A driving test was designed to gather information about the drivers and the way they use the clutch pedal. These experiments created a datasheet with several variables that would be used to create the models (statistical and fuzzy logic).

The recruitment of the volunteers was made by word of mouth, and all the subjects were volunteers. Moreover, it is important to highlight that all the methods were carried out in accordance with relevant guidelines and regulations. Experimental protocols were approved by the Universidad Carlos III de Madrid ethics committee. An informed consent with a description of the test, the objective of the study, test protocol, duration and possible risks were delivered to each volunteer. Once the volunteers had understood it completely and signed it, it must be returned to the authors.

## Experimental test

26 volunteers participated in the driving test, with ages between 21 and 56 years old, and mean weight of 120 ± 44 kg, a height of 1699.3 ± 85.6 mm and driving experience that moves from 0.2 to 38 years. Driving experience was defined as the time that has elapsed since a driver's license was obtained. It is important to mention that all the volunteers involved in the experiment drive every day. Volunteers were recruited by word of mouth.

The experimental test was split into three sections as follows.

## Step 1: explanation of the experiment

The volunteers were informed about the experiment and its risks before starting. The explanation includes 3 parts. Firstly, the informed consent was delivered with all the instructions for the experiment. Once the volunteers read it, the experiment was explained to them and any kind of questions were answered before starting. In addition, possible risks or injuries that could happen due to the test were previously underlined. The third part was to sign the consent form and fill out a short formular about some information such as their age, genre or driving experience, among others. Both documents must be returned to the researchers in charge.

It is worth noting that volunteers have the freedom to leave the experiment at any time without any kind of explanation.

## Step 2: main body measurements

For the design of the two models, it was necessary to get some anthropometric measurements such as their height or their weight. The instructions to get them were supported by the National Institute of Workplace Safety and Hygiene (INSHT) of the Ministry of Employment and Social Security of Spain [18].

The height is defined as the vertical distance from the ground to the vertex. First, the volunteers should undress heels, high-soled shoes, hair ornaments and everything that could interfere with the measure. Secondly, they must stand with the right and left heel touching and at a 45° feet angle. Also, they must stand against a wall with their heels and back touching the vertical surface (wall) and keeping the head in the Frankfort plane [19]–[22]. According to the weight, the volunteers should stay undressed on a balance until the measure becomes stable. A summary of these parameters can be seen in the Classification of the volunteers section.

## Step 3: driving test

## o Vehicle

The driving test was carried out with a real vehicle inside a close track. The vehicle was a Hyundai i30 diesel-powered with a manual gearbox of 5 gears. Inside the vehicle different systems (Fig. 1) were installed to measure the forces on the pedal. On the one hand, there is the pedal force sensor (❶) which must be supplied by DC power (❷). ❶ is connected to the data acquisition system (❸) to collect all the data. All these elements must be powered, not only by DC but also by AC. To that aim, a mobile battery (❺) is used with an AC/DC converter (❹)

Some technical information related to the instrumentation used in the experiment is shown in Table 1**¡Error! No se encuentra el origen de la referencia.**.

Table 1

Technical data of the PK-PKH HKM-Messtechnik force sensor pedal and the data acquisition module NI PXI 6230.

PK-PKH HKM-Messtechnik |

Nominal load range: 1500 N |

Accuracy: 0.5% full scale |

Output signal: 0–10 V |

NI PXI 6230 |

Analogue inputs: 8 (16 bits) |

Analogue outputs: 4 |

Sample rate: 250 KS/s |

Digital inputs: 6 |

Digital outputs: 4 |

Analog input accuracy: 3100 µV |

## o Track

The round track was located inside the facilities of the Universidad Carlos III de Madrid and covered a distance of 450 m with a gradient of 0°. Moreover, the track’s route is a loop with no sharp curves. In addition, the width of the road ensures enough space to drive in secure conditions (the driver must be focused on driving).

Before the test with volunteers, several checks were carried out to verify the design was appropriate.

## Classification of the volunteers

A summary of the characteristics of the volunteers is shown in Table 2.

