An Intelligent Predictive Algorithm for the Anti-Rollover Prevention of Heavy Vehicles for Off-Road Applications
Abstract
:1. Introduction
- The development of a non-linear three degrees-of-freedom mathematical model as simple as effective to catch the lateral load transfer dynamics even in presence of a banked road;
- The formulation of a model-based algorithm for the analytical identification of the critical rollover limits through the development of characteristic maps in the phase plane portrait, able to exhibit the influence of road local irregularities and global geometric factors, i.e., the bank angle;
- The formulation of a statistical algorithm, based on the recurrent neural network approach, for the estimation of the load transfer ratio in a realistic scenario, by considering typical measurable quantities available for an experimental implementation;
- The numerical assessment of a real-time algorithm able to predict in advance the time to reach a specific load transfer ratio considered as the incipient rollover limit.
2. Vehicle Model Description
- 1.
- All the bodies below the suspension system (tires, calipers, wheels carriers, suspension rods, etc. …) are considered as a unique rigid body, connected to the sprung mass through the virtual roll axis R, and represented by four lumped masses , where , each one placed in the the Front Left (FL), Front Right (FR), Rear Left (RL) and Rear Right (RR) wheel rotational centers, respectively;
- 2.
- The roll moment of inertia of the unsprung mass is considered negligible;
- 3.
- The road bank angle is supposed to be equal for the front and the rear axles: absolute roll angle of the unsprung mass is ;
- 4.
- The front and rear suspensions are represented as an equivalent torsional spring and damper system.
3. Load Transfer Ratio Estimation
3.1. Model-Based Estimation
- (a)
- A double lane change manouvre (ISO 3888-1) on a flat road at an initial vehicle speed of ;
- (b)
- A straight manoeuvre on a banked road, whose bank angle is smoothly increased from to , at constant vehicle speed ();
- (c)
- A straight manoeuvre on a road with a flat surface under the left vehicle side and an asymmetrical sinusoidal profile (wavelength equal to the vehicle wheelbase and height amplitude of ) under the right vehicle side, called asymmetrical waves road in the rest of the paper.
3.2. Recurrent Neural Network Estimation
- the RNN algorithm can be developed and tested with a considerable amount of simulated driving scenarios, without requiring an extensive experimental campaign, thus reducing time and costs;
- If the vehicle dynamic behavior is well described by the mathematical model, the neural network designed with a simulated data can be directly deployed on an experimental setup with a lower time and cost effort.
4. ISO-LTR Phase Plane Portrait
5. ISO-LTR Predictive Time
6. Simulation Results
- A fast ramp steering on a banked road;
- A double lane change on a flat Road (ISO 3888-1).
6.1. Fast Ramp Steering on a Banked Road
6.2. Double Lane Change on a Flat Road
7. Conclusions
- A quantitative indication of the anti rollover risk is represented by the , thus detecting the critical limit above which a wheel lifted off occurs. However, the does not represent a measurable quantity due to the extreme difficulty in estimating the vertical load transfers among the vehicle corners. The paper proposes three model-based formulations, by considering an increased level of complexity. The most generic formulation includes the influence of the road bank angle, unsprung masses and vertical dynamics. Numerical simulations of aggressive manoeuvres on flat roads, banked roads and in presence of asymmetrical speed bump waves, show the significant reliability of the generic model-based formulation when compared to the two simplified versions widespread in the literature;
- The incipient rollover occurs when a defined threshold is approached. The paper proves that the ISO-LTR characteristics, i.e., the combination of vehicle relative roll speeds and angles where the is constant, are linear in the phase plane portrait of the vehicle roll dynamics. This is analytically explained through the model-based formulation, and numerically verified with multiple simulations in IPG CarMaker®. The paper also shows that the model-based formulation provides a qualitative tool to predict how the ISO-LTR lines would change when a road perturbation, i.e., road bank angle or irregularities, is encountered. The ISO-LTR slopes are only influenced by the suspension system configuration and parameters (total roll stiffness and damping), meanwhile the severity of the manoeuvre (lateral and vertical accelerations) and the road global and local perturbations provoke an horizontal shift of the ISO-LTR lines;
- The model-based formulation is essential to analytically evaluate the main influencing factors on the load transfer dynamics between the left and right vehicle sides. However, any mathematical formulation is affected by parameters uncertainties, external disturbances and unmodeled dynamics that compromises its effectiveness for a realistic implementation, especially when noisy experimental measurements are input to the analytical formulation. For this reason, the statistical approach, based on the recurrent neural network principle, is proposed as an alternative methodology to estimate the LTR in a realistic scenario. Indeed, the input of the RNN algorithm are typical measurable quantities available for an experimental implementation, which represent the natural following step the authors are going to explore in the near future. The RNN approach provides excellent results in estimating the front and the rear load transfers even in presence of complex and realistic driving scenarios.
