An Appropriate Formulation of Nonlinear Conjugate Gradient Optimization Methods for Calculation of Structural Reliability Index

Estimation of the first-order reliability method (FORM) for computation of structural failure probability is possible by using mathematical optimization methods. Computational time and global convergence of various optimization methods are criteria for evaluating an appropriate optimization method in the reliability analysis. In this paper, the Nonlinear Conjugate Gradient (NCG) methods have been established for determination of the structural reliability index for the first time. Seven NCG methods have been proposed based on appropriate formulation of the reliability analysis for calculation of the reliability index of structures. The ability and efficiency of these methods are checked in several examples. The convergence and CPU run-times of examples are compared together. The results illustrated that the NCG methods successfully are applied for computation of the reliability index and these methods have suitable efficiency and convergence for estimation of the failure probability of structures. In the basis of problem property has been obtained irregular convergence and run-times of various NCG methods.