# A Linear Model for the Estimation of Fuel Consumption and the Impact Evaluation of Advanced Driving Assistance Systems

^{*}

## Abstract

**:**

## 1. Introduction

^{2}(DRIVEr monitoring: technologies, methodologies, and IN-vehicle INnovative systems; [2]), and its data were used for the estimation of the parameters of the model. At a later stage, data of a validation experiment were exploited in order to check the transferability of the model to different contexts.

## 2. Problem Formulation

_{2}emission and fuel consumption (eco-route, [8]). Eco-driving at the single vehicle/driver level can be achieved through an understanding what primarily affects fuel consumption, and by developing ADAS that help drivers in adopting efficient driving styles in terms of emissions and energy consumption. At both levels, the effects of the adopted solutions can be investigated by using microscopic simulation tools, which allow the simulation of the interaction of vehicles in a traffic stream and the resulting kinematics (and dynamics) of the vehicles. Microscopic models make it possible to explicitly take into account different driving behaviors [11] and engine characteristics [12,13].

^{2}): 0.76, 0.81 and 0.71. Concerning the eco-driving advisory, The University of Twente (Netherlands) in collaboration with the School of Transportation and Society (Sweden) have developed a fuel-efficiency support tool capable of performing real-time control of consumption and providing both positive and negative video feedback while driving. The support tool includes the so-called normative model, which back-calculates the minimal fuel consumption for maneuvers carried out [28]. Similarly, [29] developed an Acceleration Advisor (AA) able to signal the driver, causing a resistance on the gas pedal if s/he is accelerating too quickly. The values of the speed of pedal depression and the initial resistance were chosen after comparing driving patterns from fixed test runs involving 16 combinations of resistance variables being systematically changed. Driving pattern parameters concerning fuel efficiency (e.g., percentage time of high acceleration) were compared for each test run, as well as the perceived acceptance of the resistance level based on relative time consumption.

## 3. Data Source

#### 3.1. Principal Experiment

^{2}research project has been characterized by a large experiment. The test route was a 80 km circular ring composed by two toll-road segments with different posted speed-limits (100 and 130 km/h) and a one-lane-per-direction road with 60 km/h speed limit (and without overtaking allowed). 100 recruited subjects drove once around this route. The experiment also featured 5 professional test drivers from the FCA (Fiat Chrysler Automobiles) plant in Pomigliano d’Arco, near Naples, who drove only about the 70% of the principal test route’s total length (indeed they drove on a different test route, starting from the FCA plant). They were asked to perform eco-driving based on fuel consumption.

^{2}along the axis of motion.

#### Data Reduction

_{inst}), which expresses the fuel consumption for every second, and the liter per kilometer fuel consumption (FC

_{km}), which expresses the fuel consumption in one kilometer if the current motion conditions are maintained stationary.

_{inst}from Fuel metering [mg i] by using the following formulation:

- 4 is the number of cylinders in the engine;
- RPM is rated for two because we have one injection each 2 RPM;
- 1000 is used to switch from mg to g;
- 60 is the number of seconds in one minute; and
- 825 is the density of diesel fuel expressed g/l.

_{km}can be computed by using the current speed value as:

- fuel metering values lower than 8.62 mgi (these values are evident measurement errors, being below the value of consumption observed in engine idling speed);
- instantaneous consumption values higher than 0.12 l/km (these are measurement errors too, being over the maximum value of fuel consumption furnished by the manufacturer);
- speed values lower than 10 km/h (excluding these cuts off the stop-and-go phase, to which our model does not apply).

#### 3.2. Transferability Experiment

## 4. Results

#### 4.1. Validation of Consumption Data

_{inst}has been carried out indirectly. Indeed a direct correlations exists between fuel consumption and emissions. Thus, measuring emissions allows for an indirect estimation of fuel consumption. For this purpose we used the following formulation:

_{2}and CO are respectively the instantaneous mass of CO

_{2}and CO expressed in g/s. The development of this formulation is an outcome of experiments carried out for the DRIVE IN

^{2}project by the Istituto Motori of the National Research Council (CNR) of Italy; more details on the aim and the results of these experiments will be given in further publications.

_{diff}parameter, defined as:

**Figure 1.**(

**A**) Probability mass function (pmf) and (

**B**) cumulative mass function (cmf) versus the difference in the consumption values measured with the two instruments (FM

_{diff}) in the validation experiment.

