An efficient recursive least square-based condition monitoring approach for a rail vehicle suspension system

A model-based condition monitoring strategy for the railway vehicle suspension is proposed in this paper. This approach is based on recursive least square (RLS) algorithm focusing on the deterministic ‘input–output’ model. RLS has Kalman filtering feature and is able to identify the unknown parameters from a noisy dynamic system by memorising the correlation properties of variables. The identification of suspension parameter is achieved by machine learning of the relationship between excitation and response in a vehicle dynamic system. A fault detection method for the vertical primary suspension is illustrated as an instance of this condition monitoring scheme. Simulation results from the rail vehicle dynamics software ‘ADTreS’ are utilised as ‘virtual measurements’ considering a trailer car of Italian ETR500 high-speed train. The field test data from an E464 locomotive are also employed to validate the feasibility of this strategy for the real application. Results of the parameter identification performed indicate that estimated suspension parameters are consistent or approximate with the reference values. These results provide the supporting evidence that this fault diagnosis technique is capable of paving the way for the future vehicle condition monitoring system.     

Suspension parameter estimation in the frequency domain using a matrix inversion approach

The dynamic lumped parameter models used to optimise the ride and handling of a vehicle require base values of the suspension parameters. These parameters are generally experimentally identified. The accuracy of identified parameters can depend on the measurement noise and the validity of the model used. The existing publications on suspension parameter identification are generally based on the time domain and use a limited degree of freedom. Further, the data used are either from a simulated ‘experiment’ or from a laboratory test on an idealised quarter or a half-car model. In this paper, a method is developed in the frequency domain which effectively accounts for the measurement noise. Additional dynamic constraining equations are incorporated and the proposed formulation results in a matrix inversion approach. The nonlinearities in damping are estimated, however, using a time-domain approach. Full-scale 4-post rig test data of a vehicle are used. The variations in the results are discussed using the modal resonant behaviour. Further, a method is implemented to show how the results can be improved when the matrix inverted is ill-conditioned. The case study shows a good agreement between the estimates based on the proposed frequency-domain approach and measurable physical parameters.     

发动机液压悬置低频模型参数识别方法的研究

根据悬置低频振动模型,提出了基于DE算法的发动机液压悬置模型识别方法,由简单的低频正弦激振试验直接估计模型的关键参数值,完成模型的参数识别。基于上述理论和试验相结合的模型识别方法可以代替组件试验,识别结果可直接用于复杂结构悬置元件的动特性预测和整车NVH性能研究。     

Vehicle handling dynamics modelling by a data-driven identification method

Modelling of vehicle handling dynamics has received a renewed attention in recent years. Different from traditional vehicle modelling, a novel data-driven identification method for vehicle handling dynamics is proposed, which can avoid the problems of the under-modelling and parameter uncertainties in the first-principle modelling process. By first-order Taylor expansion, the nonlinear vehicle system can be linearised as a slowly linear time-varying system with fourth-order. In order to identify the derived identifiable model structure, a recursive subspace method is presented. Derived by optimal version of predictor-based subspace identification (PBSID_opt) and projection approximation subspace tracking (PAST), the identification method is numerical stability and gives an unbiased estimation for the closed-loop system. Based on standard road tests, the proposed modelling method is proven effective and the obtained model has good predictive ability. Additionally, it is noted that the model obtained from the initial phase of straight driving is just a mathematical model to describe the relationship between input and output. And when the vehicle is steering, the model can converge to a stable phase quickly and represent vehicle dynamic performance.     

eTS fuzzy driver model for simultaneous longitudinal and lateral vehicle control

In this paper, evolving Takagi-Sugeno (eTS) fuzzy driver model is proposed for simultaneous lateral and longitudinal control of a vehicle in a test track closed to traffic. The developed eTS fuzzy driver model can capture human operator’s driving expertise for generating desired steering angle, throttle angle and brake pedal command values by processing only information which can be supplied by the vehicle’s on-board control systems in real time. Apart from other fuzzy rule based (FRB) models requiring human expert knowledge or off-line clustering, the developed eTS driver model can adapt itself automatically, even ‘from scratch’, by an on-line learning process using eTS algorithm while human driver is supervising the vehicle. Proposed eTS fuzzy driver model’s on-line human driver identification capability and autonomous vehicle driving performance were evaluated on real road profiles created by digitizing two different intercity express ways of Turkey in IPG© CarMaker® software. The training and validation simulation results demonstrated that eTS fuzzy driver model can be used in product development phase to speed up different tests via realistic simulations. Furthermore eTS fuzzy driver model has an application potential in the field of autonomous driving.     

