基于HLRF法与修正对称秩1方法的改进可靠度方法EI北大核心CSCD

一次可靠度方法简单、高效,但在处理强非线性功能函数时存在较大误差;已有的二次可靠度方法在提高精度的同时往往降低了效率。为此,该文中在发展改进一次可靠度方法的同时提出了更好地兼顾精度与效率的改进二次可靠度方法。将修正对称秩1方法与HLRF法的步长确定策略相结合,提出了具有较好收敛性的改进一次可靠度方法,且在基本不增加计算量的前提下获得了功能函数的近似Hessian矩阵;结合坐标旋转、单变量降维近似和非中心卡方分布,提出了与改进一次可靠度方法同效率但具有更高精度的改进二次可靠度方法;通过数值算例和工程算例验证了建议方法的广泛适用性以及精度或效率上的优势。

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.