Modelling nonlinear vehicle dynamics with neural networks

The nonlinear modelling ability of neural networks has been widely recognised as an effective tool to identify and control dynamic systems, with applications including nonlinear vehicle dynamics which this paper focuses on using multi-layer perceptron networks. Existing neural network literature does not detail some of the factors which effect neural network nonlinear modelling ability. This paper investigates into and concludes on required network size, structure and initial weights, considering results for networks of converged weights. The paper also presents an online training method and an error measure representing the network's parallel modelling ability over a range of operating conditions. Copyright © 2010 Inderscience Enterprises Ltd.

Influence of the track quality and of the properties of the wheel rail rolling contact on vehicle dynamics

This work describes an analytical approach to determine what degree of accuracy is required in the definition of the rail vehicle models used for dynamic simulations. This way it would be possible to know in advance how the results of simulations may be altered due to the existence of errors in the creation of rolling stock models, whilst also identifying their critical parameters. This would make it possible to maximize the time available to enhance dynamic analysis and focus efforts on factors that are strictly necessary.In particular, the parameters related both to the track quality and to the rolling contact were considered in this study. With this aim, a sensitivity analysis was performed to assess their influence on the vehicle dynamic behaviour. To do this, 72 dynamic simulations were performed modifying, one at a time, the track quality, the wheel-rail friction coefficient and the equivalent conicity of both new and worn wheels. Three values were assigned to each parameter, and two wear states were considered for each type of wheel, one for new wheels and another one for reprofiled wheels.After processing the results of these simulations, it was concluded that all the parameters considered show very high influence, though the friction coefficient shows the highest influence. Therefore, it is recommended to undertake any future simulation job with measured track geometry and track irregularities, measured wheel profiles and normative values of wheel-rail friction coefficient.

