基于序列二次规划法的结构可靠度计算方法

Structural Reliability Calculation Method Based on Sequential Quadratic Programming

针对传统的可靠度计算方法在求解多目标函数的约束优化及高非线性结构功能函数的可靠度求解时计算效率低、收敛性不高等问题,提出了一种基于序列二次规划法的结构可靠度计算方法。该方法引入序列二次规划法的约束优化模型并结合可靠度指标计算模型,在每一迭代步通过求解一个二次规划子问题来确定目标函数的下降方向,构造价值函数确定搜索步长,使其全局收敛以获得可靠度最优解及验算点。通过三个算例验证了该方法的有效性。

Aiming at low computational efficiency and the convergence problem of traditional reliability calculation method in solving the problem of constrained optimization of multi-objective function and the reliability of high nonlinear structural function, a method of structural reliability calculation based on se- quential quadratic programming was proposed. This method introduced the constrained optimization model of sequential quadratic programming method combined with the structural reliability index calculation model, and determined the direction of the descent of the objective function by solving a quadratic programming subproblem in each iteration step and decreased the value function to determine the search step size, making it globally convergent to obtain the optimal solution of reliability and verification point. Finally, the proposed method was verified effectively through three examples.