Estimation Of Friction Coefficient Research Articles

Study on vehicle state and tire–road friction coefficient estimation based on maximum correntropy generalized high-degree cubature Kalman filter

To cope with the challenges of inadequate precision and weak robustness of tire–road friction coefficient (TRFC) and vehicle state estimation under mixed Gaussian noise circumstances, this research puts forward a method combining maximum correntropy criterion (MCC) and generalized high-degree cubature Kalman filter (GHCKF). A coupled lateral and longitudinal vehicle model and the Dugoff tire model are established. The vehicle mass is estimated using the recursive least squares approach based on a forgetting factor (FFRLS). Low-cost onboard sensors are utilized to design observers for vehicle state and TRFC. The observers’ effectiveness is tested by Carsim/Simulink co-simulation tests under the conditions of sine steering input and steering wheel angle step input. The research results indicate that in handling mixed Gaussian noise environments, maximum correntropy generalized high-degree cubature Kalman filter (MCGHCKF) method outperforms maximum correntropy cubature Kalman filter (MCCKF), GHCKF, and cubature Kalman filter (CKF) methods concerning robustness and estimation accuracy, providing stable and reliable support for systems of vehicle active safety control.

Dynamic modeling, clutch parameter adaptation, and control of automatic transmission for tracked vehicles

In this study, a novel TCU control structure and algorithms including also dynamic model of the transmission will perform the gear shifting of automatic transmissions used in tracked military vehicles are designed. In case of inherent wear of the clutches, the clutch parameters are estimated by means of an adaptation algorithm that uses only the information from the transmission input and output speed sensors. These estimated clutch parameters are used in clutch torque calculation is utilized by control algorithms. For the clutch speed control in the inertia phase, a PID control structure with a negative feedforward term that cancels the nonlinearities of the system is proposed. The feedforward term utilizes the estimated wear clutch coefficients in the calculation of friction coefficients. The parameters of the PID controller are optimized by a genetic algorithm. The designed all structure are firstly tested on a MATLAB/Simulink power train simulation model, and then tested using a unique transmission on a transmission dynamometer test bench to examine its suitability for real transmission scenarios. The performances of proposed PID control and a backstepping nonlinear controller that we constructed for the tracked vehicles are compared with and without clutch wear. Maximum tracking error is decreased by 98% with proposed adaptive PID control structure with nonlinear feedforward term compare to backstepping controller. In the case of clutch wear, the back-stepping control exists in the literature has been found to result in oscillation. By updating the estimated friction coefficient from adaptation algorithm, in the backstepping controller, it is concluded that these oscillations can be eliminated. Additionally, on-off solenoid valves, are widely used, are known to cause torque interruptions and jerks during gear shifting. It has been observed the control structure presented in this study reduced the jerks by one quarter.

Tire Road Friction Coefficient Estimation for Individual Wheel Based on Two Robust PMI Observers and a Multilayer Perceptron

Tire Road Friction Coefficient Estimation for Individual Wheel Based on Two Robust PMI Observers and a Multilayer Perceptron

Estimation of road friction coefficient based on WOA-BP neural network

The road friction coefficient is often estimated based on vehicle dynamics models, but the ideal mathematical model is difficult to describe the actual vehicle operation, which in turn leads to deviations between the estimated friction coefficient and the actual situation. In order to take full account of the actual vehicle driving conditions, back propagation (BP) neural network model is often applied to assess the friction coefficient. To further improve the generalization ability of the network model, this paper proposes a method to predict the friction coefficient using the whale optimized algorithm-BP (WOA-BP) neural network model. The whale algorithm improves the weights and thresholds of the BP neural network model to improve generalization ability and convergence speed. First, the vehicle dynamics analysis is utilized to determine the vehicle dynamics parameters as a function of the friction coefficient. Then, the WOA-BP is compared against the BP under various realistic operating scenarios. The results demonstrate that the WOA-BP estimator is accurate and efficient in estimating the friction coefficient, and the proposed method reduces the mean absolute error by 51.9% and the root mean squared error by 49.1% compared to the BP.

Acceleration-based friction coefficient estimation of a rail vehicle using feedforward NN: validation with track measurements

Low friction can lead to poor adhesion conditions between the rail and wheel, which is detrimental to rail vehicle operation and safety. Up to date knowledge of the rail-wheel friction level is currently not available across rail networks, meaning planning mitigation strategies is difficult. This paper presents a real-time friction coefficient estimation algorithm based on a feed-forward neural network (FNN). Unlike conventional methods, the FNN does not depend on slip/adhesion curves or creep force models, and only requires wheelset longitudinal acceleration and speed. The wheelset acceleration and friction measurements are obtained by running a two-car rail vehicle on a friction-modified track with five different levels of friction conditions at four different vehicle speeds. Four different FNNs are trained for four speed conditions, and their estimation performance were validated by training multiple FNNs and testing them in each speed case using new sets of data. Validation results show that the average mean absolute errors from the four FNNs remains below 0.0083.

Enhanced Vehicle Dynamics and Safety through Tire–Road Friction Estimation for Predictive ELSD Control under Various Conditions of General Racing Tracks

This study focuses on the tire–road friction estimation for the predictive control strategy of electronically limited slip differential (ELSD) to improve the handling and acceleration performance of front-wheel drive cars, which typically suffer from excessive understeer and inner drive wheel spin during acceleration while turning due to reduced vertical load on the wheel. To mitigate this, we propose a control logic for ELSD that enhances course followability and acceleration by pre-transferring the driving torque from the inside to the outside wheel, considering the estimated traction potential for rapid response. It is essential to improve the control accuracy of wheel spin prediction by predicting the friction coefficient of the road surface. Furthermore, this study extends to the analysis of vehicle dynamics during lane-change maneuvers on low-friction surfaces, emphasizing the role of accurate tire–road friction estimation in vehicle safety. A CarSim 2023-based simulation study was conducted to investigate the vehicle response on snowy roads with low friction coefficients (μ = 0.2) and low temperatures (−5 °C). The results demonstrated that even minimal steering input could result in significant side-slip angles, highlighting the nonlinear vehicle behavior and the critical need for robust traction estimation in such challenging conditions of general racing tracks. The proposed friction-estimation method was evaluated through vehicle testing and has been substantiated by patents for its originality in control and friction-estimation approaches. The outcomes of these combined methodologies underline the critical importance of tire–road friction coefficient estimation in both the effectiveness of the ELSD system and the broader context of active safety systems.

Friction coefficient estimation before gross slip for slippage prediction during prosthetic hand grasping

Slippage feedback is critical for prosthetic or bionic robotic hand to realize steady grasp. An important way to judge the slippage is to detect the maximum coefficient of static friction (µs) which is commonly measured when or after gross slip happened. Here, we proposed a new method to estimate the µs before the gross slip in order to realize slippage prediction, leaving more time for the control system to adjust grasp force. Based on a finite element model, a good linear relationship (R2 = 0.99) between the global tangential force at the time when relative slip occurs on the monitoring point (GTFRS) and the µs was obtained. An optical experiment was conducted and verified the accuracy of the simulation result. Finally, a slip sensitive soft fingertip was fabricated and tested, results show µs estimation in samples of seven different roughness is well realized with average error of 6.68 %.

Modeling and Clamping Force Tracking Control of an Integrated Electric Parking Brake System Using Sliding-Mode-Based Observer

This article proposes a hierarchical control strategy to address semi-ABS control as well as the precise clamping force control problems for an integrated electric parking brake (iEPB) system. To this end, a detailed system model, including modeling of the motor, transmission mechanism, friction and braking torque, is constructed for controller and observer design, and a sliding-mode-based observer (SMO) is proposed to estimate the load torque by using the motor rotational speed without installing a force sensor. In addition, a stable and reliable tire–road friction coefficient (TRFC) estimation method is adopted, and the desired slip ratio (DSR) is observed as the target that the rear wheels cycle around. At the upper level of the hierarchical control structure, the desired clamping forces of the rear wheels are generated using a sliding mode control (SMC) technique, and the control objective is to track the DSR to make full use of the road condition. At the lower level, the motor is controlled to track the desired clamping force generated from the upper controller. The hardware-in-the-loop (HIL) experimental results demonstrate the effectiveness and high tracking precision of the proposed strategy under different road conditions, and the estimation parameters based on the proposed observers are timely and accurate to satisfy the control requirements.

