基于交叉降阶取样的改进响应面方法

针对经典响应面法和加权响应面法存在的计算精度不高和稳定性不强的问题,提出一种新的样本点选择策略,即交叉降阶思想,并基于此发展出一种新的改进响应面方法。该方法以均值点加上0.5倍的标准差作为初始迭代点。在Bucher试验设计的基础之上,将n维坐标系降阶为n个一维坐标系。然后,依据样本点的重要性,筛选出n+1个靠近真实失效面的优秀样本点,并用这些样本点去拟合线性响应面函数。最后依据样本中心间的距离与上一次迭代得到的设计点的范数之商作为其收敛准则。通过5个数值算例与工程算例,验证了交叉降阶响应面法具有较高的精度、效率、稳定性和一定的工程适用性。

An improved response surface method based on cross order reduction sampling

Aiming at the problems of low computation accuracy and stability of classical response surface method and weighted response surface method,a new sampling point selection strategy is proposed and a new improved response surface method is developed based on cross order reduction.The sum of the mean point and half of the standard deviation is used as the initial iteration point.And the n-dimensional coordinate system is reduced to n one-dimensional coordinate systems on the basis of Bucher''s method.Then,based on the importance of the sampling points,n+1 better sampling points near the true failure surface are selected and used to fit the linear response surface.Finally,the quotient of the distance between the two central points before and after the current time instant and the norm of the design point obtained in the previous iteration is used as its convergence criterion.Through five examples,it is verified that the cross-order reduction method has high accuracy,efficiency and stability,and this method can be applied in engineering.