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TRIP-ID: A tool for a smart and interactive identification of Magic Formula tyre model parameters from experimental data acquired on track or test rig
Abstract
Tyres play a key role in ground vehicles' dynamics because they are responsible for traction, braking and cornering. A proper tyre-road interaction model is essential for a useful and reliable vehicle dynamics model. In the last two decades Pacejka's Magic Formula (MF) has become a standard in simulation field.
This paper presents a Tool, called TRIP-ID (Tyre Road Interaction Parameters IDentification), developed to characterize and to identify with a high grade of accuracy and reliability MF micro-parameters from experimental data deriving from telemetry or from test rig. The tool guides interactively the user through the identification process on the basis of strong diagnostic considerations about the experimental data made evident by the tool itself. A motorsport application of the tool is shown as a case study.
... The state-of-the-art validation model has been developed by Maserati in the context of real vehicle development, the virtual vehicle was driven by the MaxPerformance algorithm in the circuit of Balocco in dry road conditions, aiming for the lowest lap time possible. Simulation data offer the knowledge of all the time-varying variables and tyre characteristics, contrarily from experimental one, where quantities referring to adhesion condition and tyre cornering stiffness are actually unknown, despite they can be identified with offline procedures [38,39]. Those results were obtained by running the estimator at 100 Hz, adding artificial white noise to all the sensors. ...
... The described comparison is shown in Figures 7-9. To replicate experimental operating conditions, where tyre dynamic behaviour is usually unknown, tyre parameters initially set in the EKF estimator were not the same ones adopted in simulation, whose parameters in their turn were identified with the already cited procedure that is available in experimental context [39,42]. The above-mentioned methodology is able to guarantee that the differences between the estimation accuracy achieved in simulation and in experimental scenarios are minimum. ...
... Cornering stiffnesses K 1 and K 2 decrease over time due to tyres heating, particularly relevant for rear stiffness K 2 . This behaviour is coherent with expectations and with the offline analyses performed with [39,42], and will result on a slight increase of side-slip angle lap over lap. In the test shown, there are no observability issues, since the tyre is excited on all its working range, and the vehicle is never on steady state for long periods. ...
This work describes the development of a vehicle state estimator, designed to be employed onboard in real-time, based on the data acquisitions already available within the vehicle CAN bus infrastructure. The proposed estimation algorithm, taking into account the suspension elasto-kinematics, the longitudinal, lateral and combined dynamics of the tyres as well as the aligning interaction torques at the ground, represents at the current stage a significantly complete tool, since it also provides an estimation of road slope and banking angles, generalising the adoption of the presented vehicle model even on highly inclined roads. A further advantage of the presented estimator consists of its capability to identify in real-time and with a good level of accuracy the tyre/road interaction physical characteristics in terms of grip and cornering stiffness.
... The potential risks, related with the employment of empirical models, are linked with their parametrisation and the quality of data, since the adoption of numeric data-based techniques makes it possible to completely misinterpret the tyre behaviour even in case of a good fitting towards experimental results. In the literature, several approaches have been proposed to calibrate the Pacejka's model on the experimental data: in [31], a regression method, requiring a pre-determined reliable set of starting values to enable the optimisation process, has been proposed; in [32], the differential evolution algorithm has been presented, but it is still likely to fall into the local minimum; in [33], a method based on genetic algorithm has been employed to identify the MF parameters; in [34], the authors have adopted a technique solely identifying the Pacejka's scaling factors; in [21,23], a constrained regression method on the experimental indoor data has been adopted; in [35], a hybrid optimisation method, employing a genetic algorithm to solve the approximate optimal solution and a numerical optimisation algorithm to find the accurate optimal parameters' set, has been proposed; in [36], to overcome the difficulties of finding the global minimum with a limited number of iterations, a self-adaptive differential evolution optimisation algorithm (NSADE) has been designed and compared with the traditional Levenberg-Marquardt method; in [37], the author tackles the possibility to enrich the experimentally acquired dataset using Lagrange, Hermite and Spline interpolation curves, and proposes the non-linear research method on the resulting reconstructed points; in [38], the modification of the Magic Formula parameters, including the effects of road composition and tyre type, has been investigated; in [39], an integrated (TRIP-ID) tool to parametrise the standard MF micro-coefficients and to estimate micro/macro-parameters' calibration quality, comparing Pacejka's curves and tyre-road interaction characteristics for both indoor and outdoor data, has been described. ...
... In the case under study, since a distribution function isn't known and it cannot be identified a priori on the data, non-statistical or data-mining methodologies should be preferable. Furthermore, one of the main advances of the proposed technique compared to [39] regards the fact that any a-priori assumptions are assumed about the underlying data distribution. Data-mining methods do not require any prior assumptions about the data distribution and they are comparatively simple to implement, but the associated computational effort is not always negligible [42]. ...
... The model parameterisation problem can be reduced to a numerical optimisation one, which consists in a mathematical technique to find optima, minimum or maximum values of an objective function. The aim of an identification algorithm consists of finding a set of variables x minimising (or maximising) a chosen objective function in a research domain restricted by constraints G, H, and boundaries x l , x u [39,48]: ...
To cite this article: Aleksandr Sakhnevych (2021): Multiphysical MF-based tyre modelling and parametrisation for vehicle setup and control strategies optimisation, Vehicle System Dynamics, ABSTRACT Starting from the earliest phases of design of the vehicle and its control systems, the understanding of tyres is of fundamental importance to govern the overall vehicle dynamics. A properly charac-terised tyre-road interaction model is essential to achieve a reliable vehicle dynamics model on which more design variations can be studied directly in simulation environment optimising both cost and time. The possibility to count on computationally efficient and reliable formulations represents nowadays a great advantage, and the multiphysical Pacejka's Magic Formula (MF-evo) tyre model presented is one of the best trade-off solutions to meet the strict real-time requirements and to reproduce multiphysical variations of the tyre dynamic behaviour towards temperature, pressure and wear effects. A specific methodology has been developed to characterise and to identify the MF-evo parameters with a high grade of accuracy and reliability directly from experimental data. The proposed technique is based on a pre-processing procedure to remove non-physical outliers and to cluster the data, which allows to optimise the multidimensional parameterisation process. To the purpose of validation of the parametrisation routine, data from a motorsport case, exceptionally difficult to reproduce in simulation due particularly significant variations of the tyre dynamics during a single test, have been employed demonstrating the MF-evo model potential and robustness. ARTICLE HISTORY
... In particular, the relationship between interaction forces and the cited input variables is highly influenced by further effects, linked to tire temperature, tread wear, compound viscoelastic characteristics and road roughness. Among these, the influence that the thermal conditions of the different layers constituting the global thickness of tires have on the friction and on their stiffness characteristics, is highly significant and definitely not negligible in case a full reliability of the vehicle dynamics simulations is required, especially in motorsport applications [4]. The paper illustrates the basic concepts linked to the development of a novel version of a MFbased formulation, able to take into account uncommon factors affecting tire/road interaction. ...
... The paper illustrates the basic concepts linked to the development of a novel version of a MFbased formulation, able to take into account uncommon factors affecting tire/road interaction. Once described the structure and the parameters identification process [4], some results obtained with the MF-evo employed in a simulative loop with a thermal model are reported. ...
... For this reason, at the current stage, a tire characterization suite including both the characterization procedures and the software set of tools have been developed to overcome the difficulties linked to the deeper understanding of the tire behaviour and to the identification of the physical quantities necessary to properly parameterise all the physical models. The developed set of tools comprises an interaction forces estimator based on vehicle outdoor acquisitions, called TRICK [10], a "smart" parameters identifier developed for Pacejka formulations, called TRIP-ID [4], a real-time physical thermal model, called TRT [3][6] and a physical grip model, called GrETA [7]. ...
The characterization and reproduction of tire behaviour for vehicle modelling is a topic of particular interest both for real-time driving simulations and for offline performance optimization algorithms. In such contexts, the Pacejka’s Magic Formula (MF) tire model [1] represents a standard that gained in the last 25 years a role of high relevance due to its low computational request and attitude to allow an efficient parameterization for a wide range of tires working conditions. Nevertheless, the original MF formulation was conceived with the aim to provide tire/road interaction forces and moments as a function of vertical load, longitudinal and lateral slip, and inclination (or camber) angle; such variables are fundamental but not totally satisfying in the description of the complex multi-physical phenomena occurring at tire/road interface [2]. In particular, the relationship between interaction forces and the cited input variables is highly influenced by further effects, linked to tire temperature, tread wear, compound viscoelastic characteristics and road roughness. Among these, the influence that the thermal conditions of the different layers constituting the global thickness of tires have on the friction and on their stiffness characteristics, is highly significant and definitely not negligible in case a full reliability of the vehicle dynamics simulations is required, especially in motorsport applications [4]. The paper illustrates the basic concepts linked to the development of a novel version of a MF-based formulation, able to take into account uncommon factors affecting tire/road interaction. Once described the structure and the parameters identification process [4], some results obtained with the MF-evo employed in a simulative loop with a thermal model are reported.