A review of road surface recognition and tyre-road friction coefficient estimation methods

A review of road surface recognition and tyre-road friction coefficient estimation methods

Road friction estimation based on vision for safe autonomous driving

Road peak friction is a significant parameter determining vehicle driving safety. This paper focuses on road friction monitoring based on vision for autonomous vehicles. A deep learning classification model combined with training strategies adapted to the real-scenario road friction image dataset is proposed. The road peak friction coefficient is initially derived based on the classification probability and an empirical inference model. To enhance the usability and reliability of the estimated friction coefficient, a filter that concerns the classification model uncertainty and the variation of estimation output is then performed. The top-1 and top-2 classification accuracy on five road friction classes reach 94.84% and 99.22%, respectively. The developed friction preview scheme is further deployed and validated in real-vehicle scenarios. The results indicate that the proposed methods are robust to road environment change. It has potential in practical applications that provide crucial road information for safer autonomous driving.

Statistical analysis of entropy generation on the Maxwell-graphene based nanofluid passing through a squeezing channel

The present research focuses on the analysis of the flow behavior of a Graphene and Ethylene Glycol based nanofluid under the influence of magneto hydrodynamics (MHD) between two parallel plates that are being compressed or moved apart, considering the effect of thermal radiation. The study extensively investigates the system’s energy efficiency through the utilization of the Bejan number. To simplify the governing partial differential equations, a similarity transformation is employed, leading to a set of coupled non-dimensional ordinary differential equations. The numerical solution is obtained using the shooting technique in conjunction with the fourth-order Runge-Kutta method. Additionally, a statistical method is utilized to analyze the quadratic regression estimation of skin friction coefficients and Nusselt numbers, aiming to comprehend the connection between the rate of heat transfer and emerging flow parameters. Furthermore, the study examines the influence of various flow parameters viz. Magnetic field, Deborah number, squeezing parameter, radiation and Eckert number on nanofluid velocity, temperature, entropy generation (quantified by the Bejan number), skin friction coefficient, and heat transfer rate. As a result, this research holds promising applications in the fields of biomedical engineering automobile engineering and lubrication technology.

Mechanical Behavior of Seamless Pipes Using Ring Expansion Technique and Novel Hoop Stress Correlation Factor (K)

This study investigated the stress–strain behavior of seamless pipes in the hoop direction using the ring expansion test, which is a non-standardized mechanical testing technique used for evaluating the mechanical properties of round tubes. However, this technique has limitations, such as unidentified specimen geometry, strain measurement, and the estimation of friction coefficients. The study employed experimental, numerical, and analytical methodologies to address these limitations and throughout the study, a novel hoop stress correlation factor (K) was identified to be multiplied by the hoop stress derived equation for reduced section ring specimens. The experimental strain was measured using a newly derived analytical equation, and a mathematical predictive model was developed to estimate the K-factor using the Design of Experiment (DoE) and Design-Expert statistical software. The study concluded that the ring expansion test is a promising technique for evaluating the mechanical properties of seamless pipes similar to the unified axial tensile stress–strain behavior. However, future research is needed to estimate the hoop stress correlation value (K) for all ring geometries. The study's finding of the novel hoop stress correlation factor (K) in the case of a reduced section ring specimen is particularly noteworthy, as it addresses a significant research gap in the field.

Road friction coefficient estimation under low longitudinal, lateral and combined excitation

On the way to autonomous driving more and more advanced driver assistance systems (ADASs) are developed to increase safety and comfort. These functions require additional quantified information about the environment, for example information about the current road condition, which a human driver would perceive intuitively. In this paper, a road condition estimation, described by a road friction coefficient, is developed using a second order divided differences filter in combination with estimates of the time varying parameters, namely the dynamic wheel radius and the tire stiffness. Using real measurement data of commercial vehicles, the estimation algorithm is compared to a static and less complex longitudinal friction coefficient estimator. The comparison shows good results for both estimators with differences at low excitation and during cornering maneuvers.

