中国区域速度场多面函数拟合稀疏建模方法研究  

Research on Sparse Modeling Method of Multi-faceted Function Fitting of China Regional Velocity Field

作　　者：杨承午 YANG Chengwu(China Railway Design Corporation,Tianjin 300251,China)

机构地区：[1]中国铁路设计集团有限公司,天津300251

出　　处：《铁道勘察》2023年第4期27-34,共8页Railway Investigation and Surveying

基　　金：中国铁路设计集团有限公司科技开发计划重点课题(2021A240504,2023A0240103)。

摘　　要：分析多面函数建模中核函数结点选择存在的问题,探讨LASSO等变量选择及空间降维方法,在此基础上,提出多面函数拟合的稀疏建模方法和惩罚参数选取指标。该方法通过最小化正则化损失函数,实现模型参数估计与核函数结点筛选,所构建模型易于解释且具有较强的泛化能力。中国区域速度场建模结果显示,多种方案下的模型变量参数筛选保留率在19.42%~51.17%之间,外符合精度提升率达到3.29%~16.50%,表明该方法可有效降低模型结构复杂度并提高建模精度。The problems of kernel function node selection in multi-faceted function modeling were analyzed,and the methods of variable compression selection such as Lasso and spatial dimension reduction were discussed.On this basis,the sparse modeling method of multi-faceted function fitting and the selection index of penalty parameters were proposed.The method realized parameter estimation and kernel node adaptive screening by minimizing regularization loss function,and the constructed model was easy to interpret and had strong generalization ability.The results of China regional velocity field modeling show that the selection retention rate of model variable parameters under various schemes is between 19.42%and 51.17%,and the improvement rate of external coincidence accuracy is between 3.29%and 16.50%,indicating that the method can effectively reduce the model structure complexity and improve the modeling accuracy.

关 键 词：区域速度场 多面函数拟合 稀疏建模 结点筛选 

分 类 号：P221[天文地球—大地测量学与测量工程] P228[天文地球—测绘科学与技术]