... The intensification of the development of electric cars, which is related to decisions made by the European Parliament The idea itself is not new; until now, artificial neural networks and decision trees have mainly been used to identify the parameters of a tire model [14]and the influence that the conditions of pressure, load, and speed have on tire uniformity measurements [15]. These techniques have also already been used for the estimation of tire-road interactions [16] and to model tires for vehicle system dynamics and control prediction [17] or to analyze the forces acting on the tire [18,19]. The system of suspension-brakes-tire-surface is responsible for maintaining the vehicle's safe and stable trajectory [20]. ...
... The use of the described The idea itself is not new; until now, artificial neural networks and decision trees have mainly been used to identify the parameters of a tire model [14] and the influence that the conditions of pressure, load, and speed have on tire uniformity measurements [15]. These techniques have also already been used for the estimation of tire-road interactions [16] and to model tires for vehicle system dynamics and control prediction [17] or to analyze the forces acting on the tire [18,19]. The system of suspension-brakes-tire-surface is responsible for maintaining the vehicle's safe and stable trajectory [20]. ...
This article presents the current state and development directions of the tire industry. One of the main requirements that a tire must meet before it can leave the factory is achieving values of quantities describing uniformity at a defined level. Of particular importance areconicity and the components of the tire with the greatest impact on its value. This research is based on the possibility of using an ANN to meet contemporary challenges faced by tire manufacturers. In order to achieve a satisfactory level of prediction, we compared the use of a multi-layer perceptron and decision trees XGBoost, LightGbmRegression, and FastTreeRegression. Based on data analysis and similar examples from the literature, metrics were selected to evaluate the models’ ability to solve regression problems in relation to the described problem. We selected the best possible solution, standing at the top of the features covered by the criterion analysis. The proposed solutions can be the basis for acquiring new knowledge and contributions in the field of the computational analysis of industrial data in tire production. These solutions are characterized by the required accuracy and efficiency for online work, and they also contribute to the creation of the best fit elements of complex systems (including computational models). The results of this study will contribute to reducing the volume of waste in the tire industry by eliminating defective tire parts in the early stages of the production process.
... The Industry 4.0 paradigm is based on an assumption that technical inspections be performed at every stage of the production process as well as several times throughout the product life cycle. For the same reason, the use of computational analysis methods is on an upward trend [13][14][15][16][17][18]. Until now, artificial neural networks have been applied to identify tire model parameters [13] and identify tire parameters [14,15,16], or to analyze the forces acting on the tire [17,18]. ...
... For the same reason, the use of computational analysis methods is on an upward trend [13][14][15][16][17][18]. Until now, artificial neural networks have been applied to identify tire model parameters [13] and identify tire parameters [14,15,16], or to analyze the forces acting on the tire [17,18]. ...
The article presents actual challenges faced by tire manufacturers and contemporary industry. Directions of development of methods for detecting and eliminating defects generated in the tire production process were discussed, with particular emphasis on methods using artificial intelligence. An exemplary classification of tire defects is presented. It was noted that a solution to reduce the amount of tire waste due to exceeding the uniformity limits is needed. Quantities describing tire uniformity were characterized. In the frame of the main purpose of the research, it was checked whether the model based on a traditional artificial neural network (with one hidden layer) can predict the value of conicity (output variable) based on five input variables. To solve this problem, the authors used the Multi-Layer Perceptron (MLP) - machine learning method, due to its ability to train non-linear models in “almost real time”. The parameters of the network structure were determined to guarantee the achievement of root-mean-square error (RMSE) for the training set data at a very low, satisfactory level. The authors see the high potential of using the built model in the mass production of tires. Application of mentioned model will minimize the waste of time and tire components scraps, and also will actually improve the quality of the final product.
... Due to the lack of a steering wheel on the research vehicle, the traditional maneuvers used to collect data for vehicle model identification were not practical [20], [21]. We relied on information provided by the IAC organizers and tire and vehicle manufacturers, initially limiting our model to a static identification. ...
... In our work, the approach presented in [20] has been applied using data obtained by simulating ramp steer maneuvers at different speeds and road conditions in our Dymola simulator. 3) Validation: First experimental data on the real vehicle have been gathered using a simple Pure Pursuit path tracking algorithm [24] at a maximum speed of 45 m/s at IMS and performing a light warm-up maneuver at 25 m/s in the long straights of the track. ...
This paper presents a multi-layer motion planning and control architecture for autonomous racing, capable of avoiding static obstacles, performing active overtakes, and reaching velocities above 75 m/s. The used offline global trajectory generation and the online model predictive controller are highly based on optimization and dynamic models of the vehicle, where the tires and camber effects are represented in an extended version of the basic Pacejka Magic Formula. The proposed single-track model is identified and validated using multi-body motorsport libraries which allow simulating the vehicle dynamics properly, especially useful when real experimental data are missing. The fundamental regularization terms and constraints of the controller are tuned to reduce the rate of change of the inputs while assuring an acceptable velocity and path tracking. The motion planning strategy consists of a Frenét-Frame-based planner which considers a forecast of the opponent produced by a Kalman filter. The planner chooses the collision-free path and velocity profile to be tracked on a 3 seconds horizon to realize different goals such as following and overtaking. The proposed solution has been applied on a Dallara AV-21 racecar and tested at oval race tracks achieving lateral accelerations up to 25 m/s^2
... Due to the lack of a steering wheel on the research vehicle, the traditional maneuvers used to collect data for vehicle model identification were not practical [20], [21]. We relied on information provided by the IAC organizers and tire and vehicle manufacturers, initially limiting our model to a static identification. ...
... In our work, the approach presented in [20] has been applied using data obtained by simulating ramp steer maneuvers at different speeds and road conditions in our Dymola simulator. 3) Validation: First experimental data on the real vehicle have been gathered using a simple Pure Pursuit path tracking algorithm [24] at a maximum speed of 45 m/s at IMS and performing a light warm-up maneuver at 25 m/s in the long straights of the track. ...
This paper presents a multi-layer motion planning and control architecture for autonomous racing, capable of avoiding static obstacles, performing active overtakes, and reaching velocities above 75 m/s. The used offline global trajectory generation and the online model predictive controller are highly based on optimization and dynamic models of the vehicle, where the tires and camber effects are represented in an extended version of the basic Pacejka Magic Formula. The proposed single-track model is identified and validated using multi-body motorsport libraries which allow simulating the vehicle dynamics properly, especially useful when real experimental data are missing. The fundamental regularization terms and constraints of the controller are tuned to reduce the rate of change of the inputs while assuring an acceptable velocity and path tracking. The motion planning strategy consists of a Fren\'et-Frame-based planner which considers a forecast of the opponent produced by a Kalman filter. The planner chooses the collision-free path and velocity profile to be tracked on a 3 seconds horizon to realize different goals such as following and overtaking. The proposed solution has been applied on a Dallara AV-21 racecar and tested at oval race tracks achieving lateral accelerations up to 25 .
... However, this method cannot identify the longitudinal force and torque parameters. A tool called TRIP-ID was presented in Ref. [7]. The user could select the solver algorithm from the active set, pattern search, genetic algorithm (GA), and nonlinear least squares. ...
... Two typical multimodal functions, the Langermann and Damavandi, were selected as the objective functions [23][24] . The Langermann function has a local optimum f (7,9) = −3 and a global optimum in the opposite direction, which is suitable for testing an algorithm that can skip the local optimum and reach the global minimum. The Damavandi function is deceptive. ...
The magic formula (MF) tire model is a semi-empirical tire model that can precisely simulate tire behavior. The heuristic optimization algorithm is typically used for parameter identification of the MF tire model. To avoid the defect of the traditional heuristic optimization algorithm that can easily fall into the local optimum, a parameter identification method based on the Fibonacci tree optimization (FTO) algorithm is proposed, which is used to identify the parameters of the MF tire model. The proposed method establishes the basic structure of the Fibonacci tree alternately through global and local searches and completes optimization accordingly. The global search rule in the original FTO was modified to improve its efficiency. The results of independent repeated experiments on two typical multimodal function optimizations and the parameter identification results showed that FTO was not sensitive to the initial values. In addition, it had a better global optimization performance than genetic algorithm (GA) and particle swarm optimization (PSO). The root mean square error values optimized with FTO were 5.09%, 10.22%, and 3.98% less than the GA, and 6.04%, 4.47%, and 16.42% less than the PSO in pure lateral and longitudinal forces, and pure aligning torque parameter identification. The parameter identification method based on FTO was found to be effective.