Identifying Texture and Friction of Asphalt Pavement Surface with Optimized Close-Range Photogrammetry Method

Abstract An adequate pavement texture that provides sufficient brake friction is critical for drive safety. Thus, it is essential to quantify the pavement texture and friction efficiently and accurately. So far, the close-range photogrammetry (CRP) method has been manifested as a promising one. Nonetheless, related measurement parameters have not been well optimized toward its extensive promotion. For this reason, varying measurement parameters of CRP method were thoroughly discussed and optimized in this study. Additionally, the optimized CRP method was further validated using the sand patch test and X-ray computed tomography scan method. Based on this, the estimation of friction coefficients for asphalt concrete (AC-13), stone mastic asphalt (SMA-13), and open graded friction course (OGFC-13) were carried out. The results indicate the following: (1) the optimized CRP method was able to adequately feature the pavement macrotexture; (2) the mean texture depth derived from the CRP method was equivalent to the texture depth measured from sand patch method; in addition, (3) the OGFC asphalt mixture was superior to the SMA and AC asphalt mixtures in terms of the friction coefficients. The optimized CRP method could bring bright prospects for future measurements of pavement texture.

Soil friction coefficient estimation using CNN included in an assistive system for walking in urban areas

Soil friction coefficient estimation using CNN included in an assistive system for walking in urban areas

A phase plane H∞ controller for distributed drive electric vehicles with stability enhancement based on tire road friction coefficient estimation

An H∞ control strategy based on the phase plane method (phase plane H∞ controller) tracking two degrees of freedom (DOF) ideal vehicle trajectory scheme is designed for distributed drive electric vehicles with stability enhancement. Firstly, an Extended Kalman Filter (EKF) tire road friction coefficient estimation method based on Keras neural network is presented to accurately and efficiently identify the tire road friction coefficient, taking into account the huge influence of the tire road friction coefficient on vehicle equilibrium point and stability region. Secondly, the phase plane method is applied to provide a dynamic stability boundary for the switching control strategy of direct yaw moment for different tire road friction coefficients; Furthermore, based on the dynamic stability boundary, the weighted phase stability is applied to achieve more realistic stability evaluation criteria, and the fuzzy control strategy is adopted to carry out the feedback regulator of the target side slip angle and yaw rate on the purpose of limiting its maximum value max ( β) and max ( ωr). Then the torque of the four-wheel was optimized by the quadratic programming method. Finally, the presented method is verified and the results indicate that: (1) the phase plane H∞ control has the advantage in terms of stability and maneuvering performance. More importantly, under a low tire road friction coefficient, the amplitude of the side slip angle is decreased by 26.52% over the H∞; (2) the designed EKF based on Keras neural network parameter correction has a quick and accurate performance in identifying the tire road friction coefficient, and the steady-state error does not exceed 3.25%.

Tire-Road Friction Coefficient Estimation for Distributed Drive Electric Vehicles Using PMSM Sensorless Control

Many tire-road friction coefficient estimation methods require the wheel angular speed sensor to provide a signal. In this paper, a tire-road friction coefficient estimation algorithm for distributed drive electric vehicles using permanent magnet synchronous motors(PMSM) sensorless control is proposed to reduce the use of wheel angular speed sensors. The wheel angular speed signal is replaced by the rotor speed signal obtained from PMSM sensorless control. First, the three degrees of freedom vehicle dynamics model and the PMSM mathematical model are established, and a strong tracking cubature Kalman filtering algorithm based on orthogonal transformation (T-STCKF) is derived to overcome the problem that the STCKF algorithm is prone to nonlocal sampling when dealing with high dimensional systems. Second, a PMSM sensorless control system based on the adaptive exponent reaching law of sliding mode control and the T-STCKF algorithm is established, and confirmed its validity. Finally, the feasibility of the proposed algorithm is demonstrated through multicase simulation and experiment and the results shows that the T-STCKF algorithm is more accurate than the STCKF algorithm.

