A novel hybrid steepest descent map and angle condition for structural reliability analysis

Abstract

The analytical structural reliability analysis using a nonlinear iterative map without control have instabilities for searching the reliability index in some nonlinear cases. The steepest descent discrete map is simple for formulation but its iterative formulation should be enhanced for achieving stabilization. In this paper, the nonlinear discrete map given form directional steepest descent method is enhanced based on an inexact search direction vector for improving the robustness of iterative reliability method. A dynamical-accelerated step size is proposed for enhancing the instabilities of analytical reliability without controlling properties as main effort while these frameworks can be improved the computational burden of directional reliability method. An angle condition is proposed for enhancing the directional discrete map applied in the sensitivity vector as main factor in iterative formulation for approximation of failure probability. The dynamical-accelerated step size is adjusted using an inner loop based on iterative information. The instability of steepest descent method and efficiency of directional chaos control method are enhanced based on inexact step size given form the angle condition. The proposed analytical methods for searching failure probability showed a superior conveyance for both stability and efficiency compared to traditional iterative methods and these proposed reliability methods are strongly improved the computational burden of iterative chaos control formulation.