... The track session has consisted of handling tests in the widest possible range of tyre operating conditions in terms of temperature, pressure, and wear level. Following the vehicle model parametrization and the tyre parameters' estimation procedures described in [36,37], the vehicle non-linear system has been completely characterized in all the conditions of interest, being able to faithfully reproduce the experimental data in the virtual environment. ...
... Figure 3 shows the comparisons between experimental data and model outputs shown on the classic a y − δ and a y − β diagrams. An aspect that is worth pointing out is the difference between the black dashed and continuous lines: the first one is obtained using the starting parameters provided by the research partner, the second one is obtained employing the calibration procedure described in [37]. In particular, the starting under-steering characteristics (dashed lines) have been revised better identifying the parameters linked to the anti-roll bars stiffness and the steering maps, leading to a less under-steering behavior within the handling diagram, in agreement with the experimental data. ...
In recent years the increasing needs of reducing the costs of car development expressed by the automotive market have determined a rapid development of virtual driver prototyping tools that aims at reproducing vehicle behaviors. Nevertheless, these advanced tools are still not designed to exploit the entire vehicle dynamics potential, preferring to assure the minimum requirements in the worst possible operating conditions instead. Furthermore, their calibration is typically performed in a pre-defined strict range of operating conditions, established by specific regulations or OEM routines. For this reason, their performance can considerably decrease in particularly crucial safetycritical situations, where the environmental conditions (rain, snow, ice), the road singularities (oil stains, puddles, holes), and the tyre thermal and ageing phenomena can deeply affect the adherence potential. The objective of the work is to investigate the possibility of the physical model-based control to take into account the variations in terms of the dynamic behavior of the systems and of the boundary conditions. Different scenarios with specific tyre thermal and wear conditions have been tested on diverse road surfaces validating the designed model predictive control algorithm in a hardware-in-the-loop real-time environment and demonstrating the augmented reliability of an advanced virtual driver aware of available information concerning the tyre dynamic limits. The multidisciplinary proposal will provide a paradigm shift in the development of strategies and a solid breakthrough towards enhanced development of the driving automatization systems, unleashing the potential of physical modeling to the next level of vehicle control, able to exploit and to take into account the multi-physical tyre variations.
... In particular, the proposed and optimized target tracking algorithms are applied in the field of intelligent transportation, making intelligent traffic closer to our lives. In computer vision, the target tracking algorithms mainly include Optical Flow [9], Cam-Shift [10], Template Matching [11], and Particle Filter [12]. The research of target tracking algorithm mainly focuses on the accuracy of target extraction, the success rate of target tracking, the running speed of target tracking algorithm, and how to effectively overcome the background environment interference. ...
... When the hidden layer is 4,5,6,7,8,9,10,14, and 15, the error cannot be within 10 À2 . When the Hidden layer is 11, 12, 13 layers, the error can be accurate to within 10 À2 . ...
Traffic sign recognition and lane detection play an important role in traffic flow planning, avoiding traffic accidents, and alleviating traffic chaos. At present, the traffic intelligent recognition rate still needs to be improved. In view of this, based on the neural network algorithm, this study constructs an intelligent transportation system based on neural network algorithm, and combines machine vision technology to carry out intelligent monitoring and intelligent diagnosis of traffic system. In addition, this study discusses in detail the core of the monitoring system: multi-target tracking algorithm, and introduces the complete implementation process and details of the system, and highlights the implementation and tracking effect of the multi-target tracker. Finally, this study uses case identification to analyze the effectiveness of the algorithm proposed by this paper. The research results show that the proposed method has certain practical effects and can be used as a reference for subsequent system construction.
... Several models have been developed over the years for the simulation of the response of tyres, including analytical/physical models such as the Brush models [1][2][3][4], semi-empirical models such as the so-called Magic Formula models [5][6][7][8][9] and complex finite-element models such as FTire and CDTyre [10,11]. ...
One of the most used tyre models is the so-called Magic Formula, which provides the contact forces and moments as a function of the tyre slips and normal load. Among the slip inputs, there is the spin–slip, which is defined as the combination of a camber component and a path-curvature component. The two components are related to each other by the camber reduction factor, for which only a few data have been reported in the literature. In addition, these data are often obtained from indirect measurements. In this work, an experimental procedure for the direct measurement of the camber reduction factor was devised, and applied to six specimens of motorcycle tyres (three front and three rear). The approach employs a rotating-disk machine, where the tyre is intrinsically subjected to path curvature. A specific aligning procedure to mitigate sideslip disturbances is introduced and employed during testing. The three specimens of the rear tyres tested showed a camber reduction factor that was close to zero, which is the typical result suggested by the literature. On the contrary, the three specimens of front tyres showed slightly negative values, i.e., the camber component increased with respect to the curvature component. The results suggest that the classic assumption of a zero camber reduction factor does not hold valid for all motorcycle tyres.
... However, when the tire slip angle of linear tire model exceeds four degrees, the model accuracy will decrease and the stability of vehicle may be affected. To solve the aforementioned problem, many researches have been proposed to design the lateral controller by using the nonlinear tire model, such as magic formula tire model [23], UniTire model [24] and brush tire model. Although all of the results show that the lateral control based on the nonlinear tire model can improve the accuracy of path tracking under certain conditions, most researches have ignored the effect of time-varying parameters within tire model. ...
In order to improve the trajectory tracking accuracy and vehicle lateral stability, the paper proposes a lateral and longitudinal dynamics control framework of autonomous vehicles considering multi-parameter joint estimation. First, the multi-parameter joint estimation based on adaptive unscented Kalman filter (AUKF) is constructed to decouple and estimate the longitudinal position of vehicle’s center of gravity (CG), tire-road friction coefficient (TRFC), tire cornering stiffness (TCS), tire vertical force (TVF) and road grade. Then, focusing on the large lateral acceleration condition, a lateral control based on the optimal front-tire lateral force is proposed by constructing the linear quadratic regulator (LQR) and combining the multi-parameter joint estimation. Additionally, a longitudinal control based on the drive and brake force compensation to realize the accurate speed tracking by combining road slop estimation is achieved. The fuzzy system employs the drive and brake force deviation as the input to implement the compensation of the throttle and brake. The proposed estimation and control framework are verified by co-simulation on PreScan and CarSim preliminarily. In order to further verify the effectiveness and practicability of algorithm, experiments are implemented on an autonomous vehicle platform, a hybrid Lincoln MKZ. Simulation and experimental results show that the proposed estimation and control framework possess excellent performance and enhance the tracking accuracy and lateral stability.
... Detailed circuit characteristics, such as their geometry or bumps and kerbs shape and location, are directly linked to the downforce levels, braking duty and tyre loads reachable under the defined set-up conditions. The teams generally run a large number of laps in the simulator, programmed with a variety of fuel loads and grip levels, to ensure as many scenarios as possible to be covered and to analyse as many race outcomes as possible (Farroni et al., 2018). ...
This chapter deals with tyre mechanics and it has a particular focus on thermal effects on its dynamical behaviour. In the first part the typical tyre structure is introduced together with the tyre mechanical/dynamical behaviour according to a classical approach, so recalling the main kinematic and dynamic quantities involved in tyre pure and combined interactions. The core of this chapter is the description of a physical-analytical tyre thermal model able to determine the thermal status in each part of the tyre useful for vehicle dynamics modelling and driving simulations in order to take into account thermal effects on tyre interactions and consequently on vehicle dynamical behaviour. Successively also the tyre wear modelling is faced, after a brief introduction to the different models available in literature some considerations are reported concerning the thermal effects on wear.
... The tire, as said, has been modelled adopting a simplified version of the MF, conceiving the sole pure tangential interactions and the macro-parameters. The reference tire parameters have been identified employing a sedan vehicle experimental data, processed by and innovative version of TRIP-ID tool [16], able to provide MF coefficients depending on temperature, replicating the variations on grip, stiffness and shape variations due to the effects of thermal phenomena on tread polymers and carcass behaviour [17]. Figure 2, the reference tire has been hypothesized as working for the whole simulated run at an average temperature corresponding to a friction level located in the increasing part of the grip/temperature performance curve. ...
