传统代理模型技术在处理高维问题时,由于变量维数增加使得建模所需样本数量呈指数型增长,将导致计算成本显著提高.为了构建适用于高维问题的代理模型,在DIRECT优化算法基础上,改进其初始样本点位置,实现初始样本集的扩充,并将克里金(Kriging)建模方法与高维代理模型(High-dimensional model representation,HDMR)相结合,这样可避免建立的模型陷入局部最优,提出一种改进的Kriging-HDMR建模方法.iKriging-HDMR建模方法利用高维代理模型的优点,将高维问题的响应函数等效为一系列低维函数的叠加,发挥iKriging-HDMR建模方法的优势以减少建模过程所需样本点个数,提出一种新的收敛条件,从而减小代理模型的局部误差以保证建立的代理模型具有较高的精度.通过数值算例和机器人工程应用,验证了提出方法的有效性.结果表明,所提出的iKriging-HDMR建模方法可显著减少建模所需样本点数量,具有很好的计算精度和效率.
Research and Improvement of Kriging-HDMR Modeling Method
When dealing with high-dimensional problems in traditional representation model technology,the number of sample points required for modeling increases exponentially due to the increase in variable dimension,which will lead to a significant increase in computational cost.In order to build a representation model suitable for high-dimensional problems,based on the DIRECT optimization algorithm,the initial sample point position is improved,the initial sample set is expanded,and the Kriging modeling method and high-dimensional model representation(HDMR),which can avoid the established model from falling into local optimality,and proposes an improved Kriging-HDMR(iKriging-HDMR)modeling method.The iKriging-HDMR modeling method uses the advantages of HDMR to equate the response function of the high-dimensional problem to a series of low-dimensional function superpositions,taking advantage of the iKriging-HDMR modeling method to reduce the number of sample points required in the modeling process number.A new convergence condition is proposed to reduce the local error of the agent model to ensure that the established agent model has high accuracy.The effectiveness of the proposed method is verified by numerical examples and robot engineering applications.The results show that the proposed iKriging-HDMR modeling method can significantly reduce the number of sample points required for modeling,and has good calculation accuracy and efficiency.
high dimensional model representationKrigingDIRECT samplingdesign of experimentindustrial robot
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