## 3 TruckSim/Simulink Validation  
This section validates the estimation performance of the proposed ANN classifier on TruckSim/Simulink co-simulations performed under various weight conditions and several vehicle speed scenarios. The specific configuration of the vehicle is presented in Table 1. Figure 3 shows the vehicle responses generated by several conditions of engine throttle (0.2 and 0.3) and weights (5760, 7260, and 8760 kg). Specifically, Figure 3a through Figure 3c indicate the vehicle speed, the longitudinal acceleration, and the engine torque. It can be seen that the heavier the vehicle, the slower the speed response. Using the pre-processing in Equation (4) through Equation (6), those original inputs in Figure 3 are transformed to the input of ANN classifier, \(\mathrm{x}=\left[dV_{x.N},d\widetilde{E}t_{x.N},d\widetilde{a}_{x.N}\right]^{T}\).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**TruckSim** & **Model** & **Specification** & **Actual Vehicle** & **Model** & **Specification** \\ \hline \multirow{5}{*}{
\begin{tabular}{c} **Powertrain**  
To train the ANN, three cases--0.3/5760 kg, 0.2/7260 kg, and 0.3/8760 kg--are selected. Figure 4 shows the normalized training values (5760 kg: 0.576, 7260 kg: 0.726, and 8760 kg: 0.876) and the training error based on the epoch, and it is found that the training error converges below 0.01. Figure 5 shows the estimation results of three weights under engine throttle condition 0.3. Specifically, the estimated values were 5790 kg (99.48% accuracy) for actual weights of 5760 kg, 7290 kg (99.59% accuracy) for 7260 kg, and 8720 kg (99.54% accuracy) for 8760 kg. The estimates of the proposed ANN classifier converged quickly and smoothly within 1-2 s without any excessive overshoot, and the accuracy of the estimates was determined as unbeatable, which is almost close to 100% of actual values. The estimation process was interrupted within 10-20 sec, satisfying the idea that the gradient of the estimates is small (i.e., \(|m_{t+1}-m_{t}|<\epsilon\)).  
For comparison, we also presented the estimates via the RLS filter, showing relatively slower convergence and less accuracy. It is clear that the ANN classifier is much faster than the RLS filter in terms of convergence. Moreover, the final estimates of ANN are more accurate than those of RLS filters for some cases.  
Figure 6 shows the mass estimation for weights of 5760 kg, 7260 kg, and 8760 kg under engine throttle condition 0.2. Specifically, the estimated values were 5710 kg (99.13%) for the actual weights of 5760 kg (in Figure 6a), 7430 kg (97.71%) for 7260 kg (in Figure 6b) and 8520 kg (97.26%) for 8760 kg (in Figure 6c). All estimates in Figure 6 converged within 1-2 s with precise accuracy, similar to the estimation results shown in Figure 5.  
Figure 4: Training results and errors of the ANN Classifier: (**a**) training results according to three mass conditions and (**b**) error and epoch.  
Figure 3: Vehicle responses according to the condition of the engine throttle. (**a**) Vehicle Longitudinal Speed \(V_{x}\). (**b**) Longitudinal Acceleration \(a_{x}\). (**c**) Engine torque \(E_{t}\).  
Figure 5: Estimation results of TruckSim for Engine throttle 0.3. (**a**) Estimation of results mass (5760 kg). (**b**) Estimation of results mass (7260 kg). (**c**) Estimation of results mass (8760 kg).  
Detailed estimation results for Figures 5 and 6 are presented in Table 2.  
Figure 6: Estimation results of TruckSim for Engine throttle condition (0.2) (**a**) Estimation result of mass (5760 kg) (**b**) Estimation result of mass (7260 kg) (**c**) Estimation result of mass (8760 kg).