移动最小二乘代理模型支持域半径的优化方法

Optimization Method of Support Domain Radius of Moving Least Squares Agent Model

移动最小二乘代理模型描述局部波动的能力优于一般的代理模型,但其精度受支持域半径的影响。在经验公式的基础上提出了一种针对移动最小二乘代理模型支持域半径的优化方法。对支持域内抽样点数寻优获取最佳半径值,提高近似精度进而达到减少抽样点的目的。数值实验结果表明,对于不同基函数阶次和权函数的情况,提出的方法大大提高了移动最小二乘代理模型的近似精度,与基于经验公式的移动最小二乘代理模型相比,其仅需较少的抽样点即可达到相同的近似精度。

The moving least squares agent model is better than the general agent model,but its accuracy is affected by the radius of the support domain.On the basis of empirical formula,this paper proposed an optimization method for the support domain radius of the moving least square agent model.The optimal radius of sampling points in the support domain is obtained,and the approximation accuracy is improved to achieve the purpose of reducing the sampling points.Numerical experiments show that,for different base order function and weight function,the proposed method greatly improves the approximation accuracy of the moving least square agent model,and compared with the moving least squares(MLS)agent model based on empirical formula,the same approximation accuracy can be reached with only a few sampling points.