Neural ODE Tire Force Modeling for Nonlinear Vehicle Dynamics
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Solution Overview
Problem
Accurately predicting tire forces in dynamic vehicle situations is challenging due to complex nonlinear phenomena and intricate coupling effects, which existing models like the Magic Formula and single-track assumptions fail to accurately capture.
Innovation Solution
The use of neural ordinary differential equation (NODE) learned tire models to estimate tire forces by calculating inflection points and initial conditions from vehicle measurements, and integrating exponential equations to obtain a tire force function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If traditional analytical models like the Magic Formula are used to model tire forces, then the model structure is simple and easy to implement, but the prediction accuracy deteriorates due to complex nonlinear phenomena and coupling effects that cannot be accurately captured
Solution Approach 1:
The patent replaces traditional analytical mechanical models (Magic Formula, Fiala brush model) with a data-driven neural network approach. The neural network learns tire force characteristics directly from measured data, substituting the need for complex analytical formulations and parameter fitting. This allows the system to capture nonlinear phenomena and coupling effects that traditional mechanical models cannot represent accurately.
2Ease of operation
If single-track assumption is used to simplify vehicle dynamics, then control development becomes easier, but the accuracy deteriorates because intricate coupling effects from suspension dynamics and weight transfer are not captured
Solution Approach 1:
The patent introduces measured vehicle data (including suspension dynamics, weight transfer, and other coupling effects) as training inputs for the neural network. This intermediary approach allows the simple single-track model structure to be enhanced with rich physical information from actual vehicle behavior, enabling accurate tire force prediction without requiring complex model formulations.
3Measurement precision
If comprehensive vehicle dynamics effects are included in the tire model, then prediction accuracy improves, but the model complexity increases making control development more difficult
Solution Approach 1:
The patent substitutes complex analytical model structures with a neural network that automatically learns the relationships between vehicle dynamics inputs and tire forces. Instead of manually formulating complex differential equations to represent suspension dynamics and weight transfer, the neural network captures these effects through data-driven pattern recognition, maintaining model simplicity while achieving high accuracy.
Data Source
AI summary
System, methods, and other embodiments described herein relate to NODE learned tire models. In one embodiment, a method includes calculating estimated tire forces based on vehicle measurements; solving a second order differential equation in a repetitive manner until an error calculation based on a tire force function and the estimated tire forces reaches a minimum value, by: using a first predictive model to provide one or more inflection points and initial conditions based on the vehicle measurements, using a second and third predictive model to act as, respectively, exponents to a positive and a negative exponential equation based on the one or more inflection points, the initial conditions, and the vehicle measurements, and integrating the exponential equations to obtain the tire force function; and applying the tire force function to new vehicle measurements to estimate current tire forces.