Table 2

Summary of the main characteristics of the volunteers. (D.E.: Driving Experience, BMI: Body Mass Index).

| | Max | Min | Mean | σ |

♂ | Age (years) | 66.0 | 21.0 | 36.41 | 14.1 |

Weight (kg) | 120.0 | 61.6 | 79.87 | 12.9 |

Height (mm) | 1940.0 | 1570.0 | 1767.50 | 72.6 |

BMI | 36.6 | 20.6 | 25.59 | 3.8 |

D. E. (years) | 46.0 | 0.2 | 17.6 | 14.2 |

♀ | Age (years) | 60.0 | 19.0 | 35.07 | 10.7 |

Weight (kg) | 87.0 | 44.0 | 63.56 | 10.9 |

Height (mm) | 1830.0 | 1560.0 | 1665.24 | 64.2 |

BMI | 30.8 | 17.0 | 22.84 | 3.2 |

D. E. (years) | 41.0 | 1.0 | 15.5 | 10.6 |

♀+♂ | Age (years) | 56 | 21 | 31.7 | 10.0 |

Weight (kg) | 120.0 | 44.0 | 69.7 | 16.7 |

Height (mm) | 1830.0 | 1560.0 | 1699.3 | 85.6 |

BMI | 36.6 | 17.0 | 23.9 | 4.1 |

D. E. (years) | 38 | 0.2 | 12.1 | 9.9 |

## Driving test results: force applied on the pedal

This section shows the forces the volunteers applied on the pedal while driving. This force varies along the pedal stroke, and the behaviour of the curve is not the same when the driver engages or disengages. In the following lines, some examples are included to describe it in more detail.

Figure 2 shows the force a driver applies on the clutch pedal along with one experiment. As can be seen, several parts of the graph follow the same pattern. Each one represents the behaviour of the force when the driver changes the gear, and for a better understanding, some of them were highlighted with different coloured squares.

If the pattern is studied (Fig. 3), it can be seen how the force increases and decrease sharply. Firstly it is reached a local maximum ① and then a local minimum ② to continue increasing again sharply to reach a maximum peak ③. After that comes a decrease of the force to get a minimum local ④ that eventually increases again to a local maximum ⑤ that settles down to a fully downward slope.

These results present similarities with other studies carried out up to this time [15], [23].

## Force classification

Once the experiments were finished the forces (Fig. 4) were sorted by: gender Ⓐ, driving experience Ⓑ, height Ⓒ, weight Ⓓ, BMI (Body Mass Index) Ⓔ and HH/HK (Height of the Hip/Height of the Knee). This classification allows the detection of patterns to create the prediction tools.

Figure 4.a shows the force exerted by men and women, where men exerted around 30 N (23%) more than women.

According to the driving experience (Fig. 4.b), it was split into four different groups based on the existing literature [24]. The difference between the highest and lowest force is around 35 N (≈ 25% of the maximum force). Aside, it is important to highlight how volunteers with the most experience (≥ 15 years) apply the lower force. One reason that could explain that fact is the “know-how” each volunteer had. As more experience the drivers have, the more confidence they felt. On the opposite, as less experience the drivers have, they tend to feel more fear and apply more force than necessary.

Figure 4.c represents the force depending on the height of the volunteers. Results show that the force is directly connected with height. Applied forces on the clutch pedal increase as the height of the volunteers does. Around 30 N between the maximum and minimum peak force (≈ 22% of the maximum force).

(Fig. 4.d) shows the force depending on the weight of the volunteers. What stands out is that the peak force decreases at the same as the weight. The maximum peak value is located 20 N above the minimum peak value (≈ 14% of the maximum force).

The next parameter is the Index Body Mass (Fig. 4.e), an aspect that defines the relation between weight and height [25]. The force distribution based on de IBM follows a random distribution, therefore, concerning the test performed in this study, the IBM cannot be used to approach the behaviour of the driver.

Finally, the HH/HK (Height of the Hip/Height of the Knee) ratio plays an important role. Figure 4.e shows how the maximum peak force is due to the maximum value of the HH/HK ratio (HH/HK > 2.3).

## Practical approach to estimate the behaviour of the drivers

With the data collected in the driving test, two model approaches were developed. One uses statical tools and the second one the fuzzy logic algorithm. To measure the aptitude and accuracy of both models, different indicators were calculated. The information of each indicator is explained next.

## Validation Indicators

Five different indicators were used to validate the model. These five parameters were individually used.

