## 4 Experimental Validation  
This section validates the effectiveness of the proposed ANN classifier using the field test data. The field test was conducted a total of nine times, and the following data were obtained: three sets of data for 5785 kg (denoted as Data 1), three sets of data for 6785 kg (denoted as Data 2), and three sets of data for 8785 kg (denoted as Data 3). We used the first data set of each case for the training (i.e., the first cases of Data 1, Data 2, and Data 3), and Figure 7 shows the vehicle responses of the first case for each data set. Specifically, Figure 7a-c show the vehicle speed, engine torque, and estimated longitudinal acceleration  
Figure 9a-c show the estimation results of the proposed ANN classifier for the first case of Data 1/2/3, along with the estimation results of the RLS approach for comparison. In each case, the results are well synchronized with the true values within the 7% error margin, and the transients of the estimates are very short with less overshoot. According to Figure 9, the convergence rate of the estimation via ANN is shown to be 1.5-2 times faster than that of the RLS filter. Specifically, while the RLS takes about 40-60 s to converge within the 7% error margin, the ANN-based estimation typically reaches this margin within 10-35 s. The estimates of RLS hold an excessive transient response with significant overshoot. Additionally, the final steady-state values of the estimates were found to be more accurate and robust than those of the RLS approach, where we can find the variation in estimates under the steady-state conditions (i.e., less robust).  
Figure 10 shows the estimation results for the second case of Data 1/2/3, while Figure 11 presents the estimation results for the third case of Data 1/2/3. According to the results in Figures 10 and 11, it is clear that the accuracy and convergence rate of the estimates are outstanding and unmatched.  
Table 3 summarizes the estimation accuracy across all cases. Based on the estimation results for real test data shown in Figures 9-11, the proposed ANN approach with perturbed inputs can be considered one of the remarkable solutions for fast and accurate mass estimation.  
Figure 8: Training results and errors of the ANN classifier based on field test data. (**a**) Training results and (**b**) error and epoch.  
Figure 7: Vehicle responses of the first case for each data set. (**a**) Vehicle Longitudinal Speed \(V_{x}\). (**b**) Engine torque Et. (**c**) Longitudinal Acceleration \(a_{x}\).  
Figure 9: Estimation results for the first case of Data 1, 2, 3, (**a**) Estimation of results for Data 1 (5785 kg). (**b**) Estimation of results for Data 2 (6785 kg). (**c**) Estimation of results for Data 3 (8785 kg).  
Figure 10: Estimation results for the second case of Data 1, 2, 3. (**a**) Estimation of results for Data 1 (5785 kg). (**b**) Estimation of results for Data 2 (6785 kg). (**c**) Estimation of results for Data 3 (8785 kg).  
Figure 11: Estimation results for the third case of Data 1, 2, 3. (**a**) Estimation of results for Data 1 (5785 kg). (**b**) Estimation of results for Data 2 (6785 kg). (**c**) Estimation of results for Data 3 (8785 kg).