF算法时可能存在震荡、混沌的情况，甚至不收敛。针对以上问题在HL-RF算法基础上引入混沌反馈控制中的稳定转换法进行收敛控制，并利用混沌控制因子使每步迭代更加高效收敛。与此同时引入了一种迭代过程中震荡现象判定方法，当逐步收敛到验算点时利用经典HL-RF算法来进行迭代处理；如果检测到震荡的情况可通过混沌控制迭代算法来进行处理。从算例结果可以看到，对于迭代中的震荡问题，通过混沌控制迭代算法能有效解决，相对于经典HL-RF算法，该算法保证了稳定性的同时也更加高效。

Abstract: If function or limit state function has a higher degree of nonlinearity, when the HL-RF algorithm is adopted, there may be oscillation and chaos, or even no convergence. Aiming at the above problems, this paper introduces the stable transformation method in chaos feedback control based on the HL-RF algorithm for convergence control, and USES chaos control factor to make each iteration more efficient convergence. At the same time, a method to determine the oscillation phenomenon in the iterative process is introduced, and the classical HL-RF algorithm is used to perform iterative processing when it gradually converges to the checking point. If the oscillation is detected, the chaotic control iterative algorithm can be used to deal with it. It can be seen from the results of the examples that the iterative algorithm can effectively solve the oscillation problem in the iteration through the chaos control iterative algorithm. Compared with the classical HL-RF algorithm, this algorithm not only guarantees stability but also is more efficient.