79 a “normal” simulation with the driver model to provide reliable and realistic results.
Lap time
The simulated lap time is 77.55 seconds, while the registered time is 77.67. This is a difference of 1.5%.
Trajectory
The trajectory is very similar to the input one. That is to be expected, ad the driver model was controlling the vehicle to achieve this trajectory. Deviations are mostly due to the fact that the defined road has a width of 5 meters, as such the driver can deviate from the centerline to reduce lap-time. However, since the width is small, the usually negligible.
Velocity
Again, the velocity plot shows a good fit between the model and the real vehicle’s behavior, with the model reaching slightly higher speeds and having a small delay at the start.
The maximum error is 9 m/s, the mean error is 1.82 m/s, the maximum error percentage is % and the mean error percentage is 12.8%.
81
Longitudinal acceleration
The longitudinal acceleration plot shows a slightly worse fit than that of the previous signals, mainly due to noisy signals.
The maximum error is 15 m/s^2, the mean error is 4.78 m/s^2, the mean error percentage is 52%. This is skewed heavily by the many points where the denominator is small and the difference, though small in magnitude, reaches very high peaks. This condition is caused by the many intersections with the x axis of the curve (many situation where the vehicle switches from acceleration to deceleration or vice versa).
Longitudinal acceleration
The lateral acceleration plot shows a similar fit to the longitudinal one:
The maximum error is 17 m/s^2, the mean error is 4.72 m/s^2, and the mean error percentage is 12.6%. The same considerations hold true as for the longitudinal acceleration, but to a lesser degree in this case.
83
Yaw rate
Out of all the analyzed signals, the yaw rate is the one that shows the worst fit: the simulation values clearly show lower peaks than the logged ones. This may be caused by the change in trajectory: the driver tends to reduce the radius of curvature and so at similar speeds the yaw rate is reduced (more so than the lateral acceleration, that on first approximation depends on the square of the speed while the yaw rate is directly proportional)
The maximum error is 127 deg/s, the mean error is 29.6 deg/s, and the mean error percentage is 12.6%.
Sideslip angle
The sideslip angle will not be compared as the logged signal, even if not without its merits, proved to be fundamentally flawed. Thus, comparing a simulation value to a signal that is known to be wrong cannot yield good results.
Chapter 6
6.1 Conclusions
The importance of having a reliable simulation model for the design and testing phases of any product cannot be overstated: that is why this discussion is focused on the validation of a vehicle model to improve future efforts.
There are some notes to make about the procedure used: some signals could not be properly logged due to budget restrictions: accurate Sideslip angle sensors can cost tens of thousands of euros, and as such could not be sourced for this research.
The procedure used to define a substitute for this signal, while theoretically correct, relies heavily on the correct modeling of the tire behavior, as the 3d map of cornering stiffness vs Fy and Fz has been obtained through the tire property file. Modeling of a tire’s behavior is a very complex field, and while the Pacejka formulas do provide a good approximation of the tire forces, the method used to create such parameters has a great influence. In this case we know that this is a tire with an unusually low vertical load on average (50 kg), and our sponsor Pirelli told us that they had to use a new test rig for this reason and that there could be some inaccuracies due to this.
Furthermore, even a “perfect” .tir file would need to be validated to find good scaling factors for each road surface, as there is bound to be significant difference between each road and the test rig’s surface.
This leads to an output signal that cannot be considered fit as a reference behavior for the vehicle. The trajectory is also affected by this, but to a lesser extent, as sideslip angle values are usually low and the value of the yaw rate has much higher effect on the trajectory.
85 Furthermore, incorrect modeling of the tire can be even worse for the determination of correct simulation outputs. It is in fact no coincidence that most of the errors between the logged behavior and the simulated one could be explained by inconsistency in tire behavior,
It can then be surmised that having a good tire model is of the utmost importance if accurate simulation outputs are to be achieved.
However, the tire property file’s validation is outside of the scope of this discussion and some of the results achieved can be considered good if the limitations of this approach are kept in mind.
Concerning maneuvers that have been performed with input from data logs, it is clear that the magnitude of most signals cannot be trusted completely, the main exception being the vehicle’s velocity during a straight line acceleration event.
However, the fit is somewhat good for most signals, showing that the general trend of the signals can be trusted.
The best result was achieved with the autocross simulation with driver inputs:
this goes to show that while the response of the model to the same inputs od the real vehicle diverges slightly, the overall capabilities of the two are well matched when at least the peak force deliverable by the tire has been corrected.
Thus, general maneuvers performed with the driver can approximate the vehicle’s behavior well. This is mainly because even small errors that are integrated during longer periods of time can lead to large drift in the signals, while the driver can correct this by simply changing input.