Estimation of Tire-Road Friction for Road Vehicles: a Time Delay Neural Network Approach

Alexandra Moutinho; Alexandre M. Ribeiro; Andr\'e R. Fioravanti; Ely C. de Paiva

REVIEW 4 major objections 6 minor 44 references

Estimation of Tire-Road Friction for Road Vehicles: a Time Delay Neural Network Approach

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A time-delay neural network trained on simulated vehicle data estimates per-wheel tire-road friction from lateral force and slip angle, beating a model-based nonlinear least-squares baseline in simulation.

desk verdict Per-wheel TDNN friction estimation is a solid simulation study, but the fixed-μ EKF force estimator and in-distribution evaluation keep it from supporting the abstract's general claim. read the letter →

arxiv 1908.00452 v2 pith:P6YCFAAJ submitted 2019-08-01 cs.NE cs.SYeess.SY

Alexandre M. Ribeiro , Alexandra Moutinho , André R. Fioravanti , Ely C. de Paiva This is my paper · ORCID

classification cs.NEcs.SYeess.SY

keywords frictionroadestimationapproachcoefficientforcemethodtire-road

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Tire-road friction is the grip between a car's tires and the road. Safety systems like anti-lock brakes and stability control work better when they know how much grip is available. This paper tests a way to estimate that grip, called the friction coefficient, using only lateral force and the tire's slip angle, which describes how much the tire is angled relative to its direction of travel.

The authors use a time-delay neural network, a type of artificial neural network that looks at a sliding window of recent measurements rather than just one instant. They feed it the normalized lateral force and the slip angle, and train it on data from a realistic vehicle simulator where the true friction coefficient is known. They then run the trained network on three different simulated driving maneuvers with changing road surfaces, including a case where the left and right front tires have different friction. They compare it to a classical approach, nonlinear least squares, which fits a tire model to the same window of data.

In the simulations, the neural network estimates the friction coefficient with slightly lower root-mean-square error than the least-squares baseline, and it is about five times faster per time step. However, the training data and the test data come from the same simulator, and the force estimates feeding the network are produced by a Kalman filter that assumes a fixed friction value of 0.8. The paper states that no physical field test was performed. So the result is a promising simulation study, not a validated production algorithm.

Extended reading notes

Core claim

The paper's central assertion is: 'the approach is able to estimate the road friction at each wheel independently, instead of using lumped axle models simplifications' (Abstract and Section 4), with the TDNN also providing 'lower RMS errors compared with the classical regression approach' and lower computation time (Sections 5.2-5.3, Tables 7-8, Fig. 15). If correct, this means a data-driven network can replace per-wheel tire models in simulation.

Load-bearing premise

The entire estimation chain depends on the Kalman-filter force estimator, which is built on a vehicle model that fixes tire-road friction at a constant μ=0.8 (Section 4, 'Therefore, a constant μ = 0.8 is applied for the EKF forces estimation'). The authors assert this estimator is robust to TRFC variations, but no sensitivity analysis is provided. If the force estimates Fy and Fz are biased when the true friction differs from 0.8, the TDNN inputs (Fy/Fz and slip angle) are corrupted in a way that may not generalize beyond the simulator's specific conditions.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: competent simulation study of TDNN for per-wheel tire-road friction estimation; the per-wheel claim is plausible but not yet supported outside the simulator because the EKF force estimator fixes μ=0.8 and no sensitivity analysis is given.

The actual new bit is narrow but real: a time-delay neural network fed with per-wheel Fy/Fz and slip angle, trained to output friction coefficient, with an observation window sized to capture friction-change transients. The authors compare against nonlinear least squares using two tire models and show lower RMS errors and roughly six times lower computation time. That is a legitimate incremental contribution, and the simulation setup is more realistic than many NN papers: full multibody vehicle model, sensor noise per commercial IMU specs, three maneuvers including split-friction left/right.

Credit where due: they are honest about the lateral-excitation requirement, they acknowledge the NLS model discrepancy explicitly, and the conclusion admits field testing is needed. The citation pattern looks fine; the relevant prior work on NLS and NN-based estimation is cited.