The vehicle dynamic behaviour analysis is a crucial step for the evaluation of performance in terms of stability and safety. Tires play an important role by generating the interaction forces at each road-tire contact patch. The longitudinal and lateral dynamics are analysed by using instrumented vehicles with expensive high precision sensors to get a measurement of estimates of physical parameters of interest. This paper deals with the evaluation of vehicle under/oversteering behaviour and of braking performance using a Real-time (RT) simulator. The simulations were performed by using an efficient 15 Degrees of Freedoms (DOFs) Lumped-Parameter Full Vehicle Model (LPFVM), comprising a tire model with temperature-dependent properties. A virtual Driver-in-the-Loop (vDiL) scheme was used to perform test manouvers. The virtual driver is based on two PID regulators for speed and steering control. Finally, this paper reports the results of constant radius tests as defined by standard ISO4138 and of a braking manoeuvre. In both tests, a type-A road profile as defined by ISO 8608 standard was simulated.
... Farroni [15] used image processing and machine learning techniques to classify vehicles in dedicated lanes, extracted features such as windows and hollow areas to distinguish motorcycles from cars and selected K nearest neighbors and decision trees as classifier models that are robust to changes in environmental conditions. Bao [16] proposed a pseudo-long-term short-term memory (LSTM) classifier for single-image vehicle classification. ...
In recent years, researchers have proposed many methods to solve the problem of obstacle detection. However, computer vision-based vehicle detection and recognition technology is still not mature enough. This research combines machine learning technology to construct a traffic object recognition system and applies innovative technology to the computer vision recognition system to construct an automatic identification system suitable for current traffic demand and improve the stability of the traffic system. Moreover, this study uses a combination of a monocular camera and a binocular camera to sense the traffic environment and obtain vehicle position and velocity information. In addition, this study is based on the binocular stereo camera to find the obstacle space and obtain the obstacle relative to the position and speed of the vehicle and combine the obstacle space information to optimize the obstacle frame of the target vehicle. Through experimental research and analysis, it can be seen that the algorithm proposed in this study has certain recognition effect and can be applied to traffic object recognition.
... Modeling the tire-road interaction involves multiple aspects relevant to tire characteristics and to environmental factors, which make it a quite complex issue. Several tire models, e.g., the unified semi-empirical model [20], the magic formula model [21] and the Dugoff's model [22], have been developed with quite different properties. There is no doubt that modelbased control strategies rely heavily on precise mod-els to make accurate system predictions. ...
A hybrid model predictive control (HMPC) strategy is proposed in this paper to autonomously regulate intelligent vehicle longitudinal velocity considering nonlinear tire dynamics. Since the tire longitudinal dynamics, which has significant influence on vehicle longitudinal velocity control performance, exhibits highly nonlinear dynamical behaviors, the piecewise affine (PWA) identification is conducted firstly based on experimental data to accurately model the tire longitudinal dynamics. On this basis, due to that the intelligent vehicle needs to be operated in two distinct modes (drive and brake) for autonomous velocity regulation and because of the affine submodel switching behaviors of the PWA-identified tire model, the intelligent vehicle longitudinal dynamics control process considered in this work can be regarded as a hybrid system with both continuous variables and discrete operating modes. Thus, the mixed logical dynamical framework is further used to model the intelligent vehicle longitudinal dynamics, and a HMPC controller, which allows us to optimize the switching sequences of the operation modes (binary control inputs) and the torques acted on the wheels (continuous control inputs), is tuned based on online mixed-integer quadratic programming. Simulation results finally demonstrate the effectiveness of the proposed HMPC controller for intelligent vehicle longitudinal velocity regulation under typical driving conditions.
... Such torque-vectoring-based DYCs were experimentally assessed on electric vehicles with multiple motors. These controllers require the design engineer to define reference yaw rate characteristics, which are based on the desired level of understeer [16,17] and/or energy efficiency considerations [18][19][20], and depend on vehicle geometry, tire-road friction conditions [21], vehicle states, and driver inputs [16]. The reference yaw rate is usually compared online to the measured yaw rate, providing the basis for the calculation of the direct yaw moment [22]. ...
The handling characteristic is a classical topic of vehicle dynamics. Usually, vehicle handling is studied by analyzing the understeer coefficient in quasi-steady-state maneuvers. In this paper, experimental tests are performed on an electric vehicle with four independent motors, which is able to reproduce front-wheel-drive, rear-wheel-drive and all-wheel-drive (FWD, RWD and AWD, respectively) architectures. The handling characteristics of each architecture are inferred through classical and new concepts. The study presents a procedure to compute the longitudinal and lateral tire forces, which is based on a first estimate and a subsequent correction of the tire forces that guarantee the equilibrium. A yaw moment analysis is performed to identify the contributions of the longitudinal and lateral forces. The results show a good agreement between the classical and new formulations of the understeer coefficient, and allow to infer a relationship between the understeer coefficient and the yaw moment analysis. The handling characteristics vary with speed and front-to-rear wheel torque distribution. An apparently surprising result arises at low speed: the RWD architecture is the most understeering configuration. This is discussed by analyzing the yaw moment caused by the longitudinal forces of the front tires, which is significant for high values of lateral acceleration and steering angle.
... 11,13,14 In this case, the greatest challenge engineers tackle adopting the empirical models concern the tedious identification process of a suitable coefficient parameters set on the basis of tests to be carried out for each tire in analysis. 15,16 The second approach involves physical system modeling, with its geometrical and physical characteristics, resulting in obviously more onerous from the computational point of view, but it also allows a deeper understanding of the complex phenomena related to the tire behavior in its interaction with vehicle and road. 17,18 Several papers found in the literature refer to the tire modeling using the finite element method (FEM), [19][20][21] which, due to a particularly significant computational load, are adopted to evaluate static characteristics, stiffness, resonant frequencies, and vibration modes. ...
A tire is an extremely integrated and multi-physical system. From only a mechanical point of view, tires are represented by highly composite multi-layered structures, consisting of a multitude of different materials, synthesized in peculiar rubber matrices, to optimize both the performance and the life cycle. During the tire motion, due to the multi-material thermodynamic interaction within the viscoelastic tire rubber matrix, the dynamic characteristics of a tire may alter considerably. In the following paper, the multibody research comfort and handling tire model is presented. The main purpose of the research comfort and handling tire is to constitute a completely physical carcass infrastructure to correctly transmit the generalized forces and torques from the wheel spindle to the contact patch. The physical model structure is represented by a three-dimensional array of interconnected nodes by means of tension and rotational stiffness and damper elements, attached to the rim modeled as a rigid body. Research comfort and handling tire model purpose is to constitute a structural physical infrastructure for the co-implementation of additional physical modules taking into account the modification of the tire structural properties with temperature, tread viscoelastic compound characteristics, and wear degradation. At the stage, the research comfort and handling tire discrete model has been validated through both static and dynamic shaker test procedures. Static test procedure adopts contact sensitive films for the contact patch estimation at different load and internal pressure conditions, meanwhile the specifically developed sel test regards the tire dynamic characterization purpose at the current stage. The validation of the tire normal interaction in both static and dynamic conditions provided constitutes a necessary development step to the integration of the tangential brush interaction model for studying the handling dynamics and to the analysis of the model response on the uneven surfaces.
... Since the motion of a ground vehicle is primarily determined by the friction forces transferred from roads via tyres, information about the tyre/road interaction is critical to many active vehicle safety control systems, including longitudinal control, yaw stability control and rollover prevention control systems. In particular friction formation is crucial tool for Brake Assist Systems (BAS), Electronic Stability Control (ESC-ESP) and Adaptive Cruise Control (ACC) systems that have recently become essential for active safety systems, as shown in [1][2][3][4][5]. For instance, in the case of adaptive cruise control, estimation of friction force enables the braking distances to be adjusted in real time. ...
To guarantee the braking performance and safety of electric vehicles (EVs) and to improve their regenerative energy performance, a regenerative braking recuperation control strategy based on hierarchical coordinated control of an electrohydraulic brake system (eBooster) is proposed in this paper. First, considering the EV braking system characteristics, the eBooster model, vehicle dynamics model and energy recuperation model are established. Then, a hierarchical coordinated control strategy (HCCS) is proposed, and the top-level controller based on model predictive control (MPC) reasonably coordinates the braking torque according to the control objectives and constraints. Additionally, as per the eBooster characteristics, the bottom-level controller adopts a double closed-loop controller to improve the control accuracy and response speed. Finally, verification in the Simulink/AMESim joint simulation environment shows that the eBooster and the HCCS enable combined regenerative and hydraulic braking, which improves brake safety and performance.
Tire dynamics model is the basis of vehicle dynamic performance research, however, due to the limitation of safety and environmental conditions, the six-component physical test can not fully characterize the dynamic mechanical response characteristics of tire under special conditions such as low service inflation pressure, high load, and large range of operation temperature. To accurately describe the dynamic response of the tire under special operating conditions with the magic formula (MF) tire model, this paper combines the nonlinear finite element analysis and the experimental test. The finite element model of the tire is verified by the dynamic characteristic experiments, and the tire dynamics simulation under special operating conditions are also conducted based on the verification results. The MF tire model is modified and the parameter identification is performed for the prediction results to extend the operating conditions of the tire dynamic model. The results of the comparison show that the method proposed in this paper can realize the condition expansion of MF tire model under special conditions.
