Non-steady state modelling of wheel-rail contact problem for the dynamic simulation of railway vehicles

Abstract

This paper deals with the solution of the non-steady state wheel-rail contact problem. Firstly, the existing models are analysed and it is concluded that none of them have the computational efficiency and/or accuracy characteristics required to be used in a railway simulation programme. Following this, a new solution is proposed to the problem that allows obtaining sufficiently accurate results with a relatively low computational cost. During the development of the proposed method it has been assumed that only one type of creepage is variable with respect to the time. Further work is necessary to extend it to more general cases.     

Carpooling problem: A new mathematical model,branch-and-bound,and heuristic beam search algorithm

Carpooling is an environmentally friendly transportation system. It can efficaciously help resolve a variety of societal concerns of the urban areas, ranging from traffic congestion to environmental pollution. In this paper, we propose a new mathematical model to solve the carpooling problem. The model simultaneously minimizes the costs of travel times, the vehicle use, and the vehicle delays. An exact solution method based on Branch-and-Bound (B&B) algorithm is proposed to efficiently obtain the optimal solution of the problem. In order to find the near-optimal solutions for large-scale problems, a heuristic beam search algorithm is introduced, which is based on the partial relaxation of some fathoming criteria applied in our proposed B&B. The computational experiments are conducted, based upon the transportation network of Isfahan city, Iran. The results demonstrate the great capability of the proposed exact solution method in terms of both computational solving time required and the number of the evaluated nodes, in comparison with CPLEX software package. The findings of this research can be applied to solve the carpooling problem compatible to the real-life situations.     

Tangential problem solution for non-elliptical contact areas with the FastSim algorithm

This article deals with the application of the FastSim algorithm to the solution of the tangential contact problem for non-elliptical contact areas. At first, the causes creating problems for the solution of non-hertzian contact areas with this algorithm shall be analyzed. Then, different currently existing methods shall be studied, analyzing their accuracy characteristics and computational cost to determine whether or not they are appropriate to use in dynamic simulations. Finally, a new strategy shall be proposed that, in the opinion of the authors, offers good characteristics of precision and computational cost.     

Tangential problem solution for non-elliptical contact areas with the FastSim algorithm

This article deals with the application of the FastSim algorithm to the solution of the tangential contact problem for non-elliptical contact areas. At first, the causes creating problems for the solution of non-hertzian contact areas with this algorithm shall be analyzed. Then, different currently existing methods shall be studied, analyzing their accuracy characteristics and computational cost to determine whether or not they are appropriate to use in dynamic simulations. Finally, a new strategy shall be proposed that, in the opinion of the authors, offers good characteristics of precision and computational cost.     

基于多用户类型随机用户平衡的连续网络设计

用多用户类型随机用户平衡描述实际路网中出行者的路径选择行为。根据出行者对路网状况认识的不同程度,将出行者划分为具有相同特性的多个类型。将多用户类型随机用户平衡问题表示为一个无约束极小化问题,并提出了该问题的一种基于路段水平的灵敏度分析方法。建立了多用户类型随机用户平衡条件下的连续网络设计问题的双层规划模型,并给出了基于灵敏度分析的启发式算法。实例的结果表明模型具有一般性和适应性。     

基于混合粒子群算法的土钉支护结构设计参数优化

在土层工程地质情况一定的条件下,如何寻找一组最佳设计参数,以达到既经济又安全的目的,是土钉支护设计的一个重要问题。这是一个复杂的优化设计问题。就此,提出基于混合粒子群优化(PSO)算法的基坑土钉支护优化设计方法,以单位长度土钉墙的土钉材料造价作为优化的目标函数。该方法保持了PSO算法结构简单的特点,改善了PSO算法的全局寻优能力,提高了算法的收敛速度和计算精度,不活动粒子的处理使算法避免了“早熟”现象的出现。工程实例计算表明,该方法是进行土钉支护结构优化设计的有效方法。     

Design of robust-stable and quadratic finite-horizon optimal controllers with low trajectory sensitivity for uncertain active suspension systems