Co-simulation Methodologies for Hybrid and Electric Vehicle Dynamics

In recent decades, full electric and hybrid electric vehicles have emerged as an alternative to conventional cars due to a range of factors, including environmental and economic aspects. These vehicles are the result of considerable efforts to seek ways of reducing the use of fossil fuel for vehicle propulsion. Sophisticated technologies such as hybrid and electric powertrains require careful study and optimization. Mathematical models play a key role at this point. Currently, many advanced mathematical analysis tools, as well as computer applications have been built for vehicle simulation purposes. Given the great interest of hybrid and electric powertrains, along with the increasing importance of reliable computer-based models, the author decided to integrate both aspects in the research purpose of this work. Furthermore, this is one of the first final degree projects held at the ETSII (Higher Technical School of Industrial Engineers) that covers the study of hybrid and electric propulsion systems. The present project is based on MBS3D 2.0, a specialized software for the dynamic simulation of multibody systems developed at the UPM Institute of Automobile Research (INSIA). Automobiles are a clear example of complex multibody systems, which are present in nearly every field of engineering. The work presented here benefits from the availability of MBS3D software. This program has proven to be a very efficient tool, with a highly developed underlying mathematical formulation. On this basis, the focus of this project is the extension of MBS3D features in order to be able to perform dynamic simulations of hybrid and electric vehicle models. This requires the joint simulation of the mechanical model of the vehicle, together with the model of the hybrid or electric powertrain. These sub-models belong to completely different physical domains. In fact the powertrain consists of energy storage systems, electrical machines and power electronics, connected to purely mechanical components (wheels, suspension, transmission, clutch…). The challenge today is to create a global vehicle model that is valid for computer simulation. Therefore, the main goal of this project is to apply co-simulation methodologies to a comprehensive model of an electric vehicle, where sub-models from different areas of engineering are coupled. The created electric vehicle (EV) model consists of a separately excited DC electric motor, a Li-ion battery pack, a DC/DC chopper converter and a multibody vehicle model. Co-simulation techniques allow car designers to simulate complex vehicle architectures and behaviors, which are usually difficult to implement in a real environment due to safety and/or economic reasons. In addition, multi-domain computational models help to detect the effects of different driving patterns and parameters and improve the models in a fast and effective way. Automotive designers can greatly benefit from a multidisciplinary approach of new hybrid and electric vehicles. In this case, the global electric vehicle model includes an electrical subsystem and a mechanical subsystem. The electrical subsystem consists of three basic components: electric motor, battery pack and power converter. A modular representation is used for building the dynamic model of the vehicle drivetrain. This means that every component of the drivetrain (submodule) is modeled separately and has its own general dynamic model, with clearly defined inputs and outputs. Then, all the particular submodules are assembled according to the drivetrain configuration and, in this way, the power flow across the components is completely determined. Dynamic models of electrical components are often based on equivalent circuits, where Kirchhoff’s voltage and current laws are applied to draw the algebraic and differential equations. Here, Randles circuit is used for dynamic modeling of the battery and the electric motor is modeled through the analysis of the equivalent circuit of a separately excited DC motor, where the power converter is included. The mechanical subsystem is defined by MBS3D equations. These equations consider the position, velocity and acceleration of all the bodies comprising the vehicle multibody system. MBS3D 2.0 is entirely written in MATLAB and the structure of the program has been thoroughly studied and understood by the author. MBS3D software is adapted according to the requirements of the applied co-simulation method. Some of the core functions are modified, such as integrator and graphics, and several auxiliary functions are added in order to compute the mathematical model of the electrical components. By coupling and co-simulating both subsystems, it is possible to evaluate the dynamic interaction among all the components of the drivetrain. ‘Tight-coupling’ method is used to cosimulate the sub-models. This approach integrates all subsystems simultaneously and the results of the integration are exchanged by function-call. This means that the integration is done jointly for the mechanical and the electrical subsystem, under a single integrator and then, the speed of integration is determined by the slower subsystem. Simulations are then used to show the performance of the developed EV model. However, this project focuses more on the validation of the computational and mathematical tool for electric and hybrid vehicle simulation. For this purpose, a detailed study and comparison of different integrators within the MATLAB environment is done. Consequently, the main efforts are directed towards the implementation of co-simulation techniques in MBS3D software. In this regard, it is not intended to create an extremely precise EV model in terms of real vehicle performance, although an acceptable level of accuracy is achieved. The gap between the EV model and the real system is filled, in a way, by introducing the gas and brake pedals input, which reflects the actual driver behavior. This input is included directly in the differential equations of the model, and determines the amount of current provided to the electric motor. For a separately excited DC motor, the rotor current is proportional to the traction torque delivered to the car wheels. Therefore, as it occurs in the case of real vehicle models, the propulsion torque in the mathematical model is controlled through acceleration and brake pedal commands. The designed transmission system also includes a reduction gear that adapts the torque coming for the motor drive and transfers it. The main contribution of this project is, therefore, the implementation of a new calculation path for the wheel torques, based on performance characteristics and outputs of the electric powertrain model. Originally, the wheel traction and braking torques were input to MBS3D through a vector directly computed by the user in a MATLAB script. Now, they are calculated as a function of the motor current which, in turn, depends on the current provided by the battery pack across the DC/DC chopper converter. The motor and battery currents and voltages are the solutions of the electrical ODE (Ordinary Differential Equation) system coupled to the multibody system. Simultaneously, the outputs of MBS3D model are the position, velocity and acceleration of the vehicle at all times. The motor shaft speed is computed from the output vehicle speed considering the wheel radius, the gear reduction ratio and the transmission efficiency. This motor shaft speed, somehow available from MBS3D model, is then introduced in the differential equations corresponding to the electrical subsystem. In this way, MBS3D and the electrical powertrain model are interconnected and both subsystems exchange values resulting as expected with tight-coupling approach.When programming mathematical models of complex systems, code optimization is a key step in the process. A way to improve the overall performance of the integration, making use of C/C++ as an alternative programming language, is described and implemented. Although this entails a higher computational burden, it leads to important advantages regarding cosimulation speed and stability. In order to do this, it is necessary to integrate MATLAB with another integrated development environment (IDE), where C/C++ code can be generated and executed. In this project, C/C++ files are programmed in Microsoft Visual Studio and the interface between both IDEs is created by building C/C++ MEX file functions. These programs contain functions or subroutines that can be dynamically linked and executed from MATLAB. This process achieves reductions in simulation time up to two orders of magnitude. The tests performed with different integrators, also reveal the stiff character of the differential equations corresponding to the electrical subsystem, and allow the improvement of the cosimulation process. When varying the parameters of the integration and/or the initial conditions of the problem, the solutions of the system of equations show better dynamic response and stability, depending on the integrator used. Several integrators, with variable and non-variable step-size, and for stiff and non-stiff problems are applied to the coupled ODE system. Then, the results are analyzed, compared and discussed. From all the above, the project can be divided into four main parts: 1. Creation of the equation-based electric vehicle model; 2. Programming, simulation and adjustment of the electric vehicle model; 3. Application of co-simulation methodologies to MBS3D and the electric powertrain subsystem; and 4. Code optimization and study of different integrators. Additionally, in order to deeply understand the context of the project, the first chapters include an introduction to basic vehicle dynamics, current classification of hybrid and electric vehicles and an explanation of the involved technologies such as brake energy regeneration, electric and non-electric propulsion systems for EVs and HEVs (hybrid electric vehicles) and their control strategies. Later, the problem of dynamic modeling of hybrid and electric vehicles is discussed. The integrated development environment and the simulation tool are also briefly described. The core chapters include an explanation of the major co-simulation methodologies and how they have been programmed and applied to the electric powertrain model together with the multibody system dynamic model. Finally, the last chapters summarize the main results and conclusions of the project and propose further research topics. In conclusion, co-simulation methodologies are applicable within the integrated development environments MATLAB and Visual Studio, and the simulation tool MBS3D 2.0, where equation-based models of multidisciplinary subsystems, consisting of mechanical and electrical components, are coupled and integrated in a very efficient way.

