The Effect of Driving Cycle Duration on Its Representativeness

Abstract

There is an increasing interest in properly representing local driving patterns. The most frequent alternative to describe driving patterns is through a representative time series of speed, denominated driving cycle (DC). However, the DC duration is an important factor in achieving DC representativeness. Long DCs involve high testing costs, while short DCs tend to increase the uncertainty of the fuel consumption and tailpipe emissions results. There is not a defined methodology to establish the DC duration. This study aims to study the effect of different durations of the DCs on their representativeness. We used data of speed, time, fuel consumption, and emissions obtained by monitoring for two months the regular operation of a fleet of 15 buses running in two flat urban regions with different traffic conditions. Using the micro-trips method, we constructed DCs with a duration of 5, 10, 15, 20, 25, 30, 45, 60, and 120 min for each region. For each duration, we repeated the process 500 times in order to establish the trend and dispersion of the DC characteristic parameters. The results indicate that to obtain driving pattern representativeness, the DCs must last at least 25 min. This duration also guarantees the DC representativeness in terms of energy consumption and tailpipe emissions.

1. Introduction

Recently, there is an increasing interest in studying the manner that drivers drive the vehicles in a region, and its impact on energy consumption, in the case of electric vehicles, and fuel consumption and tailpipe emissions in the case of vehicles with an internal combustion engine. Conceptually, local driving pattern is a term used to define the average driving characteristics of the region. The driving patterns frequently are described by a speed-time series, denominated driving cycle (DC) [1,2].

DCs are mainly used to evaluate vehicles’ fuel consumption and emissions compliances before they enter into a country automotive market. Moreover, DCs can be used for the powertrain design, to compare vehicles’ performance, and to develop emissions inventories [3,4]. In the latest years, due to the deployment of hybrid and pure electric vehicles, as an alternative to reduce greenhouse gases (GHG), new DCs have been developed for evaluating energy management, batteries, energy storage capacity, and vehicle mileage [5]. The representativeness of the local driving pattern is the key issue of a DC, and it depends mainly on three factors: (a) the quality and quantity of vehicle operation data, (b) the DC construction method, and (c) the CPs used to assess the DC representativeness [6].

All these factors have been the subject of extensive research work. However, a fourth factor that could affect the local DC representativeness and the results of the vehicle energy consumption and the tailpipe emissions is the DC duration. Long DCs involve high costs associated with the implementation of the type approval tests, while short DCs tend to generate high uncertainty in the fuel consumption and emissions results [7]. The duration of a DC must be defined as a balance between the precision of the fuel consumption and tailpipe results and testing costs [8]. However, little research has been conducted to elucidate this issue.

Currently, researchers defined the DC duration based on their experience and knowledge of the driving conditions of the study region. Amirjamshidi et al. [9] suggested that a DC generated by the micro-trips method must have a duration between 10 and 30 min. Ho et al. [10] noted down that random approaches to construct DCs like micro-trips involve defining a pre-determined duration of more than 1000 s without rational scientific justification, which is a shortcoming in their methodology. Ho et al. [10] performed a trip distance and duration survey. The trip distance result was used to define the DC length according to the percentage of each type of road segment. A driving cycle with a duration of 2344 s was obtained for Singapore. A difference of 2.3% between the trip survey (2400 s) and the proposed DC was established. The process followed in Singapore’s DC assures the similarity between the DC and the city trip duration. However, this method does not solve the question of the minimum duration of a DC to reach representativeness in terms of local driving patterns, fuel consumption, and emissions. Knez et al. [11] developed the Celje driving cycle and found a relation between the increase of the average speed, the reduction of the trip time, and the traffic conditions. Figure 1 shows a summary of the duration and average speed of different DC used in the type approval test developed for different regions around the world.

The aim of this study is to analyze the effects of the DCs durations on the representativeness of local driving patterns and the reproducibility of the observed vehicle fuel consumption and tailpipe emissions when the vehicle reproduces the DC on a chassis dynamometer. The methodology used and the results obtained are the main contribution to new knowledge of this work.