This paper presents a design method for designing the robust-stable and quadratic-finite-horizon-optimal controllers of uncertain active suspension systems. The method integrates a robust stabilisability condition, the orthogonal functions approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA). Using the integrative computational method, a robust-stable and quadratic-finite-horizon-optimal controller with low-trajectory sensitivity can be obtained such that (i) the active suspension system with elemental parametric uncertainties is stabilised and (ii) a quadratic-finite-horizon-integral performance index including a quadratic trajectory sensitivity term for the nominal active suspension system is minimised. The robust stabilisability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal active suspension feedback dynamic equations. By using the OFA and the LMI-based robust stabilisability condition, the dynamic optimisation problem for the robust-stable and quadratic-finite-horizon-optimal controller design of the linear uncertain active suspension system is transformed into a static-constrained-optimisation problem represented by the algebraic equations with constraint of LMI-based robust stabilisability condition; thus greatly simplifies the design problem. Then, for the static-constrained-optimisation problem, the HTGA is employed to find the robust-stable and quadratic-finite-horizon-optimal controllers of the linear uncertain active suspension systems. A design example is given to demonstrate the applicability of the proposed integrative computational approach.     

Design of safety-oriented control allocation strategies for overactuated electric vehicles

The new vehicle platforms for electric vehicles (EVs) that are becoming available are characterised by actuator redundancy, which makes it possible to jointly optimise different aspects of the vehicle motion. To do this, high-level control objectives are first specified and solved with appropriate control strategies. Then, the resulting virtual control action must be translated into actual actuator commands by a control allocation layer that takes care of computing the forces to be applied at the wheels. This step, in general, is quite demanding as far as computational complexity is considered. In this work, a safety-oriented approach to this problem is proposed. Specifically, a four-wheel steer EV with four in-wheel motors is considered, and the high-level motion controller is designed within a sliding mode framework with conditional integrators. For distributing the forces among the tyres, two control allocation approaches are investigated. The first, based on the extension of the cascading generalised inverse method, is computationally efficient but shows some limitations in dealing with unfeasible force values. To solve the problem, a second allocation algorithm is proposed, which relies on the linearisation of the tyre–road friction constraints. Extensive tests, carried out in the CarSim simulation environment, demonstrate the effectiveness of the proposed approach.     

基于改进稀疏正则化的扩展卡尔曼滤波损伤识别研究

基于传统扩展卡尔曼滤波方法（EKF）的损伤识别过程是一个典型的反问题求解，反问题的不适定性使EKF识别结果容易受噪声干扰，导致EKF算法收敛困难、识别精度下降。基于l₁正则化的EKF算法在一定程度上可以缓解此问题，但其不能获得足够准确的稀疏解。为此，提出了一种改进稀疏正则化的EKF方法。该方法采用Arctangent罚函数代替l₁范数以施加损伤稀疏性约束；通过伪测量技术将稀疏性约束嵌入到EKF中，获得施加约束方程后的递推解。采用3层剪切结构和悬臂梁2个试验算例验证了该方法的有效性。研究结果表明：即使在噪声干扰下，所提方法也可以准确识别出结构损伤；相比传统l₁正则化EKF方法，该方法需要的观测信息更少，能获得更准确的稀疏解。     

Precision analysis and dynamic stability in the numerical solution of the two-dimensional wheel/rail tangential contact problem

ABSTRACT

In this paper the two-dimensional contact problem is analysed through different mesh topologies and strategies for approaching equations, namely; the collocation method, Galerkin, and the polynomial approach. The two-dimensional asymptotic problem (linear theory) associated with very small creepage (or infinite friction coefficient) is taken as a reference in order to analyse the numerical methods, and its solution is tackled in three different ways, namely steady-state problem, dynamic stability problem, and non-steady state problem in the frequency domain. In addition, two elastic displacements derivatives calculation methods are explored: analytic and finite differences. The results of this work establish the calculation conditions that are necessary to guarantee dynamic stability and the absence of numerical singularities, as well as the parameters for using the method that allows for maximum precision at the minimum computational cost to be reached.     