A modelling strategy for vehicle dynamics using Pro/ENGINEER

Vehicle dynamics modelling can provide vehicle designers with vehicle performance data that can assist with the efficient development of more refined cars. However, such models are notoriously complicated requiring the user to have a considerable understanding of vehicle dynamics.

Race car vehicle dynamics and design applied to formula student

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Fusion of in-vehicle sensor data to develop Intelligent Driver Training System (IDTS)

The over represented number of novice drivers involved in crashes is alarming. Driver training is one of the interventions aimed at mitigating the number of crashes that involve young drivers. To our knowledge, Advanced Driver Assistance Systems (ADAS) have never been comprehensively used in designing an intelligent driver training system. Currently, there is a need to develop and evaluate ADAS that could assess driving competencies. The aim is to develop an unsupervised system called Intelligent Driver Training System (IDTS) that analyzes crash risks in a given driving situation. In order to design a comprehensive IDTS, data is collected from the Driver, Vehicle and Environment (DVE), synchronized and analyzed. The first implementation phase of this intelligent driver training system deals with synchronizing multiple variables acquired from DVE. RTMaps is used to collect and synchronize data like GPS, vehicle dynamics and driver head movement. After the data synchronization, maneuvers are segmented out as right turn, left turn and overtake. Each maneuver is composed of several individual tasks that are necessary to be performed in a sequential manner. This paper focuses on turn maneuvers. Some of the tasks required in the analysis of ‘turn’ maneuver are: detect the start and end of the turn, detect the indicator status change, check if the indicator was turned on within a safe distance and check the lane keeping during the turn maneuver. This paper proposes a fusion and analysis of heterogeneous data, mainly involved in driving, to determine the risk factor of particular maneuvers within the drive. It also explains the segmentation and risk analysis of the turn maneuver in a drive.

Correlating eye gaze direction, depth and vehicle information on an interactive map for driver training

The over represented number of novice drivers involved in crashes is alarming. Driver training is one of the interventions aimed at mitigating the number of crashes that involve young drivers. Experienced drivers have better hazard perception ability compared to inexperienced drivers. Eye gaze patterns have been found to be an indicator of the driver's competency level. The aim of this paper is to develop an in-vehicle system which correlates information about the driver's gaze and vehicle dynamics, which is then used to assist driver trainers in assessing driving competency. This system allows visualization of the complete driving manoeuvre data on interactive maps. It uses an eye tracker and perspective projection algorithms to compute the depth of gaze and plots it on Google maps. This interactive map also features the trajectory of the vehicle and turn indicator usage. This system allows efficient and user friendly analysis of the driving task. It can be used by driver trainers and trainees to understand objectively the risks encountered during driving manoeuvres. This paper presents a prototype that plots the driver's eye gaze depth and direction on an interactive map along with the vehicle dynamics information. This prototype will be used in future to study the difference in gaze patterns in novice and experienced drivers prior to a certain manoeuvre.

