变f响应面法及其在重力坝结构可靠性分析中的应用

响应面法已经成为求解大型复杂结构可靠度的常用方法,尤其适用于求解结构极限状态方程具有较强的非线性或是在结构分析中引入有限元进行可靠性分析而导致方程呈隐式的问题.针对传统响应面法中中心复合抽样因子f值取值不同导致计算结果波动且精度不高的问题,首次提出在响应面法计算流程中引入"变f"的概念.算例结果表明,本文提出的变f响应面法相比于经典响应面法、加权响应面法以及JC法精度更高,收敛速度更快,且可突破f取值1~3的限制,适用于非线性极限状态方程可靠度的计算.此外,通过变f响应面法与加权响应面结果的对比可知,本文提出的方法精度更高,改变f值的作用可以替代加权响应面法中加权函数的作用.最后,结合某简单的重力坝模型,对于该方法在重力坝抗拉可靠度计算中的应用作了有益的探索.

Improved Response Surface Method with Variable f and Its Application to Structural Reliability Analysis of Gravity Dam

Response surface method（RSM） has become a common method for analyzing the structural reliabil- ity of large complex systems, especially appropriate for solving the limit state equation characterized by strong nonlinearity or in terms of the introduction of finite element reliability analysis which often leads to the limit equation being implicit. As is well-known, the traditional RSM based on central composite sampling may re- sult in volatility when factor f is determined differently and the precision of traditional RSM is not well e- nough. Thus, RSM with variable f is first proposed in this paper and is illustrated with two case studies. Nu- merical results show that the proposed method with variable f possesses higher accuracy and faster conver- gence, compared to the classical RSM, the weighted RSM and JC method. What＇s more, the proposed method is able to break restriction of the value of f which customarily ranges from one to three. In addition, by com- paring the results of the proposed method and the weighted RSM, the proposed method bears better accuracy and the role played by the weight matrix can be replaced by the function of variable f. Finally, by utilizing a simple gravity dam model, the RSM with variable f is found suitable for analyzing the tensile reliability of gravity dams.