基于蚁群算法的军事配送车辆调度问题研究

针对军事配送的特点,以"等待损失"和运输成本最小化为目标,建立了问题的数学模型,并应用蚁群算法求解了这一问题.算法中改进了状态转移规则,设计了局部搜索模块.为测试算法性能,应用改进的蚁群算法求解了文献中的21个基准算例.计算结果表明,这一算法明显优于已有算法.     

Stress sensitivity analysis and optimization of automobile body frame consisting of rectangular tubes

At conceptual design stage, beam element is extensively used to create the frame structure of automobile body, which can not only archive the accurate stiffness but also reduce much computational cost. However, the stress definition of beam element is very complex so that the stress sensitivity and optimization are difficult to analytically derive and numerically program. This paper presents an solution to this problem and an application in the lightweight optimization design of automobile frame. Firstly, maximal Von Mises stress of rectangular tube is calculated by using the superposition of stress, which is together induced by the axial force, bending moments, torsional moment and shear force. Secondly, the sensitivity of Von Mises Stress with respect to size design variables: breadth, height and thickness are derived, respectively. Thirdly, an optimal criterion is constructed by Lagrangian multiplier method to solve the frame optimization with stress constraints. Lastly, numerical example of car frame proves that the proposed method can guarantee the stress of each beam element almost fully reaches at the yielding stress.     

New methodology for fast prediction of wheel wear evolution

In railway applications wear prediction in the wheel–rail interface is a fundamental matter in order to study problems such as wheel lifespan and the evolution of vehicle dynamic characteristic with time. However, one of the principal drawbacks of the existing methodologies for calculating the wear evolution is the computational cost. This paper proposes a new wear prediction methodology with a reduced computational cost. This methodology is based on two main steps: the first one is the substitution of the calculations over the whole network by the calculation of the contact conditions in certain characteristic point from whose result the wheel wear evolution can be inferred. The second one is the substitution of the dynamic calculation (time integration calculations) by the quasi-static calculation (the solution of the quasi-static situation of a vehicle at a certain point which is the same that neglecting the acceleration terms in the dynamic equations). These simplifications allow a significant reduction of computational cost to be obtained while maintaining an acceptable level of accuracy (error order of 5–10%). Several case studies are analysed along the paper with the objective of assessing the proposed methodology. The results obtained in the case studies allow concluding that the proposed methodology is valid for an arbitrary vehicle running through an arbitrary track layout.     

Robust traffic assignment model: Formulation,solution algorithms and empirical application

ABSTRACT

The deterministic traffic assignment problem based on Wardrop's first criterion of traffic network utilization has been widely studied in the literature. However, the assumption of deterministic travel times in these models is restrictive, given the large degree of uncertainty prevalent in urban transportation networks. In this context, this paper proposes a robust traffic assignment model that generalizes Wardrop's principle of traffic network equilibrium to networks with stochastic and correlated link travel times and incorporates the aversion of commuters to unreliable routes.

The user response to travel time uncertainty is modeled using the robust cost (RC) measure (defined as a weighted combination of the mean and standard deviation of path travel time) and the corresponding robust user equilibrium (UE) conditions are defined. The robust traffic assignment problem (RTAP) is subsequently formulated as a Variational Inequality problem. To solve the RTAP, a Gradient Projection algorithm is proposed, which involves solving a series of minimum RC path sub-problems that are theoretically and practically harder than deterministic shortest path problems. In addition, an origin-based heuristic is proposed to enhance computational performance on large networks. Numerical experiments examine the computational performance and convergence characteristics of the exact algorithm and establish the accuracy and efficiency of the origin-based heuristic on various real-world networks. Finally, the proposed RTA model is applied to the Chennai road network using empirical data, and its benefits as a normative benchmark are quantified through comparisons against the standard UE and System Optimum (SO) models.     

Vehicle dynamic stability improvements through gain-scheduled steering and braking control

This paper is concerned with the synthesis of a robust gain-scheduled ?_∞ MIMO vehicle dynamic stability controller (VDSC) involving both steering and rear braking actuators. This VDSC aims at improving automotive vehicle yaw stability and lateral performances. The aim of this work is to provide a methodology to synthesise such a controller while taking into account the braking actuator limitations and use the steering actuator only if it is necessary. These objectives are treated in an original way by the synthesis of a parameter-dependent controller built in the LPV framework and by the solution of an LMI problem. The proposed solution is coupled with a local ABS strategy to guarantee slip stability and make the solution complete. Nonlinear time and frequency domain simulations on a complex full vehicle model (which has been validated on a real car), subject to critical driving situations, show the efficiency and robustness of the proposed solution.     

