# Filtering Process to Optimize the Technical Data of Prototype Race Cars
## 4 Description of the Filtering Process
### The Filtering Process  
As an initial step, we calculated the uncertainty in the simulated maximum vehicle speed (40 [km/h]) caused by applying a 5% relative uncertainty to each input parameter individually while assuming zero uncertainty for all other parameters. The resulting relative uncertainties in the output are visualized in Figure 7. (The tabulated data can be found in Table A1 in Appendix A). It can be concluded that optimization should be restricted to those parameters whose induced uncertainties, as shown in Figure 7, are significant. It should be remarked here that the Gaussian error propagation method is very effective in early filtering, as it assumes linearity between inputs and outputs, but as a result, it can oversimplify the effect of nonlinear interactions inherent in vehicle dynamics. In the case where the simulated value is highly sensitive to the uncertainty of an input parameter, the calculated error might be inaccurate. Therefore, if, after filtering is performed assuming the linearity above, we are uncertain whether a parameter should be excluded from the optimization or not, then it can be advisable to perform the error calculation also with a nonlinear approximation for the given parameter. As a second step, we demonstrated that to ensure a simulated vehicle speed uncertainty of less than 10%, the relative uncertainty caused by each input parameter must be limited to 2%, assuming that all inputs contribute equally. Figure 8 illustrates the relative uncertainties of each input parameter that would individually result in a 2% uncertainty in  
Figure 7: Relative percentage uncertainties of the simulated maximum vehicle speed (40 [km/h]) caused by 5% uncertainties in each input data separately. As shown in Figure 8, the 2% uncertainty in the simulated vehicle speed is the result of applying 1.6% and 4% relative uncertainties to the battery terminal voltage (\(U\)) and the vehicle mass (\(m_{0}\)), respectively. The corresponding values for the electric resistance (\(R_{r}\)) and moment of inertia (\(J_{r}\)) of the rotor of the electric motor are 34% and 75%, respectively. Practically, this implies that the battery terminal voltage (\(U\)) and vehicle mass (\(m_{0}\)) must be determined with much greater precision than the electric resistance (\(R_{r}\)) or moment of inertia (\(J_{r}\)) of the rotor. Naturally, while all parameters should ideally be determined as accurately as possible, uncertainties of 20-30% in the electric resistance or the rotor's moment of inertia would not introduce significant errors in the simulated vehicle speed. In the example analyzed, it is advisable to maintain the input parameter uncertainties within or below the limits indicated in Figure 8. This requirement implies that the uncertainty in the battery terminal voltage (\(U\)) should be \(\leq\)2%, potentially necessitating more detailed dynamic battery modeling [48; 49] or measuring the battery terminal voltage in real-time during the drag race and then using these voltages as input data when running the simulation. It can be solved, e.g., by applying a NI 9239 voltage input module in real-time in in situ measurements. Regarding the vehicle mass (\(m_{0}\)), an uncertainty of \(\leq\)4% is sufficient, which is easily achievable, as mass (\(m_{0},m_{f}\) and \(m_{b}\)) can typically be measured with less than 1% uncertainty. It is advisable to know the chain drive efficiency (\(\eta\)) with an uncertainty of less than 7%, but according to the literature, it is typically known with an uncertainty of 2% or less [50]. In the case of the brush voltage (\(U_{brush}\)), an uncertainty of less than 8% is required, for which it is advisable to measure the value of the brush voltage as a function of the intensity of the current flowing through the motor as accurately as possible. The resistances of the motor windings (\(R_{r}\) and \(R_{s}\)) should ideally have uncertainties of 20% or less, though, in practice, measurement accuracies better than 2% are readily achievable [38].