Estimation of Tire-Road Friction Using Observer Based Identifiers

This paper presents methods for identifying the tire-road friction coefficient. The proposed methods are: an observer-based least square method and an observer/filtered-regressor-based method. These methods were designed assuming that some of the states are not available since physical parameter identification methods developed assuming that the system states are available are not attractive from a practical point of view. The observer is used to estimate signals which are difficult or expensive to measure. Using the estimated states of the system and the filtered-regressor, the parameter estimates are obtained. The proposed methods are evaluated on an eight state nonlinear vehicle/transmission simulation model with a Bakker-Pacejka's formula tire model. Vehicle tests have been performed on dry and wet roads to verify the performance of the methods. It has been shown through simulations and vehicle tests how the RPM sensors can be used with observer based identification methods to estimate the tire-road friction from measurements of engine rpm, transmission output speed and wheel speed. The proposed methods will be useful in the implementation and adaptation of vehicle collision warning/avoidance algorithm since the tire-road friction can be estimated only using the RPM sensors which are currently being used in production vehicles.     

An approach for the validation of railway vehicle models based on on-track measurements

This paper proposes an approach for the validation of railway vehicle models based on on-track measurements. The validation of simulation models has gained importance with the introduction of new applications of multi-body simulation in railway vehicle dynamics as the assessment of track geometry defects, the investigation of derailments and the analysis of gauging. These applications are not only interested in qualitative predictions of the vehicle behaviour but also in precise quantitative results of the safety and comfort relevant vehicle responses. The validation process aims at guaranteeing that the simulation model represents the dynamic behaviour of the real vehicle with a sufficient good precision. A misfit function is defined which quantifies the distance between the simulated and the measured vehicle response allowing to evaluate different models at different running conditions. The obtained modelling errors are compared to the measurement uncertainty estimated for one vehicle using repeatability analysis.     

Dynamic model for automotive side impact crashes

A rigid body model to represent a side impact crash is constructed using five degrees-of-freedom (dof) for the vehicle and three dof for each occupant in the vehicle. Nonlinear stiffness and damping elements and the presence of physical gaps between several components make the model highly nonlinear. The model is validated using experimental crash test data from a National Highway Traffic Safety Administration (NHTSA) database. To simplify the parameter identification process and reduce the number of parameters to be identified at each stage, a two-step process is adopted in which the vehicle is first assumed to be unaffected by the presence of the occupants, and its model parameters are identified. Subsequently, the parameters in the occupant models are identified.

The active set method with a performance index that includes both the L₂ and L_∞ norms is used for parameter identification. A challenge is posed by the fact that the optimisation problem involved is non-convex. To overcome this challenge, a large set of random initial values of parameter estimates is generated and the optimisation method is applied with all these initial conditions. The values of parameters that provide the minimal performance index from the entire set of initial conditions are then chosen as the best parameter values. The optimal parameters values thus identified are shown to significantly improve the match between the model responses and the experimentally measured sensor signals from the NHTSA crash test.     

Identification of linear handling models for road vehicles

This study reports the identification of linear handling models for road vehicles starting from structural identifiability analysis, continuing with the experiments to acquire data on a vehicle equipped with a sensor set and data acquisition system, and ending with the estimation of parameters using the collected data. The model structure originates from the well-known linear bicycle model that is frequently used in handling analysis of road vehicles. Physical parameters of the bicycle model structure are selected as the unknown parameter set that is to be identified. Global identifiability of the model structure is analysed, in detail, and concluded according to various available sensor sets. Physical parameters of the bicycle model structure are estimated using prediction error estimation method. Genetic algorithms are used in the optimisation phase of the identification algorithm to overcome the difficulty in the selection of initial values for parameter estimates. Validation analysis of the identified model is also presented. The identified model is shown to track the system response successfully.     

