Comparison study on measurement of rail weld joint between inertial reference method and multi-point chord reference method

Purpose – Straightness measurement of rail weld joint is of essential importance to railway maintenance. Dueto the lack of efficient measurement equipment, there has been limited in-depth research on rail weld joint with a5-m wavelength range, leaving a significant knowledge gap in this field.Design/methodology/approach – In this study, the authors used the well-established inertial referencemethod (IR-method), and the state-of-the-art multi-point chord reference method (MCR-method). Two methodshave been applied in different types of rail straightness measurement trollies, respectively. These instrumentswere tested in a high-speed rail section within a certain region of China. The test results were ultimatelyvalidated through using traditional straightedge and feeler gauge methods as reference data to evaluate the railweld joint straightness within the 5-m wavelength range.Findings – The research reveals that IR-method and MCR-method produce reasonably similar measurementresults for wavelengths below 1 m. However, MCR-method outperforms IR-method in terms of accuracy forwavelengths exceeding 3 m. Furthermore, it was observed that IR-method, while operating at a slower speed,carries the risk of derailing and is incapable of detecting rail weld joints and low joints within the track.Originality/value – The research compare two methods’ measurement effects in a longer wavelength rangeand demonstrate the superiority of MCR-method.

A RELAXED INERTIAL FACTOR OF THE MODIFIED SUBGRADIENT EXTRAGRADIENT METHOD FOR SOLVING PSEUDO MONOTONE VARIATIONAL INEQUALITIES IN HILBERT SPACES

In this paper,we investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces.For solving this problem,we propose a new method that combines the advantages of the subgradient extragradient method and the projection contraction method.Some very recent papers have considered different inertial algorithms which allowed the inertial factor is chosen in[0;1].The purpose of this work is to continue working in this direction,we propose another inertial subgradient extragradient method that the inertial factor can be chosen in a special case to be 1.Under suitable mild conditions,we establish the weak convergence of the proposed algorithm.Moreover,linear convergence is obtained under strong pseudomonotonicity and Lipschitz continuity assumptions.Finally,some numerical illustrations are given to confirm the theoretical analysis.

Weak and Strong Convergence of Self Adaptive Inertial Subgradient Extragradient Algorithms for Solving Variational Inequality Problems

Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.

STRONG CONVERGENCE OF AN INERTIAL EXTRAGRADIENT METHOD WITH AN ADAPTIVE NONDECREASING STEP SIZE FOR SOLVING VARIATIONAL INEQUALITIES

In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our method requires only to compute one projection onto the feasible set per iteration and without any linesearch procedure or additional projections as well as does not need to the prior knowledge of the Lipschitz constant and the sequentially weakly continuity of the variational inequality mapping.A strong convergence is established for the proposed method to a solution of a variational inequality problem under certain mild assumptions.Finally,we give some numerical experiments illustrating the performance of the proposed method for variational inequality problems.

Modified Subgradient Extragradient Method for Variational Inequality Problems and Fixed Point Problems

Many approaches inquiring into variational inequality problems have been put forward,among which subgradient extragradient method is of great significance.A novel algorithm is presented in this article for resolving quasi-nonexpansive fixed point problem and pseudomonotone variational inequality problem in a real Hilbert interspace.In order to decrease the execution time and quicken the velocity of convergence,the proposed algorithm adopts an inertial technology.Moreover,the algorithm is by virtue of a non-monotonic step size rule to acquire strong convergence theorem without estimating the value of Lipschitz constant.Finally,numerical results on some problems authenticate that the algorithm has preferable efficiency than other algorithms.

Subgradient Extragradient Methods for Equilibrium Problems and Fixed Point Problems in Hilbert Space

Inspired by inertial methods and extragradient algorithms,two algorithms were proposed to investigate fixed point problem of quasinonexpansive mapping and pseudomonotone equilibrium problem in this study.In order to enhance the speed of the convergence and reduce computational cost,the algorithms used a new step size and a cutting hyperplane.The first algorithm was proved to be weak convergence,while the second algorithm used a modified version of Halpern iteration to obtain strong convergence.Finally,numerical experiments on several specific problems and comparisons with other algorithms verified the superiority of the proposed algorithms.

