# Design of an Estimator Using the Artificial Neural Network Technique to Characterise the Braking of a Motor Vehicle

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

- The proposal of a novel methodology for the analysis of the data acquired by the sensors during the experiments. New indicators were defined in order to characterise the braking manoeuvre of a vehicle, providing information on type of braking, intensity or evolution over time.
- The development of an ANN-based estimation algorithm to estimate the pressure in the brake circuit and the type of braking. The system was implemented with the experimental data obtained from the sensors during the experiments. Therefore, the system will brake by imitating human behaviour.
- The proposed braking system automatically decides how to apply the brake when faced with the risk of a collision. It achieves this by using the information obtained by the sensors about the obstacle. Depending on the position of the obstacle and the speed of the vehicle, the actions on the braking system to reduce the speed will be to perform (1) maintained, (2) progressive and (3) emergency braking. In other words, the automatic braking offers safe and comfortable brake control, without braking too early or too late.

## 2. Materials and Methods

#### 2.1. Instrumented Vehicle

#### 2.1.1. Pressure Sensors

#### 2.1.2. Thermocouple

#### 2.1.3. Load Cell

#### 2.1.4. Data Acquisition System

#### 2.2. Methodology of the Experimental Phase

#### 2.2.1. Types of Braking Performed in the Experimental Tests

- Maintained braking

- Progressive braking

- Emergency braking

#### 2.2.2. Variables Analysed in the Experimental Tests

- Braking time

- 2.
- Braking distance

- 3.
- Pressure in the brake circuit

#### 2.2.3. Test Conditions

- Tyre pressure should be within the manufacturer’s recommended range for the vehicle’s load.
- The temperature range allowed on the brake disc before each braking manoeuvre must be between 18 and 31 °C.
- There shall always be a second person in the co-driver’s seat in charge of controlling the acquisition system. No other persons are allowed in the vehicle.
- The clutch must be disengaged to avoid the influence of engine retention in braking capacity.

## 3. Data Collected by Sensors

#### 3.1. Output Signal of the Pressure Sensors Installed for the Driving Braking Tests

#### 3.2. Statistical Study of the Driver Set

#### 3.3. Methodology for Analysing Data Collected by Pressure Sensors

_{t}”. This indicator defines the integral of the fitted function from the beginning of the braking (t

_{0}) to the end of the braking (t) and provides significant information about the magnitude of the braking (see Figure 9c), but it is also important to know how the braking is distributed over time.

_{v}” (see Figure 9d).

_{t}” is divided by the time taken to execute the braking, the indicator called “vfill

_{t}” is obtained (see Figure 10a). This factor is an indicator of the total braking intensity (see Figure 10b).

_{t}” is integrated by divisions as a function of time, the time representation of the braking evolution is obtained. This concept is a vector called “vfill

_{v}” and provides information on the braking intensity for each division (see Figure 10c). Each value of this vector represents the intensity of braking over time.

_{v}” vector: average, standard deviation and quartiles. Figure 11a shows, by way of example, how the vector “q

_{v}” obtained for the same driver evolves at a speed of 80 km/h for the three types of braking. Figure 11b shows the statistical values obtained from the data represented in Figure 11a. The average and standard deviation values provide information on the magnitude of the braking. Q1, Q2, Q3 and Q4 provide information on the evolution of braking over time.

_{t}, q

_{v}, vfill

_{t}and vfill

_{v}.

## 4. Feed-Forward Neural Networks

#### 4.1. ANN Model

_{max}= 1 and y

_{min}= −1, x corresponds to the original data to be normalised, and x

_{max}and x

_{min}are the maximum and minimum values of the original data to be processed, respectively.

_{v}y vfill

_{v}parameters. The neurons in the output layer contain information about the type of braking and defined indicators for right and left pressure sensors in Section 3.3 (q

_{t}, q

_{v}, vfill

_{t}, vfill

_{v}and statistics).

^{2}) while minimising the MSE. R

^{2}measure the correlation between the outputs and targets.

