径向基函数随机响应面法

针对随机响应面法对非正态分布响应与标准正态分布输入之间的复杂非线性隐函数拟合不够理想的问题,基于径向基函数在杂散数据拟合方面的优异性能,提出使用径向基函数替换Hermite多项式来解决复杂非线性隐函数拟合问题。以若干个非线性解析函数和钢管混凝土肋拱极限承载力不确定性问题作为算例,验证该方法对非正态分布响应拟合的精确性和对工程问题的适用性。算例结果表明,基于径向基函数随机响应面法对高度非线性的响应与输入隐函数拟合较好;在多参数钢管混凝土拱极限承载力不确定性问题中,精度较高,且比Hermite多项式样本点数量少。

Stochastic Response Surface Method Based on Radial Basis Functions

For non-ideal interpolation results of complex implicit nonlinear functions between non-normal distribution response and standard normal distribution inputs using stochastic response surface method, radial basis functions was used to replace Hermite polynomials so as to solve complex implicit nonlinear function interpolation problem for its excellent performance on scattered data interpolation. A few nonlinear analytical functions and uncertainty problems of the load carrying capacity of single circular concrete filled steel tubule (CFST) arch were used as examples to test and verify the precision of proposed method in non-normal distribution response interpolation and its engineering applicability. The results show that stochastic response surface method based on radial basis functions performs well in fitting highly nonlinear input implicit functions, and can achieve high precision on multi-parameters CFST arch load carrying capacity uncertainty problems. Meanwhile, the method has less sample points compared to the Hermite polynomials method.