一种新的改进响应面法的结构可靠性计算方法

A new improved response surface method for structural reliability computing

针对经典响应面方法计算结构的可靠度时计算量大、不够精确、易产生奇异解等问题,首先通过计算原来响应面函数的梯度函数得到方位向量,由方位向量得到旋转矩阵;然后,按照该旋转矩阵通过旋转坐标轴得到新的坐标系,在该新的坐标系用新的样本点构造逼近函数,所构造的逼近函数和原来极限状态函数在形式上接近;最后,通过反复迭代,得到极限状态函数的最大失效点,从而得到结构的失效概率。研究结果表明:本文方法改进了传统响应面法,提高计算精度,降低计算次数,是有效和可行的。

Considering that the classical response surface method can easily produce large amount of calculation, errors and singular solution, the original response surface function gradient orientation vector was firstly computed to obtain the rotation matrix, and then the axes were rotated in accordance with the rotation matrix to get the new coordinate system by using the rotation matrix. In the new coordinate system, the new sample points were used to construct the approximation function and the original limit state function approximation function in the close form. Finally, the most failure point of the limit state function and the structural failure probability were obtained by using the mutual replacement method. The results show that the calculation accuracy of the traditional response surface method can be improved, and the computational times can be reduced. The algorithm is effective and feasible.