基于单变量分析的自适应响应面法

A NEW ADAPTIVE RESPONSE SURFACE METHOD BASED ON UNIVARIATE ANALYSIS

由于简便易行,响应面法在结构可靠度分析中获得了众多关注,其中尤以不考虑交叉项的二次响应面应用最为广泛。然而,对于与强非线性相对应的复杂极限状态曲面,二次响应面的近似精度显然不够,从而引起可靠度估计的较大误差。虽然理论上高次响应面法可以解决这一问题,但待定系数的急剧增长导致计算效率降低甚至无法实现。为此,该文以多变量函数的单变量分析为基础,提出了一种合理确定高次响应面形式的算法,可以有效地减少响应面中待定系数的数量,降低了计算的困难,并且针对可能出现的问题提出了改进措施;此外,基于数论选点策略,发展了一类适用于响应面法的数论选点方案。最后,通过算例分析对建议算法进行验证,结果表明该算法具有较好的精度和效率。

Response surface method has won numerous concerns in the reliability analysis of structures due to its simplicity and practicability, especially the quadratic response surface is most widely used because it contains no cross terms. However, for the complex ultimate state curved surface associated with strong nonlinearity, the accuracy of quadratic response surface is not good enough, introducing a big error in the estimation of reliability. Although, theoretically, higher order response surface method can overcome this problem, the sharp increase of the undetermined coefficient reduces calculation efficiency. Therefore, on the basis of univariate analysis of the multivariable function, an algorithm which can reasonably determine the form of higher order response surface is presented in this article, and it is able to effectively reduce the number of undetermined coefficients in response surface, so as to reduce computational difficulties; In addition, a scheme of number-theoretic selecting point applicable to response surface method has been developed. Finally, illustrative examples show that the suggested algorithm has good accuracy and efficiency.