利用连续多模态特性探索的自适应Kriging模型构建方法

Adaptive Kriging Modeling Using Continuous and Multi-modal Characteristics Exploration

为了高效率地构建高精度的代理模型,提出一种利用连续多模态特性探索的自适应Kriging模型构建方法.首先在获得一个初始Kriging模型后,利用留一交叉验证策略计算出代理模型的精度;然后利用相对误差准则,从样本库中挑选出误差最大的样本点;再通过泰勒级数展开式快速获得新样本点及其近似响应值;如此不断地更新样本库及Kriging模型,最终使模型精度达到预定要求.对2个数学算例和1个工程实例进行了应用分析,结果表明,该方法能够以较快的速度得到较高精度的Kriging模型.

To build a highly accurate metamodel with high efficiency, an adaptive Kriging modeling method using the exploration of continuous and multi-modal characteristics was proposed. After obtaining an initial Kriging model, the leave-one-out cross-validation strategy was utilized to calculate the metamodel＇s accuracy. Then the sample point with the maximum error was selected from the sample database according to the relative error criterion. A new sample point and its approximate response value were acquired quickly by using the Taylor Series expansion. With the above procedures repeated, the sample database and the Kriging model were updated in order to make the Kriging model achieve the required accuracy. The method was applied to two mathematical problems and an engineering problem. Results show that the method can get a higher accurate Kriging model with higher efficiency.