^{2}increases. Furthermore, the MSE decreases as the number of divisions performed in the output data vector increases. However, there is no relationship between the number of neurons in the hidden layer and the MSE. The best of the three algorithms tested was BR, followed by LM and, lastly, SCG. All models have a high degree of regression, however, and given that the computational cost is negligible (network training is not performed in real time, only the simulation and parameter estimation process take place in real time), an ANN with the following parameters has been chosen (see Figure 14).

- Number of neurons in the input layer: 2.
- Number of neurons in the hidden layer: 20.
- Number of neurons in the output layer: 217.
- Type of training: Bayesian Regularization.
- Divisions of the data vectors: 50.

- Position 1: Represents the type of braking that has been performed (maintained = 1, progressive = 2 or emergency = 3). It is contemplated that decimal values appear in position 1 of the output vector.
- Position 2: Represents the braking capacity value measured by the right pressure sensor (q
_{t}). - Positions 3–52: Vector dividing by 50 the braking capacity value measured by the right pressure sensor according to the time the vehicle takes to stop (q
_{v}). - Position 53: Represents how the right pressure sensor reaches full braking capacity, providing information on “how braking occurs over time” (vfill
_{t}). - Position 54–103: Vector dividing by 50 the value of vfill
_{t}relative to the right pressure sensor (vfill_{v}). - Positions 104–109: Statistical values for braking characterisation relating to the right pressure sensor.
- Position 110: Represents the braking capacity value measured by the left pressure sensor (q
_{t}). - Positions 111–160: Vector dividing by 50 the braking capacity value measured by the left pressure sensor according to the time the vehicle takes to stop (q
_{v}). - Position 161: Represents how the left pressure sensor reaches full braking capacity, providing information on “how braking occurs over time” (vfill
_{t}). - Positions 162–211: Vector dividing by 50 the value of vfill
_{t}relative to the left pressure sensor (vfill_{v}). - Position 212–217: Statistical values for braking characterisation relating to the left pressure sensor.

^{10}). This indicates that the network convergence is correct. The value of R obtained for the training and test phase is shown in Figure 15. As a combination of these phases, the R value obtained for the total system is 0.99566 (expressed over 1).

## 5. Results of Braking Parameter Estimation

_{t}, vfill

_{t}, q

_{v}, vfill

_{v}and statistical values of the two pressure sensors, as well as the type of braking.

_{t}) for the two pressure sensors (right and left).

_{v}) for the right pressure sensor over the 50 divisions performed.

_{t}over the 50 divisions performed for the left pressure sensor.

_{t}.

_{v}).

_{v}parameter corresponding to the left pressure sensor.

_{t}for the two pressure sensors, the data simulated by ANN for the above parameters and the error of these values compared to the target data.

_{t}target values for the two pressure sensors, the ANN-simulated data for these parameters and the error of these values against the target data.

_{t}, vfill

_{t}and the type of braking for each type of braking.

## 6. Validation of Results against Direct Sensor Readings

_{t}and vfill

_{t}.

## 7. Discussion

^{2}value and the lowest MSE value.

_{t}) of all simulations was 1.345 and 1.946% for the right pressure sensor and left pressure sensor, respectively. The mean error of the parameter estimating the braking intensity (vfill

_{t}) of all simulations was 3.959 and 3.775% for the right pressure sensor and left pressure sensor, respectively. It is worth mentioning that the braking type estimations contain the highest error, mainly for maintained braking (23.024%). It has been found that for the emergency braking type the system does not exceed the braking type set in the training, which offers a higher degree of safety and comfort because the braking system will be controlled from the safety side and less aggressively.

