结构体系隐式极限状态方程概率分析的改进响应面法

ADVANCED RESPONSE SURFACE METHOD FOR THE FAILURE PROBABILITY OF COMPLEX STRUCTURE WITH MULTIPLE IMPLICIT LIMIT STATE EQUATIONS

提出一种新的处理隐式极限状态方程概率安全分析的响应面法,在原响应面法的基础上,通过引入高阶修正项和概率等效变换,建立原隐式极限状态方程的等效显式极限状态方程,以利用已有的各种针对显式极限状态方程的可靠性分析方法,得到等效显式极限状态方程的失效概率。该方法被推广应用到所有极限状态方程均为隐式的结构体系的可靠性分析中去,依次建立每个失效模式的等效极限状态方程,并采用MonteCarlo法和重要抽样法计算具有多个极限状态方程的结构体系的失效概率。算例表明,文中方法不用差分方法计算隐式极限状态对基本随机变量的导数,适于解决隐函数的概率可靠性分析问题,由于采用了高阶项的修正,能够得到更高精度的结果。

An advanced response surface method is presented for implicit limit state equation. Based on the conventional response surface method, the higher order correction and equivalent probability transform are considered in the advanced response surface method. The equivalent explicit limit state equation can be established by the advanced response surface method so that the available reliability analysis method for explicit limit state can be used. The advanced surface response method can be extended to the complex structure with multiple implicit limit state equations. After the equivalent explicit limit state is established for every implicit limit state equation in the complex structure, Monte Carlo method and the extended importance sampling method can be employed to calculate the structure system failure probability. Illustrative examples show that the gradient is avoided in the presented method, and the higher accuracy is attained by taking the correlation of the failure modes into consideration.