- The detection of current is not sufficient to predict the incipient risk of rollover. A ISO-LTR Predictive Time is then derived to proactively calculate the necessary time to reach a particular threshold. The proposed predictive index is then successfully verified through a fast ramp steering maneuver on a banked road and during an aggressive double lane change manoeuvre. In both cases, the demonstrates promising predictive capabilities, compatible with the intervention of a control active strategy.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Type | Description | Parameter | Value |
---|---|---|---|
Springs | Total roll stiffness | K | |
Dampers | Total roll damping | C | |
Masses and inertia | Roll sprung mass moment of inertia | ||
Sprung mass | |||
FR unsprung mass | |||
FL unsprung mass | |||
RR unsprung mass | |||
RL unsprung mass | |||
Total mass | m | ||
Distances | Front axle from the sprung mass CoG | a | |
Rear axle from the sprung mass CoG | b | ||
Wheelbase | L | ||
Track width | T | ||
Unsprung mass CoG height | |||
Roll centre height | |||
Sprung mass CoG from the roll centre | |||
Front tyre radius | |||
Rear tyre radius |
Type | Description | Units |
---|---|---|
Inputs | Longitudinal speed | |
Longitudinal acceleration | ||
Lateral acceleration | ||
Vertical acceleration | ||
roll rate | ||
yaw rate | ||
pitch rate | ||
steer angle | ||
Outputs | Roll angle | |
Front load transfer ratio | − | |
Rear load transfer ratio | − |
Type | Description | Characteristics |
---|---|---|
Layers | Sequence input | Number of features (8) |
LSTM | Number of hidden units (100) | |
Fully connected | Number of Responses (3) | |
Regression | ||
Main Hyperparameters | Adam | Adaptive moment estimation |
MaxEpochs | 850 | |
GradientThreshold | 1 | |
InitialLearnRate | 0.01 | |
LearnRateDropPeriod | 425 | |
LearnRateDropFactor | 0.2 |
Maneuver | Error | Values |
---|---|---|
Bernina | MAE Front | |
MAE Rear | ||
MAE Roll | ||
MSE Front | × | |
MSE Rear | × | |
MSE Roll | ||
Stelvio | MAE Front | |
MAE Rear | ||
MAE Roll | ||
MSE Front | × | |
MSE Rear | × | |
MSE Roll | ||
FishHook | MAE Front | |
MAE Rear | ||
MAE Roll | ||
MSE Front | × | |
MSE Rear | × | |
MSE Roll |
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Tota, A.; Dimauro, L.; Velardocchia, F.; Paciullo, G.; Velardocchia, M. An Intelligent Predictive Algorithm for the Anti-Rollover Prevention of Heavy Vehicles for Off-Road Applications. Machines 2022, 10, 835. https://doi.org/10.3390/machines10100835
Tota A, Dimauro L, Velardocchia F, Paciullo G, Velardocchia M. An Intelligent Predictive Algorithm for the Anti-Rollover Prevention of Heavy Vehicles for Off-Road Applications. Machines. 2022; 10(10):835. https://doi.org/10.3390/machines10100835
Chicago/Turabian StyleTota, Antonio, Luca Dimauro, Filippo Velardocchia, Genny Paciullo, and Mauro Velardocchia. 2022. "An Intelligent Predictive Algorithm for the Anti-Rollover Prevention of Heavy Vehicles for Off-Road Applications" Machines 10, no. 10: 835. https://doi.org/10.3390/machines10100835