TREAD Acceleration in Tire Dynamics

• TREAD Acceleration is the study of acceleration processes in tire treads, using sensor data and advanced signal processing to quantify tire-road interactions.
• Machine learning frameworks, including neural networks and random forests, process tread acceleration data to accurately estimate tire forces and slip ratios.
• Applications span vehicle dynamics control, emission reduction, and hybrid model integration, with implications also in fluid, plasma, and robotic systems.

TREAD Acceleration refers to methodologies, measurement systems, and modeling frameworks that quantify or exploit acceleration phenomena associated with treaded surfaces, primarily in tire dynamics for terrestrial vehicles, vehicle-terrain interaction, and related control applications. The concept can also encompass analogues in aerodynamic, robotic, and plasma environments where tread or surface acceleration drives key physical processes or enables adaptive control. The following sections provide a detailed survey of the core principles, methodologies, measurement systems, and control applications defined by TREAD Acceleration in contemporary research.

1. Measurement and Analysis of Tread Acceleration in Intelligent Tires

Direct measurement of acceleration within the tire tread, typically via a triaxial accelerometer mounted on or within the inner liner, enables precise quantification of tire–road interaction forces. This sensor architecture records high-frequency (order 10 kHz) acceleration time series in the longitudinal ($a_x$), lateral ($a_y$), and vertical ($a_z$) channels as the tread passes through the contact patch (Xu et al., 2020, Xu et al., 2021). Real-time signal processing includes:

• Filtering with a low-pass filter (e.g., 400 Hz cutoff) to suppress high-frequency noise and isolate deformation-driven frequency content.
• Synchronous segmentation per tire revolution using circumferential encoder signals, refining the analysis to the interval where tread is in the contact patch.
• Resampling of time series to spatial series at fixed angular increments over the contact patch, decoupling feature extraction from vehicle speed.
• Min–max normalization:

$$x_{\text{norm}} = \frac{x - x_{\min}}{x_{\max} - x_{\min}}$$

where $x$ is a measured acceleration value.

The processed acceleration data serve as input features to various machine learning models for real-time estimation of tire forces (longitudinal $F_x$, lateral $F_y$, vertical $F_z$) and slip ratio ($\kappa = \frac{V_w - V_x}{V_x}$, where $V_w$ is wheel velocity and $V_x$ vehicle longitudinal velocity), realizing a purely sensor-driven estimation architecture.

2. Machine Learning Frameworks Leveraging Tread Acceleration

Tread acceleration features extracted as described above are the primary input to regression models trained to estimate force and slip in real time:

• Feedforward neural networks using resilient backpropagation (Rprop) achieve normalized root mean squared errors (NRMS) as low as 0.81% for $F_z$ and 2.89% for $F_x$; similar performance is observed for $F_y$ except at high slip angles (Xu et al., 2020).
• Additional methods include random forests (RF), gradient boosting machines (GBMs), recurrent neural networks (RNNs), and support vector machines (SVMs), with cross-validated NRMS errors for slip ratio estimation reaching $\sim$4.88% with ANN using $a_z$ alone (Xu et al., 2021).

The selection of input channels (e.g., using only vertical acceleration $a_z$ versus a combination of all axes) and the choice of machine learning model critically affect estimation accuracy. Empirical results show that $a_z$ is the most robust input for slip ratio estimation across driving conditions and tire loads.

ML Model	Typical Use Case	Best NRMS Error
NN (Rprop)	Force ($F_x$, $F_y$, $F_z$)	0.81–4.23%
ANN (Rprop), GBM	Slip ratio ($\kappa$)	4.88%
Random Forest	Rapid convergence	$>$4.88%
RNN	Sequence modeling	$\sim$4.9%

The models are trained and validated on data from instrumented tire testbeds (such as an MTS Flat-Trac platform) under varied loads, angles, and velocities.

3. Tread Acceleration in Vehicle Dynamics Control: Emissions and Performance

The acceleration signature in the tread is used not only for state estimation but also as input to advanced control systems that optimize vehicle performance for specific objectives, including minimal tire emissions. In the context of electric vehicles (EVs), control schemes have been developed to:

• Deploy heterogeneous tire profiles (low-wear, low-traction tire on one axle; high-wear, high-traction tire on the other).
• Apply dynamic steering correction $\Delta\sigma$ and torque distribution, computed via a greedy search, to mimic the base-vehicle response despite differing tire characteristics (Pham et al., 14 Apr 2025).