1. Coefficient of determination (R2): this parameter defines the quality of the model in order to reproduce the real data and it is calculated by Eq. (1). This coefficient reaches a value equal to or close to 1 when the compared samples are similar. As it moves away from this value, the dispersion increases.

$${R}^{2}=\frac{{\sigma }_{xy}^{2}}{{\sigma }_{x}^{2}{\sigma }_{y}^{2}}$$

1

2. Spearman’s correlation: calculates the monotonic relation of two variables and assesses the monotonic correlation of two variables. This one goes from − 1 to 1. 1 happens when there is a match of 100% and − 1 when it is -100%. Some other authors used this correlation to compare signals with good findings [26], [27]. 3. Energy ratio (2): it is the fraction between the energy of both signals (real and model) [28]. As close to 1 the signals seem to be more similar. The ratio was assessed point by point.

$$ER=\frac{{\int }_{0}^{t}{\left|x\left(t\right)\right|}^{2}dt}{{\int }_{0}^{t}{\left|y\left(t\right)\right|}^{2}dt}$$

2

4. Linear correlation coefficient (LC): calculated by means of Eq. (3). This coefficient moves from − 1 to 1. In case LC is over 0 the correlation is positive, but if it is under 0 the correlation is negative. When LC is equal to 0 there is no correlation between signals [29].

$$LC=\frac{\sum \left(x-\stackrel{-}{x}\right)\left(y-\stackrel{-}{y}\right)}{\sqrt{\sum {\left(x-\stackrel{-}{x}\right)}^{2}\sum {\left(y-\stackrel{-}{y}\right)}^{2}}}$$

3

5. Cross-correlation coefficient (CC): as the previous parameter, it gets a value between − 1 and 1. -1 is equal to an uncorrelated relationship and 1 positive correlation of the signals. Some examples comparing signals can be found in the work undertaken by Harrison et al. [30] and in the manuscript of Winter et al. [31]. Eq. (4) defines it.

$$CC=\frac{n(\sum xy)-(\sum x\left)\right(\sum y)}{\sqrt{\left[n\left(\sum {x}^{2}\right)-{\left(\sum x\right)}^{2}\right]\left[n\left(\sum {y}^{2}\right)-{\left(\sum y\right)}^{2}\right]}}$$

4

## Statistic model

This section describes the first model, the statistical one. To that aim, the most significant points of Fig. 2 and only the most relevant parameters (driving experience, height, weight, and HH/HK factor), were considered.

The assessment was done using polynomial regression and the results consist of a set of equations (1) that estimates the force in every single point tagged in Fig. 2.

F = ƒ (Driving experience, Height, Weight, HH/KH) (5)

## Results of the statistical model

The five indicators explained in the previous section (Validation Indicators) were evaluated. The assessment (Table 3) was done by analyzing the complete model and for every single characteristic point (①, ②, ③, ④, ⑤), depending on the indicator.

Table 3

Results of the validation indicators based on the Fig. 2 for the statistical model. SC (Spearman’s Correlation), ER (Energy ratio), LC (linear correlation) CC (Cross-correlation).

Point | ① | ② | ③ | ④ | ⑤ | Mean | SD |

R2 | 0.83 | 0.83 | 0.82 | 0.92 | 0.94 | 0.87 | 0.05 |

SC | - | - | - | - | - | 0.93 | 0.10 |

ER | 0.98 | 0.88 | 0.98 | 0.90 | 0.91 | 0.93 | 0.05 |

LC | - | - | - | - | - | 0.94 | 0.27 |

CC | - | - | - | - | - | 0.71 | - |

## Fuzzy Logic model

This section, it is described the second model designed by employing fuzzy logic.

Fuzzy logic is a computational tool that allows for describing a fuzzy system to estimate the output response according to a set of rules and a knowledge database. The working method consists of different actions: define the inputs, define the rules and define the output. The inputs are the driving experience, the height, the weight and the HH/KH ratio. The output is the force applied to the clutch pedal. Rules were defined to create the relationships between inputs and outputs with a set of membership functions by means the Mamdani’s method and some trapezoidal mathematical expressions (Fig. 5).

## Results of the Fuzzy Logic model

As it was done for the statistical method, the five indicators were solved (Table 4). Depending on the indicator, the assessment was done for every single characteristic point (①, ②, ③, ④, ⑤) and the complete model.

Table 4

Results of the validation indicators based on the Fig. 2 for the fuzzy logic model. SC (Spearman’s Correlation), ER (Energy ratio), LC (linear correlation) CC (Cross-correlation).

Point | ① | ② | ③ | ④ | ⑤ | ߃ | σ |

R2 | 0.99 | 0.97 | 0.99 | 0.98 | 0.99 | 0.99 | 0.01 |

SC | - | - | - | - | - | 0.97 | 0.05 |

ER | 0.99 | 1 | 1 | 0.98 | 1 | 1 | 0.1 |

LC | - | - | - | - | - | 0.99 | 0.01 |

CC | - | - | - | - | - | 0.96 | - |

## Comparison between the statical and the fuzzy logic model

In the following figure (Fig. 6) it is plotted an example that compares the signal from the experiment of one volunteer, the result achieved by the statical model and the result from the fuzzy logic model of the same volunteer.