基于不平稳假设的序贯近似建模方法

在工业设计中常涉及复杂、耗时的仿真,建立简单的近似模型可以简化分析和优化过程.元模型的构建和仿真试验的设计是其中的两个关键问题.针对元模型的构建,分析指出传统的基于平稳性假设的Kriging方法并不适合常见的不规则系统的建模,接着采用非线性映射方法,提出了一种基于不平稳假设的Kriging方法.实例说明:相对于传统的Kriging方法,该方法不仅可以建立精度较高的预测模型,而且对模型的预测不确定性的描述也更符合直观认识;针对计算机试验设计,提出了一种基于改进的Kriging方法的序贯准则,使得试验点序贯产生在不确定性大且距离现有试验点远的位置.算例表明:该序贯设计比一步设计效果好,能节约试验样本.

Non-stationary covariance-based sequential meta-modeling of engineering design simulation

Surrogate models are usually developed to facilitate the analysis and optimization of engineering systems that involve computationally expensive simulations. The two key problems in constructing the surrogate model are meta-modeling and design of computer experiment. As for the meta-modeling, the widely used Kriging method is under the assumption of a stationary covariance structure, which does not hold in situations where the level of smoothness of a response varies significantly. Thus, we adopt a non-linear mapping approach to incorporate the non-stationary covariance structure into Kriging meta-modeling for simulations. Examples show that the proposed method is superior to the classical Kriging method in producing kriging meta-models with higher prediction accuracy and in quantifying prediction uncertainty associated with the use of meta-models. As for the design of computer experiment, we proposed a sequential criterion based on the improved Kriging method to generate new design points with high prediction uncertainty and with great distance to the current design points. Examples show that the sequential design is superior to the single-stage design in saving samples.