IMPROVED RELIABILITY METHOD BASED ON HLRF AND MODIFIED SYMMETRIC RANK 1 METHOD

The first-order reliability method (FORM) is simple and efficient, but the error is significant when dealing with strong nonlinear functions. With existing second-order reliability methods (SORM), the calculation accuracy is improve, but the efficiency is reduced. In this research, an improved SORM, which can achieve better balance between accuracy and efficiency, is presented. The modified symmetric rank 1 method is combined with the determination of step length of the HLRF method, and an improved FORM with better convergence is proposed, in which the approximate Hessian matrix of performance function is obtained without increasing the amount of function evaluations. Combining the coordinate rotation with the univariate dimensional reduction approximation of the performance function according to its known gradient vector and Hessian matrix, and introducing the non-central chi-square distribution, the paper proposes an improved SORM with the same efficiency but higher accuracy. The wide applicability and advantages in both accuracy and efficiency of the proposed methods are verified by several numerical examples and engineering examples.