Finite-element model calibration of a railway vehicle based on experimental modal parameters

This article describes the experimental calibration of a three-dimensional numerical model of an Alfa Pendular train vehicle based on modal parameters. The dynamic tests of the carbody and bogie of the vehicle allowed the determination of the frequencies and modal configurations of 13 vibration modes, by applying the data-driven stochastic subspace identification method. In addition, a dynamic characterisation test of the passenger-seat system was also conducted. The calibration of the model was performed using a submodelling/multistep approach involving two phases, the first one focused on the calibration of the model of the bogie under test conditions and the second one focused on the calibration of the complete model of the vehicle. The calibration was performed through an iterative method based on a genetic algorithm and allowed to obtain optimal values of 17 parameters of the numerical model. For the pairing of the vibration modes, real and complex, a recent technique was used based on the calculation of the modal strain energy. The stability of a significant number of parameters considering different initial populations demonstrated the robustness of the algorithm. The comparison of experimental and numerical responses before and after calibration revealed significant improvements in the numerical model and a very good correlation between the responses obtained with the calibrated model and the experimental responses.     

Improved calibration of simulation models in railway dynamics: application of a parameter identification process to the multi-body model of a TGV train

This paper aims at estimating the vehicle suspension parameters of a TGV (Train à Grande Vitesse) train from measurement data. A better knowledge of these parameters is required for virtual certification or condition monitoring applications. The estimation of the parameter values is performed by minimising a misfit function describing the distance between the measured and the simulated vehicle response. Due to the unsteady excitation from the real track irregularities and nonlinear effects in the vehicle behaviour, the misfit function is defined in the time domain using a least squares estimation. Then an optimisation algorithm is applied in order to find the best parameter values within the defined constraints. The complexity of the solution surface with many local minima requires the use of global optimisation methods. The results show that the model can be improved by this approach providing a response of the simulation model closer to the measurements.     

Tyre pressure monitoring using a dynamical model-based estimator

In the last few years, various control systems have been investigated in the automotive field with the aim of increasing the level of safety and stability, avoid roll-over, and customise handling characteristics. One critical issue connected with their integration is the lack of state and parameter information. As an example, vehicle handling depends to a large extent on tyre inflation pressure. When inflation pressure drops, handling and comfort performance generally deteriorate. In addition, it results in an increase in fuel consumption and in a decrease in lifetime. Therefore, it is important to keep tyres within the normal inflation pressure range. This paper introduces a model-based approach to estimate online tyre inflation pressure. First, basic vertical dynamic modelling of the vehicle is discussed. Then, a parameter estimation framework for dynamic analysis is presented. Several important vehicle parameters including tyre inflation pressure can be estimated using the estimated states. This method aims to work during normal driving using information from standard sensors only. On the one hand, the driver is informed about the inflation pressure and he is warned for sudden changes. On the other hand, accurate estimation of the vehicle states is available as possible input to onboard control systems.     

驾驶机器人车辆动态制动力矩补偿

为了减小长期自动驾驶过程中制动性能下降带来的影响,提出了一种驾驶机器人车辆动态制动力矩补偿方法。首先建立了以车速和制动踏板力为输入,制动力矩为输出的驾驶机器人车辆制动性能离线自学习模型。然后考虑到驾驶机器人车辆长期自动驾驶导致离线自学习模型可靠性下降,建立了以车速和制动踏板力为输入,制动力矩为输出的扩展自回归在线辨识模型,并采用模糊变遗忘因子递推最小二乘法进行参数辨识。模糊变遗忘因子递推最小二乘法通过引入遗忘因子的方式,对数据施加时变加权系数,以避免出现数据增长导致的数据饱和现象。模糊变遗忘因子控制器以制动力矩辨识误差为输入,经模糊规则推理实时输出合适的遗忘因子进行参数辨识,能够有效均衡驾驶机器人车辆制动性能参数辨识的稳定性与收敛速度。驾驶机器人车辆自动驾驶过程中,根据当前车速与目标车速的大小计算出所需的制动力矩,加上反馈回来的制动力矩误差,并结合当前时刻的车速,利用制动性能离线自学习模型与机械腿逆向运动学模型实时计算出制动电机输出位移量,实现对驾驶机器人车辆制动力矩的在线补偿。仿真与试验结果表明:利用所提出的方法对车辆动态制动力矩进行辨识时,通过调节遗忘因子,辨识结果能够快速收敛且辨识误差较小。在此基础上,控制驾驶机器人车辆进行纵向车速跟踪时,能够有效减小制动性能下降造成的影响,保证控制车速跟踪误差在±1km·h-1之内。     