## 8. Conclusions

_{t}, vfill

_{t}, q

_{v}and vfill

_{v}. Each of these indicators provided relevant information to characterise vehicle braking.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 3.**Onboard sensors: (

**a**) pressure sensor in the brake circuit and thermocouple on the brake disc and (

**b**) load cell on the brake pedal.

**Figure 4.**(

**a**) Twin antennas located longitudinally on the roof of the vehicle and (

**b**) vehicle dashboard data acquisition equipment.

**Figure 5.**Force exerted on the brake pedal as a function of braking time for the three types of braking studied.

**Figure 6.**Curves of the data obtained during maintained braking for the different speeds by (

**a**) the right pressure sensor and (

**b**) left pressure sensor.

**Figure 7.**Curves of the data obtained during progressive braking for the different speeds by (

**a**) the right pressure sensor and (

**b**) left pressure sensor.

**Figure 8.**Curves of the data obtained during emergency braking for the different speeds by (

**a**) the right pressure sensor and (

**b**) left pressure sensor.

**Figure 9.**Methodology for the analysis of the data acquired by the pressure sensors to obtain the indicators. (

**a**) raw sensor measurement, (

**b**) fitted function, (

**c**) q

_{t}and (

**d**) q

_{v}for 50 divisions.

**Figure 10.**Methodology for the analysis of the data acquired by the pressure sensors to obtain (

**a**) vfill

_{t}, (

**b**) q

_{t}/t and (

**c**) vfill

_{v}for 50 divisions.

**Figure 11.**Example of the three types of braking at 80 km/h performed by one of the drivers (

**a**) q

_{v}and (

**b**) statistical data.

**Figure 13.**ANN sensitivity of the different models designed for the training type: (

**a**) BR, (

**b**) LM, and (

**c**) SCG.

**Figure 16.**Comparison between the complete data simulated by ANN and the target data for braking at a speed of 70 km/h for type: (

**a**) maintained, (

**b**) progressive and (

**c**) emergency.

**Figure 17.**Comparison between ANN-simulated data and target q

_{t}data for the two pressure sensors for braking at a speed of 70 km/h for the type: (

**a**) maintained, (

**b**) progressive and (

**c**) emergency.

**Figure 18.**Comparison between ANN-simulated data and target q

_{v}data for the right pressure sensor for braking at a speed of 70 km/h for the type: (

**a**) maintained, (

**b**) progressive and (

**c**) emergency.

**Figure 19.**Comparison between the ANN-simulated data and target q

_{v}data for the left pressure sensor for braking at a speed of 70 km/h for the type: (

**a**) maintained, (

**b**) progressive and (

**c**) emergency.

**Figure 20.**Comparison between the ANN-simulated data and vfill

_{t}target data for the two pressure sensors for braking at a speed of 70 km/h for the type: (

**a**) maintained, (

**b**) progressive and (

**c**) emergency.

**Figure 21.**Comparison between ANN-simulated data and vfill

_{v}target data for the right pressure sensor for braking at a speed of 70 km/h for the type: (

**a**) maintained, (

**b**) progressive and (

**c**) emergency.

**Figure 22.**Comparison between ANN simulated data and vfill

_{v}target data for the left pressure sensor for braking at a speed of 70 km/h for the type: (

**a**) maintained, (

**b**) progressive and (

**c**) emergency.

**Figure 23.**Comparison between the ANN-simulated data and target braking type data for braking at a speed of 70 km/h for the type: (

**a**) maintained, (

**b**) progressive and (

**c**) emergency.

**Figure 24.**Comparison between the ANN-simulated data and actual data collected by the right pressure sensor for braking at a speed of 70 km/h for the type: (

**a**) maintained, (

**b**) progressive and (

**c**) emergency.

**Figure 25.**Comparison between the ANN-simulated data and actual data collected by the left pressure sensor for braking at a speed of 70 km/h for the type: (

**a**) maintained, (

**b**) progressive and (

**c**) emergency.

Test Speed (km/h) | Type of Braking |
---|---|

20 | Maintained braking Progressive braking Emergency braking |

30 | Maintained braking Progressive braking Emergency braking |

40 | Maintained braking Progressive braking Emergency braking |

50 | Maintained braking Progressive braking Emergency braking |

60 | Maintained braking Progressive braking Emergency braking |

70 | Maintained braking Progressive braking Emergency braking |

80 | Maintained braking Progressive braking Emergency braking |

Speed (km/h) | Sensor | Maximum | Minimum | Average | Standard Deviation |
---|---|---|---|---|---|

