Chapter 4 Vehicle Rollover Prediction System
4.5 Block Diagram for the Prediction System
Figure 4.4 shows the block diagram of the proposed vehicle rollover prediction system.
As shown in the diagram, the driver maneuver, such as steering, braking, tracking and etc are fed into estimator as the system inputs. The estimator produces vehicle states information in real-time with information from system inputs and sensor outputs. These states real-time information is then fed into predictor to obtain the vehicle roll angle in future time. A rollover incidence is declared based on the rollover angle in future time.
Chapter 5
Simulation and Results
The following simulations are meant to elucidate the feasibility of the proposed rollover prediction method. In these simulations, the vehicle is moving at the longitudinal speed of 90 km/hr and making a quick turn at the 4th second. The simulation includes five situations and each differs from the steering wheel maneuvering and/or vehicle on a slanted road. The simulation results are shown in figure 5.1~5.6 and the plot is arranged in the following order:
steering wheel angle in the upper left, lateral acceleration in the lower left, roll angle in upper the middle, roll rate in lower the middle, yaw angle in the upper right and yaw rate in the lower right. Furthermore, the yaw-roll model outputs are drawn in solid-blue lines while the predictor output is drawn in dash-green lines. The vehicle parameters utilized in simulations are listed in Appendix B.
For the comparison purpose, the output of the predictor is intentionally set to obtain current states information, instead of states information in future time. Furthermore, three sensors (lateral acceleration sensor, longitudinal velocity sensor and suspension displacement sensors) are turned on between 0~5 second and then turned off to the end of the simulation.
Also, during 5~8 second, the steering wheel angle is kept at the same. With the above arrangements, the simulation results shown in solid-blue lines can be treated as the real vehicle response; the green-dash lines can be treated as the estimator output for the timeline within 0~5 second and as the predictor output for the timeline after the 5th second.
In the reminder of this section, we will verify the vehicle rollover prediction system by the real vehicle, which is the integrated yaw-roll model as shown in chapter 3. On one hand, the convergence of the observer-based estimator will be checked between 0~5 second. On the other hand, the accuracy of the model-based predictor will be checked between 5~10 second.
Additionally, keeping the same driving maneuver during 5~8 second looks like the future dynamic behavior at the 5th second. And, changing the driving maneuver after the 8th second will check the inactivity of sensors. Lastly, we will declare the vehicle rollover by the vehicle roll angle in the future time.
5.1 Case I
Case I shows a vehicle doing a smooth turn on a flat road. As shown in figure 5.1, the estimator observes the vehicle roll motion very well and the predictor successfully predicts the vehicle roll motion. There is an obvious deviation between vehicle response and predictor output after 8th second. That is because the steering wheel angle changes again at 8th second and this command input, as expected, is not aware of by the predictor. Furthermore, both estimator and predictor do not work well for the vehicle yaw angle.
5.2 Case II
Case II shows a vehicle doing a quick turn on a flat road. As shown in figure 5.2, the vehicle roll angle diverge and a rollover happening. Again, the estimator can observe the vehicle roll motion very well and the predictor can successfully predict the vehicle rollover. In addition, the estimation of vehicle yaw angle still does not follow the vehicle yaw angle.
5.3 Case III
Case III shows a vehicle doing a slow turn on a slanted road with the slop of -25 degrees from the horizontal. As shown in figure 5.3, the vehicle rollover and the prediction system successfully predict this situation. The only difference between simulation conditions in Case I and Case III is the road bank angle.
This example demonstrates how the road bank angle can initiate a rollover incidence.
Additionally, the estimator successfully observes the vehicle yaw angle in this case but not the other. This is because the lateral acceleration is affected by the yaw angle when the vehicle is on a slope and thus the yaw angle being observed through lateral acceleration sensor.
Figure 5.1 Comparison of vehicle response and rollover prediction system output in Case I, in which the vehicle does not rollover.
Figure 5.2 Comparison of vehicle response and rollover prediction system output in Case II, in which the vehicle rollover.
Figure 5.3 Comparison of vehicle response and rollover prediction system output in Case III, in which the vehicle rollover due to road bank angle.
Figure 5.4 Comparison of vehicle response and rollover prediction system output in Case IV, in which the vehicle rollover but the prediction failed, due to neglecting the road bank condition.
5.4 Case IV
Case IV shows a vehicle doing a slow turn on a slanted road with the slop of -25 degrees from the horizontal, while the prediction system exclude the road bank condition in the modeling. As shown in figure 5.4, the prediction system can neither estimate the states nor predict the states correctly.
Case IV and Case III are mean to demonstrate the importance of incorporating the road bank condition in the vehicle model.
5.5 Case V
Case V shows a vehicle doing a smooth turn on a flat road. The simulation condition is the same as in Case I, except the car response (solid-blue lines) are obtained from the full-car model. As shown in figure 5.5, the prediction system, which based on the yaw-roll model, failed to estimate the system states.
The deviation shown in figure 5.5 obviously came from the difference between full-car model and yaw-roll model. To identify which step in the model simplification process results in this big deviation, we compare the vehicle response obtained from full-car model, separated yaw-roll model and separated yaw-roll model with pitch motion. As shown in figure 5.6, the response of yaw-roll model with pitch motion is very close to the response of full car model, except at some high frequency content.
This simulation results suggest that, when focused on the vehicle roll dynamics, broken down the full-car model into several subsystems is feasible. However, neglecting the Euler pitch motion may be erroneous.
Figure 5.5 Comparison of vehicle response and rollover prediction system output in Case V.
Figure 5.6 Comparison between full-car model, separated yaw-roll model with pitch motion and separated yaw-roll model.
5.6 Conclusions
A vehicle rollover prediction system proposed in this thesis achieves two goals: the estimation in real-time vehicle dynamics and the prediction in future vehicle dynamics. In these predicted vehicle states, we especially observe the vehicle roll angle in future time. With this physical quantity, we can declare the vehicle rollover in future time while keeping the same driving maneuver. Additionally, we can also take these predicted vehicle states to present the relative orientation of the vehicle in future time.
Simulation results indicated that road bank condition plays an important role in rollover incidences. This factor should be dealt with in two phases. Firstly, the road bank condition should be included in the vehicle model. Secondly, the selected sensor should be truly reflecting the vehicle roll angle relative to the road bank angle. These two challenges are solved by introducing the “road frame” into vehicle modeling and adopting suspension displacement sensors.
Simulation results also indicated that the Euler pitch motion has less effect on the vehicle roll angle estimation but may still result in intolerable deviation when it is neglected. More research work should be done in investigating the effect of neglecting vehicle pitch motion instead of Euler pitch motion for a better approximation to real driving situations.
Furthermore, simulation results also suggest that a separated yaw-roll-pitch model could be a possible solution to this application.
Chapter 6
Conclusions and Future Works
6.1 Conclusions
In this thesis, we touched upon several topics for the vehicle rollover prediction system.
The main contributions of this thesis include the full-car modeling, the novel observability matrix, the ADI-like method and its stability analysis, and the vehicle rollover prediction system. The work done in each topic is summarized as follows.
Full-car model
The proposed vehicle rollover prediction system is developed based on the vehicle full-car model, which is obtained from the vehicle physical features, performance, road conditions, etc, instead of a set of empirical parameters. Therefore, this prediction method can be easily tailored for various types of four-wheels vehicles and accommodate for different driving maneuvers. This approach presents a strong evidence for the vehicle rollover prediction.
A vehicle rollover is declared for the vehicle roll angle relative to the road. Therefore, the consideration of road condition in a rollover prediction system should be a must. Simulation results also indicated that a full-car model, incorporated with the road condition, can successfully predict a rollover event for the case that a car doing a quick turn on a slope, while a full-car model without road condition does not.
Novel observability matrix
The novel system observability matrix is developed to reveal the connection between vehicle roll motion and other vehicle dynamics. It provides firm evidence for the modeling reduction task. This approach, using covariance matrix to reveal the states relations, is
particularly suitable to a complicated nonlinear system with a wide operation range. However, more theoretical work should be done to investigate the reliability of this new observability matrix.
Switching scheme in the ADI-like method
A vehicle rollover prediction system based on the separated yaw-roll model is developed and verified by simulation results. The separated yaw-roll model, accompanied with switching computation scheme, enables the nonlinear observer design, which the observer design is almost impossible for the complicated full-car model. Furthermore, the stability analysis, as shown in chapter 4, indicates that the switching computation scheme can perform a stable computing by a proper choice of simulation time-step.
Vehicle rollover prediction system
A vehicle rollover prediction system proposed in this thesis is developed and verified by simulation results. The observer-based estimator, the first part of this prediction system, can obtain more states information in real-time by deploying limited amount of sensors.
Additionally, the estimated vehicle states can be recorded in a so-called “Vehicle Black Box”
for multiple vehicle applications. The model-based predictor, the second part of this prediction system, can predict vehicle states in future time by the integrated yaw-roll model.