#### 4.2. Model Specification and Estimation of the Parameters

^{2}) and acceleration (a). Indeed these variables were selected as more significant by the stepwise algorithm. Then the linear regression model is calibrated as follows:

_{mgi}= β

_{0}+ β

_{1}v

^{2}+ β

_{2}a+ β

_{3}GasPedal + β

_{4}IntakeAir

_{i}, is the complementary to 1 of ${R}_{i}^{2}$, where ${R}_{i}^{2}$ is the coefficient of determination of a regression of explanatory on all the other explanators. Whereas the VIF index is the reciprocal of the tolerance index. In other words:

**Table 1.**Index of determination, model coefficients, and their statistical significance within the full model (identification against 50 drivers).

Constant | v^{2} | a | Gas Pedal | Intake Air | |
---|---|---|---|---|---|

β | 7.750 | 0.005 | 6.420 | 0.212 | 0.004 |

t | 123,000 | 77.600 | 84.500 | 186,000 | 36.400 |

sig. | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 |

std. β | - | 0.205 | 0.225 | 0.490 | 0.098 |

T | - | 0.797 | 0.786 | 0.797 | 0.763 |

VIF | - | 1.255 | 1.273 | 1.254 | 1.311 |

R^{2} | 0.483 | ||||

std. error | 3.759 |

_{inst}, have been depicted:

_{mgi}.

**Figure 3.**(

**A**) Probability mass function (pmf) and (

**B**) cumulative mass function (cmf) versus the percentage error (ERR

_{inst}) of the three sub-samples.

- RMSE (root mean square error), which is the ratio between the inner deviance and the total numerosity, n$$RMSE=\sqrt{\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({x}_{i}-{\widehat{x}}_{i}\right)}^{2}}{n}}$$
- MAPE (mean absolute percentage error), which is a measure of accuracy of a method for constructing fitted time series values$$MAPE=\frac{1}{n}{\displaystyle \sum}_{i=1}^{n}\frac{\left|{x}_{i}-{\widehat{x}}_{i}\right|}{{x}_{i}}$$

RMSE | MAPE | |
---|---|---|

Specification Sample | 3.790 | 0.188 |

Control Sample | 3.670 | 0.184 |

Fiat Sample | 3.330 | 0.161 |

_{mgi}= β

_{0}+ β

_{1}v

^{2}+ β

_{2}a+ β

_{3}GasPedal

**Table 3.**Index of determination and beta coefficients and their significance within the reduced.1 model (identification against 50 drivers).

Constant | v^{2} | a | Gas Pedal | |
---|---|---|---|---|

β | 9.530 | 0.005 | 7.300 | 0.222 |

t | 238.000 | 88.200 | 101.000 | 199.000 |

sig. | <0.001 | <0.001 | <0.001 | <0.001 |

std. β | - | 0.228 | 0.255 | 0.513 |

T | - | 0.845 | 0.873 | 0.846 |

VIF | - | 1.183 | 1.145 | 1.182 |

R^{2} | 0.476 | |||

std. error | 3.785 |

**Figure 4.**(

**A**) The probability mass function (pmf) and (

**B**) cumulative mass function (cmf) of the gap between the responses of the full model and the reduced.1 evaluated for the three sub-samples.

^{2}(model reduced.2) and the a (model reduced.3). Results associated with these models have been reported in Table 4. Removing Intake Air causes a negligible reduction of the R-square value (and consistently causes a negligible increase in the standard error of the model). The decrease of the model performance becomes significant once the reduced.2 and reduced.3 specifications are considered.

**Table 4.**Index of determination and beta coefficients and their significance within the reduced.2 and reduced.3 models (identification against 50 drivers).

reduced.2 | Constant | v^{2} | a | Gas Pedal | |

β | 12.497 | - | 5.430 | 0.255 | |

t | 551.674 | - | 75.144 | 233.576 | |

sig. | <0.001 | - | <0.001 | <0.001 | |

std. β | - | - | 0.190 | 0.590 | |

R^{2} | 0.432 | ||||

std. error | 3.940 | ||||

reduced.3 | |||||

β | 12.935 | - | - | 0.272 | |

t | 573.849 | - | - | 248.090 | |

sig. | <0.001 | - | - | <0.001 | |

std. β | - | - | - | 0.631 | |

R^{2} | 0.398 | ||||

std. error | 4.058 |

#### 4.3. Model Transferability

_{inst}and have been reported in Figure 5. ERR

_{inst}distribution has been computed for each of the different driving contexts studied, and for the whole validation path. The ERR

_{inst}distribution concerning the control sample of the DRIVE IN

^{2}experiment has been also reported (dashed line) for comparison.

