Effects of Parameter Selections on Fitting Vertical Curves to Data

Song, Zhanfeng; Ma, Xiaotong; Schonfeld, Paul; Li, Jun

doi:10.1061/(asce)su.1943-5428.0000394

Cited by 2 publications

(4 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A steepest descent algorithm of the dynamics model (SDADM) with optimal step length in the gradient direction of the energy functional is established by setting 𝑣 𝑖𝑖 in Equation ( 37) as (Song et al 2022)…”

Section: Two Algorithms For the Dynamics Modelmentioning

confidence: 99%

“…A steepest descent algorithm of the dynamics model (SDADM) with optimal step length in the gradient direction of the energy functional is established by setting

{v}_{ii}

in Equation () as (Song et al. 2022)

\begin{equation}\ {v}_{ii} = \frac{{{{{{\bf \dot{\Theta }}}}}^T{{\bf \dot{\Theta }}}}}{{{{{{\bf \dot{\Theta }}}}}^T{{\bf W\dot{\Theta }}}}}{\bf{\ }}\end{equation}

…”

Section: Dynamics Model For Vertical Alignment Reconstructionmentioning

confidence: 99%

“…It cannot dynamically deal with constraints. Further, the different units (meters and radians) of independent parameters may affect the search results (Song et al, 2022). Adeli and Park (1995a) first proposed a neural dynamics model for structural optimization and applied it to linearly optimal plastic design of steel structures in a companion paper (Park & Adeli, 1995).…”

Section: Introductionmentioning

confidence: 99%

“…It cannot dynamically deal with constraints. Further, the different units (meters and radians) of independent parameters may affect the search results (Song et al., 2022).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Two algorithms for reconstructing vertical alignments exploring the neural dynamics model of Adeli and Park

Song,

Chen,

Schonfeld

et al. 2023

Computer aided Civil Eng

Self Cite

View full text Add to dashboard Cite

Vertical alignment reconstruction obtains alignment parameters by fitting geometric components to a set of measured points representing the profile of an existing road or railroad, which is essential in alignment consistency analysis and maintenance to ensure safety and comfort. The neural dynamics model of Adeli and Park is explored and improved for reconstructing vertical alignments with constraints. The structure of the dynamics model is modified to include three layers: parameter layer, intermediate layer, and energy layer. The number of nodes in the parameter or intermediate layers corresponds to the number of independent parameters defining a vertical alignment. The number of nodes in the energy layer is the sum of the number of deviations and the number of constraints in the alignment reconstruction problem. The coefficients connecting nodes between the parameter layer and the intermediate layer determine the integral operations, which define the Levenberg–Marquardt algorithm of the dynamics model (LMADM) and the steepest descent algorithm of the dynamics model (SDADM). Both the LMADM and SDADM methods satisfy the Lyapunov stability theorem, but the LMADM method outperforms the SDADM method in its objective function value and computation time. Experiment results demonstrate that there are multiple local optima for a vertical alignment reconstruction, and the solutions obtained by the LMADM method are the best obtained so far, compared with those reported in the literature, with 57.1% and 23.4% decreases of the mean squared error for the highway and the railroad examples, respectively.

show abstract

Section: Two Algorithms For the Dynamics Modelmentioning

confidence: 99%

“…A steepest descent algorithm of the dynamics model (SDADM) with optimal step length in the gradient direction of the energy functional is established by setting

{v}_{ii}

in Equation () as (Song et al. 2022)

\begin{equation}\ {v}_{ii} = \frac{{{{{{\bf \dot{\Theta }}}}}^T{{\bf \dot{\Theta }}}}}{{{{{{\bf \dot{\Theta }}}}}^T{{\bf W\dot{\Theta }}}}}{\bf{\ }}\end{equation}

…”

Section: Dynamics Model For Vertical Alignment Reconstructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…It cannot dynamically deal with constraints. Further, the different units (meters and radians) of independent parameters may affect the search results (Song et al., 2022).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations