# The Effect of Driving Cycle Duration on Its Representativeness

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Common Trip Database

^{2}> 0.9) obtained in a correlation analysis between the results obtained by these two methods, we concluded that the OBD produces reliable data. Tailpipe emissions were monitored with a Portable Emission Measurement System (PEMS), SEMTECH ECOSTAR model from Sensors Inc. with the modules for measuring CO, CO

_{2}, NO, and NO

_{2}. With the SEMTECH-FEM module, CO and CO

_{2}emissions were measured using a non-dispersive infrared analyzer, and the SEMTECH-NOx module for NO and NO

_{2}emissions using a non-dispersive ultraviolet gas analyzer. Both concentration measurement systems are recommended by the US Environmental Protection Agency (USEPA) for these purposes. At the beginning and at the end of each measurement, the recommended calibration procedure by the manufacturer was carried out using NIST traceable calibration gas tanks.

_{2}emissions [13]. After analyzing the monitoring campaign results, 46 monitored trips were included in the sample trips database.

#### 2.2. Construction of Representative DCs

_{i}, Table 1). CP

_{i}are metrics, like mean speed or mean positive acceleration, calculated from the speed and time data collected in the monitored trips. A DC is a time series of speeds, and they also can be described by the same set of CP

_{i}. We use CP

_{i}to denote the characteristic parameters that describe the local driving patterns, while CP

_{i}* for the characteristic parameter that describes the DCs. Relative differences between CP

_{i}and CP

_{i}* (RD

_{i,}Equation (1)) close to zero indicate that the DC represents the local driving patterns [18].

_{i,}Equation (1)). RDi values equal to or smaller than 5% are used as an acceptable threshold for selecting a DC. Otherwise, the method restarts and selects a new group of micro-trips and proposes a new candidate DC. Within this method, only 3 $C{P}_{i}$ are considered, and they are referred to as assessment criteria. In this work, we used as assessment criteria average speed, percentage of idling time, and specific fuel consumption (SFC), following up the results reported in Quirama et al. [21], who identified the main characteristic parameters to construct DC. They also found that by including SFC in the assessment criteria, the resulting DC reproduce other $C{P}_{i}$ and emissions. Including additional CP

_{i}within the set of CP

_{i}used as assessment criteria would results into excessive computational time or into convergence problems.

_{2}, CO, and NO

_{x}. Table 1 presents the characteristic parameters used in this study.

_{i}). Aiming to observe the trend and dispersion of the representativeness of the obtained DCs, the process was repeated 500 times. This value was used after the work of Quirama et al. [22], who determined that after 500 repetitions, convergence in the results is obtained. The trend was calculated through the Mean Relative absolute Difference (MRD

_{i}), Equation (2), while the dispersion was calculated through the Inter-quartile range (IQR

_{i}).

_{i}and ARD

_{i}values close to zero indicate that the obtained DCs, with a high probability, tend to be highly representative of the local driving, respectively.

#### 2.3. Determination of the Appropriate DC Duration

_{i}at the iteration j (MRD

_{j}*, Equation (3)). Similarly, the MIQR

_{j}* (Equation (4)) were obtained. Finally, the average of the MRD

_{j}* ($\overline{MRD}$) and MIQR

_{j}* ($\overline{MIQR}$) were calculated.

_{i}listed in Table 1, while j refers to the iteration number that ranges from 1 to 500. The MRD

_{i}described in the previous section (Section 2.2) are the mean value of the 500 iterations for each CPi, while the MRD

_{j}* are the mean value of RD

_{i}for all CP

_{i}at iteration j.

## 3. Results

_{i}obtained for the 500 DCs for a duration of 20 min, the urban 1 region, and the cases of average speed, positive kinetic energy, specific fuel consumption, and NOx emissions. Vertical red lines in this figure represent their respective MRD

_{i}. We highlight that average speed and specific fuel consumption are two of the three CP

_{i}used as assessment criteria within the micro-trip construction method, and therefore by design, their RDi should be less than 5%. Figure 2 also shows that the RD

_{i}do not exhibit a normal distribution. Kolmogorov–Smirnov tests confirmed this observation for all CP

_{i}with a p_value lower than 0.01. Therefore, the use of average values of RD

_{i}is not an appropriate descriptor of their respective distribution. Thus, in the subsequent analysis, we will use box plots, and the mean values of RD

_{i}(MRD

_{i}) will be used only for reference purposes.

_{i}obtained for the 500 DCs as a function of their duration in the Urban 1 region for all CP

_{i}and emission indexes. In this figure, the dots inside the boxes indicate the average value, while the vertical red lines indicate the obtained median values. These two metrics are associated with the tendency of the RD

_{i}. The vertical green lines indicate the threshold of 10%, which is used as a criterion of representativeness. We highlight that during the construction of the representative DC, a 5% threshold was used in the assessment criteria of representativeness, but that is used only for the three CP

_{i}included within the assessment. In this analysis for reference purposes, we adopted a value of 10% for the rest of CP

_{i}and emission indexes, which is still within the range frequently used in the literature for representativeness.

_{i}decrease, that is, by increasing DC duration, there is a tendency of the micro-trip method to produce more representative DCs. Similarly, Figure 3 shows that for all CP

_{i}the IQR

_{i}(size of the boxes in Figure 3) tend to decrease, that is, by increasing the DC duration, the micro-trip method tends to produce with a higher probability more representative DC. However, these tendencies are not necessarily a monotonic function of DC duration. In some instances, and for some CP

_{i,}such as maximum speed (max speed) and standard deviation of speed (SD speed), the RD

_{i}and IQR

_{i}show the opposite behavior between two consecutive bins of DC duration. This phenomenon happens most of the time from the 5 to 10 bins. It could be due to the fact that to construct a 5 min DC, all micro-trips lasting more than 5 min are excluded, biasing the representativeness of the constructed DC.

_{i}results for each of the CP

_{i}for the Urban 1 and Urban 2 regions, respectively, as a function of the DC duration. They show that the number of CP

_{i}with MRD

_{i}below the 10% threshold increase with the DC duration. For example, Table 2; Table 3 show that for a DC duration of 10 min, 11 and 16 out of the 21 MRD

_{i}fall below the 10% threshold for the Urban 1 and Urban 2 region, respectively. However, when the DC duration increase to 25 min, the number of MRD

_{i}below the 10% threshold increase to 19 and 21, respectively. This observation confirms that increasing the DC duration tends to increase the representativeness of the DC obtained.

_{j}*. They are grouped by the characteristic parameters and the vehicle’s emissions. We recall that j refers to the iteration number. Vertical red lines inside the boxed are the respective $\overline{MRD}$. Figure 4a shows that, for the case of characteristic parameters and the Urban 1 region, DCs with a duration of 5 min exhibit the highest MRD

_{j}* (>10%) with $\overline{MRD}$ ≈ 22%. The increase of the DC duration decreases the MRD

_{j}* values. After a duration of 25 min, the MRD

_{j}* becomes below 10%, and the lowest values MRD

_{j}* are obtained at 120 min with $\overline{MRD}$ ≈ 4%. Similar results are obtained for the cases of the emissions (Figure 4b) and for the case of the Urban 2 region (Figure 4c,d). These observations confirm again that by increasing the DC duration, the obtained DC tends to increase the representativeness of the driving pattern and of the tailpipe emissions.

## 4. Discussion

_{i}for all CP

_{i}and emission indexes to become less than 10%. Figure 4 and Table 2; Table 3 show that it happens when the DC last at least 25 min. They also show that Emission Indexes for the Urban 1 region are the limiting case (Figure 4b). Figure 3 shows that the only CP

_{i}that, with this criterion, does not fall within the condition MRD

_{i}< 10% is the number of accelerations per km (Accel/km) for the case of the Urban 1 region. However, for this CP

_{i}, none of the DC durations considered in this study make the MRD

_{i}< 10%. We emphasize that this fact does make the DCs unrepresentative. We recall that up to today, there is not an agreement on which CP

_{i}to use to describe driving patterns. Perhaps this CP

_{i}is irrelevant for the purpose of describing driving patterns.

## 5. Conclusions

_{i}) between the 21 characteristic parameters (CP

_{i}*) of the obtained DC with respect to CP

_{i}used to describe the measured driving pattern. This comparison was extended to the specific fuel consumption and the emissions of CO

_{2,}CO, and NO

_{x.}

_{i}and their interquartile range (IQR

_{i}). These results mean that by increasing the DC duration, the micro-trips method tends to produce more representative driving cycles with higher probability. Finally, based on literature, a threshold of 10% for RD

_{i}was established as criteria of minimum acceptable representativeness. Under this definition, results indicate that a minimum DC duration of 25 min is needed. This duration is slightly higher than the duration of the type approval DC most frequently used worldwide. However, additional work is needed to confirm these conclusions for the case of fleets of different vehicle sizes working in different urban regions.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Symbol | Description | Units |

CP_{i} | Values of the ith characteristic parameter that describe the driving pattern | - |

CP_{i}^{*} | Values of the ith characteristic parameter that describe the driving cycle | |

DC | Driving Cycle | |

IQR_{i} | Interquartile range of the ith characteristic parameter | - |

MRD_{i} | Mean of the relative difference of the ith characteristic parameter obtained after 500 iterations | % |

MRD_{j}* | Mean of the relative difference of all CP_{i}* obtained at the jth iteration. | % |

RD_{i} | Relative difference of the ith characteristic parameter | % |

SFC | Specific Fuel Consumption | L/km |

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**Figure 1.**DC duration and average speed for DC developed for different regions or cities. * denotes DC for motorcycles.

**Figure 2.**Frequency distribution of the RD

_{i}obtained for the 500 DCs for a duration of 20 min and Urban 1 region and the cases of (

**a**) average speed, (

**b**) positive kinetic energy, (

**c**) specific fuel consumption, and (

**d**) NOx emissions. Vertical red lines in these figures represent their respective MRD

_{i}.

**Figure 3.**Box-plot of the RDi obtained in the Urban 1 region for the following characteristic parameters and emissions: (

**a**) maximum speed, (

**b**) standard deviation of speed, (

**c**) average acceleration, (

**d**) maximum acceleration, (

**e**) standard deviation of acceleration, (

**f**) average deceleration, (

**g**) maximum deceleration, (

**h**) standard deviation of deceleration, (

**i**) percentage of acceleration, (

**j**) percentage of deceleration, (

**k**) percentage of cruising time, (

**l**) positive kinetic energy, (

**m**) root mean square of acceleration, (

**n**) accelerations per kilometer, (

**o**) kinetic energy, (

**p**) emission index of CO

_{2}, (

**q**) emission index of CO, (

**r**) emission index of NOx. Boxes indicate interquartile ranges, and red + signs indicate outlier data. Blue dots inside the boxes indicate the average value, while vertical red lines indicate the median values. The vertical green lines indicate threshold values for acceptable representativeness.

**Figure 4.**Results of $MR{D}_{j}$ as a function of DC duration for the cases of (

**a**) characteristic parameters and (

**b**) Emissions in the Urban 1 region; (

**c**) characteristic parameters and (

**d**) Emissions in the Urban 2 region. Boxes indicate interquartile ranges, and red + signs indicate outlier data. Blue dots inside the boxes indicate the average value, while vertical red lines indicate the mean values ($\overline{MRD}$). The vertical green lines indicate threshold values for acceptable representativeness.

**Table 1.**Characteristics parameters (CP

_{i}), emissions, and fuel consumption used to describe driving patterns and driving cycles in this study.

Type | Name | Symbol | Unit | Driving Pattern | ||
---|---|---|---|---|---|---|

Urban 1 | Urban 2 | |||||

Characteristic parameters | 1 | Average speed * | Ave Speed | m/s | 7.3 | 10.0 |

2 | Maximum speed | Max Speed | m/s | 22.3 | 26.2 | |

3 | Standard deviation of speed | SD speed | m/s | 6.9 | 7.7 | |

4 | Maximum acceleration | Max a+ | m/s^{2} | 1.3 | 1.3 | |

5 | Maximum deceleration | Max a− | m/s^{2} | −2.1 | −2.1 | |

6 | Average acceleration | Ave a+ | m/s^{2} | 0.5 | 0.4 | |

7 | Average deceleration | Ave a− | m/s^{2} | −0.5 | −0.5 | |

8 | Standard deviation of acceleration | SD a+ | m/s^{2} | 0.2 | 0.2 | |

9 | Standard deviation of deceleration | SD a− | m/s^{2} | 0.4 | 0.4 | |

10 | Percentage of idling time * | % idling | - | 15.1 | 13.6 | |

11 | Percentage Acceleration | % a+ | - | 32.9 | 33.8 | |

12 | Percentage Deceleration | % a− | - | 29.3 | 29.1 | |

13 | Percentage Cruising | % cruising | - | 22.7 | 25.9 | |

14 | No. of acceleration per kilometer | Accel/km | km^{−1} | 8.6 | 6.1 | |

15 | Root mean square of accel. | RMS | m/s^{2} | 0.5 | 0.5 | |

16 | Positive kinetic energy | PKE | m/s^{2} | 0.4 | 0.3 | |

17 | Speed acceleration probability distribution | SAPD | - | N/A | N/A | |

18 | Vehicle Specific Power | VSP | kW/t | 4.8 | 7.0 | |

19 | Kinetic Intensity | KI | km^{−1} | 0.8 | 0.7 | |

Fuel consumption and emissions | 20 | Specific fuel consumption * | SFC | L/km | 0.4 | 0.4 |

21 | Emission index of CO_{2} | EI CO_{2} | g/km | 839.0 | 749.2 | |

22 | Emission index of CO | EI CO | g/km | 37.2 | 39.4 | |

23 | Emission index of NOx | EI NOx | g/km | 5.0 | 3.9 |

**Table 2.**MRD

_{i}of 500 DCs obtained by the micro-trip method using the same trip database for the case of the Urban 1 region.

DC Duration (min) | |||||||||
---|---|---|---|---|---|---|---|---|---|

Characteristic Parameters | 5 | 10 | 15 | 20 | 25 | 30 | 45 | 60 | 120 |

Ave Speed * | 3.4 | 2.7 | 1.9 | 2.5 | 2.6 | 2.5 | 2.5 | 2.5 | 2.5 |

Max Speed | 26.8 | 17.1 | 10.0 | 6.6 | 2.5 | 2.2 | 4.6 | 5.9 | 10.8 |

SD Speed | 22.3 | 25.6 | 23.3 | 17.9 | 8.1 | 8.1 | 6.1 | 6.7 | 5.4 |

Max a+ | 0.2 | 2.4 | 6.1 | 1.8 | 0.6 | 0.6 | 0.0 | 0.0 | 0.0 |

Max a− | 4.2 | 9.7 | 11.8 | 9.1 | 4.9 | 3.5 | 1.8 | 0.7 | 0.1 |

Ave a+ | 8.9 | 8.0 | 6.3 | 3.9 | 2.9 | 2.8 | 2.3 | 1.9 | 1.3 |

Ave a− | 22.5 | 9.5 | 7.0 | 4.7 | 5.5 | 5.1 | 3.4 | 3.7 | 2.7 |

SD a+ | 27.1 | 9.6 | 7.5 | 5.0 | 3.1 | 3.2 | 2.5 | 2.2 | 1.5 |

SD a− | 37.1 | 16.5 | 8.3 | 7.6 | 7.9 | 6.8 | 5.1 | 4.8 | 3.4 |

% Idling * | 2.2 | 3.1 | 2.4 | 2.5 | 2.4 | 2.5 | 2.5 | 2.6 | 2.4 |

% a+ | 8.2 | 6.5 | 3.6 | 2.2 | 2.5 | 2.4 | 1.8 | 1.9 | 1.4 |

% a− | 5.9 | 3.0 | 3.5 | 2.9 | 2.5 | 2.5 | 2.4 | 2.0 | 1.4 |

% cruising | 18.3 | 11.6 | 8.6 | 4.2 | 3.6 | 4.1 | 3.7 | 3.3 | 2.4 |

Accel/km | 18.5 | 5.7 | 35.8 | 25.1 | 17.2 | 15.8 | 12.2 | 13.8 | 12.9 |

RMS | 25.2 | 12.4 | 8.3 | 4.9 | 4.4 | 4.1 | 3.0 | 3.0 | 2.1 |

PKE | 22.6 | 11.7 | 8.3 | 5.3 | 5.0 | 4.6 | 5.1 | 4.2 | 2.9 |

SAPD | 17.8 | 13.0 | 10.5 | 7.5 | 3.7 | 3.5 | 2.3 | 2.2 | 1.6 |

VSP | 6.0 | 7.0 | 2.6 | 4.0 | 3.3 | 3.1 | 3.7 | 3.1 | 2.5 |

KI | 121.6 | 91.7 | 67.6 | 53.4 | 26.2 | 26.0 | 19.0 | 20.3 | 18.6 |

SFC* | 3.5 | 3.4 | 1.2 | 2.5 | 2.6 | 2.5 | 2.6 | 2.5 | 2.6 |

EI CO2 | 7.9 | 15.9 | 1.8 | 4.4 | 4.9 | 4.1 | 3.8 | 3.3 | 3.4 |

EI CO | 16.7 | 12.9 | 17.3 | 9.0 | 6.8 | 6.3 | 5.2 | 4.7 | 4.2 |

EI NOx | 5.2 | 21.0 | 9.9 | 8.7 | 7.5 | 8.8 | 6.9 | 7.3 | 6.5 |

*****Characteristic parameter used in the assessment criteria.

**Table 3.**MRD

_{i}obtained for the 500 DCs obtained by the micro-trip method using the same trip database for the case of the Urban 2 region.

DC Duration (min) | |||||||||
---|---|---|---|---|---|---|---|---|---|

Characteristic Parameters | 5 | 10 | 15 | 20 | 25 | 30 | 45 | 60 | 120 |

Ave Speed * | 1.9 | 2.4 | 2.6 | 2.4 | 2.5 | 2.5 | 2.4 | 2.5 | 2.3 |

Max Speed | 11.0 | 7.2 | 5.4 | 4.6 | 4.1 | 4.0 | 4.3 | 4.4 | 5.6 |

SD Speed | 10.4 | 6.8 | 6.9 | 5.2 | 4.6 | 4.9 | 4.9 | 4.1 | 3.1 |

Max a+ | 0.7 | 4.2 | 1.8 | 1.5 | 0.9 | 0.6 | 0.2 | 0.1 | 0.0 |

Max a− | 37.6 | 10.7 | 7.4 | 4.7 | 3.4 | 2.1 | 0.8 | 0.4 | 0.0 |

Ave a+ | 11.6 | 4.6 | 4.2 | 3.9 | 4.0 | 3.9 | 3.1 | 2.5 | 2.0 |

Ave a− | 14.4 | 11.0 | 8.5 | 6.2 | 6.5 | 6.3 | 5.3 | 4.6 | 3.5 |

SD a+ | 6.9 | 6.2 | 7.0 | 5.9 | 4.9 | 4.7 | 3.9 | 3.3 | 2.5 |

SD a− | 25.2 | 14.8 | 11.0 | 7.4 | 7.1 | 7.3 | 5.9 | 5.3 | 3.9 |

% Idling * | 1.7 | 2.7 | 2.5 | 2.5 | 2.5 | 2.4 | 2.5 | 2.5 | 2.5 |

% a+ | 3.6 | 5.2 | 5.6 | 4.4 | 4.0 | 3.6 | 3.3 | 3.0 | 2.9 |

% a− | 10.8 | 9.2 | 7.9 | 6.6 | 6.0 | 5.9 | 5.3 | 5.5 | 6.3 |

% cruising | 11.0 | 13.4 | 12.8 | 10.6 | 9.8 | 8.6 | 7.0 | 6.1 | 4.8 |

Accel/km | 6.8 | 11.3 | 12.4 | 11.4 | 9.3 | 9.3 | 8.3 | 8.3 | 9.3 |

RMS | 16.2 | 5.6 | 5.4 | 4.3 | 4.4 | 3.9 | 3.6 | 3.1 | 3.2 |

PKE | 19.0 | 6.4 | 7.0 | 5.7 | 5.5 | 4.8 | 4.3 | 3.9 | 3.3 |

SAPD | 8.0 | 5.9 | 4.9 | 3.4 | 2.8 | 2.5 | 1.9 | 1.5 | 0.8 |

VSP | 3.0 | 6.4 | 5.9 | 6.8 | 6.5 | 6.1 | 6.0 | 6.0 | 6.4 |

KI | 28.6 | 11.1 | 8.9 | 8.6 | 8.6 | 7.8 | 6.3 | 6.0 | 4.8 |

SFC* | 1.9 | 2.8 | 2.7 | 2.6 | 2.4 | 2.4 | 2.3 | 2.4 | 2.3 |

EI CO2 | 8.3 | 7.2 | 6.2 | 4.4 | 4.1 | 4.3 | 3.5 | 3.0 | 2.4 |

EI CO | 15.1 | 11.7 | 11.8 | 9.3 | 7.9 | 8.4 | 7.0 | 6.0 | 4.9 |

EI NOx | 21.5 | 8.8 | 8.1 | 7.7 | 7.3 | 7.5 | 6.9 | 7.3 | 7.6 |

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## Share and Cite

**MDPI and ACS Style**

Giraldo, M.; Quirama, L.F.; Huertas, J.I.; Tibaquirá, J.E.
The Effect of Driving Cycle Duration on Its Representativeness. *World Electr. Veh. J.* **2021**, *12*, 212.
https://doi.org/10.3390/wevj12040212

**AMA Style**

Giraldo M, Quirama LF, Huertas JI, Tibaquirá JE.
The Effect of Driving Cycle Duration on Its Representativeness. *World Electric Vehicle Journal*. 2021; 12(4):212.
https://doi.org/10.3390/wevj12040212

**Chicago/Turabian Style**

Giraldo, Michael, Luis F. Quirama, José I. Huertas, and Juan E. Tibaquirá.
2021. "The Effect of Driving Cycle Duration on Its Representativeness" *World Electric Vehicle Journal* 12, no. 4: 212.
https://doi.org/10.3390/wevj12040212