Transport and health in China : recent collaborative research relating to vehicle factors and pollution

The nature of the transport system contributes to public health outcomes in a range of ways. The clearest contribution to public health is in the area of traffic crashes, because of their direct impact on individual death and disability and their direct costs to the health system. Other papers in this conference address these issues. This paper outlines some collaborative research between the Centre for Accident Research and Road Safety - Queensland (CARRS-Q) at QUT and Chinese researchers in areas that have indirect health impacts. Heavy vehicle dynamics: The integrity of the road surface influences crash risk, with ruts, pot-holes and other forms of road damage contributing to increased crash risks. The great majority of damage to the road surface from vehicles is caused by heavy trucks and buses, rather than cars or smaller vehicles. In some cases this damage is due to deliberate overloading, but in other cases it is due to vehicle suspension characteristics that lead to occasional high loads on particular wheels. Together with a visiting researcher and his colleagues, we have used both Queensland and Chinese data to model vehicle suspension systems that reduce the level of load, and hence the level of road damage and resulting crash risk(1-5). Toll worker exposure to vehicle emissions: The increasing construction of highways in China has also involved construction of a large number of toll roads. Tollbooth workers are potentially exposed to high levels of pollutants from vehicles, however the extent of this exposure and how it relates to standards for exposure are not well known. In a study led by a visiting researcher, we conducted a study to model these levels of exposure for a tollbooth in China(6). Noise pollution: The increasing presence of high speed roads in China has contributed to an increase in noise levels. In this collaborative study we modelled noise levels associated with a freeway widening near a university campus, and measures to reduce the noise(7). Along with these areas of research, there are many other areas of transport with health implications that are worthy of exploration. Traffic, noise and pollution contribute to a difficult environment for pedestrians, especially in an ageing society where there are health benefits to increasing physical activity. By building on collaborations such as those outlined, there is potential for a contribution to improved public health by addressing transport issues such as vehicle factors and pollution, and extending the research to other areas of travel activity. 1. Chen, Y., He, J., King, M., Chen, W. and Zhang, W. (2014). Stiffness-damping matching method of an ECAS system based on LQG control. Journal of Central South University, 21:439-446. DOI: 10.1007/s1177101419579 2. Chen, Y., He, J., King, M., Feng, Z. and Chang, W. (2013). Comparison of two suspension control strategies for multi-axle heavy truck. Journal of Central South University, 20(2): 550-562. 3. Chen, Y., He, J., King, M., Chen, W. and Zhang, W. (2013). Effect of driving conditions and suspension parameters on dynamic load-sharing of longitudinal-connected air suspensions. Science China Technological Sciences, 56(3): 666-676. DOI: 10.1007/s11431-012-5091-3 4. Chen, Y., He., J., King, M., Chen, W. and Zhang, W. (2013). Model development and dynamic load-sharing analysis of longitudinal-connected air suspensions. Strojniški Vestnik - Journal of Mechanical Engineering, 59(1):14-24. 5. Chen, Y., He, J., King, M., Liu, H. and Zhang, W. (2013). Dynamic load-sharing of longitudinal-connected air suspensions of a tri-axle semi-trailer. Proceedings of Transportation Research Board Annual Conference, Washington DC, 13-17 January 2013, paper no. 13-1117. 6. He, J., Qi, Z., Hang, W., King, M., and Zhao, C. (2011). Numerical evaluation of pollutant dispersion at a toll plaza based on system dynamics and Computational Fluid Dynamics models. Transportation Research Part C, 19(2011):510-520. 7. Zhang, C., He, J., Wang, Z., Yin, R. and King, M. (2013). Assessment of traffic noise level before and after freeway widening using traffic microsimulation and a refined classic noise prediction method. Proceedings of Transportation Research Board Annual Conference, Washington DC, 13-17 January 2013, paper no. 13-2016.

