Generalized Method for Estimating Best-Fit Vertical Alignments for Profile Data
When the profile information of an existing road is
missing or not up-to-date and the parameters of the vertical
alignment are needed for engineering analysis, the engineer has to recreate
the geometric design features of the road alignment using
collected profile data. The profile data may be collected using
traditional surveying methods, global positioning systems, or digital
imagery. This paper develops a method that estimates the parameters
of the geometric features that best characterize the existing vertical
alignments in terms of tangents and the expressions of the curve, that
may be symmetrical, asymmetrical, reverse, and complex vertical
curves. The method is implemented using an Excel-based
optimization method that minimizes the differences between the
observed profile and the profiles estimated from the equations of the
vertical curve. The method uses a 'wireframe' representation of the
profile that makes the proposed method applicable to all types of
vertical curves. A secondary contribution of this paper is to introduce
the properties of the equal-arc asymmetrical curve that has been
recently developed in the highway geometric design field.
[1] S. M. Easa, Y. Hassan, and Z. Karim, "Establishing highway vertical
alignment using field data," ITE J. on the Web, 1998, pp. 81-86.
[2] D. Ben-Arieh, S. Chang, M. Rys, and G. Zhang, "Geometric modeling of
highways using GPS data and B-spline approximation," J. Transp. Eng.,
vol. 130, no. 5, 2004, pp. 632-636.
[3] J. M. Anderson, and E. M. Mikhail, Surveying: Theory and Practice.
New York: McGraw-Hill, 1998, ch. 16.
[4] B. F. Kavanagh, Surveying: Principles and Applications. New York:
Prentice Hall, 2005, ch. 10.
[5] F. H. Moffitt, and J. D. Bossler, Surveying. New York: Addison Wesley,
1998, ch. 13.
[6] C. D. Ghilani, and P. R. Wolf, Elementary Surveying: An Introduction to
Geomatics. 12th Edition, Upper Saddle River, New Jersey: Pearson
Prentice-Hall, 2008, ch. 25.
[7] T. Hickerson, Route Location and Design. New York: McGraw-Hill,
1964, ch. 5.
[8] S. M. Easa, "New and improved unsymmetrical vertical curve for
highways," J. Transp. Res. Rec., TRB, no. 1445, 1994, pp. 94-100.
[9] S. M. Easa, "Sight distance model for unsymmetrical crest curves," J.
Transp. Res. Rec., TRB, no. 1303, 1991, pp. 39-49.
[10] S. M. Easa, "Sight distance models for unsymmetrical sag curves," J.
Transp. Res. Rec., TRB, no. 1303, 1991, pp. 51-62.[11] S. M. Easa, and Y. Hassan, "Design requirements of equal-arc
unsymmetrical curves," J. Transp. Eng., ASCE, vol. 124, no. 5, 1998,
pp. 404-410.
[12] S. M. Easa, "Optimum vertical curves for highway profiles," J. Surv.
Eng., ASCE, vol. 125, no. 3, 1999, pp. 147-157.
[13] L. Schrage, Optimization Modeling with LINGO. Palo Alto, California:
LINDO Systems, 2006, ch. 1-5.
[14] W. C. Hu, F. Tan, A. and Barnes, "New solutions to vertical curve
problem," J. Surv. Eng., ASCE, vol. 130, no. 3, 2004, pp. 119-125.
[15] S. M. Easa, "Efficient method for estimating globally optimal simple
vertical curves," J. Surv. Eng., ASCE, vol. 134, no. 1, 2008, pp. 33-37.
[16] G. Nehate, and M. Rys, "3D calculation of stopping-sight distance from
GPS data," J. Transp. Eng., vol. 132, no. 9, 2006, pp. 691-698.
[17] J. Marshall, and J. Bethel, "Basic concepts of L1 norm minimization for
surveying applications," J. Surv. Eng., ASCE, vol. 122, no. 4, 1996, pp.
168-179.
[18] Frontline Systems. Premium Solver Platform - User Guide. Incline
Village, Nevada: Frontline Systems, Inc., 2005.
[19] B. P. Carlin, and T. A. Louis, Bayesian Methods for Data Analysis. Boca
Raton, Florida: Chapman & Hall/CRC, 2008.
[1] S. M. Easa, Y. Hassan, and Z. Karim, "Establishing highway vertical
alignment using field data," ITE J. on the Web, 1998, pp. 81-86.