Smart power grid is a two-way interconnected network in which information plays a fundamental role in the process of energy transmission and distribution. The smart grid is based on combining ICT with the processing capabilities of computers and electrical systems to increase communication between users. However, smart grids are exposed to a variety of malicious cyber-attacks that can lead to the destruction of basic infrastructure and disrupt communication between the grid and users. Meanwhile, by authenticating the authenticated users, cyber-security can be created in the smart grid. One of the main components of a smart power grid is smart meters. However, to maintain security in a communication, smart meter authentication alone is not enough and it must be ensured that the electricity company’s server is not forgery. Therefore, there is a need for two-way authentication between the smart meter on the home side and the electricity company server. The present work provides a key management layout (based on the elliptic curve cryptography) with two-way authentication for communication outside the home area network The proposed solution is two-way authentication among the smart meter and the security associate in the power company. In other words, the proposed methodology creates a solution to establish a connection between valid users and the smart grid. The proposed protocol evaluates the behavior of cyber-attacks on the smart grid. Attacks such as man-in the middle attacks and retransmission attacks are considered. It was found that, the proposed methodology improves the reliance between smart grid and authenticated users with the increase of secure communications. Moreover, the proposed protocol can prevent an extensive experiment attack. The results also showed that, as the false factor increases, the detection time by the proposed algorithm increases. As the false factor increases from 0.1 to 0.3, the detection time increases by 1.4 s.
Accurate modeling of tire characteristics is one of the most challenging tasks. Many mathematical models can be used to fit measured data. Identification of the parameters of these models usually relies on least squares optimization techniques. Different researchers have shown that the proper selection of an initial set of parameters is key to obtain a successful fitting. Besides, the mathematical process to identify the right parameters is, in some cases, quite time-consuming and not adequate for fast computing. This paper investigates the possibility of using Artificial Neural Networks (ANN) to reliably identify tire model parameters. In this case, the Pacejka's "Magic Formula" has been chosen for the identification due to its complex mathematical form which, in principle, could result in a more difficult learning than other formulations. The proposed methodology is based on the creation of a sufficiently large training dataset, without errors, by randomly choosing the MF parameters within a range compatible with reality. The results obtained in this paper suggest that the use of ANN to directly identify parameters in tire models for real test data is possible without the need of complicated cost functions, iterative fitting or initial iteration point definition. The errors in the identification are normally very low for every parameter and the fitting problem time is reduced to a few milliseconds for any new given data set, which makes this methodology very appropriate to be used in applications where the computing time needs to be reduced to a minimum.
The performance of the vehicle’s active safety systems depends on accurate knowledge of the vehicle state, and the frictional forces resulting from tyre contact and the road surface. This paper aims to estimate the vehicle states and tyre-road coefficient of friction through and Extended Kalman Filter (EKF), integrated with the Double-Track model and the Pacejka Magic Formula that allows knowledge of the lateral force of the tyre. Besides, this approach can estimate the overall coefficient of lateral friction on each side of the vehicle, left and right respectively. Simulations based on a reference vehicle model are performed on different road surfaces and driving manoeuvres to verify the effectiveness of the proposed estimation method, in order to obtain good performance from different vehicle control systems.
Measuring and modeling vehicle response delays is a fundamental prerequisite for dynamic simulations, both in real-time driving platforms and in offline systems. With a human driver the delays have a heavy influence on the driving feeling and for the achievement of the optimal lap times. If artificial intelligence is driving, lap times can be improved by using algorithms able to calculate vehicle states, whose reliable reproduction is deeply linked to the delay’s evaluation.
Soft robots have been extensively studied for their ability to provide both good performance and safe human-robot interaction. In this paper, we present and compare the performance of two model-based control techniques with the common aim to independently and simultaneously control position and stiffness of a pneumatic soft robot’s joint. The dynamic system of a robot arm with flexible joints actuated by a pneumatic antagonistic pair of actuators, so-called McKibben artificial muscles, will be regarded, while its dynamic parameters will be considered imprecise. Simulation results are provided to verify the performance of the algorithms.
Measurement of tire deformation is a hot spot in the research of intelligent tire, which not only provides deep insights into the mechanism of generating tire forces and moments, but also has a significant influence on assessing the health condition of bridges. This paper proposed a tire deformation measurement method by monitoring tire hoop strain with long-gauge Fiber Bragg Grating (FBG) sensors, which can achieve real-time continuous measurement of the tire deformation by the modified conjugate beam method. Taking advantage of the FBG sensor’s high sensitivity, high durability and macro–micro, the modified conjugate beam method transforms the problem of solving the tire deformation into a more convenient solution to the bending moment of the conjugate structure. Intelligent bridge impact vehicle experiments and high-speed experiment were carried out to validate the proposed method, from which the estimated tire deformations under different wheel loads and tire pressures show good agreements with reference measurements.
In the field of path tracking control for wheeled mobile robots, researchers generally believe that the motion of robots meets non-holonomic constraints. However, the robot may sideslip by centrifugal force when it is steering. This kind of slip is usually uncontrollable and dangerous. In order to prevent sideslip and improve the performance of path tracking control, we propose a controller based on tire mechanics. Moreover, the new controller is based on model predictive control, and this control method has proven to be suitable for path tracking of wheeled mobile robots. The proposed controller was verified by simulation and compared with a model predictive controller based on kinematics (non-holonomic constraints). As for the simulation results, the maximum values of displacement error, heading error, lateral velocity, and slip angle of the dynamic-based model predictive controller are 0.2086m, 0.1609rad, 0.1546m/s, and 0.0576rad, respectively. Compared with the kinematics-based model predictive controller, the maximum values of the above parameters of the dynamic-based controller reduce by 86.55%, 72.25%, 96.30%, and 90.02%, respectively. The above results show that the proposed controller can effectively improve the accuracy of path tracking control and avoid sideslip.
In this study, combining the membrane feature with inflation pressure and the structural deformation caused by sidewall curvature, rigid-elastic coupling tyre model with analytical multi-stiffness sidewall is proposed for a heavy-loaded radial tyre with a large section ratio. The membrane pre-tension of sidewall arc resulting from inflation pressure is investigated. By means of virtual work principle, the structural deformation of sidewall curved arc resulting from the arc curvature, including stretching, bending and shearing deformation is derived. The structural stiffness caused by the sidewall curvature and membrane pre-tension caused by the inflation pressure are combined for the multi-stiffness sidewall model. The influence of the sidewall structural and geometrical parameters on the sidewall multi-stiffness, modal resonant frequency and transfer function is researched and discussed. The non-linear characteristic of sidewall multi-stiffness with respect to the sidewall radial deformation is investigated. Experimental and theoretical results show that: (1) the multi-stiffness of sidewall can characterise the membrane-tension stiffness caused by inflation pressure and the structural stiffness led by the sidewall curvature and material properties; (2) the different multi-stiffnesses of upper and lower sidewall arcs results from the different interval angles; (3) the multi-stiffness of sidewall is non-linear to the radial sidewall deformation. Taking the flexible deformation of tyre carcass and the analytical multi-stiffness of tyre sidewall into consideration, rigid-elastic coupling tyre model with multi-stiffness sidewall is suitable for the heavy-loaded radial tyre with a large section ratio or tyres under impulsive loading and large deformation.
Fully electric vehicles with individually controlled drivetrains can provide a high degree of drivability and vehicle safety, all while increasing the cornering limit and the ‘fun-to-drive’ aspect. This paper investigates a new approach on how sideslip control can be integrated into a continuously active yaw rate controller to extend the limit of stable vehicle cornering and to allow sustained high values of sideslip angle. The controllability-related limitations of integrated yaw rate and sideslip control, together with its potential benefits, are discussed through the tools of multi-variable feedback control theory and non-linear phase-plane analysis. Two examples of integrated yaw rate and sideslip control systems are presented and their effectiveness is experimentally evaluated and demonstrated on a four-wheel-drive fully electric vehicle prototype. Results show that the integrated control system allows safe operation at the vehicle cornering limit at a specified sideslip angle independent of the tire-road friction conditions.
Designers and technicians involved in vehicle dynamics face during their daily activities with the need of reliable data regarding tyres and their physical behaviour. The solution is often provided by bench characterizations, rarely able to test tyres in real working conditions as concerns road surface and the consequential thermal and frictional phenomena. The aim of the developed procedure is the determination of the tyre/road interaction curves basing on the data acquired during experimental sessions performed employing the whole vehicle as a sort of moving lab, taking into account effects commonly neglected.
