This paper discusses a new sequential adaptive design of experiments (DoE) approach for global Kriging metamodeling applications. The sequential implementation is established by using the current metamodel, formulated based on the existing experiments, to guide the selection of the optimal new experiment(s). The score function, defining the DoE objective, combines two components: (1) the metamodel prediction variability, expressed through the predictive variance, and (2) the metamodel bias, approximated through the leave-one-out cross validation (LOOCV) error. The latter is used as a weighting factor to extend traditional DoE approaches that focus solely on the metamodel prediction variability. Two such approaches are considered here, adopting either the integrated mean squared error or the maximum mean squared error as the basic component of the score function. The incorporation of bias information as weighting within these well-established approaches facilitates a direct extension of their respective computational workflows, making the proposed implementation attractive from computational perspective. An efficient optimization scheme for identification of the next experiment, as well as the balancing of exploration and exploitation between the two components of the score function, are also discussed. The incorporation of LOOCV weightings is shown to be highly beneficial in a total of six analytical and engineering examples. Furthermore, these examples demonstrate that for DoE approaches which use LOOCV information as weights, it is preferable to update the predictive variance to explicitly consider the impact of the new experiment, rather than relying strictly on the current metamodel variance.

本文讨论了用于全局Kriging元建模应用程序的新的顺序自适应实验设计（DoE）方法。通过使用基于现有实验制定的当前元模型来建立顺序实现，以指导最佳新实验的选择。定义DoE目标的得分函数结合了两个组成部分：（1）通过预测方差表示的元模型预测变异性；以及（2）通过留一法交叉验证（LOOCV）误差近似的元模型偏差。后者被用作加权因子，以扩展传统的DoE方法，该方法只专注于元模型预测的可变性。这里考虑两种这样的方法，采用积分均方误差或最大均方误差作为得分函数的基本组成部分。将偏差信息作为权重并入这些公认的方法中有助于直接扩展其各自的计算工作流程，从而从计算角度使所提出的实现更具吸引力。还讨论了用于识别下一个实验的有效优化方案，以及评分函数的两个组件之间的探索与开发之间的平衡。在总共六个分析和工程示例中，LOOCV权重的合并被证明是非常有益的。此外，这些示例表明，对于使用LOOCV信息作为权重的DoE方法，