2. Materials and Methods

Seeking to accomplish the objective described above: (i) we used a common trip database obtained monitoring a large sample of vehicles during a long period of time in an arbitrary region. (ii) selected the most frequent technique to construct DC and constructed DCs with a time length of 5, 10, 15, 20, 25, 30, 45, 60, and 120 min. For each duration, we built 500 DCs in order to establish the trend and dispersion of the representativeness of the obtained DC [2,12] (iii) Based on the results obtained, we selected the most appropriate duration of the DC, including additional criteria than just representativeness. Next, we will describe each of these steps.

2.1. Common Trip Database

In this study, we used the trip database obtained by Giraldo et al. [13] monitoring transit busses in central Mexico. Considering the relevance of that database for the present work, next, we summarize how it was obtained.

We developed this study in two urban regions located at high altitudes: Mexico City (2255 m.a.s.l.) and Toluca City (2611 m.a.s.l.). In each region, we selected road segments that have lengths 11.5 and 18.8 km, respectively. Mexico City’s roads are characterized by highly congested traffic (LoS = F) while Toluca’s roads by medium congested traffic (LoS = F). LoS (Level of Service) is the level of quality of a traffic facility and represents a range of operating conditions, typically in terms of service measures such as speed and travel time, freedom to maneuverer, traffic interruptions, and comfort and convenience [14].

A total of 15 buses were used during the monitoring campaign. The selected vehicles presented the same maintenance, route of operation, and technology characteristics. They were built between 2012 and 2014, have a 49-passenger capacity and a gross vehicle weight of 13,850 kg. They operated with a diesel engine Cummins ISM 425 with emission control EURO IV, power of 425 HP, and torque of 2102 Nm [15].

The vehicle location (Altitude, Latitude, and Longitude) and speed were measured by using a global position system (GPS) Garmin 16x. The data sample frequency was 1 Hz. Regarding fuel consumption, the On-Board Diagnostics (OBD) system was used to read this variable from the Engine Control Unit (ECU). These diesel vehicles have an electronic fuel injection system that, according to the opening time of the injector, the instantaneous fuel consumption is determined. The data obtained in this way were validated by using an external graduated tank, which is the standard procedure to determine the fuel consumption of vehicles [16,17]. Based on the determination coefficient (R² > 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, CO₂, NO, and NO₂. With the SEMTECH-FEM module, CO and CO₂ emissions were measured using a non-dispersive infrared analyzer, and the SEMTECH-NOx module for NO and NO₂ 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.

The measurements were made for two months. During this time, the vehicles were operated by their usual drivers at different times of the day and different days of the week. Then, a data quality analysis was carried out to identify and discard atypical data or incomplete trip data (i.e., trips with less than 95% of data availability). The analysis included a synchronization process where data readings from the three different instruments were manually synchronized by observing the correlation of variables that from physics should be correlated, such as fuel consumption and CO₂ emissions [13]. After analyzing the monitoring campaign results, 46 monitored trips were included in the sample trips database.

2.2. Construction of Representative DCs

The key issue in constructing DCs is their representativeness of the local driving pattern. This last term refers to the way drivers drive their vehicles, and usually, it is described by a set of characteristic parameters (CP_i,

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/s2	1.3	1.3
	5	Maximum deceleration	Max a−	m/s2	−2.1	−2.1
	6	Average acceleration	Ave a+	m/s2	0.5	0.4
	7	Average deceleration	Ave a−	m/s2	−0.5	−0.5
	8	Standard deviation of acceleration	SD a+	m/s2	0.2	0.2
	9	Standard deviation of deceleration	SD a−	m/s2	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/s2	0.5	0.5
	16	Positive kinetic energy	PKE	m/s2	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 CO2	EI CO2	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

* indicates the parameters used as assessment criteria to evaluate the DC representativeness in the MT method.

). 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].

$$R{D}_i=\frac{{\displaystyle \sum }\left(C{P}_i^{*}-C{P}_i\right)}{C{P}_i}$$

(1)

Then, we selected the micro-trips method to build representative DCs of different durations. The micro-trips method is the most frequently used method to construct representative DC. In this method, the speed-time data collected in the vehicle monitoring campaign is partitioned into segments of trips bounded by vehicle speed equal to 0 km/h. These segments are called “micro-trips.” micro-trips are often clustered as a function of their average speed and average acceleration. Then, some of them are quasi-randomly selected based on the frequency distribution of the clusters and later spliced to build a candidate DC [19,20]. The representativeness between the candidate DC and the local driving patterns is calculated through the relative difference of characteristic parameters (RD_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.

