Effects of Parameter Selections on Fitting Vertical Curves to Data
Publication: Journal of Surveying Engineering
Volume 148, Issue 2
Abstract
Vertical curve fitting is important both for road safety management and railway maintenance. Different parameterizations were proposed to specify a vertical curve satisfying the constraint of continuity between its components. The vertical curve-fitting model was developed to explore the effects of different parameter sets on the fitting performance for a vertical curve. The steepest descent (SD), Gauss-Newton (GN), and Levenberg-Marquardt (LM) algorithms were used to search for the optimum solution. Experiments showed that the different parameterizations have different effects on the performance of the three algorithms. For one parameter set, the three algorithms converged to different solutions. For the other, the three algorithms converged to the same optimal solution. The two parameterizations responded differently to initial values, which were illustrated visually. From six different initial values, the LM algorithm converged to different solutions for one parameterization, but to the same optimum for the other. The condition number (CN), an index for evaluating the extent of ill-posed problems as well as correlations between parameter pairs, was examined to interpret the reasons of one parameterization outperformed the other in both robustness and effectiveness. Results also showed that the LM algorithm outperformed the GN algorithm in robustness and outperformed the SD algorithm in efficiency.
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Data Availability Statement
All data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
This research is supported by the National Natural Science Foundation of China (Grant No. 51678574) and the Laboratory Foundation of Central South University (Grant No. TMSY202107). The authors would like to thank the anonymous reviewers for their constructive comments and valuable suggestions to improve the quality of the article.
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Published In
Journal of Surveying Engineering
Volume 148 • Issue 2 • May 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jul 25, 2021
Accepted: Dec 2, 2021
Published online: Jan 24, 2022
Published in print: May 1, 2022
Discussion open until: Jun 24, 2022
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