Formally, the lateral and longitudinal dynamics are modeled (standard bicycle model), with explicit modulation for tire parameters:

$$\frac{dv}{dt} = \frac{1}{m} \left( F_{v,r} + F_{v,f}\cos\sigma - F_{u,f}\sin\sigma - C_d v^2 \right) + u \delta$$

where $F_{*,*}$ are tire force components.

Emission minimization is posed as a quadratic objective in the longitudinal force on each tire:

$PN(F_v, p) = p_2 F_v^2 + p_1 F_v + p_0$

The control algorithm computes reference forces and distributes torque to minimize total emissions while preserving base-vehicle handling even under emergency braking and cornering, achieving $\sim$48–63% emission reductions in simulation.

4. Integration of Tread Acceleration with Hybrid Vehicle Dynamics Models

Tread acceleration informs hybrid dynamics models used in autonomous off-road driving and high-speed locomotion. In state-of-the-art approaches, high-dimensional visual features (e.g., DINOv2 vision transformer outputs) are compressed via learned encoders and associated, by projection, with local 3D terrain voxels relevant for each wheel (Gibson et al., 30 Nov 2024). These features, together with physical vehicle states and controls, parameterize:

• Physics-based models (e.g., bicycle model with Pacejka tire slip component),
• Data-driven corrections (LSTM modules) that explicitly utilize wheel-centric visual features correlated with surface and tread acceleration signals.

The model equations are designed to represent the mechanical and terramechanical state transitions:

$$\dot{v}_x = \frac{(1 + \cos\delta) F_x - F_{y,f}\sin\delta}{m} - C_{x,d} v_x^2 - C_{x,g} \eta_x + v_y r$$

with lateral forces $F_{y,*}$ derived from empirically tuned tire models, robust to terrain-induced fluctuations in traction. Integration of tread acceleration and its visual correlates reduces prediction errors in high-speed off-road autonomous driving, substantially improving the reaction to sudden dynamics changes (termed “TREAD Acceleration” in the adaptive sense).

5. Impact of Tread Depth and Velocity on Tractive Performance

Changes in tread depth—tread wear states—and velocity directly affect the measured and modeled tread acceleration, which in turn influences tire–road force transfer and vehicle stability (Singh et al., 2023, Rodríguez-Martínez et al., 2023).

• Decreasing tread depth increases carcass contribution to stiffness and may raise peak friction near the wear-out limit; adapted Pacejka tire models use quadratic terms in tread depth to scale cornering stiffness and friction.
• At higher forward velocities ($>$0.2 m/s in planetary rover contexts), both drawbar pull coefficient and tractive efficiency decrease, while wheel sinkage increases, an effect directly observable in the measured vertical tread acceleration.
• Flexible wheels maintain higher drawbar pull and lower sinkage at high speeds, highlighting a strong dependence of tractive performance on real-time tread acceleration characteristics.

Updated models integrate such effects dynamically, improving controller robustness under nonlinear, velocity-dependent conditions.

6. Tread Acceleration in Broader Physical Contexts

Acceleration effects at the interface or “tread” of moving surfaces have significant implications across other domains:

• In turbulent flow drag reduction, the non-dimensional acceleration parameter ($a^+$) of the oscillating wall surface, representing the rate of momentum transfer, is the primary scaling variable that collapses diverse experimental results for drag reduction. The acceleration is defined as:

$a^+ = \frac{A^+}{T^+} = \frac{A\nu}{T u_{\tau0}^3}$

with $A$ amplitude, $T$ period, $\nu$ kinematic viscosity, $u_{\tau0}$ friction velocity (Ding et al., 2023).

• In plasma and astrophysical phenomena, analogous “TREAD Acceleration” constraints arise from the necessity to produce a specific ambient-particle-normalized acceleration rate. For example, in solar flare models, the specific acceleration rate $\eta(\geq E_0)$ serves as the primary criterion for model validation (Guo et al., 2013).

7. Future Directions and Methodological Challenges

Continued advancement in TREAD Acceleration research depends on:

• Expansion of sensor arrays (in-tread acceleration) and improved spatial calibration in emerging intelligent tire platforms.
• Development of physics-informed, velocity- and wear-dependent terramechanics models grounded in empirical high-speed data.
• Further integration of semantic vision models and sensor fusion strategies to correlate tread acceleration with environmental context in real time.
• Extension of hybrid-tire control methodologies to onboard implementation and validation in closed-loop vehicle fleets, particularly in EVs.
• Theoretical investigation into acceleration-based scaling laws in complex mechanical and plasma systems where “tread”-driven acceleration is a core phenomenon.

Research across these axes will further refine both the estimation and control of systems for optimal performance, emissions, and safety, leveraging the unique measurement and modeling advantages of TREAD Acceleration.