**Figure 5.**(

**A**) Probability mass function (pmf) and (

**B**) cumulative mass function (cmf) of the gap between the responses of the reduced.1 model once applied in the driving contexts of the validation experiment.

#### 4.4. Parameters Dispersion

**Table 5.**The minimum, maximum, first, second and third quartiles of the values assumed by the parameters (together with R-square and RMSE) estimated for each of the trajectories in the dataset.

Min | Max | Q1 | Q2 | Q3 | |
---|---|---|---|---|---|

β_{0} | 4.580 | 13.500 | 7.440 | 8.970 | 10.200 |

β_{1} | 1.53 × 10^{−4} | 1.02 × 10^{−2} | 4.01 × 10^{−3} | 6.40 × 10^{−3} | 7.65 × 10^{−3} |

β_{2} | −5.620 | 21.200 | 1.750 | 11.800 | 14.200 |

β_{3} | 0.115 | 0.518 | 0.184 | 0.236 | 0.288 |

R^{2} | 0.226 | 0.785 | 0.474 | 0.545 | 0.630 |

RMSE | 2.320 | 5.400 | 3.020 | 3.420 | 3.760 |

#### 4.5. Aggregate Analysis

_{aggr}variable.

**Figure 6.**(

**A**) Probability mass function (pmf) and (

**B**) cumulative mass function (cmf) versus the aggregate error evaluated in the sample used for the model verification.

## 5. Discussion

_{inst}), but on the other hand we showed that in about 10% of the cases this discrepancy is greater than 50%. The performance of the model in terms of instantaneous fuel consumption gets worse when applied to the estimation of the fuel consumed during the transferability experiment. On the other hand two of the models presented in Section 2, those compatible with our experiments, have been calibrated using our data, and both of them present even worse performances. Indeed, the best of the functional forms within those introduced by Lee et al. [27], corresponds to our reduced.3 specification, which we showed to be less convincing than reduced.1 (Table 4); it is worth noting that in the original work the throttle was used instead of the gas pedal as independent variable, but this difference seems to be not enough to justify the great decrease in the performance of the model (the authors reported an R-square coefficient of 0.81 in their dataset). Similarly the best of the models presented in [25], the Model M, exhibits an R-square of 0.27 (and an RMSE of 4.459) once calibrated by using data of our specification sample; moreover six of the estimated coefficients (of a total of fifteen) are not statistically significant.

_{2}) estimated for each of the driving sessions (Table 5).

## 6. Conclusions

_{2}emission savings can be created by adopting environmentally friendly policies, by implementing traffic congestion reducing strategies, by choosing ecological routes, and, in particular, by enacting more efficient driving styles. Our research addresses this last point through the development of real-time microscopic fuel consumption model. The data used in the paper were collected during a huge experimental campaign (more than 8000 Km of driving data over 100 subjects) near Naples, Italy, by an instrumented vehicle under extra-urban driving conditions. We proposed a simple and efficient fuel consumption model based only on data from OBD port and IMU and, therefore, one that is easy to implement in an integrated simulation environment.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Bifulco, G.N.; Galante, F.; Pariota, L.; Spena, M.R.
A Linear Model for the Estimation of Fuel Consumption and the Impact Evaluation of Advanced Driving Assistance Systems. *Sustainability* **2015**, *7*, 14326-14343.
https://doi.org/10.3390/su71014326

**AMA Style**

Bifulco GN, Galante F, Pariota L, Spena MR.
A Linear Model for the Estimation of Fuel Consumption and the Impact Evaluation of Advanced Driving Assistance Systems. *Sustainability*. 2015; 7(10):14326-14343.
https://doi.org/10.3390/su71014326

**Chicago/Turabian Style**

Bifulco, Gennaro Nicola, Francesco Galante, Luigi Pariota, and Maria Russo Spena.
2015. "A Linear Model for the Estimation of Fuel Consumption and the Impact Evaluation of Advanced Driving Assistance Systems" *Sustainability* 7, no. 10: 14326-14343.
https://doi.org/10.3390/su71014326