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

Song, Zhanfeng; Yang, Fei; Schonfeld, Paul; Li, Jun; Pu, Hao

doi:10.1061/(asce)su.1943-5428.0000307

Cited by 14 publications

(8 citation statements)

References 18 publications

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“…Therefore, many experts and scholars put forward a variety of methods to improve the algorithm performance. Currently, the commonly used optimization algorithms of BP neural network include BP neural network with additional momentum term combined with adaptive learning rate [38,39], GA-BP neural network combined BP neural network with genetic algorithm [40], PSO-BP neural network combined BP neural network with particle swarm optimization [41], BP learning algorithm improved by Levenberg-Marquardt method [42,43]. Due to the different inherent characteristics of the problems to be simulated, the improvement effect of each optimization method is limited.…”

Section: The Operating Principle Of Bp Neural Networkmentioning

confidence: 99%

Catalyst Optimization Design Based on Artificial Neural Network

Sun

2022

AJRCoS

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Artificial neural network (ANN) has the characteristics of self-adaptation, self-learning, parallel processing and strong nonlinear mapping ability. Compared with traditional experimental analysis modeling, ANN has obvious advantages in dealing with multivariable nonlinear complex relationships in the process of industrial catalyst design. In the face of the complex structure of catalyst, the unclear reaction mechanism and conditions, the use of neural network for small-scale experimental data analysis can save the time and energy invested in large-scale experimental research and obtain more perfect results in catalyst formulation optimization and condition selection. This paper summarizes the development of artificial neural network. The application principle, construction method and research progress of BP artificial neural network model in catalyst optimization design are summarized and analyzed. The development and innovation of artificial neural network in the future, as well as its continuous application and accumulation, will provide a powerful tool for the research of catalyst design and optimization in the future.

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Section: The Operating Principle Of Bp Neural Networkmentioning

confidence: 99%

Catalyst Optimization Design Based on Artificial Neural Network

Sun

2022

AJRCoS

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“…The GN search converges much faster than the SD search when

Θ_{k}

is close to the optimum. However, the GN search may diverge while the SD search can guarantee the decrease of

f (Θ)

when

Θ_{k}

is far from the optimum (Song et al., 2020).…”

Section: Parameter Estimationmentioning

confidence: 99%

“…Dong, Easa, and Li (2007) also presented an approximate method for extracting a compound horizontal curve consisting of a circular curve and a spiral curve. Song, Yang, Schonfeld, Li, and Pu (2020) proposed a robust algorithm for fitting transition curves. Easa (2008) proposed an efficient method for estimating vertical curves.…”

Section: Introductionmentioning

confidence: 99%

Integrating segmentation and parameter estimation for recreating vertical alignments

Song

Yang

Schonfeld

et al. 2020

Computer aided Civil Eng

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A major problem of vertical alignment recreation is to automatically attribute the measured points to geometric elements (i.e., grades and vertical curves) and to efficiently recreate the vertical alignment with constraints. Most existing methods are nonoptimal in theory, semiautomatic, or inefficient in recreating an alignment. A new approach is proposed for automatically determining segmentation into geometric elements from measured points and efficiently optimizing a recreated alignment with constraints. First, independent parameters defining an alignment, are proposed to represent a vertical alignment. Then, a statistical deflection angle (SDA) method is proposed to determine segmentation by exploring statistical features of the geometric elements. Analysis shows that the SDA method outperforms the curvature method in distinguishing between grades and curves. Patterns of the segmentation process are found, and a segmentation algorithm is provided. Further, an optimization model is proposed to recreate the alignment with constraints. Experiment results demonstrate that this approach is highly efficient and effective compared with existing methods, reducing the number of searched alignments from tens of thousands to tens, while improving the value of the objective function.

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“…Easa and Wang (2010), Cellmer et al (2016), and Tong et al (2010) proposed an optimization model that can continuously estimate the parameters of each section of the curve by fitting the horizontal and vertical curve components with the least-squares method. Song et al (2020Song et al ( , 2021 selected the least-squares residual as the objective function, combined it with a heuristic strategy, and employed the Levenberg-Marquardt algorithm to fit the optimal alignment of the transition curve. Camacho-Torregrosa et al (2015) proposed using a heuristic algorithm to fit the geometric elements of different combined alignments.…”

Section: Introductionmentioning

confidence: 99%

“…Song et al. (2020, 2021) selected the least‐squares residual as the objective function, combined it with a heuristic strategy, and employed the Levenberg–Marquardt algorithm to fit the optimal alignment of the transition curve. Camacho‐Torregrosa et al.…”

Section: Introductionmentioning

confidence: 99%

A smoothness optimization method for horizontal alignment considering ballasted track maintenance

Jin

Zhang

Chen

et al. 2022

Computer aided Civil Eng

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This paper proposes a smoothness optimization method of horizontal alignment based on orthogonal least squares and the theory of controlling the track smoothness. With this method, multiple curve types can be fitted simultaneously according to the maintenance requirements, and the residual deviation in the track is optimized according to the smoothness standard. The target alignment of the tamping operation is constructed, providing support for the maintenance of the ballasted track. The implementation results show that the proposed method fully adapts to operating railway maintenance conditions, and the optimized design parameters resemble the field observation results. The lateral profile track quality index is reduced from 0.78 to 0.39, the amplitudes of the 10 and 60 m mid‐chord offset decrease by 73% and 52%, respectively, and the 30‐m vector distance difference decreased by 53%, indicating effective improvement.

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

Cited by 14 publications

References 18 publications

Catalyst Optimization Design Based on Artificial Neural Network

Catalyst Optimization Design Based on Artificial Neural Network

Integrating segmentation and parameter estimation for recreating vertical alignments

A smoothness optimization method for horizontal alignment considering ballasted track maintenance

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