The soft spots are real but not disqualifying. The load-bearing one is the force estimator. The EKF uses a Dugoff model with fixed μ=0.8; the paper asserts robustness to TRFC variations based on earlier work, but does not show any sensitivity analysis for off-nominal friction. The TDNN inputs are Fy/Fz and α, so any bias in the estimated forces at e.g. μ=0.4 feeds straight into the network. The stress-test worry that inertial acceleration corrects total force but not its axle/wheel distribution is exactly right and is not addressed. Also, the text does not make unambiguous whether the 200,000 training samples are the raw simulated tire outputs or the EKF-filtered estimates; that matters because the deployed network sees EKF outputs. If the training data skip the EKF, the train/test distribution mismatch is another unverified link.

Other issues are minor: single simulation runs, no variance across noise seeds; RMS differences between TDNN and NLS (0.0346 vs 0.0421) are small, so the 'lower RMS' claim is modest; no code or data released. But none of this undermines the paper's internal validity; the authors never overclaim beyond simulation.

Who this is for: people working on practical friction estimation for chassis control, especially those wanting a fast inference alternative to recursive least squares. It deserves serious peer review. My recommendation: send it to review, but request (a) a sensitivity study of the EKF force estimates across the μ range, (b) clarification of the training-data pipeline, and (c) reporting of multiple runs.

Referee Report

4 major / 6 minor

Summary. The paper presents a hierarchical estimator for the tire-road friction coefficient (TRFC) at each wheel. A cascade of extended Kalman filters estimates per-wheel lateral and vertical forces using a vehicle model whose internal Dugoff tire model fixes the friction coefficient at μ=0.8; the slip angle is computed kinematically; and a time-delay neural network (TDNN) with a 50-sample observation window maps (F_y/F_z, α) to a per-wheel estimate of μ. The TDNN is trained on about 200,000 simulated samples with μ ranging from 0.3 to 1.2 and evaluated in three simulated maneuvers: a ramp steer on constant μ=0.8, a constant steer with step changes in μ for all wheels (1.0→0.6), and a constant steer with different μ for left and right front wheels (0.9/0.8→0.8/0.7). The TDNN is compared with nonlinear least-squares (NLS) fits using Dugoff and Brush tire models; the reported RMS errors are slightly lower for the TDNN (e.g., 0.0346 vs 0.0421 in case 1), and the average computation time per iteration is 0.594 ms vs 3.379 ms for the NLS.

Significance. If the claims hold, the approach would offer a real-time, per-wheel friction estimate without an explicit tire model in the network itself, which is of practical interest for active-safety and vehicle-control systems. The paper's strengths are the use of a realistic 32-state vehicle simulation with sensor noise, a comparison against two NLS model-based baselines, and a clear demonstration of the computational advantage of the TDNN. The central novelty—using a TDNN for per-wheel TRFC estimation from lateral force information—is clearly stated. However, the significance is tempered because the evaluation is entirely in the same simulated environment used for training, the training-data pipeline is not fully specified, and the fixed-μ EKF force estimator's robustness is asserted without sensitivity analysis.

major comments (4)

