Improvement of Stability Transformation Method for First Order Reliability Analysis

The stability transformation method (STM) of chaos feedback control is a simple and efficient approach to implement the convergence control of the first order reliability method (FORM). The robustness and efficiency of the STM are depended on selected parameters of this algorithm such that involuntary matrix and step size in structural reliability analysis. When involuntary matrix and step size are inappropriately selected, the STM iterative formula can be prematurely and slowly converged. In this paper, the STM scheme was improved based on a simple dynamical step size and the involuntary matrix equals to unit matrix. The proposed dynamical step size can be computed using the new and previous results of the FORM iterative formula. The efficiency and robustness of improved STM was compared with the STM and finite-step length methods from five numerical and mechanical examples taken through the literature. The results impales that the improved STM not only ensured the numerical stability of nonlinear mechanical problems but also is more efficient than the STM to approximate the failure probability.