中国公路车-桥耦合振动车辆模型研究（双语出版）

为了提出适用于中国车-桥耦合振动分析的车辆动力分析模型,首先基于中国桥梁规范中的设计车辆荷载,结合大量调查统计数据和等效静力分析方法,初步拟定车辆动力分析模型的几何尺寸、质量、刚度、阻尼等参数取值,并与国内外广泛采用的几种车辆模型的参数取值进行对比。接着选取4座钢筋混凝土简支梁桥并建立其三维有限元模型,基于车-桥耦合振动数值模拟分析车辆模型的刚度、阻尼等参数对桥梁上动力冲击系数的影响,并对比几个不同车辆模型对动力冲击系数的影响。最后,选择中国湖南省境内一座实桥和几辆不同轴数的重车开展实桥试验,将实测动力冲击系数与所提车辆模型数值模拟获得的冲击系数进行对比。结果表明：动力冲击系数随车辆总质量的增大而减小,随车辆整体刚度的增大而增大,但随车辆整体阻尼的增大呈先减小后增大的趋势;单个车轴的刚度和阻尼对动力冲击系数的影响不明显;车辆总质量是导致不同车辆模型作用下动力冲击系数差异的主要因素;数值模拟结果与实测结果吻合良好,验证了所提车辆模型及参数取值的合理性;该车辆模型可用于中国的设计车辆荷载作用下桥梁的动力响应分析和相关研究,也可用于估算重量相当的不同类型车辆对桥梁的动力冲击效应。     

Development of an electric active rollcontrol (ARC) algorithm for a SUV

Cornering maneuvers with reduced body roll and without loss in comfort are leading requirements for car manufacturers. An electric active roll control (ARC) system controls body roll angle with motor-driven actuators installed in the centers of the front and rear stabilizer bars. A vehicle analysis model developed using a CarSim S/W was validated using vehicle test data. Two ARC algorithms for a sports utility vehicle (SUV) were designed using a sliding-mode control algorithm based on a nonlinear roll model and an estimated lateral acceleration based on a linearized roll model. Co-simulation with the Matlab simulink controller model and the CarSim vehicle model were conducted to evaluate the performance of two ARC control algorithms. To validate the ARC performance in a real vehicle, vehicle tests were conducted at KATECH proving ground using a small SUV equipped with two ARC actuators, upper and lower controllers and a few subsystems. From the simulation and vehicle validation test results, the proposed ARC control algorithm for the developed ARC actuator prototypes improves the vehicle’s dynamic performance.     

Effect of vehicle model on the estimation of lateral vehicle dynamics

A methodology is presented for estimating vehicle handling dynamics, which are important to control system design and safety measures. The methodology, which is based on an extended Kalman filter (EKF), makes it possible to estimate lateral vehicle states and tire forces on the basis of the results obtained from sinusoidal steering stroke tests that are widely used in the evaluation of vehicle and tire handling performances. This paper investigates the effect of vehicle-road system models on the estimation of lateral vehicle dynamics in the EKF. Various vehicle-road system models are considered in this study: vehicle models (2-DOF, 3-DOF, 4-DOF), tire models (linear, non-linear) and relaxation lengths. Handling tests are performed with a vehicle equipped with sensors that are widely used by vehicle and tire manufacturers for handling maneuvers. The test data are then used in the estimation of the EKF and identification of lateral tire model coefficients. The accuracy of the identified values is validated by comparing the RMS error between experimentally measured states and regenerated states simulated using the identified coefficients. The results show that the relaxation length of the tire model has a notable impact on the estimation of lateral vehicle dynamics.     

