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Volume 55 Issue 1
Jan.  2020
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Journal of Southwest Jiaotong University  > 2020  >  55(1): 144-149.
ZHU Yunfang, WU Zhiyu, GAO Yan, HOU Yishuang, LIU Zhengjie. Recognition Method for Multi-scale Sparse Power Quality Disturbance[J]. Journal of Southwest Jiaotong University, 2020, 55(1): 18-26. doi: 10.3969/j.issn.0258-2724.20180606
Citation: SONG Zhanfeng, WANG Jian, LI Jun. Levenberg-Marquardt Algorithm for Orthogonal Fitting of Transition Curves[J]. Journal of Southwest Jiaotong University, 2020, 55(1): 144-149. doi: 10.3969/j.issn.0258-2724.20190130
shu

Levenberg-Marquardt Algorithm for Orthogonal Fitting of Transition Curves

doi: 10.3969/j.issn.0258-2724.20190130
  • Received Date: 05 Mar 2019
  • Rev Recd Date: 11 Jun 2019
    • Available Online: 18 Sep 2019
  • Publish Date: 01 Feb 2020
    Abstract
  • To identify the parameters of transition curves in as-built alignments by measured points, orthogonal least-squares fitting is studied on the basis of the parameter equation of transition curves. First, eigenvalue analysis has clarified that the Gauss-Newton (GN) algorithm usually fails to converge because of the existence of the ill-condition. Next, a bi-objective optimization model is proposed and the Levenberg-Marquardt (LM) algorithm combining the GN algorithm with the steepest descent method is constructed to fit a transition curve to points orthogonally. The LM parameter is updated dynamically during iterations according to the evaluation of the distance between the current and the optimum locations. Finally, Monte Carlo simulations are employed to test the performances of the GN and LM algorithms with measured points and the same 5 000 initial values. Experimental results show that the GN algorithm diverges while the LM algorithm converges to the same optimum under different initial values. The number of iterations, with an average of 16.8 times and the minimum of 5 times and the maximum of 50 times, is related to the distance between the initial and the optimum locations. The LM algorithm shows a better robustness than the GN algorithm.

     

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    • References(12)
  • GIBREEL G M, EASA S M, EL-DIMEERY I A. Prediction of operating speed on three-dimensional highway alignments[J]. Journal of Transportation Engineering, 2001, 127(1): 21-30. doi: 10.1061/(ASCE)0733-947X(2001)127:1(21)
    BASSANI M, MARINELLI G, PIRAS M. Identification of horizontal circular arc from spatial data sources[J]. Journal of Surveying Engineering, 2016, 142(4): 1-14.
    丁克良,欧吉坤,赵春梅. 正交最小二乘法曲线拟合法[J]. 测绘科学,2007,32(3): 18-19. doi: 10.3771/j.issn.1009-2307.2007.03.006

    DING Keliang, OU Jikun, ZHAO Chunmei. Methods of the least-squares orthogonal distance fitting[J]. Science of Surveying and Mapping, 2007, 32(3): 18-19. doi: 10.3771/j.issn.1009-2307.2007.03.006
    丁克良,刘全利,陈翔. 正交距离圆曲线拟合方法[J]. 测绘科学,2008,33(S1): 72-73.

    DING Keliang, LIU Quanli, CHEN Xiang. Fitting of circles based on orthogonal distance[J]. Science of Surveying and Mapping, 2008, 33(S1): 72-73.
    AHN S J, RAUH W, WARNECKE H. Least-squares orthogonal distances fitting of circle,sphere,ellipse,hyperbola,and parabola[J]. Pattern Recognition, 2001, 34(12): 2283-2303. doi: 10.1016/S0031-3203(00)00152-7
    宋占峰,彭欣,吴清华. 基于中线坐标的地铁调线优化算法[J]. 西南交通大学学报,2014,49(4): 656-661. doi: 10.3969/j.issn.0258-2724.2014.04.015

    SONG Zhanfeng, PENG Xin, WU Qinghua. Optimization algorithm for horizontal realignment based on coordinate of metro centerline[J]. Journal of Southwest Jiaotong University, 2014, 49(4): 656-661. doi: 10.3969/j.issn.0258-2724.2014.04.015
    DONG H, EASA S M, LI J. Approximate extraction of spiralled horizontal curves from satellite imagery[J]. Journal of Surveying Engineering, 2007, 133(1): 36-40. doi: 10.1061/(ASCE)0733-9453(2007)133:1(36)
    LEVENBERG K. A method for the solution of certain non-linear problems in least squares[J]. Quarterly of Applied Mathematics, 1944, 2(2): 164-168. doi: 10.1090/qam/10666
    MARQUARDT D W. An algorithm for least-squares estimation of nonlinear parameters[J]. Journal of the Society for Industrial and Applied Mathematics, 1963, 11(2): 431-441. doi: 10.1137/0111030
    ZHAO R, FAN J. On a new updating rule of the Levenberg-Marquardt parameter[J]. Journal of Scientific Computing, 2018, 74(2): 1146-1162. doi: 10.1007/s10915-017-0488-6
    SONG Z, DING H, LI J, et al. Circular curve fitting method for field surveying data with correlated noise[J]. Journal of Surveying Engineering, 2018, 144(4): 1-9.
    FAN J, YUAN Y. On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption[J]. Computing, 2005, 74(1): 23-39. doi: 10.1007/s00607-004-0083-1
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