[Section 4, Fig. 3 and paragraph 'The aforementioned works...'] The claim that the EKF force estimator is robust to TRFC variations is not supported in this paper. The EKF uses a Dugoff model with constant μ=0.8, and the TDNN's inputs are the estimated F_y/F_z and slip angle α. If the true friction departs from 0.8, a systematic bias in the per-wheel force estimates—especially in the distribution of lateral force between front/rear and left/right wheels, which inertial acceleration does not constrain—propagates directly into the network inputs. Please provide a sensitivity analysis that varies the true μ while keeping the EKF's μ fixed, quantifies the force-estimation error, and shows that the TDNN's per-wheel μ estimates remain accurate; alternatively, close the loop by updating the EKF's μ.
[Section 4, paragraph 'In the neural network data collecting stage...'] It is not stated whether the 200,000 training samples are raw outputs of the simulated tire model (the Pacejka model in the vehicle simulator) or the EKF-estimated forces and kinematically computed slip angles that are actually fed to the network in deployment (Fig. 3). If training uses clean model outputs, the training and deployment input distributions differ (the deployed inputs are filtered EKF estimates with estimator bias), and the reported R≈0.94 and mse values do not demonstrate the accuracy of the deployed system. Please specify the pipeline precisely and, if necessary, train on the actual deployed input features.
[Section 5, Tables 7-8 and Figs. 11-14] All test maneuvers use friction values (0.6-1.0) inside the training range (0.3-1.2) and the same simulation environment as the training data. The results are therefore interpolation within the fitted envelope and do not provide evidence of generalization to out-of-range conditions or to a different vehicle or tire model. Add a hold-out test with a friction value not in the training grid (e.g., μ=0.5) or with a mismatched tire model in the simulator, and report the resulting RMS errors. The conclusion's own statement that a field test is needed should be reflected in the abstract's unqualified per-wheel claim.
[Section 5, Tables 7-8] The RMS values are computed from a single simulation run for each scenario. Because the measurements are corrupted with Gaussian sensor noise, the reported small differences between TDNN and NLS (e.g., 0.0346 vs 0.0421 in Table 7) could be within run-to-run variability. Please report the mean and standard deviation (or at least the range) of the RMS errors over several Monte Carlo runs for each maneuver to assess the significance of the TDNN's advantage.

minor comments (6)

[Abstract and Section 4] The phrase 'avoiding the use of standard mathematical tire models' overstates the architecture, since the EKF force estimator uses a Dugoff tire model with μ=0.8; please qualify the claim to say the TDNN itself is model-free.
[Equation (6)] The displayed summation has a typo: 'F (x)−Fk=1' should be 'F(x)-F_k' with the subscript on F_k.
[Section 5.3] The text first describes a 'constant left turn maneuver' and then refers to a 'right-hand steer maneuver'; please clarify which steering direction is simulated and ensure Fig. 13 matches the text.
[Section 4, data collection] Please state whether overlapping sliding windows were used to form the N=50 delayed input vectors from the 200,000 samples and report how many training windows resulted.
[Table 2] The correlation coefficients are presented without a statement of the data source or the number of samples; add this information for reproducibility.
[Fig. 15] The histograms do not show the mean or standard deviation of the computation-time distributions; include the reported means (0.594 ms vs 3.379 ms) in the figure or caption for clarity.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central estimator rests on a small set of hand-chosen hyperparameters, a constant friction assumption in the force estimator, and simulation-generated training data. No invented entities are introduced.

free parameters (6)

TDNN weights = Not released
The mapping from inputs to friction coefficient is determined by weights trained on simulated data; they are not provided, so independent users cannot reproduce the estimator.
Observation window N = 50 samples (0.5 s)
Chosen as approximately twice the rise time of the slip angle response; affects how much temporal context the network sees.
Hidden layer neuron count = 50
Selected without a stated hyperparameter search; no evidence that 50 is optimal.
Low-pass filter cutoff = 5 Hz
Applied to forces and slip angle to suppress noise; no sensitivity analysis is given.
Slip angle threshold alpha_thres = 1 degree
Estimation holds at initial value until slip angle exceeds threshold; directly affects transient estimation behavior.
EKF constant friction value = 0.8
The force estimator's prediction model fixes tire-road friction at 0.8; the authors assert robustness without a sensitivity study.

assumptions (5)

domain assumption The Pacejka tire model used in the full-vehicle simulator is an accurate ground truth for the friction coefficient.
The training and test data are generated by a multibody model that uses the Pacejka tire model; if this model is wrong, both the TDNN ground truth and the comparison are invalid.
domain assumption The EKF force estimator remains accurate under varying tire-road friction even with constant μ=0.8 in its internal model.
Stated in Section 4: 'a constant μ=0.8 is applied for the EKF forces estimation' and the estimator is asserted to be robust. No supporting sensitivity analysis is provided.
domain assumption The training data distribution covers the conditions of the test maneuvers.
Test slip angles and forces lie within the Table 3 ranges used to generate training data; no out-of-distribution test is reported.
standard math Newton's laws and planar vehicle kinematics underlie the slip angle equations.
Eq. 1 relates slip angle to velocities and yaw rate; this is standard vehicle kinematics treated as background.
domain assumption Measured signals are available with noise according to the MTi Xsens sensor specifications.
Simulated Gaussian noise is added to measurements; the actual sensor behavior on a vehicle is assumed to match.

