基于最小范数点的响应面方法

Response surface method based on minimum norm point for structure reliability analysis

针对传统的响应面法难以实现大范围精度近似,可靠度计算效率和精度偏低的问题,本文从可靠度指标的几何意义入手,提出一种基于最小范数点的改进响应面方法。该方法在响应面上的最小范数点附近选取新的试验点,再对这些样本点进行二次多项式插值校正,从而构建出更加逼近极限状态方程的响应面形式,一定程度上提高了计算的精度。另一方面,本文引入了一种双重收敛准则进行判断性评估,能够有效地节省迭代的过程,提高计算效率。最后,算例分析验证了本文方法的合理性和适用性。

It is difficult to achieve high precision using the traditional response surface method,which suffers from low reliability calculation efficiency and accuracy.The proposed method starts with the geometric significance of the reliability index and proposes a method based on the minimum norm point to improve the response surface.New test points are selected near the minimum norm point on the response surface.These sample points are improved by two polynomial interpolations.Then,a better response surface is constructed which is closer to that for the limit state equation.It improves the accuracy of the calculation.In addition,the proposed method introduces a dual convergence criterion for evaluation.It can not only effectively shorten the iterative process,but also improve its efficiency.At last,numerical examples are given to show the advantages and applicability of the proposed method.