An adaptive sampling approach for Kriging metamodeling by maximizing expected prediction error
An adaptive sampling approach for Kriging metamodeling by maximizing expected prediction error
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DOI：
10.1016/j.compchemeng.2017.05.025
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发表时间：
2017-11
期刊：
影响因子：
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通讯作者：
Haitao Liu;Jianfei Cai;Y. Ong
中科院分区：
文献类型：
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作者：
Haitao Liu;Jianfei Cai;Y. Ong
作为一种著名的近似方法，克立格法被广泛应用于过程工程设计和优化中，以节省计算预算。目标函数的克立格模型是用一组样本点来拟合的，这些样本点的响应在实际中是昂贵的，而这些样本点的分布对模型的预测质量有很大的影响。因此，Kriging元模型自适应采样的一个主要任务是收集信息点，以便用尽可能少的点建立一个准确的模型。为此，我们提出了一种偏差-方差分解框架下的自适应采样方法。这种新的采样方法通过最大化同时考虑偏差和方差信息的预期预测误差准则来顺序地选择新点。特别地，它提出了一种自适应平衡策略，通过前一次迭代的误差信息动态平衡局部开发和全局开发。用4个基准算例和4个工程算例从低维到高维对该方法的性能进行了评估。数值结果表明，这种自适应采样方法对于构造具有不同特征的问题的精确克立格模型是非常有前途的。
As a well-known approximation method, Kriging is widely used in process engineering design and optimization for saving computational budget. The Kriging model for a target function is fitted to a set of sample points, the responses of which are expensive to obtain in practice and the sample distribution of which has a great impact on the model prediction quality. Therefore, a main task in adaptive sampling for Kriging metamodeling is to gather informative points in order to build an accurate model with as few points as possible. To this end, we propose an adaptive sampling approach under the bias-variance decomposition framework. This novel sampling approach sequentially selects new points by maximizing an expected prediction error criterion that considers both the bias and variance information. Particularly, it presents an adaptive balance strategy to dynamically balance the local exploitation and global exploration via the error information from the previous iteration. Four benchmark cases and four engineering cases from low to high dimensions are used to assess the performance of the proposed approach. Numerical results reveal that this adaptive sampling approach is very promising for constructing accurate Kriging models for problems with diverse characteristics.