20 | Right pressure (V) | 0.618 | 0.206 | 0.410 | 0.153 |

Left pressure (V) | 0.573 | 0.184 | 0.377 | 0.145 | |

Braking time (s) | 3.53 | 1.25 | 2.118 | 0.697 | |

Braking distance (m) | 10.949 | 4.031 | 6.629 | 2.105 | |

30 | Right pressure (V) | 0.792 | 0.264 | 0.458 | 0.173 |

Left pressure (V) | 0.734 | 0.220 | 0.419 | 0.163 | |

Braking time (s) | 3.73 | 1.7 | 2.901 | 0.612 | |

Braking distance (m) | 19.215 | 8.581 | 14.292 | 3.092 | |

40 | Right pressure (V) | 0.799 | 0.328 | 0.549 | 0.164 |

Left pressure (V) | 0.740 | 0.293 | 0.507 | 0.156 | |

Braking time (s) | 4.71 | 1.98 | 3.3 | 0.699 | |

Braking distance (m) | 31.757 | 12.136 | 21.376 | 4.967 | |

50 | Right pressure (V) | 1.165 | 0.411 | 0.643 | 0.225 |

Left pressure (V) | 1.082 | 0.375 | 0.594 | 0.211 | |

Braking time (s) | 5.44 | 2.45 | 3.847 | 0.884 | |

Braking distance (m) | 40.604 | 17.194 | 29.967 | 7.311 | |

60 | Right pressure (V) | 1.530 | 0.519 | 0.774 | 0.351 |

Left pressure (V) | 1.388 | 0.478 | 0.709 | 0.317 | |

Braking time (s) | 5.5 | 2.75 | 3.917 | 0.751 | |

Braking distance (m) | 49.273 | 24.040 | 37.255 | 6.631 | |

70 | Right pressure (V) | 1.586 | 0.584 | 0.803 | 0.279 |

Left pressure (V) | 1.481 | 0.536 | 0.739 | 0.262 | |

Braking time (s) | 5.93 | 2.34 | 4.259 | 0.885 | |

Braking distance (m) | 61.163 | 26.138 | 45.701 | 9.021 | |

80 | Right pressure (V) | 1.679 | 0.652 | 0.942 | 0.374 |

Left pressure (V) | 1.596 | 0.595 | 0.868 | 0.353 | |

Braking time (s) | 6.23 | 3 | 4.426 | 0.869 | |

Braking distance (m) | 76.692 | 38.014 | 54.596 | 10.266 |

Speed (km/h) | Sensor | Maximum | Minimum | Average | Standard Deviation |
---|---|---|---|---|---|

