## 6 Individual Brake Force Estimation
The ANN classification performance of each wheel is shown in Figure 11, where comparison results indicate well trained ANN for a wide range



Figure 8: Input training data set (**a**) Normalized initial velocity at the braking (\(V_{0}\)), (**b**) normalized average deceleration (\(dV_{aver}\)), (**c**) average front-left wheel slip ratio (FL), (**d**) average front-right wheel slip ratio (FR), (**e**) average rear-left wheel slip ratio (RL), (**f**) average rear-right wheel slip ratio (RR), and (**g**) normalized vehicle mass. Figure 10: ANN training diagram. Figure 9: True references for training data (road friction coefficients). (**a**) Front left wheel (FL), (**b**) front right wheel (FR), (**c**) rear left wheel (RL), and (**d**) rear right wheel (RR). ### The Validation Phase

Figure 12 explores the effectiveness of the proposed mass estimation approach as described in Algorithm 1. In Figure 12, the performance of the system has been verified by three different masses \(m_{v}=1780\) kg, \(m_{v}=1980\) kg, and \(m_{v}=2180\) kg. Again, it should be noted that the estimation is disabled when the longitudinal velocity becomes greater than 10 km/h (i.e., \(V_{x}>10\) km/h). In addition, as shown in Figure 12b,e,h, the suspension springs are varied by the corresponding sprung mass when the vehicle is accelerated from 0 velocity. The estimated mass quickly converges to the true value almost less than 0.3 s, as shown in Figure 12c,f,i. Here, we discussed the performance of the trained ANN classifier presented in Algorithm 2 and the incorporation of brake force estimation described in Algorithm 3. First, based on the scenario shown in Figure 13a, the loaded vehicle with mass \(m_{v}=1800\) kg has been accelerated to 100 km/h and then was braked (\(P_{m}>0\)) at 10 s until the vehicle completely stops. After the first stop, a second acceleration was initiated and proceeded to reach 60 km/h, and then a brake (\(P_{m}>0\)) was again applied at 27 s. As shown in Figure 13b, the road frictions are assumed to be randomly changed during each brake. Figure 11: Comparison between true references and trained outputs. (**a**) Front left wheel (FL), (**b**) front right wheel (FR), (**c**) rear left wheel (RL), and (**d**) rear right wheel (RR). Figure 13b indicates that the vehicle experiences four-times abrupt changes in friction level during the first brake and twice at the second brake. It can be seen that the estimated friction excellently tracks the abrupt changes of the true friction. Although there are small errors at 15 s, the overall results are acceptable. Moreover, the brake forces estimated by the proposed method accurately track their true values as seen in Figure 13c-f. The most challenging change was the one occurred at 10 s, where the car takes a longer time to reach the trigger value (\(V_{x}\) = 0.97 \(V_{0}\)) due to the

\[FX_{0}=(1-a)FX_{02}+aFX_{01} \tag{27}\]0 Mass estimation results. **(a)** Longitudinal velocity (1780 kg), **(b)** suspension deflections (1780 kg), **(c)** mass estimation (1780 kg), **(d)** longitudinal velocity (1980 kg), **(e)** suspension deflections (1980 kg), **(f)** mass estimation (1980 kg), **(g)** longitudinal velocity (2180 kg), **(h)** suspension deflections (2180 kg), and **(i)** mass estimation (2180 kg). \[FX_{0}=(1-a)FX_{02}+aFX_{01} \tag{27}\]1 Estimation results of road friction coefficients and brake forces with \(m_{v}\) = 1800 kg. **(a)** Vehicle speed and brake scenarios, **(b)** estimates of road friction coefficients, **(c)** brake force of FL wheel, **(d)** brake force of FR wheel, **(e)** brake force of RL wheel, and **(f)** brake force of RR wheel. low road friction (\(\mu\) = 0.1). Therefore, the convergence to the reference brake forces exhibits a small delay right after the first brake. Moreover, the friction estimation mainly affects the accuracy of the estimated brake force since estimation results are varied by the accuracy of road friction.