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    Heuristic Strategies of Modified Levenberg–Marquardt Algorithm for Fitting Transition Curves

    Source: Journal of Surveying Engineering:;2020:;Volume ( 146 ):;issue: 002
    Author:
    Zhanfeng Song
    ,
    Fei Yang
    ,
    Paul Schonfeld
    ,
    Jun Li
    ,
    Hao Pu
    DOI: 10.1061/(ASCE)SU.1943-5428.0000307
    Publisher: ASCE
    Abstract: Horizontal curve identification is important both for road safety management and railway maintenance. Parameters of a transition curve are introduced to perform an orthogonal least-squares fitting. During such a fitting process, the Gauss-Newton (GN) method may fail to converge because of an ill-conditioned Hessian matrix. A biobjective fitting model is introduced, and the Levenberg–Marquardt (LM) algorithm is specified to perform the fitting of transition curves. The LM parameter is updated heuristically during iterations according to the specific information explored instead of the standard preset way. Further, another heuristic strategy is proposed to search a path to the optimum instead of the traditional greedy strategy. The heuristic strategies were compared with traditional ones by fitting a transition curve of a railway to the measured points. Monte Carlo simulations were employed to test the robustness and efficiency of the modified LM algorithm, with different initial values, all converging to the same optimum. Results showed that the heuristic strategy for updating the LM parameter has a better robustness than the preset way, and the heuristic strategy for searching a path converges much faster than the traditional one, for which visual interpretations are provided.
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      Heuristic Strategies of Modified Levenberg–Marquardt Algorithm for Fitting Transition Curves

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4266732
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    contributor authorZhanfeng Song
    contributor authorFei Yang
    contributor authorPaul Schonfeld
    contributor authorJun Li
    contributor authorHao Pu
    date accessioned2022-01-30T20:14:03Z
    date available2022-01-30T20:14:03Z
    date issued2020
    identifier other%28ASCE%29SU.1943-5428.0000307.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4266732
    description abstractHorizontal curve identification is important both for road safety management and railway maintenance. Parameters of a transition curve are introduced to perform an orthogonal least-squares fitting. During such a fitting process, the Gauss-Newton (GN) method may fail to converge because of an ill-conditioned Hessian matrix. A biobjective fitting model is introduced, and the Levenberg–Marquardt (LM) algorithm is specified to perform the fitting of transition curves. The LM parameter is updated heuristically during iterations according to the specific information explored instead of the standard preset way. Further, another heuristic strategy is proposed to search a path to the optimum instead of the traditional greedy strategy. The heuristic strategies were compared with traditional ones by fitting a transition curve of a railway to the measured points. Monte Carlo simulations were employed to test the robustness and efficiency of the modified LM algorithm, with different initial values, all converging to the same optimum. Results showed that the heuristic strategy for updating the LM parameter has a better robustness than the preset way, and the heuristic strategy for searching a path converges much faster than the traditional one, for which visual interpretations are provided.
    publisherASCE
    titleHeuristic Strategies of Modified Levenberg–Marquardt Algorithm for Fitting Transition Curves
    typeJournal Paper
    journal volume146
    journal issue2
    journal titleJournal of Surveying Engineering
    identifier doi10.1061/(ASCE)SU.1943-5428.0000307
    page04020001
    treeJournal of Surveying Engineering:;2020:;Volume ( 146 ):;issue: 002
    contenttypeFulltext
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