20 | Right pressure (V) | 0.720 | 0.334 | 0.502 | 0.118 |

Left pressure (V) | 0.670 | 0.312 | 0.466 | 0.110 | |

Braking time (s) | 2.6 | 1.58 | 2.029 | 0.357 | |

Braking distance (m) | 8.075 | 5.505 | 6.423 | 0.841 | |

30 | Right pressure (V) | 0.929 | 0.418 | 0.639 | 0.150 |

Left pressure (V) | 0.864 | 0.391 | 0.595 | 0.141 | |

Braking time (s) | 3.09 | 1.88 | 2.323 | 0.348 | |

Braking distance (m) | 15.135 | 8.688 | 11.378 | 1.915 | |

40 | Right pressure (V) | 1.177 | 0.540 | 0.817 | 0.222 |

Left pressure (V) | 1.066 | 0.502 | 0.755 | 0.200 | |

Braking time (s) | 3.3 | 2.07 | 2.568 | 0.398 | |

Braking distance (m) | 24.314 | 12.955 | 17.186 | 3.197 | |

50 | Right pressure (V) | 1.349 | 0.571 | 0.959 | 0.255 |

Left pressure (V) | 1.259 | 0.526 | 0.888 | 0.233 | |

Braking time (s) | 4.12 | 2.27 | 2.845 | 0.522 | |

Braking distance (m) | 33.805 | 18.447 | 23.480 | 4.075 | |

60 | Right pressure (V) | 1.597 | 0.641 | 1.044 | 0.342 |

Left pressure (V) | 1.488 | 0.599 | 0.966 | 0.309 | |

Braking time (s) | 3.87 | 2.4 | 3.196 | 0.545 | |

Braking distance (m) | 41.490 | 22.292 | 31.409 | 5.698 | |

70 | Right pressure (V) | 1.983 | 0.731 | 1.265 | 0.450 |

Left pressure (V) | 1.701 | 0.702 | 1.161 | 0.391 | |

Braking time (s) | 4.5 | 2.18 | 3.377 | 0.714 | |

Braking distance (m) | 49.581 | 23.706 | 37.905 | 8.934 | |

80 | Right pressure (V) | 1.992 | 0.807 | 1.379 | 0.404 |

Left pressure (V) | 1.814 | 0.748 | 1.243 | 0.329 | |

Braking time (s) | 4.58 | 2.52 | 3.415 | 0.596 | |

Braking distance (m) | 58.596 | 26.537 | 43.271 | 9.542 |

Speed (km/h) | Sensor | Maximum | Minimum | Average | Standard Deviation |
---|---|---|---|---|---|

20 | Right pressure (V) | 1.871 | 0.759 | 1.286 | 0.479 |

Left pressure (V) | 1.749 | 0.701 | 1.197 | 0.446 | |

Braking time (s) | 1.15 | 0.64 | 0.952 | 0.153 | |

Braking distance (m) | 4.148 | 2.321 | 3.202 | 0.613 | |

30 | Right pressure (V) | 1.879 | 1.01 | 1.471 | 0.374 |

Left pressure (V) | 1.786 | 0.937 | 1.374 | 0.321 | |

Braking time (s) | 1.5 | 1 | 1.266 | 0.132 | |

Braking distance (m) | 8.337 | 5.004 | 6.176 | 0.947 | |

40 | Right pressure (V) | 1.958 | 0.997 | 1.687 | 0.305 |

Left pressure (V) | 1.894 | 0.904 | 1.527 | 0.278 | |

Braking time (s) | 2.01 | 1.28 | 1.607 | 0.218 | |

Braking distance (m) | 15.594 | 8.649 | 10.494 | 2.198 | |

50 | Right pressure (V) | 1.986 | 1.235 | 1.737 | 0.235 |

Left pressure (V) | 1.942 | 1.122 | 1.635 | 0.244 | |

Braking time (s) | 2.04 | 1.71 | 1.887 | 0.092 | |

Braking distance (m) | 17.149 | 13.480 | 14.848 | 1.159 | |

60 | Right pressure (V) | 2.014 | 1.476 | 1.875 | 0.149 |

Left pressure (V) | 1.946 | 1.360 | 1.709 | 0.156 | |

Braking time (s) | 3.01 | 1.98 | 2.4 | 0.266 | |

Braking distance (m) | 28.524 | 17.495 | 21.891 | 3.187 | |

70 | Right pressure (V) | 2.245 | 1.768 | 1.999 | 0.148 |

Left pressure (V) | 2.055 | 1.637 | 1.798 | 0.122 | |

Braking time (s) | 2.67 | 2.36 | 2.523 | 0.098 | |

Braking distance (m) | 27.838 | 24.990 | 26.264 | 1.103 | |

80 | Right pressure (V) | 2.351 | 1.312 | 2.001 | 0.244 |

Left pressure (V) | 2.164 | 1.155 | 1.785 | 0.251 | |

Braking time (s) | 2.93 | 2.51 | 2.677 | 0.121 | |

Braking distance (m) | 39.404 | 28.348 | 32.543 | 3.523 |

**Table 5.**Target and simulated values of braking type (Tb), right pressure sensor q

_{t}(pr), left pressure sensor q

_{t}(pl) and error.