As a result of this method, a representative DC is obtained. Then to evaluate the level of representativeness of the obtained DC, the relative differences were calculated for nineteen characteristic parameters. Moreover, the relative difference between the average specific fuel consumption of the local driving patterns and the specific fuel consumption of the DC was calculated. This analysis was extended to the CO₂, CO, and NO_x. Table 1 presents the characteristic parameters used in this study.

Due to the stochastic nature of the micro-trip method, despite using the same trip database, each time the micro-trip method is implemented, it produces a different representative DC with a different level of representativeness (different RD_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).

$$MR{D}_i=\frac{{{\displaystyle \sum }}_{j=1}^n\left|C{P}_{i,j}^{*}-C{P}_i\right|}{n C{P}_i}$$

(2)

In Equation (2), $n$ is the total number of iterations performed (n = 500), and j is the iteration number. IQR_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

As stated before, this work aims to analyze the effects of the DC duration on its representatives. To accomplish this objective, for a given duration, 500 representative DC were obtained by the micro-trip method. Then, the level of representativeness of each DC was obtained through the mean value of all RD_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.

$$MR{D}_j{}^{*}=\frac{{{\displaystyle \sum }}_{i=1}^{k}R{D}_{i,j}}{k}$$

(3)

$$MIQ{R}_j{}^{*}=\frac{{{\displaystyle \sum }}_{i=1}^{k}IQ{R}_{i,j}}{k}$$

(4)

We highlight that in Equations (3) and (4), the subscript i refers to any of the CP_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.

$\overline{MRD}$ ranges from 0 to infinity and low values of $\overline{MRD}$ indicate that the selected time duration generates driving cycles highly representative of the local driving patterns, fuel consumption, and emissions. Low $\overline{MIQR}$ values are associated with a high probability of occurrence of the obtained $\overline{MRD}$.

This analysis was extended to the specific fuel consumption and specific emissions. Finally, the process was repeated for durations of 5, 10, 15, 20, 25, 30, 45, 60, and 120 min.

3. Results

As an illustrative example, Figure 2 presents the frequency distribution of the RD_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.

Figure 3 shows the boxplots of the RD_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.

Figure 3 shows that by increasing the DC duration, the average and median values of RD_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.

Alternatively, the same analysis can be done using

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.

and

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

* Characteristic parameter used in the assessment criteria.

; They list the MRD_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.

To further explore the effects of the DC duration on the DC representatives, Figure 4 depicts the results obtained for the MRD_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

Besides a representation of the local pattern, the DCs are designed to reproduce the observed real fuel consumption and tailpipe emissions of the vehicles under normal conditions of operation when those vehicles are tested on a chassis dynamometer following the DC. Thus, increasing the duration of the DC will increase the duration of these tests and, therefore, the costs associated with carrying them out. On the opposite side, DC too short could be no representative of the local driving pattern and with a low probability of reproducing observed fuel consumption and tailpipe emissions.

We used as criteria for fixing the minimum duration of the DCs as the duration that makes the MRD_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.

We also underline that, previously, results were obtained for the case of a fleet of 15 buses operating in two urban regions in central Mexico. Therefore, additional work is needed to confirm the conclusion presented in this paper for the case of vehicle fleets of several sizes and technologies operating in several regions. We also point out that in this discussion, the fact that vehicles need time to reach their normal operating temperature and that the engine performance varies with it is not considered. That is, in this work, we assume that vehicles are tested after being warmed up to their operating temperature.

5. Conclusions

In this study, we proposed a methodology to analyze the effects of driving cycle (DC) duration on the level of representativeness of the local driving pattern and on the level of reproducibility of fuel consumption and tailpipe emissions when vehicles are tested on a chassis dynamometer following that DCs. Toward that end, we implemented the proposed methodology, which involves the construction of at least 500 representative DCs using a well-accepted method (the micro-trip method) and a common database of trips, which were obtained monitoring a fleet of 15 buses operating during two months in two urban regions located in flat and densely populated regions with different traffic conditions. The process was repeated for DC durations of 5, 10, 15, 20, 25, 30, 45, 60, and 120 min. The level of representativeness was evaluated by means of the relative differences (RD_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.

Results showed that in both regions, increasing the duration of DCs reduces the RD_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.