[2] D. Ben-Arieh, S. Chang, M. Rys, and G. Zhang, "Geometric modeling of
highways using GPS data and B-spline approximation," J. Transp. Eng.,
vol. 130, no. 5, 2004, pp. 632-636.
[3] J. M. Anderson, and E. M. Mikhail, Surveying: Theory and Practice.
New York: McGraw-Hill, 1998, ch. 16.
[4] B. F. Kavanagh, Surveying: Principles and Applications. New York:
Prentice Hall, 2005, ch. 10.
[5] F. H. Moffitt, and J. D. Bossler, Surveying. New York: Addison Wesley,
1998, ch. 13.
[6] C. D. Ghilani, and P. R. Wolf, Elementary Surveying: An Introduction to
Geomatics. 12th Edition, Upper Saddle River, New Jersey: Pearson
Prentice-Hall, 2008, ch. 25.
[7] T. Hickerson, Route Location and Design. New York: McGraw-Hill,
1964, ch. 5.
[8] S. M. Easa, "New and improved unsymmetrical vertical curve for
highways," J. Transp. Res. Rec., TRB, no. 1445, 1994, pp. 94-100.
[9] S. M. Easa, "Sight distance model for unsymmetrical crest curves," J.
Transp. Res. Rec., TRB, no. 1303, 1991, pp. 39-49.
[10] S. M. Easa, "Sight distance models for unsymmetrical sag curves," J.
Transp. Res. Rec., TRB, no. 1303, 1991, pp. 51-62.[11] S. M. Easa, and Y. Hassan, "Design requirements of equal-arc
unsymmetrical curves," J. Transp. Eng., ASCE, vol. 124, no. 5, 1998,
pp. 404-410.
[12] S. M. Easa, "Optimum vertical curves for highway profiles," J. Surv.
Eng., ASCE, vol. 125, no. 3, 1999, pp. 147-157.
[13] L. Schrage, Optimization Modeling with LINGO. Palo Alto, California:
LINDO Systems, 2006, ch. 1-5.
[14] W. C. Hu, F. Tan, A. and Barnes, "New solutions to vertical curve
problem," J. Surv. Eng., ASCE, vol. 130, no. 3, 2004, pp. 119-125.
[15] S. M. Easa, "Efficient method for estimating globally optimal simple
vertical curves," J. Surv. Eng., ASCE, vol. 134, no. 1, 2008, pp. 33-37.
[16] G. Nehate, and M. Rys, "3D calculation of stopping-sight distance from
GPS data," J. Transp. Eng., vol. 132, no. 9, 2006, pp. 691-698.
[17] J. Marshall, and J. Bethel, "Basic concepts of L1 norm minimization for
surveying applications," J. Surv. Eng., ASCE, vol. 122, no. 4, 1996, pp.
168-179.
[18] Frontline Systems. Premium Solver Platform - User Guide. Incline
Village, Nevada: Frontline Systems, Inc., 2005.
[19] B. P. Carlin, and T. A. Louis, Bayesian Methods for Data Analysis. Boca
Raton, Florida: Chapman & Hall/CRC, 2008.
@article{"International Journal of Architectural, Civil and Construction Sciences:53682", author = "Said M. Easa and Shinya Kikuchi", title = "Generalized Method for Estimating Best-Fit Vertical Alignments for Profile Data", abstract = "When the profile information of an existing road is
missing or not up-to-date and the parameters of the vertical
alignment are needed for engineering analysis, the engineer has to recreate
the geometric design features of the road alignment using
collected profile data. The profile data may be collected using
traditional surveying methods, global positioning systems, or digital
imagery. This paper develops a method that estimates the parameters
of the geometric features that best characterize the existing vertical
alignments in terms of tangents and the expressions of the curve, that
may be symmetrical, asymmetrical, reverse, and complex vertical
curves. The method is implemented using an Excel-based
optimization method that minimizes the differences between the
observed profile and the profiles estimated from the equations of the
vertical curve. The method uses a 'wireframe' representation of the
profile that makes the proposed method applicable to all types of
vertical curves. A secondary contribution of this paper is to introduce
the properties of the equal-arc asymmetrical curve that has been
recently developed in the highway geometric design field.", keywords = "Optimization, parameters, data, reverse, spreadsheet,vertical curves", volume = "3", number = "9", pages = "327-9", }