FULL DISCRETE NONLINEAR GALERKIN METHOD FOR THE NAVIER-STOKES EQUATIONS

This paper deals with the inertial manifold and the approximate inertialmanifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore,we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.

Modified Inertial Projection Method for Solving Pseudomonotone Variational Inequalities with Non-Lipschitz in Hilbert Spaces

This paper deals with a class of inertial gradient projection methods for solving a vari-ational inequality problem involving pseudomonotone and non-Lipschitz mappings in Hilbert spaces.The proposed algorithm incorporates inertial techniques and the projection and contraction method.The weak convergence is proved without the condition of the Lipschitz continuity of the mappings.Meanwhile,the linear convergence of the algorithm is established under strong pseudomonotonicity and Lipschitz continuity assumptions.The main results obtained in this paper extend and improve some related works in the literature.

Automated pavement horizontal curve measurement methods based on inertial measurement unit and 3D profiling data

Pavement horizontal curve is designed to serve as a transition between straight segments, and its presence may cause a series of driving-related safety issues to motorists and drivers. As is recognized that traditional methods for curve geometry investigation are time consuming, labor intensive, and inaccurate, this study attempts to develop a method that can automatically conduct horizontal curve identification and measurement at network level. The digital highway data vehicle （DHDV） was utilized for data collection, in which three Euler angles, driving speed, and acceleration of survey vehicle were measured with an inertial measurement unit （IMU）. The 3D profiling data used for cross slope calibration was obtained with PaveVision3D Ultra technology at 1 mm resolution. In this study, the curve identification was based on the variation of heading angle, and the curve radius was calculated with ki- nematic method, geometry method, and lateral acceleration method. In order to verify the accuracy of the three methods, the analysis of variance （ANOVA） test was applied by using the control variable of curve radius measured by field test. Based on the measured curve radius, a curve safety analysis model was used to predict the crash rates and safe driving speeds at horizontal curves. Finally, a case study on 4.35 km road segment demonstrated that the proposed method could efficiently conduct network level analysis.

A Symmetric Inertial Alternating Direction Method of Multipliers for Elliptic Equation Constrained Optimization Problem

A new algorithm,called symmetric inertial alternating direction method of multipliers(SIADMM),is designed for separable convex optimization problems with linear constraints in this paper.The convergence rate of the SIADMM is proved to be O(1/√k).Two kinds of elliptic equation constrained optimization problems,the un-constrained cases as well as the box-constrained cases of the distributed control and the Robin boundary control,are analyzed theoretically and solved numerically.First,the existence and uniqueness of the solutions to these problems are proved.Second,these continuous optimization problems are transformed into discrete optimization problems by thefinite element method,and then the discrete optimization problems are solved by the proposed SIADMM.Numerical experiments with different problems are investigated to demonstrate the efficiency of the SIADMM.And the numerical per-formance of the SIADMM is better than the performance of the ADMM.Moreover,the numerical results show that the convergence rate of the SIADMM tends to be faster than O(1/√k)in calculation process.

Relaxed inertial proximal Peaceman-Rachford splitting method for separable convex programming

The strictly contractive Peaceman-Rachford splitting method is one of effective methods for solving separable convex optimization problem, and the inertial proximal Peaceman-Rachford splitting method is one of its important variants. It is known that the convergence of the inertial proximal Peaceman- Rachford splitting method can be ensured if the relaxation factor in Lagrangian multiplier updates is underdetermined, which means that the steps for the Lagrangian multiplier updates are shrunk conservatively. Although small steps play an important role in ensuring convergence, they should be strongly avoided in practice. In this article, we propose a relaxed inertial proximal Peaceman- Rachford splitting method, which has a larger feasible set for the relaxation factor. Thus, our method provides the possibility to admit larger steps in the Lagrangian multiplier updates. We establish the global convergence of the proposed algorithm under the same conditions as the inertial proximal Peaceman-Rachford splitting method. Numerical experimental results on a sparse signal recovery problem in compressive sensing and a total variation based image denoising problem demonstrate the effectiveness of our method.