基于k-fold交叉验证的代理模型序列采样方法

在代理模型序列采样框架下,针对现有研究中的不足之处,通过引入k-fold交叉验证计算样本的预测误差,并结合泰森多边形法和最大距离最小化准则,发展了一种适用于任意代理模型的k-fold CV-Voronoi自适应序列采样方法。相较于传统序列采样方法,本文方法具有计算简单和自适应性强等显著优势。通过数值算例和工程算例对比分析发现所提序列采样方法具有较高的近似精度和计算效率,此外,进一步讨论了k-fold交叉验证中k的不同取值对于代理模型精度的影响,总结出k的最优取值范围以供参考。

A sequential sampling method of surrogate model based on k-fold cross validation

Under the framework of sequence sampling of surrogate models,in view of the shortcomings of existing methods,a k-fold CV-Voronoi adaptive sequential sampling method was developed,which is suitable for arbitrary surrogate models.In this method,the k-fold cross-validation was introduced to calculate the prediction error of sample points,and the Voronoi diagram and maxmin criterion were combined.Compared with the traditional sequential sampling method,the proposed method has the advantages of calculation simplicity and strong adaptability.Through the numerical examples and engineering example,it is shown that the proposed sequential sampling method has high accuracy and calculation efficiency.In addition,the influence of different k values on the accuracy of surrogate model is further discussed in the k-fold cross-validation,and the optimal range of k values is summarized for reference.