A self-adaptive finite-step length method based on the inverse tangent function for accurate and efficient structural reliability analysis

In first-order reliability estimation, the finite step length (FSL) method can bring improvements, but can only conditionally reduce step length and is restricted by its inability to achieve a self-adaptive step length. Thus, it often fails to balance efficiency, accuracy and robustness. This article proposes a self-adaptive finite-step length method based on the inverse tangent function ITF-FSL) to address the deficiencies of FSL. The proposed method elucidates the nonlinear relationship between the distance of iteration points and the ideal FSL step length. It introduces the inverse tangent function lTF to achieve self-adaptive step length, replacing the fixed one. The parameters involved are discussed. Using the adjustment approach, the proposed method converges stably and efficiently with comparable or superior accuracy. The performance of the method is demonstrated through 10 numerical and engineering examples. Lastly, the optimal parameters of the lTF model are suggested.