An Armijo-based hybrid step length release first order reliability method based on chaos control for structural reliability analysis

In structural reliability analysis, the HL-RF method may not converge in some nonlinear cases. The chaos control based first-order second-moment method (CC) achieves convergence by controlling the step length with chaotic control factors, but it commonly requires very time-consuming computation. In this paper, an Armijo-based hybrid step length release method based on chaos control is proposed to surmount the above issue. An iterative control angle is introduced for the proposed method to select an adaptive adjustment step length strategy. Then, a step length release method is proposed to speed up the convergence when the iterative rotation angle is less than the rotation control angle. When the iterative rotation angle exceeds the rotation control angle, an adaptive adjustment method for step length is defined based on the Armijo rule to provide an optimal choice of adaptive step length for the iterative process and guarantee convergence. After that, the robustness and efficiency of the proposed method are proved through several examples. The examples show that the proposed method is capable of generating a suitable adaptive step length, therefore accessing a more stable and accurate solution with greater efficiency in both high and low nonlinearity cases. It can well combine the advantages of HL-RF and the CC methods, and the efficiency is further improved without sacrificing its robustness. Finally, a discussion is brought out to investigate the selection of optimal parameters and how the two step length selection strategy cooperates and co-action with one another. It can be seen that the efficiency improvement of the proposed method mainly contributed to the step length release method, while the Armijo-based adaptive adjustment method for step length guaranteed convergence.