Test Speed (km/h) | Tb Target | Tb ANN | Error Tb (%) | q_{t} pr Target (−) | q_{t} pl Target (−) | q_{t} pr ANN (−) | q_{t} pl ANN (−) | Error q _{t} pr (%) | Error q _{t} pl (%) |
---|---|---|---|---|---|---|---|---|---|

20 | 1 | 1.198 | 19.790 | 61.666 | 55.066 | 62.325 | 51.528 | 1.068 | 6.426 |

30 | 1 | 1.267 | 26.690 | 83.841 | 76.920 | 83.896 | 74.716 | 0.066 | 2.866 |

40 | 1 | 1.339 | 33.870 | 144.547 | 132.640 | 143.452 | 132.713 | 0.758 | 0.055 |

50 | 1 | 1.268 | 26.780 | 176.539 | 161.390 | 175.466 | 163.674 | 0.608 | 1.415 |

60 | 1 | 1.273 | 27.340 | 196.110 | 176.927 | 200.004 | 182.471 | 1.986 | 3.134 |

70 | 1 | 0.934 | 6.640 | 212.132 | 189.399 | 210.982 | 189.003 | 0.542 | 0.209 |

80 | 1 | 0.799 | 20.060 | 256.899 | 224.802 | 257.644 | 224.558 | 0.290 | 0.109 |

20 | 2 | 1.839 | 8.075 | 68.920 | 64.861 | 67.529 | 63.509 | 2.018 | 2.084 |

30 | 2 | 2.175 | 8.755 | 91.568 | 85.262 | 91.926 | 85.583 | 0.391 | 0.376 |

40 | 2 | 2.345 | 17.255 | 149.352 | 139.339 | 149.797 | 138.186 | 0.298 | 0.827 |

50 | 2 | 1.749 | 12.560 | 174.557 | 162.725 | 174.978 | 162.466 | 0.241 | 0.160 |

60 | 2 | 1.931 | 3.475 | 256.852 | 237.602 | 242.019 | 228.535 | 5.775 | 3.816 |

70 | 2 | 1.899 | 5.040 | 304.726 | 284.060 | 304.717 | 283.668 | 0.003 | 0.138 |

80 | 2 | 1.872 | 6.425 | 351.586 | 315.649 | 347.118 | 316.410 | 1.271 | 0.241 |

20 | 3 | 2.302 | 23.283 | 84.704 | 80.895 | 79.247 | 73.292 | 6.443 | 9.399 |

30 | 3 | 2.694 | 10.213 | 121.171 | 108.838 | 122.686 | 114.119 | 1.250 | 4.852 |

40 | 3 | 2.502 | 16.610 | 153.193 | 141.558 | 149.638 | 138.841 | 2.321 | 1.920 |

50 | 3 | 2.850 | 5.010 | 218.325 | 193.090 | 216.281 | 194.676 | 0.936 | 0.821 |

60 | 3 | 2.656 | 11.470 | 284.893 | 256.028 | 282.748 | 258.274 | 0.753 | 0.877 |

70 | 3 | 2.560 | 14.673 | 330.512 | 289.901 | 328.298 | 291.454 | 0.670 | 0.536 |

80 | 3 | 2.723 | 9.220 | 367.199 | 333.607 | 365.160 | 331.577 | 0.555 | 0.609 |

**Table 6.**Target and simulated values of vfill

_{t}of the right pressure sensor (pr), vfill

_{t}of the left pressure sensor (pl) and error.

Test Speed (km/h) | Tb | vfill_{t} pr Target (−) | vfill_{t} pl Target (−) | vfill_{t} pr ANN (−) | vfill_{t} pl ANN (−) | Error vfill_{t} pr (%) | Error vfill_{t} pl (%) |
---|---|---|---|---|---|---|---|