Analysis of handling performance based on simplified lateral vehicle dynamics

In this article, the analysis methods for vehicle handling performance are studied. Using simple models, dynamic characteristic parameters such as yaw, natural frequency, and the damping coefficient of a vehicle can be theoretically formulated. Here, the vehicle is simplified by a bicycle (single-track) model, and the tire is modeled by an equivalent cornering stiffness and first order lag. From the experimental road data, the tire model parameters (equivalent cornering stiffness and time lag constant) are extracted. These parameters are then inserted into the theoretically formulated equations of dynamic characteristic parameters. For the purpose of validating the efficiency of the suggested methods, experimental road tests (where the cars have different handling performances) are performed. The results show that vehicle handling performance can be sufficiently represented by the suggested dynamic characteristic parameters. So, it is concluded that the proposed method has practical use for the development of new cars or for the comparison of similar cars since the evaluations of the vehicle handling performance can be efficiently determined by the suggested dynamic characteristic parameters.     

Design,manufacturing and evaluation of glass/polyester composite crash structures for lightweight vehicles

The development and validation of a modular composite impact structure is presented in the present paper. Quasi-static and dynamic impact tests of the composite components and a full frontal crash test of a vehicle prototype with composite impact structures manufactured by a new UV-pultrusion process have been performed. The results have demonstrated the feasibility of composite impact structures for crash applications with high specific energy absorption values compared with current metallic crash structures. Furthermore, due to the high production capacity of this new manufacturing process, cost-effective composite impact structures for mass-production of conventional cars may be feasible. Finally, a multimaterial numerical model as design tool for crashworthiness applications has also been validated. Different accelerations measured in the crash test have been accurately predicted as well as the crash behaviour of the composite impact structures.     

基于位移测量的非线性涡激力模型参数识别方法

利用半经验数学模型来近似表示涡激力是目前研究涡激共振所采用的主要方法，但关于非线性涡激力模型参数的试验识别研究还较少，现有识别方法也有待改进。为了更方便可靠地识别非线性涡激力模型中的参数，根据能量等效原理推导出一种基于节段模型位移响应的气动参数识别新方法。通过节段模型风洞试验测得中央开槽箱梁断面的扭转涡激共振位移响应，应用新方法识别简化非线性涡激扭矩模型中的气动参数，并对参数识别精度做出评价。将新方法与Ehsan等所建议的位移法以及基于实测力时程的三步最小二乘拟合法进行了对比。结果表明：利用新方法识别得到的气动参数可以较好地预测系统的扭转涡激共振位移响应；基于一致的系统线性机械参数，新方法识别得到的气动参数与Ehsan等所建议位移法的识别结果基本相同，而新方法能进一步考虑对识别结果影响较为显著的机械参数非线性特性；当新方法考虑非线性机械参数时，其识别结果和基于实测力时程的三步最小二乘拟合法相比也十分吻合，并且新方法更为简便。     

Identifying tyre models directly from vehicle test data using an extended Kalman filter

Individual tyre models are traditionally derived from component tests, with their parameters matched to force and slip measurements. They are imported into vehicle models which should, but do not always properly provide suspension geometry interaction. Recent advances in Global Positioning System (GPS)/inertia vehicle instrumentation now make full state measurement viable in test vehicles, so tyre slip behaviour is directly measurable. This paper uses an extended Kalman filter for system identification, to derive individual load-dependent tyre models directly from these test vehicle state measurements. The resulting model therefore implicitly compensates for suspension geometry and compliance. The paper looks at two variants of the tyre model, and also considers real-time adaptation of the model to road surface friction variations. Test vehicle results are used exclusively, and the results show successful tyre model identification, improved vehicle model state prediction – particularly in lateral velocity reproduction – and an effective real-time solution for road friction estimation.