Additionally, the predicted vehicle states can be the evidence for declaring a vehicle rollover.
6.2 Future Works
In this thesis, some of the conceptual work for the proposed vehicle rollover prediction system is verified by simulation results. However, more mathematical work should be done for the reliability and optimization analysis. Some future works for this study are summarized in the following.
Full-state vehicle model with automotive engine
Simulation result indicates that the dynamic response of the full-car model is different from that of the separated yaw-roll model, but similar to the separated yaw-roll-pitch model.
However, in this thesis, we take the separated yaw-roll model as an example for simple verification. In order to get close to the real situation, a vehicle rollover prediction system should adopt the separated yaw-roll-pitch model for the subsequent observer construction work.
Currently, the simulation wok does not include the engine and power-train system in the full-car modeling, and thus the driver has very limited control over the vehicle dynamics. The next step is to include more vehicle components, such as engine and power-train system, in the simulation work so that we can investigate more driver maneuvers during a rollover incidence.
Optimal sensor type and location
The sensor type and location, in this thesis, are chosen for the reasons shown in chapter 4.
However, the choice of the sensor type and location is not optimal yet. The sensor choice could be determined by the observability covariance matrix [24]. Therefore, it is possible to combine a cost function with observability covariance matrix to achieve the optimal sensor location and selection for this prediction system.
Rollover prevention measures
This vehicle rollover prediction system proposed in this thesis can provide the vehicle states information for the subsequent rollover warning or prevention system. Since the information provided by this prediction technique is much richer than other approaches, we can design various prevention measures and determine which one to be in effect according to the rollover conditions. This approach can provide a safety measure for the driver while minimize the unnecessary interferences to the driver maneuvering.
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Appendix
A. The Separation of the Integrated Yaw-Roll Model from Euler Transformation
After neglecting the vehicle pitch motion, the governing equation of the rotational motion is shown in equation (3.1) by Euler transformation. The equations are rewritten as follows:
( )
During most of the vehicle maneuvering, the vehicle roll motion (φ ) is small, the above equations can be written as:
z
Therefore, the integrated yaw-roll model can be broken into two sub-models: roll model and yaw model. The angular momentum along ( ) consists of lateral force and vertical force while the angular momentum along ( ) consists of longitudinal force and lateral force. Therefore the lateral force is presented in both roll dynamics as well as yaw dynamics.
B
ex Mx
B
ey My
B. Parameters of the Full-Car Model
In this appendix, the vehicle parameters utilized in simulations are mainly taken the Feng’s dissertation [7] and Hingwe’s dissertation [13] as reference. Furthermore, vehicle parameters, shown in the following section, consist of three parts: vehicle inertial and geometric parameters, suspension coefficients, and tire geometric and experiential parameters.
B.1 Vehicle Inertial and Geometric Parameters
Vehicle parameters Symbol Value Unit
Total mass of the vehicle mvehicle 1740 kg
Sprung mass of the vehicle m s 1600 kg
Front unsprung mass of the vehicle mu1,2 40 kg Rear unsprung mass of the vehicle mu3,4 30 kg
Roll moment of inertia I x 420 kg⋅m2
Pitch moment of inertia Iy 2594 kg⋅m2
Yaw moment of inertia Iz 3214 kg⋅m2
Front tread width sb1 1.45 m
Rear tread width sb2 1.45 m
Distance from the CG to the front axis l1 1.05 m Distance from the CG to the rear axis l2 1.4 m
Height of the vehicle shell h 0.6 m
Distance from the CG to the road Z 0.7 m
Gravitational constant g 9.81 m/ s2
Table B.1 The inertial and geometric parameters of the full-car model
B.2 Suspension Coefficients
The equations of the suspension, shown in section 2.3.2, contain the nonlinear stiffness coefficient and the damper coefficient. Then, suspension coefficients are listed in table B.2.
B.3 Tire Geometric and Experiential Parameters
Tire geometric parameters, shown in section 2.3, are listed in table B.3.
Tire experiential parameters of the nonlinear tire model, shown in section 2.3.3, are verified by Feng [7]. Furthermore, these tire experiential parameters, which consist of two parts: parameters in the longitudinal direction and parameters in the lateral direction, are listed in table B.4 and table B.5, respectively. Additionally, the more information for this nonlinear tire model is shown in Pacejka [15] [16].
Suspension coefficients Symbol Value Unit
Suspension coefficients Symbol Value Unit