考虑整体趋势的最佳子集Kriging模型

Optimal Subset Kriging Surrogate Model Considering Global Trend

代理建模是用于解决具有隐式工程设计问题的有效方法,可广泛应用于航空航天等领域。代理模型方法主要寻求2个方面突破:一是降低模型构建成本,二是提高模型计算精度。基于以上2点,提出一种改进Kriging模型,通过一至三阶响应面确定隐式函数的整体趋势,选取拟合程度较高的趋势备选函数的阶数作为Kriging模型趋势项的阶数,并通过遗传算法排除趋势函数中不必要的项。通过引入主动学习函数,在尽量减少构建成本的同时,进一步提升代理模型的计算精度。算例结果表明:在样本数量相近的情况下,所提方法比其他方法具有更好的计算精度。

Surrogate modeling is an effective method to solve implicit engineering design issues,which can be widely used in aerospace engineering and other engineering fields.The surrogate model approach mainly seeks for two breakthroughs:The first way is to reduce the construction cost of the surrogate model,and the second way is to improve the calculation accuracy of the surrogate model.An improved Kriging model was proposed and its details were as follows.The trend item of the implicit function was determined by using the first-order to third-order response surface methods.The order of the trend alternative function with the higher degree of fitting was selected as the order of the trend item in Kriging model.The unnecessary items of the trend function were eliminated by the genetic algorithm.The calculation accuracy of Kriging model was further improved by the active-learning function while the construction cost of the Kriging model was reduced.The numerical examples show that the calculation accuracy of the proposed method is higher than the one of other methods when the number of samples is almost the same.