Robust Reentry Guidance of a Reusable Launch Vehicle Using Model Predictive Static Programming

A robust suboptimal reentry guidance scheme is presented for a reusable launch vehicle using the recently developed, computationally efficient model predictive static programming. The formulation uses the nonlinear vehicle dynamics with a spherical and rotating Earth, hard constraints for desired terminal conditions, and an innovative cost function having several components with associated weighting factors that can account for path and control constraints in a soft constraint manner, thereby leading to smooth solutions of the guidance parameters. The proposed guidance essentially shapes the trajectory of the vehicle by computing the necessary angle of attack and bank angle that the vehicle should execute. The path constraints are the structural load constraint, thermal load constraint, bounds on the angle of attack, and bounds on the bank angle. In addition, the terminal constraints include the three-dimensional position and velocity vector components at the end of the reentry. Whereas the angle-of-attack command is generated directly, the bank angle command is generated by first generating the required heading angle history and then using it in a dynamic inversion loop considering the heading angle dynamics. Such a two-loop synthesis of bank angle leads to better management of the vehicle trajectory and avoids mathematical complexity as well. Moreover, all bank angle maneuvers have been confined to the middle of the trajectory and the vehicle ends the reentry segment with near-zero bank angle, which is quite desirable. It has also been demonstrated that the proposed guidance has sufficient robustness for state perturbations as well as parametric uncertainties in the model.

Rollover-Preventive Force Synthesis at Active Suspensions in a Vehicle Performing a Severe Maneuver With Wheels Lifted Off

Among the intelligent safety technologies for road vehicles, active suspensions controlled by embedded computing elements for preventing rollover have received a lot of attention. The existing models for synthesizing and allocating forces in such suspensions are conservatively based on the constraints that are valid until no wheels lift off the ground. However, the fault tolerance of the rollover-preventive systems can be enhanced if the smart/active suspensions can intervene in the more severe situation in which the wheels have just lifted off the ground. The difficulty in computing control in the last situation is that the vehicle dynamics then passes into the regime that yields a model involving disjunctive constraints on the dynamics. Simulation of dynamics with disjunctive constraints in this context becomes necessary to estimate, synthesize, and allocate the intended hardware realizable forces in an active suspension. In this paper, we give an algorithm for the previously mentioned problem by solving it as a disjunctive dynamic optimization problem. Based on this, we synthesize and allocate the roll-stabilizing time-dependent active suspension forces in terms of sensor output data. We show that the forces obtained from disjunctive dynamics are comparable with existing force allocations and, hence, are possibly realizable in the existing hardware framework toward enhancing the safety and fault tolerance.

Design trade-offs for energy regeneration and control in vehicle suspensions

This paper investigates the fundamental trade-offs involved in designing energy-regenerative suspensions, in particular, focusing on efficiency of power extraction and its effect on vehicle dynamics and control. It is shown that typical regenerative devices making use of linear-to-rotational elements can be modelled as a parallel arrangement of an inerter and a dissipative admittance. Taking account of typical adjustable parameters of the generator, it is shown, for a given suspension damping coefficient, that the power efficiency ratio scales with inertance. For a typical passenger vehicle, it is shown that there is a feasible compromise, namely that good efficiency is achievable with an inertance value that is not detrimental to vehicle performance. A prototype is designed and tested with a resistive termination and experimental results show good agreement between ideal and experimental admittances. The possibility to use dynamic (rather than purely resistive) loads to improve vehicle control without limiting the energy recovery is discussed. © 2013 Copyright Taylor and Francis Group, LLC.

Model Predictive Control for Vehicle Stabilization at the Limits of Handling

Recent developments in vehicle steering systems offer new opportunities to measure the steering torque and reliably estimate the vehicle sideslip and the tire-road friction coefficient. This paper presents an approach to vehicle stabilization that leverages these estimates to define state boundaries that exclude unstable vehicle dynamics and utilizes a model predictive envelope controller to bound the vehicle motion within this stable region of the state space. This approach provides a large operating region accessible by the driver and smooth interventions at the stability boundaries. Experimental results obtained with a steer-by-wire vehicle and a proof of envelope invariance demonstrate the efficacy of the envelope controller in controlling the vehicle at the limits of handling.

Large school bus design vehicle dimensions.

Arkansas State Highway and Transportation Department, Little Rock

Computer simulation of the effect of road roughness on tire-pavement forces for an articulated vehicle performing braking and cornering maneuvers. Phase report.

Federal Highway Administration, Washington, D.C.