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Pith. "Pith review of Estimation of Tire-Road Friction for Road Vehicles: a Time Delay Neural Network Approach." pith.science (2026). https://pith.science/paper/P6YCFAAJ

@misc{pith2026190800452,
  author       = {Pith},
  title        = {Pith review of: Estimation of Tire-Road Friction for Road Vehicles: a Time Delay Neural Network Approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P6YCFAAJ}},
  note         = {Machine review of arXiv:1908.00452}
}

read the original abstract

The performance of vehicle active safety systems is dependent on the friction force arising from the contact of tires and the road surface. Therefore, an adequate knowledge of the tire-road friction coefficient is of great importance to achieve a good performance of different vehicle control systems. This paper deals with the tire-road friction coefficient estimation problem through the knowledge of lateral tire force. A time delay neural network (TDNN) is adopted for the proposed estimation design. The TDNN aims at detecting road friction coefficient under lateral force excitations avoiding the use of standard mathematical tire models, which may provide a more efficient method with robust results. Moreover, the approach is able to estimate the road friction at each wheel independently, instead of using lumped axle models simplifications. Simulations based on a realistic vehicle model are carried out on different road surfaces and driving maneuvers to verify the effectiveness of the proposed estimation method. The results are compared with a classical approach, a model-based method modeled as a nonlinear regression.

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Estimation of tire–road friction coeﬃcient and its application in chassis control systems

Kanwar Bharat Singh and Saied Taheri. Estimation of tire–road friction coeﬃcient and its application in chassis control systems. Systems Science & Control Engineering, 3(1):39–61, December 2014. 12 Alexandre M. Ribeiro et al

work page 2014

[2] [2]

Robust road friction estimation during vehicle steering

Liang Shao, Chi Jin, Cornelia Lex, and Arno Eichberger. Robust road friction estimation during vehicle steering. Vehicle System Dynamics , 57(4):493–519, 2019

work page 2019

[3] [3]

A method to estimate the fric- tion coeﬃcient and tire slip angle using steering torque

Yung-Hsiang J Hsu, Shad Laws, Christopher D Gadda, and J Christian Gerdes. A method to estimate the fric- tion coeﬃcient and tire slip angle using steering torque. In ASME 2006 International Mechanical Engineering Congress and Exposition , pages 515–524. American So- ciety of Mechanical Engineers, 2006

work page 2006

[4] [4]

Ali I. H. Al-Zughaibi. Experimental and analytical inves- tigations of friction at lubricant bearings in passive sus- pension systems. Nonlinear Dynamics, 94(2):1227–1242, Oct 2018

work page 2018

[5] [5]

Robust estimation of road friction co- eﬃcient for vehicle active safety systems

Chang Sun Ahn. Robust estimation of road friction co- eﬃcient for vehicle active safety systems . PhD thesis, University of Michigan, 2011

work page 2011

[6] [6]

de Castro, R

R. de Castro, R. E. Araujo, J. S. Cardoso, and D. Freitas. A new linear parametrization for peak friction coeﬃcient estimation in real time. In 2010 IEEE Vehicle Power and Propulsion Conference, pages 1–6, Sep. 2010

work page 2010

[7] [7]

W. R. Pasterkamp and H. B. Pacejka. The tyre as a sensor to estimate friction. Vehicle System Dynamics , 27(5-6):409–422, jun 1997

work page 1997

[8] [8]

Estimation and control of lateral tire forces using steering torque

Yung-Hsiang Judy Hsu. Estimation and control of lateral tire forces using steering torque . PhD thesis, Stanford University, 2009

work page 2009