an enhanced hl-rf method for the computation of structural failure probability based on relaxed approach

the computation of structural failure probability is vital importance in the reliability analysis and may be carried out on the basis of the first-order reliability method using various mathematical iterative approaches such as hasofer-lind and rackwitz-fiessler (hl-rf). this method may not converge in complicated problems and nonlinear limit state functions, which usually shows itself in the form of periodic, bifurcation and chaos solution. in this paper, the hl-rf method has been improved based on the relaxed method to overcome these numerical instabilities. an appropriate relaxed coefficient has been defined, ranging between 0 and 1, to enhance the hl-rf method. this coefficient can be computed using the information from the new and previous iterations of the hl-rf algorithm based on second-order fitting. capability, robustness and efficiency of the proposed algorithm have been studied by results of several examples compared to the hl-rf. results illustrated that the proposed method is more efficient and robust in the computation of the failure probability compared to the hl-rf method.