## 6 Individual Brake Force Estimation
From Figure 13d, we can see that the estimation error of the front-right wheel at 14 s is larger than others because the front-right friction (\(\hat{\mu}_{FR}\)) is underestimated (see Figure 13b). The second test has been obtained from the same setup but with a different vehicle mass \(m_{v}\) = 2100 kg and other road friction patterns during two brake cycles. Again, the results shown in Figure 14b indicate that the individually estimated road friction adapts the actual value quickly and accurately. Figure 14c-f describes the estimation of the longitudinal braking forces. Nevertheless, there are momentarily differences between the true values and estimates when the friction level is abruptly changed. The main source of these discrepancies is the delay of averaging data process. The values of averaged slip ratio \(\overline{\sigma}_{i}\) and averaged deceleration \(d\overline{V}_{x}\) do not update to new values until satisfying \(count\) = 20 (see Algorithm 2). This can be observed clearly at the 12 s of the first brake. Table 2 shows the correlation between actual brake force and the estimated one based on the following performance index, the correlation coefficient,

\[FX_{0}=(1-a)FX_{02}+aFX_{01} \tag{27}\]2

where n is the sample size, \(x\) is the true value from CarSim of the concerned wheel, and \(y\) is the estimated value of the concerned wheel. According to the correlation coefficient in Table 2, the braking force coincides with the actual one by more than 87%, at least. \[FX_{0}=(1-a)FX_{02}+aFX_{01} \tag{27}\]3 Estimation results of road friction coefficients and brake forces with \(m_{v}\) = 2100 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. \[FX_{0}=(1-a)FX_{02}+aFX_{01} \tag{27}\]4 Estimation results of road friction coefficients and brake forces for split-friction road. (**a**) Longitudinal vehicle speed, (**b**) split-friction road condition (\(\hat{\mu}=0.7\) for left and \(\hat{\mu}=0.5\) for right), (**c**) friction estimation of FL wheel, (**d**) brake force of FL wheel, (**e**) friction estimation of FR wheel, (**f**) brake force of FR wheel, (**g**) friction estimation of RL wheel, (**h**) brake force of RL wheel, (**i**) friction estimation of RR wheel, and (**j**) brake force of RR wheel. ## 9 Conclusions

This paper presents a novel longitudinal brake force estimation strategy for individual wheels using an artificial neural network classifier and data-driven technique together. (i) The vehicle mass was instantly estimated by monitoring the static suspension deflections. (ii) Road friction identification used an artificial neural network and average data set from currently available standard sensors. (iii) A combination of estimated mass, estimated road friction, and data-driven technique was utilized to estimate brake forces. The proposed approach was verified through several co-simulation between CarSim and Matlab/Simulink with different velocities, road friction, and masses. In several brak

\[FX_{0}=(1-a)FX_{02}+aFX_{01} \tag{27}\]5 Estimation results of road friction coefficients and brake forces for split-friction road. (**a**) Longitudinal vehicle speed, (**b**) split-friction road condition (\(\dot{\mu}=0.3\) for left and \(\dot{\mu}=0.5\) for right), (**c**) friction estimation of FL wheel, (**d**) brake force of FL wheel, (**e**) friction estimation of FR wheel, (**f**) brake force of FR wheel, (**g**) friction estimation of RL wheel, (**h**) brake force of RL wheel, (**i**) friction estimation of RR wheel, and (**j**) brake force of RR wheel. ing cycles, the estimation performance of the brake force was satisfactory, the minimum correlation coefficient was 87% match between the estimated force and its actual value. It can be concluded that the proposed method can guarantee robustness for a wide range of road friction (including abrupt changes in road conditions) and mass variation.