Enriched FR conjugate search directions for robust and efficient structural reliability analysis

Abstract

This paper proposes three modified conjugate Fletcher- Reeves (FR) algorithms including improved FR (IFR), the spectral-variant FR (SVFR) and modified FR (MFR) for first-order reliability method (FORM) for nonlinear reliability problems. An adaptive finite-step length is proposed to improve the efficiency and robustness of FORM formula using both steepest descent and conjugate search directions. These conjugate nonlinear maps for computing the search direction of FORM are adjusted based on sufficient decent condition to control instabilities of FORM formula. The efficiency and robustness of three proposed conjugate methods are compared with conjugate Hasofer and Lind-Rackwitz and Fiessler (CHL-RF), limited FR (LFR), HL-RF and finite-step length (FSL) through five nonlinear limit state functions. Numerical experiments illustrated that the modified FR versions of conjugate search direction are robust methods for highly nonlinear performance functions and the IFR is more efficient than the other reliability algorithms.