A theoretical tyre model was developed analytically using the proposed middle plane for predicting the three-dimensional global tyre wear qualitatively and quantitatively as a function of the road roughness and the dynamic characteristics of the vehicle. Diagrams of the tyre wear pattern across the tyre width and along the tyre circumference were drawn for different road roughnesses, camber angles and vehicle dynamic characteristics. The numerical results show how the three-dimensional tyre wear pattern varied when these factors changed. Numerical calculations also reveal that a unique wear pattern may be caused by the system’s inherent dynamic features, e.g. the modal shape. In addition, a sensitivity analysis shows that the slip ratio, the longitudinal stiffness, the tyre width, the velocity and the vertical force have the greatest effects on the frictional dissipation energy, in that order. With the established wear model, good tyre wear distribution predictions can be given qualitatively and quantitatively for the rolling surface of the tyre. Moreover, guidelines for obtaining less tyre wear are provided for tyre and car manufacturers.
Nowadays, application of active control systems in vehicles has been developed in order to increase safety and steerability. In these systems, using an appropriate dynamic model can be very effective in increasing the accuracy of simulations and analysis. Tire-road forces are crucial in vehicle dynamics and control since they are the only forces that a vehicle experiences from the ground and have maximum uncertainty on vehicle dynamic model. In order to simulate the non-linear regimes of vehicle motion, the ‘Pacejka’ tire model is being utilized. In this paper, a dynamic model with Dual Unscented Kalman Filter algorithm has been utilized to identify the lateral forces, side slip angle, and normal forces of tires. In order to solve the non-linear least squares problem, these parameters were given as input to the hybrid Levenberg–Marquardt and quasi Newton algorithm to find the Pacejka tire model coefficients in the offline mode. Four degrees of freedom vehicle model combined with Pacejka tire model are used for simulation in various maneuvers. Results show appropriate compatibility with CarSim software.
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THE MORE YOU KNOW VEHICLE DYNAMICS, THE MORE YOU'LL BE SURPRISED
Vehicle dynamics is often perceived as a quite intuitive subject. As a matter of fact, lots of people are able to drive a car. Nevertheless, without a rigorous mathematical formulation it is very difficult to truly understand the physical phenomena involved in the motion of a road vehicle.
In this book, mathematical models of vehicles are developed, always paying attention to state the relevant assumptions and to provide explanations for each step. This approach allows for a deep, yet simple, analysis of the dynamics of vehicles, without having to resort to foggy concepts. The reader will soon achieve a clear understanding of the subject, which will be of great help both in dealing with the challenges of designing and testing new vehicles and in tackling new research topics.
However, there is much more than that. Quite surprisingly, it is shown that several classical concepts, such as the understeer gradient or the roll axis, are either wrong or inadequate and need to be replaced.
The book covers handling and performance of both road and race cars. A new approach, called MAP (Map of Achievable Performance), is presented and thoroughly discussed. It provides a global and intuitive picture of the handling features of a vehicle. Moreover, the book also deals with several relevant topics in vehicle dynamics that have never been discussed before. Even very experienced people should find the book interesting and stimulating.
This new book is not a translation of the Italian Dinamica del Veicolo; by the same author. Actually, in some sense, this new book is totally different, with new topics and with new points of view for the topics covered in the Italian book as well.
In the paper a new physical tyre thermal model is presented. The model, called Thermo Racing Tyre (TRT) was developed in collaboration between the Department of Industrial Engineering of the University of Naples Federico II and a top ranking motorsport team.
The model is three-dimensional and takes into account all the heat flows and the generative terms occurring in a tyre. The cooling to the track and to external air and the heat flows inside the system are modelled.
Regarding the generative terms, in addition to the friction energy developed in the contact patch, the strain
energy loss is evaluated. The model inputs come out from telemetry data, while its thermodynamic parameters come either from literature or from dedicated experimental tests.
The model gives in output the temperature circumferential distribution in the different tyre layers (surface,
bulk, inner liner), as well as all the heat flows.
These information have been used also in interaction models in order to estimate local grip value.
In this paper an experimental test rig aimed to characterize mechanical properties of a pneumatic tyre, together with some results, is presented.
The objective is to determine tyre mechanical characteristics useful to physically model its behaviour; in particular: the normal interaction characteristic, the radial stiffness, the total stiffness and the longitudinal hysteretic cycles.
To this aim two different kind of tests have been executed: radial and longitudinal.
In the radial test the load is statically applied to the tyre, along the vertical direction, by means of an hydraulic press and it is measured together with the consequent radial deformation, so allowing the estimation of the tyre normal interaction characteristic and of its radial stiffness. Different radial tests can be conducted for an assigned tyre varying the inflation pressure.
The longitudinal tests are conducted applying, under an assigned constant vertical load, a variable horizontal strain to the tyre by means of a linear actuator, two profile rail guides and a system to transfer the horizontal motion to the contact patch of the tyre, opportunely placed on a moving steel plate placed on the two linear guide rails. During the tests the horizontal load and the resulting deformations are measured and acquired so allowing the estimation of tyre total stiffness and of its longitudinal hysteretic cycles.
Longitudinal tests can be conducted varying the assigned vertical load, the horizontal displacement law in terms of frequency and amplitude, the tyre inflation pressure.
All the different types of rim can be mounted on the test rig thanks to a universal quick flange.
A new analytical–physical tyre model for which the paternity has to be ascribed to Professor Giuseppe Capone was developed at the Department of Mechanical Engineering for Energetics at Naples University ‘Federico II’ with the support of the Bridgestone Technical Centre Europe. The whole model allows to obtain the road–tyre interactions so it can be used in vehicle dynamic simulations. The model has been named Ph.An.Ty.M.H.A., acronym of ‘PHysical ANalytical TYre Model for Handling Analysis’ and it includes the normal, longitudinal and lateral tyre–road interaction. Considering that Ph.An.Ty.M.H.A. is an analytical ‘deductive’ model, it is necessary to develop it starting just from the normal interaction, described in this paper, and then the other ones will be described in future papers. In fact, the normal interaction, i.e. the relationship between the normal load and the normal deflection, influences the tangential (longitudinal plus lateral) one, which determines the vehicle handling behaviour. The parameters used in this model are physical and geometrical so they can be measured on the real tyre. This property allows to better understand the tyre–road interaction mechanism. The tyre behaviour is modelled by analytical expressions based on equilibrium conditions and geometrical relations. To reproduce the experimental normal interaction and the pressure distribution, once the tyre geometrical quantities are known, it is necessary to identify some parameters, related to the tyre structure, by a comparison with the experimental data. Moreover, the predictive ability of the whole model, combined with a vehicle model, is very careful in analysing the vehicle handling [J.C. Dixon, Tyres, Suspensions and Handling, Cambridge University Press, Cambridge, 1991].
In 2004, a new searching algorithm for Magic Formula tyre model parameters was presented. Now, a summary of the results, for pure and combined slip, that this algorithm is able to achieve is presented. The Magic Formula tyre model needs a set of parameters to describe the tyre properties. The determination of these parameters is dealt with in this article. A new method, called IMMa Optimization Algorithm (IOA), based on genetic techniques, is used to determine these parameters. Here, we show the computational cost that has been used to obtain the optimum parameters of every characteristic of the Magic Formula tyre model, called Delft Tyre 96. The main advantages of the method are its simplicity of implementation and its fast convergence to optimal solution, with no need of deep knowledge of the searching space. Hence, to start the search, it is not necessary to know a set of starting values of the Magic Formula parameters (null sensitivity to starting values). The search can be started with a randomly generated set of parameters between [0, 1]. Nowadays, MF-Tool, an application developed by TNO, uses an optimization technique to fit Magic Formula parameters from Matlab toolbox [van Oosten, J.J.M. and Bakker, E., 1993, {Determination of magic tyre model parameters}. Vehicle System Dynamics, 21, 19–29; van Oosten, J.J.M., Savi, C., Augustin, M., Bouhet, O., Sommer, J. and Colinot, J.P., 1999, {Time, tire, measurements, forces and moments, a new standard for steady state cornering tyre testing}. EAEC Conference, Barcelona, 30 June–2 July.]. We refer to that algorithm as the starting value optimization technique. The comparison between the optimization technique employed by TNO and the proposed IOA method is discussed in this article. In order to give a relative idea of adjustment accuracy, the sum-squared error and the mean-squared error, from the curves of the tyre model with the parameters optimized by both applications compared with test data are evaluated.
