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中南大学学报(自然科学版)

Journal of Central South University

第50卷    第7期    总第299期    2019年7月

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文章编号:1672-7207(2019)07-1696-08
基于U曲线法的半参数模型中正则化参数确定
周岩1,靳奉祥2,梁庆华3,马德鹏4

(1. 山东科技大学 资源与土木工程系,山东 泰安,271019;
2. 山东建筑大学 测绘地理信息学院,山东 济南,250101;
3. 中煤科工集团 重庆研究院有限公司,重庆,400039;
4. 山东农业大学 水利土木工程学院,山东 泰安,271018
)

摘 要: 针对半参数模型补偿最小二乘估计中正则化参数合理确定的问题,研究一种正则化参数确定方法即U曲线法,基于该方法确定合适的正则化参数,能够有效地控制残差范数与信号范数之间的平衡,得到较准确的参数估值;通过仿真算例分析,将基于U曲线法确定正则化参数的半参数模型的参数估计解和其他方法进行比较,研究结果表明:模拟的系统误差为周期性时,应用L曲线法、U曲线法确定的正则化参数进而求得的参数估值与其真值差值向量的范数分别为4.632 4×10-4 和3.497 0×10-4;当模拟的系统误差呈线性周期性时,应用L曲线法和U曲线法确定的正则化参数进而求得的参数估值与其真值差值向量的范数分别为7×10-4 和4×10-4,故采用U曲线法确定的正则化参数所求得的参数估值的精度比L曲线法的高,能较好地将观测值中的系统误差分离出来。

 

关键词: 半参数模型;正则化参数;L曲线法;U曲线法

Determination of regularization parameter in semiparametric model based on U curve method
ZHOU Yan1, JIN Fengxiang2, Liang Qinghua3, MA Depeng4

1. Department of Resources and Civil Engineering, Shandong University of Science and Technology, Tai’an 271019, China;
2. College of Surveying and Geo-Informatics, Shandong Jianzhu University, Jinan 250101, China;
3. CCTEG Chongqing Research Institute, Chongqing 400039, China;
4. School of Water Conservancy and Civil Engineering, Shandong Agricultural University, Tai''an 271018, China

Abstract:To solve the problem of the regularization parameter in the semiparametric model, the U curve method was researched as a regularization parameter selection method. By determining the appropriate regularization parameters, the balance between the residual part and the smoothness part was better controlled, and more accurate parameter estimation was obtained. Through the simulation examples and real examples, the parametric estimation solution of the semiparametric model based on the U curve method to determine the regularization parameters was compared with other methods. The results show that when the simulated system error is periodic, the parameter estimation is obtained by using the regularized parameters determined by U-curve method and L-curve method respectively, and the norm of the difference vector between it and its true value is respectively 4.632 4×10-4 and 3.497 0×10-4. When the simulated system error is linear periodicity, the parameter estimation is also obtained by using the regularized parameters determined by U-curve method and L-curve method respectively,and the norm of the difference vector between it and its true value is respectively 7×10-4 and 4×10-4. By comparison, the accuracy of parameter estimation by using the regularized parameters determined by U-curve method is better than that by L-curve method, and the U-curve method can better separate the systematic errors from the observed values.

 

Key words: semiparametric model; regularization parameter; L curve method; U curve method

中南大学学报(自然科学版)
  ISSN 1672-7207
CN 43-1426/N
ZDXZAC
中南大学学报(英文版)
  ISSN 2095-2899
CN 43-1516/TB
JCSTFT
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