Tire-road friction coefficient estimation for automatic guided vehicle under multiple road conditions

The traditional unscented Kalman filter (UKF) will have the problem of reduced accuracy or even divergence in the estimation process due to state model perturbation, unknown noise of the system, and other factors, which in turn affect the estimation results of the tire-road friction coefficient. By this problem, the paper investigates the tire-road friction coefficient estimation by taking an automatic guided vehicle (AGV) as the research object and proposes an adaptive singular value decomposition unscented Kalman filter (ASVD-UKF) with a noise estimator. Singular value decomposition (SVD) is introduced into the unscented Kalman filter (UKF) for Sigma sampling to suppress the negative definiteness of the state covariance matrix in UFK. The paper considered estimation schemes for joint road, μ-split road, and μ-different road and constructed corresponding ASVD-UKF observers to reduce the dimension of the road estimation model and real-time observation of four tire-road friction coefficients. Results show that the average absolute error of the μ-split road, joint road, and μ-different road proposed in this paper is significantly smaller than that of UFK, and the estimation accuracy is improved by 13.39%, 6.74%, and 5.71%, respectively. A Distributed Drive AGV prototype was developed for a real vehicle verification experiment, with only a 1.14% error between simulation and experiment. It is further proved that the designed observers are practical. The research can provide a theoretical basis and experimental foundation for the tire-road friction coefficient estimation.

Accuracy requirements for the road friction coefficient estimation of a friction-adaptive automatic emergency steer assist (ESA)

The number of traffic accidents resulting in personal injury and property damage is increasingly being reduced by effective advanced driver assistance systems (ADAS). Nevertheless, many traffic accidents still cannot be prevented today because they are due to wet, snow- and ice-covered roads. For this reason, the Institute of Automotive Engineering (IAE) of the Technical University of Braunschweig is investigating the road friction coefficient sensitivity and adaptation of advanced driver assistance systems (ADAS) currently in series production from 2018 to 2021 as part of the ‘Road Condition Cloud’ research project funded by the German Research Foundation (DFG) to increase driving safety, particularly on wet, snow- and ice-covered roads. In this article, the road friction coefficient sensitivity and adaptation of an automatic emergency steer assist is simulatively investigated. This assist overrides the driver to automatically execute an evasive maneuver. The driving maneuver used is a standardized obstacle-avoidance maneuver that is simulatively repeated on a dry, wet, snow- and ice-covered road. The road friction coefficient sensitivity shows that this test is already failed on a wet road because the simulated vehicle does not pass the second lane without errors. Subsequently, a road friction coefficient adaptation of the emergency steer assist is investigated. This adaptation varies the maximum lateral acceleration of the evasive trajectory depending on an estimated value of the road friction coefficient in order not to exceed the maximum adhesion coefficient of the wheels during the evasive maneuver. Ideally, the estimated value matches the true road friction coefficient so that the second lane is passed without errors even on a wet, snow- and ice-covered road. In contrast, an existing difference determines whether the second lane is reached. Finally, the necessary accuracy requirements of the road friction coefficient estimation are determined in an novel estimation error diagram. A road friction coefficient adaptation increases the driving safety of driver advanced assistance systems (ADAS) that are in series production today and future highly automated driving functions (HAF) and is necessary for automated driving because the driver is not present as a fallback level. The described results were presented before in [1].

Pavement Friction Evaluation Based on Vehicle Dynamics and Vision Data Using a Multi-Feature Fusion Network

The tire–road friction coefficient is a critical evaluation index of the service performance of roads: it governs the stopping distance, traction control, and stability of vehicles. Moreover, friction information is also needed in many function units of modern vehicles. This paper proposes a novel data-driven approach for inference of the maximum tire–road friction coefficient using a combination of vehicle dynamics signal and machine vision data. The approach is aimed at robust road condition perception that can provide frequent measurements over large areas across all weather conditions. Two different neural network architectures were adopted to extract in-depth features behind vehicle dynamics signals and road surface images. Features from these two types of data were then fused in two different levels, namely feature level and decision level, forming a multi-feature fusion neural network. The proposed network performs better than models based only on dynamic signals or vision data. The method proposed was applied to real data obtained from an electric car in a highway driving scenario. For classification of the maximum tire–road friction coefficient, the proposed network can yield F1-score increments of 0.09 and 0.18 from dynamics-based and vision-based sub-models, respectively. For the maximum tire–road friction coefficient value regression, the proposed model also achieves the highest R-square score of 0.71. Of these two types of data collected under highway driving scenarios, the vision data contribute more to the overall performance of the proposed model. Nevertheless, the dynamics data possess excellent potential in poor lighting conditions. With these fused features, the proposed multi-feature fusion network can not only improve the accuracy of maximum tire–road friction coefficient estimation but also is deemed workable for a broader range of scenarios.