基于合理子域的改进响应面方法

基于结构可靠性分析理论，给出了合理子域概念.合理子域能够明确在设计点附近对失效概率起主要贡献区域尺寸，且能够保证失效点以一定概率落在其内，解决了对失效概率起主要贡献区域尺寸难以量化问题.基于合理子域概念，给出了一种改进响应面方法.该方法能够保证响应函数在设计点处是无误差的、且在合理子域内对极限状态函数具有较好近似.采取蒙特卡罗重要抽样方法求解失效概率，结合抽样点位置采取分区域评估方法以提高失效概率求解精度.算例表明，所提方法在处理具有显式和隐式极限状态函数的可靠性分析时，均具有较好的计算精度和较高的计算效率. 

AN IMPROVED RESPONSE SURFACE METHOD BASED ON THE RESONABLE SUBDOMAIN

The concept of reasonable subdomain is defined based on the theory of structural reliability in the paper. The size of domain around the design point which gives the main contribution to the failure probability is well-defined by using the reasonable subdomain. The failure points can be distributed in the reasonable subdomain in terms of a given probability. The proposed reasonable subdomain can solve the problem that the size of main domain influencing failure probability is not given obviously. Then, an improved response surface method is also proposed based on the reasonable subdomain. The proposed method can ensure that there is no fitting error of the response function at the design point, and can better fit the limit state function in the reasonable subdomain. The failure probability is evaluated by using the importance sampling Monte Carlo simulation. In order to improve the evaluation accuracy of failure probability, the evaluation method of subdomain is applied according to the locations of sample points. Numerical examples are shown that the proposed method has high accuracy and efficiency for both explicit and implicit limit states.