Summary Tyre behavior plays an important role in vehicle dynamics research. Knowledge of tyre properties is necessary to properly design vehicle components and advance control system. For that purpose mathematical models of the tyre are being used in vehicle simulation models. The Magic Formula Tyre Model is a semi-empirical tyre model which describes tyre behavior quite accurately. The Magic Formula Tyre Model needs a set of parameters to describe the tyre properties; the determination of these parameters is dealt with in this paper. A new method based on genetic techniques is used to determine these parameters. The main advantages of the method are its simplicity of implementation and its fast convergence to optimal solution, with no need of deep knowledge of the searching space. So to start the search, it is not necessary to know a set of starting values of the Magic Formula parameters. The comparison between analytical optimization methods and the method proposed is discussed in this paper.
. We consider the global and local convergence properties of a class of Lagrangian barrier methods for solving nonlinear programming problems. In such methods, simple bound constraints may be treated separately from more general constraints. The objective and general constraint functions are combined in a Lagrangian barrier function. A sequence of Lagrangian barrier functions are approximately minimized within the domain defined by the simple bounds. Global convergence of the sequence of generated iterates to a first-order stationary point for the original problem is established. Furthermore, possible numerical difficulties associated with barrier function methods are avoided as it is shown that a potentially troublesome penalty parameter is bounded away from zero. This paper is a companion to our previous work (see, Conn et al., 1991) on augmented Lagrangian methods. 1 Mathematical Sciences Department, IBM T.J. Watson Research Center, PO Box 218, Yorktown Heights, NY 10598, USA 2 C...
: This paper contains a new analysis for the Generalized Pattern Search (GPS) methods of Torczon and Lewis and Torczon. The two novel aspects are that the proofs are much shorter and simpler, and they use weaker dierentiability assumptions. Specically, under very mild conditions, the method nds an interesting limit point even if the objective function is not continuous and is even extended valued. If the objective is Lipschitz near the limit point, then appropriate directional derivatives of the objective are nonnegative. If the objective is strictly dierentiable at the limit point, then the gradient exists and the limit point satises the KKT conditions. Key words: Pattern search algorithm, linearly constrained optimization, surrogate -based optimization, nonsmooth optimization, derivative-free convergence analysis. Acknowledgments: Work of the rst author was supported by NSERC (Natural Sciences and Engineering Research Council) fellowship PDF-207432-1998 during a pos...
The tire and vehicle setup definition, able to optimise grip performance and thermal working conditions, can make the real difference as for motorsport racing teams, used to deal with relevant wear and degradation phenomena, as for tire makers, requesting for design solutions aimed to obtain enduring and stable tread characteristics, as finally for the development of safety systems, conceived in order to maximise road friction, both for worn and unworn tires. The activity discussed in the paper deals with the analysis of the effects that tire wear induces in vehicle performance, in particular as concerns the consequences that tread removal has on thermal and frictional tire behaviour. The physical modelling of complex tire–road interaction phenomena and the employment of specific simulation tools developed by the Vehicle Dynamics UniNa research group allow to predict the tire temperature local distribution by means of TRT model and the adhesive and hysteretic components of friction, thanks to GrETA model. The cooperation between the cited instruments enables the user to study the modifications that a reduced tread thickness, and consequently a decreased SEL (Strain Energy Loss) and dissipative tread volume, cause on the overall vehicle dynamic performance.
Filling the gaps between subjective vehicle assessment, classical vehicle dynamics and computer-based multibody approaches, The Multibody Systems Approach to Vehicle Dynamics offers unique coverage of both the virtual and practical aspects of vehicle dynamics from concept design to system analysis and handling development. The book provides valuable foundation knowledge of vehicle dynamics as well as drawing on laboratory studies, test-track work, and finished vehicle applications to gel theory with practical examples and observations. Combined with insights into the capabilities and limitations of multibody simulation, this comprehensive mix provides the background understanding, practical reality and simulation know-how needed to make and interpret useful models. New to this edition you will find coverage of the latest tire models, changes to the modeling of light commercial vehicles, developments in active safety systems, torque vectoring, and examples in AView, as well as updates to theory, simulation, and modeling techniques throughout. © 2015 Michael Blundell and Damian Harty. Published by Elsevier Ltd. All rights reserved.
The most powerful engine, the most sophisticated aerodynamic devices or the most complex control systems will not improve vehicle performances if the forces exchanged with the road are not optimized by proper employment and knowledge of tires. The vehicle interface with the ground is constituted by the sum of small surfaces, wide about as one of our palms, in which tire/road interaction forces are exchanged. From this it is clear to see how the optimization of tire behavior represents a key-factor in the definition of the best setup of the whole vehicle.Nowadays, people and companies playing a role in automotive sector are looking for the optimal solution to model and understand tire's behavior both in experimental and simulation environments. The studies carried out and the tool developed herein demonstrate a new approach in tire characterization and in vehicle simulation procedures. This enables the reproduction of the dynamic response of a tire through the use of specific track sessions, carried out with the aim to employ the vehicle as a moving lab.The final product, named TRICK tool (Tire/Road Interaction Characterization and Knowledge), comprises of a vehicle model which processes experimental signals acquired from vehicle CAN bus and from sideslip angle estimation additional instrumentation. The output of the tool is several extra "virtual telemetry" channels, based on the time history of the acquired signals and containing force and slip estimations, useful to provide tire interaction characteristics. TRICK results can be integrated with the physical models developed by the Vehicle Dynamics UniNa research group, providing a multitude of working solutions and constituting an ideal instrument for the prediction and the simulation of the real tire dynamics.
A new automotive controllable differential is proposed and tested, firstly in software environment and, successively, following a hardware in the loop procedure based on the employment of the physical prototype. The device is based on the employment of magnetorheological fluid, whose magnetization allows to generate the locking torque and, consequently, the corrective yaw moment. A vehicle model has been derived and adopted for the design of a yaw moment controller based on the sliding mode approach. Some feedbacks requested by the controller have been estimated by means of an extended Kalman filter. The obtained results show the effectiveness of the device in terms of vehicle dynamics improvement. Indeed, the results reached by the vehicle in presence of the new differential confirm the improved performances for both steady and unsteady state manoeuvres. Moreover, the hardware in the loop testing allows to overcome the limits due to the modelling of the differential, fully validating the physical prototype.
In this paper, we consider the problem of estimating unknown parameters of the so-called Pacejka's model of a tyre from measurements of the car behavior. Differently from other estimation problems, the tyre parameters may change during the car life due to tyre aging, the variability of the inflation pressure, or many further reasons. Rather then solving a single estimation problem, thus, the issue is to set-up an automatic estimator, able to to supply reliable estimates of the Pacejka's parameters for any type of tyre and any type of operating condition. Existing methods for parameter estimation have been conceived for the estimation of the value taken by the parameter in a given functioning condition, and are not suitable for the problem here considered. In this paper we present a novel approach, the TS (two-stage) approach, specifically tailored to the problem of returning accurate estimates notwithstanding the tyres changeability. We compare its performances with those achievable with other parameter estimation techniques such as Prediction Error and Kalman Filter based methods. It turns that the TS approach offers significant improvements.
This paper deals with the frictional behaviour of a tyre tread elementary volume in sliding contact with road asperities. Friction is supposed as composed by two main components: adhesion and deforming hysteresis. The target, fixed in collaboration with a motorsport racing team and with a tyre manufacturing company, is to provide an estimation of local grip for on-line analyses and real time simulations and to evaluate and predict adhesive and hysteretic frictional contributions arising at the interface between tyre tread and road. A way to approximate asperities, based on rugosimetric analyses on macro and micro scale, has been introduced. The adhesive component of friction has been estimated by means of a new approach based on two different models found in literature, whose parameters have been identified thanks to a wide experimental campaign previously carried out. The hysteretic component of friction has been estimated by means of an energy balance taking into account rubber viscoelastic behaviour, characterized by means of proper DMA tests, and internal stress / strain distribution due to indentation with road. Model results are finally shown and discussed and the validation experimental procedure is described. The correct reproduction of friction phenomenology and the model prediction capabilities are highlighted making particular reference to grip variability due to changes in working conditions.
The purpose of this paper is to provide an overview of the research that was conducted in the development of a virtual prototype of a real vehicle. For that purpose the ADAMS/CAR software was chosen because it is a sophisticated mechanical dynamic modelling tool typically used by some of the main car manufacturers. The main motivation of this virtual prototyping was to test different control techniques in an active suspension of a full scale vehicle model. This is a preliminary approach to the virtual prototyping process and how it can be used to solve forward and reverse engineering problems.
The paper presents an anti-lock braking system (ABS) control logic based on the measurement of the longitudinal forces at the hub bearings. The availability of force information allows to design a logic that does not rely on the estimation of the tyre–road friction coefficient, since it continuously tries to exploit the maximum longitudinal tyre force.The logic is designed by means of computer simulation and then tested on a specific hardware in the loop test bench: the experimental results confirm that measured wheel force can lead to a significant improvement of the ABS performances in terms of stopping distance also in the presence of road with variable friction coefficient.