State estimation in roll dynamics for commercial vehicles

Accurate lateral load transfer estimation plays an important role in improving the performance of the active rollover prevention system equipped in commercial vehicles. This estimation depends on the accurate prediction of roll angles for both the sprung and the unsprung subsystems. This paper proposes a novel computational method for roll-angle estimation in commercial vehicles employing sensors which are already used in a vehicle dynamic control system without additional expensive measurement units. The estimation strategy integrates two blocks. The first block contains a sliding-mode observer which is responsible for calculating the lateral tyre forces, while in the second block, the Kalman filter estimates the roll angles of the sprung mass and those of axles in the truck. The validation is conducted through MATLAB/TruckSim co-simulation. Based on the comparison between the estimated results and the simulation results from TruckSim, it can be concluded that the proposed estimation method has a promising tracking performance with low computational cost and high convergence speed. This approach enables a low-cost solution for the rollover prevention in commercial vehicles.     

序列响应面方法在覆盖件成形过程优化中的应用研究

为求解覆盖件最佳成形方案,将设计探索转化为满足特定目标和约束的待优化模型;提出采用逐次逼近方法,通过动态多项式响应面技术构造子优化目标和约束的近似响应面进行全局寻优,避免数值模拟易受噪声干扰且响应相对设计变量存在强非线性特征而导致的传统梯度法求解困难和过程发散等问题。该方法无须求解函数灵敏度,在保证拟合精度的前提下,能光滑响应并最大程度减少精确分析计算量,分析前翼子板回弹补偿优化设计实例,证明其具有很高的精度和鲁棒性。     

基于混沌神经网络的最优路径选择算法

研究车载交通流诱导系统的最优路径选择问题。采用广义路阻的定义,考虑了驾驶员在路径选择中的不同要求,并借助一种具有暂态混沌和时变增益的神经网络(NNTCTG),针对最优路径选择问题设计了神经网络结构,构造了能量函数,提出了一种能够满足不同出行者偏好的最优路径选择算法。所提出的算法具有很多优良特性,即暂态混沌特性和平稳收敛性,能有效地避免传统Hopfield神经网络极易陷入局部极值的缺陷。它通过短暂的倒分叉过程,能很快进入稳定收敛状态。仿真结果表明,NNTCTG求解指定起讫点对之间的最优路径问题时,总能收敛到全局最优,同时具有更高的搜索效率。     

Reliable Shortest Path Problems in Stochastic Time-Dependent Networks

This study investigates the time-dependent reliable shortest path problem (TD-RSPP), which is commonly encountered in congested urban road networks. Two variants of TD-RSPP are considered in this study. The first variant is to determine the earliest arrival time and associated reliable shortest path for a given departure time, referred to as the “forward” TD-RSPP. The second problem is to determine the latest departure time and associated reliable shortest path for a given preferred arrival time, referred as the “backward” TD-RSPP. It is shown in this article that TD-RSPP is not reversible. The backward TD-RSPP cannot be solved by the algorithms designed for the forward problem using the reverse search from destination to origin. In this study, two efficient solution algorithms are proposed to solve the forward and backward TD-RSPP exactly and the optimality of proposed algorithms is rigorously proved. The proposed solution algorithms have potential applications in both advanced traveler information systems and stochastic dynamic traffic assignment models.     

短时交通流预测系统的效率优化研究

针对短时交通流预测系统的功能需求特点,提出了一个分布式的系统框架,将系统的计算任务按照功能划分到不同的服务器上,从而降低了单个服务器的负荷,提高了整体的效率。通过对系统在北京市实际路网上运行的性能测试,找出了程序执行效率的瓶颈,分析了执行效率问题的主要原因,并给出了对效率问题的具体优化措施。经过实际验证,该技术方案很好地解决了系统的执行效率问题,满足了系统的实时性要求。