[1] Hu Wusheng, Sun Lu,. Neural network based method for compensating model error [J]. Journal of Southeast University (English Edition), 2009, 25 (3): 400-403. [doi:10.3969/j.issn.1003-7985.2009.03.024]

Copy

Neural network based method for compensating model error()

Share：

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

25

Issue:

2009 3

Page:

400-403

Research Field:

Surveying and Mapping and Navigation

Publishing date:

2009-09-30

Info

Title:

Neural network based method for compensating model error

Author(s):

Hu Wusheng¹;  2;  Sun Lu²

¹ School of Transportation, Southeast University, Nanjing 210096, China
² School of Civil Engineering, Catholic University of America, Washington DC 20064, USA

Keywords:

model error;  neural network;  BP algorithm;  compensating

PACS:

P207

DOI:

10.3969/j.issn.1003-7985.2009.03.024

Abstract:

Two traditional methods for compensating function model errors, the method of adding systematic parameters and the least-squares collection method, are introduced.A proposed method based on a BP neural network(called the H-BP algorithm)for compensating function model errors is put forward.The function model is assumed as y=f(x₁1, x₂2, …, x_n), and the special structure of the H-BP algorithm is determined as(n+1)×p×1, where(n+1)is the element number of the input layer, and the elements are x₁1, x₂2, …, x_n and y′(y′ is the value calculated by the function model); p is the element number of the hidden layer, and it is usually determined after many tests;1 is the element number of the output layer, and the element is Δy=y_0-y′0(y₀ is the known value of the sample).The calculation steps of the H-BP algorithm are introduced in detail.And then, the results of three methods for compensating function model errors from one engineering project are compared with each other.After being compensated, the accuracy of the traditional methods is about ±19 mm, and the accuracy of the H-BP algorithm is ±4.3 mm. It shows that the proposed method based on a neural network is more effective than traditional methods for compensating function model errors.

References:

[1] Tao Benzao. Statistical analyses of surveying data [M].Beijing:Surveying and Mapping Press, 1992:55-87.(in Chinese)
[2] Baarda W.A testing procedure for use in geodetic networks[J]. Neth Geod Comm Publ on Geodesy, 1968, 2(5):27-55.
[3] Craven P, Wahba G.Smoothing noisy data with spline functions [J].Numer Math, 1979, 31(2):377-403.
[4] Cook R D, Weisberg S.Residuals and influence in regression [M].London:Chapmanand Hall Press, 1982:23-41.
[5] Aduol F W O.Geodetic parameter estimation through iterative weighting[J].Survey Review, 1994, 32(252):359-367.
[6] Marshall J, Bethel J.Basic concepts of L1 norm minimization for surveying applications [J].Journal of Surveying Engineering, 1996, 122(4):168-179.
[7] Ding X, Colemen R.Multiple outlier detection by evaluating redundancy contributions of observations [J].Journal of Geodesy, 1996, 70(8):489-498.
[8] Fischer B, Hegland M.Collocation filtering and nonparametric regression [J].Zeitschrift für Vermessungswesen, 1999, 124(1):17-24.
[9] Hu Wusheng, Sha Yuejin, Kuang Shanlong.New method for transforming global positioning system height into normal height based on neural network [J].Journal of Surveying Engineering, 2004, 130(1):36-39.
[10] Kuhar M, Stopar B, Turk G, et al.The use of artificial neural network in geoid surface approximation[J].Allgemeine Vermessungs-Nachrichten, 2001, 108(1):22-27.
[11] Kavzoglu T, Saka M H.Modeling local GPS/leveling geoid undulations using artificial neural networks [J].J Geodesy, 2005, 78(9):520-527.
[12] Lin Laosheng.Application of a back-propagation artificial neural network to regional grid-based geoid model generation using GPS and leveling data [J].Journal of Surveying Engineering, 2007, 133(2):81-89.
[13] Hu Wusheng.The theory of neural network and its applications in engineering [M].Beijing:Surveying and Mapping Press, 2006:63-92.(in Chinese)
[14] Rao M A, Srinivas J.Neural networks:algorithms and applications [M].Pangbourne:Alpha Science International Ltd, 2003:17-113.

Memo

Memo:

Biography: Hu Wusheng(1965—), male, doctor, professor, wusheng.hu@163.com.
Foundation items: The National Basic Research Program of China(973 Program)(No.2006CB705501), the National High Technology Research and Development Program of China(863 Program)(No.2007AA12Z228).
Citation: Hu Wusheng, Sun Lu.Neural network based method for compensating model error[J].Journal of Southeast University(English Edition), 2009, 25(3):400-403.

Common functions