Chaotic conjugate stability transformation method for structural reliability analysis

The efficiency and robustness are two important issues in First Order Reliability Method (FORM). The Hasofer and Lind-Rackwitz and Fiessler (HL-RF) algorithm is widely used in FORM, but it produces unstable results as periodic and chaotic solutions for highly nonlinear problems. Hence, the stability transformation method (STM) with chaos feedback control was proposed to overcome the numerical instabilities of FORM, but it is inefficient for both concave and convex reliability problems. In this paper, a stability transformation method with chaotic conjugate search direction is proposed to improve both the robustness and efficiency of FORM formula, where a chaos control factor is proposed based on Logistic map, and a transformation matrix is adaptively defined based on the reliability index and the Logistic map at each iteration. Eight nonlinear mathematical and structural/mechanical examples are selected to demonstrate the efficiency and robustness of the proposed chaotic conjugate stability transformation method (CCSTM). Results illustrate that the CCSTM is more robust than the HL-RF and more efficient than other existing reliability methods.