The lateral tyre force versus slip angle and vertical load is obtained through specific tests on the single tyre or with a theoretical-empirical analysis with physical models. This study is about the possibility to use a third way: Executing a particular handling test, known as Force-Moment test, using a Flat Track Roadway Simulator (the Fiat-Elasis MTS FTRS). The understanding and the project of vehicle handling is strongly based on the knowledge of lateral tyre force response [1, 2, 3, 7].
A methodology is presented for identifying lateral tyre force dynamics by studying the vehicle dynamics. The methodology is based on the EKF (extended Kalman filter) and makes it possible to determine lateral tyre force dynamics on the basis of the results obtained from standard on-road handling manoeuvres. The experimental activity, a vehicle model, and an appropriate identification algorithm are described. The vehicle model has four degrees of freedom where the lateral tyre forces are described by the Magic formula with transient behaviour. The test vehicle is equipped with standard sensors used by vehicle and tyre manufacturers in handling manoeuvres. Handling tests are performed, and the results of standard tests are for off-line identification of the coefficients of lateral tyre dynamics using EKF data. The identified lateral tyre dynamics are validated, and the results show good agreement between simulation and measurement, which confirms the validity and accuracy of the estimated lateral tyre model.
This paper investigates the use of GPS to estimate vehicle sideslip and tire information. Both a one antenna GPS antenna/receiver and dual GPS antenna method are studied. Analysis of the accuracy that can be achieved using the two different GPS solutions is provided. The algorithms are then validated on a fully instrumented Infiniti G35 sedan. Experimental data is given showing the performance of the GPS based sideslip estimates compared against a simple bicycle model and a DatronTM velocity sensor. NOMENCLATURE r Vehicle yaw rate
Individual tire model parameters are traditionally derived from expensive component indoor laboratory tests as a result of an identification procedure minimizing the error with respect to force and slip measurements. These parameters are then transferred to vehicle models used at a design stage to simulate the vehicle handling behavior. A methodology aimed at identifying the Magic Formula-Tyre (MF-Tyre) model coefficients of each individual tire for pure cornering conditions based only on the measurements carried out on board vehicle (vehicle sideslip angle, yaw rate, lateral acceleration, speed and steer angle) during standard handling maneuvers (step-steers) is instead presented in this paper. The resulting tire model thus includes vertical load dependency and implicitly compensates for suspension geometry and compliance (i.e., scaling factors are included into the identified MF coefficients). The global number of tests (indoor and outdoor) needed for characterizing a tire for handling simulation purposes can thus be reduced. The proposed methodology is made in three subsequent steps. During the first phase, the average MF coefficients of the tires of an axle and the relaxation lengths are identified through an extended Kalman filter. Then the vertical loads and the slip angles at each tire are estimated. The results of these two steps are used as inputs to the last phase, where, the MF-Tyre model coefficients for each individual tire are identified through a constrained minimization approach. Results of the identification procedure have been compared with experimental data collected on a sport vehicle equipped with different tires for the front and the rear axles and instrumented with dynamometric hubs for tire contact forces measurement. Thus, a direct matching between the measured and the estimated contact forces could be performed, showing a successful tire model identification. As a further verification of the obtained results, the identified tire model has also been compared with laboratory tests on the same tire. A good agreement has been observed for the rear tire where suspension compliance is negligible, while front tire data are comparable only after including a suspension compliance compensation term into the identification procedure. [DOI: 10.1115/1.4003093]
We propose a new trust region approach for minimizing a nonlinear function subject to simple bounds. Unlike most existing methods, our proposed method does not require that a quadratic programming subproblem, with inequality constraints, be solved in each iteration. Instead, a solution to a trust region subproblem is defined by minimizing a quadratic function subject only to an ellipsoidal constraint. The iterates generated are strictly feasible. Our proposed method reduces to a standard trust region approach for the unconstrained problem when there are no upper or lower bounds on the variables. Global and local quadratic convergence is established. Preliminary numerical experiments are reported indicating the practical viability of this approach.
A set of scaling factors has been introduced by Pacejka into his `magic formula' tyre model to take into account the influence of a number of external overall parameters such as road roughness, weather conditions and suspension characteristics. These scaling factors are important for a correct prediction of tyre-road contact forces but are not a function of the tyre itself. From a different point of view, one could say that scaling factors should remain constant for different tyres on the same circuit, with the same weather conditions and with the same car. After having characterized different tyres through indoor tests (which do not consider external overall parameters) and after having identified Pacejka's coefficients with scaling factors assumed to be one, several outdoor experimental tests have been carried out to determine the influence of vehicle and road surface conditions on scaling factors. These experimental data allowed us to identify, through a minimization approach, the `best' set of Pacejka's scaling factors for that vehicle and that tyre on that track. Scaling factors for the same track and vehicle but for different tyres were compared to check whether their values remained constant. All experimental data shown in this paper comes from tests carried out within the VERTEC project (vehicle, road, tyre and electronic control systems interaction: increasing active vehicle safety by means of a fully integrated model for behaviour prediction in potentially dangerous situations) (official contract G3RD-CT-2002-00805), a European funded research project that puts together knowledge from vehicle manufacturers (Volvo, Porsche and (CRF)), tyre manufacturers (Pirelli and Nokian Tyres), control logic manufacturers (Lucas Varity GmbH), road maintenance experts (CETE), transport research organizations (TRL) and (VTI) and universities (HUT) and (UNIFI)). The results shown in this paper are obtained by tests performed during tasks 2a ( Reference tyre characterizations and tests ) and 2b ( Development and validation of tyre-pavement interaction model ) of VERTEC project. The partners involved in these tasks are Pirelli, Nokian, Porsche, CRF, CETE, VTI, HUT and UNIFI.
. The automotive industry and their suppliers will have to face increasing demands in term of fuel economy and safety in the next years and decades. Consistent improvements of vehicle safety could be obtained if accurate information of the interactions between road and tires could be extracted and transmitted to the vehicle in real time: new control logics can be defined and implemented to better utilize the new available information. The paper describes the two main directions of the research: both in the field of features extraction from sensors applied on the inner liner of a tire and their possible utilization to improve the present vehicle control systems. This activity has implied the realization of some facilities to easily implement and test new algorithms, such as hardware in the loop test bench of the ABS and ESP. 1 INTRODUCTION Chassis active systems are generally designed to support the driver to prevent accidents and at the same time increase vehicle dynamics performance. The design of active safety systems for passenger cars dates back to the eighties and it involved brakes, suspensions, steer and transmission. Due to the object of safety, the former applications regarded firstly the longitudinal dynamics improving acting, in particular, the vehicle stability through a more effective braking (ABS) and Traction Control (TC) systems. In nineties the Electronic Stability Control (ESC, ESP, VDC, IVD, DSC) added a significant increasing to the active safety acting, essentially, on brakes and engine torque to stabilize the vehicle in limit handling situations through controlling the yaw motion and, recently, the sideslip angle. Other chassis control systems act e.g. on roll bar (ARC), air spring, steering system (AFS), transmissions (AMT, DCT) with the object of safety and vehicle dynamics performance. Nowadays it seems that the performance obtainable using a stand-alone current chassis control system joined almost its target performance depending on the sensors actually available to support their control strategy. Usually an active chassis control strategy is based on estimation of fundamental characteristics quantities on the vehicle dynamics like, e.g., sideslip angle, slip, tire-road friction and forces applied. The performance could significantly increase if more detailed information could be real-time measured directly by new sensors economically sustainable. Many activities concerning the chassis control systems integration are in developing to overcome the fundamental problem of the lack of more information directly related to the vehicle dynamics. Nevertheless, it is well-known that the availability of either sideslip angle measurement or, especially, the forces applied in the contact between tire and road can increase significantly the chassis active system currently performed.
Rolling Tyre: Real-Time Detection of Patch-Contact and Dissipation
- N Roveri
- G Pepe
- F Coppo
- A Carcaterra
N. Roveri, G. Pepe, F. Coppo, A. Carcaterra, Rolling Tyre: Real-Time Detection of Patch-Contact and Dissipation, Conference paper, ID 602, ISMA 2016,
University of Leuven, Belgium, 2016.
An Evolved Version of Thermo Racing Tyre for Real Time Applications
- F Farroni
- A Sakhnevych
- F Timpone
F. Farroni, A. Sakhnevych, F. Timpone, An Evolved Version of Thermo Racing Tyre for Real Time Applications, World Congress on Engineering, London,
2015.