20 | 1 | 0.453 | 0.420 | 0.461 | 0.430 | 1.674 | 2.306 |

30 | 1 | 0.448 | 0.408 | 0.412 | 0.384 | 8.110 | 5.841 |

40 | 1 | 0.315 | 0.284 | 0.307 | 0.279 | 2.699 | 1.759 |

50 | 1 | 0.354 | 0.324 | 0.339 | 0.307 | 4.191 | 5.244 |

60 | 1 | 0.484 | 0.437 | 0.478 | 0.437 | 1.306 | 0.081 |

70 | 1 | 0.358 | 0.319 | 0.387 | 0.358 | 8.295 | 12.057 |

80 | 1 | 0.412 | 0.361 | 0.405 | 0.370 | 1.736 | 2.456 |

20 | 2 | 0.428 | 0.403 | 0.433 | 0.404 | 1.150 | 0.332 |

30 | 2 | 0.430 | 0.400 | 0.453 | 0.424 | 5.463 | 5.962 |

40 | 2 | 0.692 | 0.645 | 0.745 | 0.694 | 7.579 | 7.675 |

50 | 2 | 0.619 | 0.577 | 0.626 | 0.580 | 1.099 | 0.548 |

60 | 2 | 0.895 | 0.828 | 0.847 | 0.774 | 5.392 | 6.545 |

70 | 2 | 0.896 | 0.835 | 0.950 | 0.860 | 5.952 | 2.960 |

80 | 2 | 0.623 | 0.581 | 0.616 | 0.568 | 1.011 | 2.310 |

20 | 3 | 0.538 | 0.510 | 0.530 | 0.495 | 1.475 | 2.893 |

30 | 3 | 0.927 | 0.817 | 0.892 | 0.829 | 3.795 | 1.418 |

40 | 3 | 0.876 | 0.747 | 0.853 | 0.793 | 2.644 | 6.233 |

50 | 3 | 1.200 | 1.061 | 1.110 | 1.021 | 7.485 | 3.792 |

60 | 3 | 1.217 | 1.094 | 1.170 | 1.065 | 3.942 | 2.663 |

70 | 3 | 1.306 | 1.146 | 1.251 | 1.129 | 4.254 | 1.454 |

80 | 3 | 1.429 | 1.298 | 1.373 | 1.236 | 3.898 | 4.752 |

**Table 7.**Mean error in the results of the braking type, q

_{t}and vfill

_{t}simulations of the pressure sensors.

Tb | Mean Error Tb (%) | Mean Error q_{t} pr (%) | Mean Error q_{t} pl (%) | Mean Error vfill_{t} pr (%) | Mean Error vfill_{t} pl (%) |
---|---|---|---|---|---|

1 | 23.024 | 0.760 | 2.030 | 4.002 | 4.249 |

2 | 8.798 | 1.428 | 1.092 | 3.949 | 3.762 |

3 | 12.926 | 1.847 | 2.716 | 3.927 | 3.315 |

Total | 14.916 | 1.345 | 1.946 | 3.959 | 3.775 |

**Table 8.**Standard deviation in the results of the brake type, q

_{t}and vfill

_{t}simulations of pressure sensors.

Tb | Standard Deviation Tb (%) | Standard Deviation q _{t} pr (%) | Standard Deviation q _{t} pl (%) | Standard Deviation vfill _{t} pr (%) | Standard Deviation vfill _{t} pl (%) |
---|---|---|---|---|---|

1 | 8.675 | 0.629 | 2.328 | 3.024 | 3.980 |

2 | 4.731 | 2.044 | 1.384 | 2.773 | 2.965 |

3 | 5.913 | 2.113 | 3.317 | 1.846 | 1.755 |

Total | 6.439 | 1.595 | 2.343 | 2.548 | 2.900 |

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**MDPI and ACS Style**

Garrosa, M.; Olmeda, E.; Díaz, V.; Mendoza-Petit, M.F.
Design of an Estimator Using the Artificial Neural Network Technique to Characterise the Braking of a Motor Vehicle. *Sensors* **2022**, *22*, 1644.
https://doi.org/10.3390/s22041644

**AMA Style**

Garrosa M, Olmeda E, Díaz V, Mendoza-Petit MF.
Design of an Estimator Using the Artificial Neural Network Technique to Characterise the Braking of a Motor Vehicle. *Sensors*. 2022; 22(4):1644.
https://doi.org/10.3390/s22041644

**Chicago/Turabian Style**

Garrosa, María, Ester Olmeda, Vicente Díaz, and Mᵃ Fernanda Mendoza-Petit.
2022. "Design of an Estimator Using the Artificial Neural Network Technique to Characterise the Braking of a Motor Vehicle" *Sensors* 22, no. 4: 1644.
https://doi.org/10.3390/s22041644