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Comparison of bus driving cycles elaborated for
vehicle dynamic simulation
Attila V
amosi
1
p, Levente Cz
eg
e
2
and Imre Kocsis
1
1
Department of Basic Technical Studies, Faculty of Engineering, University of Debrecen, Debrecen,
Hungary
2
Department of Mechanical Engineering, Faculty of Engineering, University of Debrecen, Debrecen,
Hungary
Received: July 12, 2020 •Accepted: December 14, 2020
ABSTRACT
Due to the technological progress, new approaches such as model-based design are spreading in the
development process in the automotive industry to meet the increased requirements related to lower
fuel consumption and reduced emission. This work is part of a research project which focuses on
dynamic modeling of vehicles aimed at analyzing and optimizing the emission and fuel consumption.
To model the driver behavior, the simulation control algorithm requires a predetermined speed-time
curve as an input. The completeness of this driving cycle is a crucial factor in the simulation, and as far
as the legislative driving cycles are not accurate enough, it is indispensable to develop our own one
representing our narrower area and driving conditions. This article considers two common drive cycle
design methods, comparing the micro-trip-based approach and the Markov-chain approach. The new
driving cycle has been developed applying the Markov-chain approach and compared to a driving cycle
introduced in our recent paper using the micro-trip method. The comparison basis is the Speed-Ac-
celeration Probability Distribution, which sufficiently reflects the dynamic behavior of the vehicle, and
the root mean square error, including parameters such as the average speed, average cruising speed,
average acceleration, average deceleration, root mean square acceleration, and idle time percentage. The
representative Bus Driving Cycle for Debrecen is prepared to be applied in the vehicle dynamics
simulation for evaluating and improving the fuel economy of vehicles, selecting the proper power source
for various applications and the optimization of the powertrain and the energy consumption in re-
searches to be continued.
KEYWORDS
driving cycle, real traffic data, urban bus route, Markov chain, micro-trip method
1. INTRODUCTION
As a result of the increasingly stringent measures of the governments as well as the market
requirements large efforts are made to reduce fuel consumption and emission in the auto-
motive industry. At the same time, due to technological progress new methods and tools are
involved in the development process such as computer modeling and simulation. At the
University of Debrecen, the project has been launched with emphasis on vehicle dynamics
simulation. Among the goals we find the optimization of fuel consumption of various vehicle
design concepts of propulsion system, such as internal combustion engine, fuel cell, electric
drive, and hybrid systems. The basis of the analysis and optimization is a dynamic model
which consists of a simplified vehicle model and discrete control algorithms to execute the
desired driving cycle inputs for the vehicle. The math model representing the vehicle me-
chanics is a simplified longitudinal “bicycle”model including the power loss effects like drag
and rolling resistance, the drivetrain, the brake system and the model of the power source
(internal combustion engine or electric motor). The control algorithm is based on PID
controllers to model the driver behavior.
International Review of
Applied Sciences and
Engineering
DOI:
10.1556/1848.2020.00153
© 2020 The Author(s)
ORIGINAL RESEARCH
PAPER
pCorresponding author.
E-mail: vamosi.attila@eng.unideb.hu
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The input of the PID controllers is the speed of the
vehicle, which is given by a predetermined time-speed curve.
This is the so-called driving cycle, which represents the
driving pattern of the analyzed vehicle. The level of the
representativeness of the driving cycle is a crucial factor in
the vehicle dynamics simulation, therefore it is an important
task to find the appropriate method of data collection, data
processing, and driving cycle development. The existing
methods are fundamentally based on the analysis of large
amounts of long-term data collected under real-world con-
ditions and apply some statistical procedures to develop a
representative driving cycle of the desired length. It has also
been proven in several papers that the legislative driving
cycles are not accurate enough to estimate the fuel and en-
ergy consumption or emission data for vehicles, because the
driving patterns can be very different in various areas and
cities [1]. The conclusion that can be drawn from these
studies is that the development of alternative driving cycle
characteristics of driving conditions in our area is necessary
to get accurate results from the dynamic vehicle simulation.
In this paper two driving cycles for Debrecen are over-
viewed and compared. They were obtained by the two
common driving cycle development techniques, namely the
micro-trip-based approach and the Markov-chain approach.
In V
amosi et al. [2] a driving cycle is introduced constructed
with the micro-trip method for city buses in Debrecen,
Hungary. Now a new driving cycle is presented developed
with the Markov-chain approach using the same dataset.
Finally, the two approaches are being compared based on
the root mean square error and the Speed-Acceleration
Probability Distribution (SAPD), which precisely reflects the
dynamic behavior of the vehicle.
2. LITERATURE REVIEW
The different versions of the micro-trip-based approach
have several advantages. But the parameters used for micro-
trip-based cycles are not directly related to emissions, while
applications aiming at emission reduction of vehicles need
emission sensitive driving characteristics, as it is emphasized
in several publications, see e.g., Silvas [3] or Delgado-Neira
[4].
The Markov modal events studied in Lin and Niemeier
[5] demonstrate the stochastic nature of the driving data. In
practice it is a significant contribution to the estimation of
emissions that this model can represent the modal events
and driving changeableness, while modal operating condi-
tions are not significantly distinguished by the micro-trip
approach [5]. The Markov process allows us to replicate the
global driving characteristics while preserving small time-
scale speed fluctuations that contain the information related
to driving variability [6].
The Markov process theory was applied to depict how
real driving occurs according to a transition probability
matrix by Lin and Niemeier [5]. Dai et al. [7] got a more
sophisticated approach modifying the Markov process. They
applied several variables related to emissions, matching with
the modal distributions and SAPD, furthermore, a complex
parameter for assessment was used to allow the driving
mode to fit small accelerations while considering significant
acceleration rates to be classified as acceleration modes,
respectively.
The micro-trip-based and Markov theory-based methods
were compared and the limitations of both methods were
presented in many papers. According to Dai et al. [7] the
feature that the micro-trip approach does not make differ-
ence between various types of driving conditions could be
considered as a limitation. If, for example, a vehicle does not
have to stop frequently due to smooth traffic conditions,
several diverse road segments or traffic conditions could be
included in a single micro-trip. Traffic signals and conges-
tion generate most of the stop-go driving patterns and lead
to higher fuel consumption, since more fuel is consumed by
vehicles during stop-go conditions [8]. Consequently, mi-
cro-trip-based methods have been applied primarily in sit-
uations where the goal is to develop a driving cycle for a
single type of trip or for region-wide driving conditions [7].
Lin and Niemeier [5] compared two frequently referred
cycles, namely the LA01 cycle (based on the Markov process
theory) and the Unified Cycle (based on micro-trips). Sig-
nificant differences were obtained related to frequencies,
durations and intensities of modal events, though both cy-
cles represent the global characteristics in connection with
observed speed and acceleration in the driving dataset.
Compared with the Unified Cycle, the LA01 contains modal
events with frequencies and durations more similar to those
of the sample dataset. The stochastic method deals with a
couple of major problems appearing in the construction
procedure of the Unified Cycle. In the Unified Cycle the
global characteristics is preserved, while small timescale
activities, for example small accelerations are lost, in spite of
their crucial role in increased emissions. If we use micro-
trips, within a micro-trip, we cannot distinguish significantly
the modal operating conditions. This can result an imprecise
representation of the modal events. Considering the fre-
quency, average duration and intensity, generally, LA01
replicates the vehicle operation modes in the sample dataset
better than the Unified Cycle. Some limitations of the
Markov method are also mentioned. For instance, the
segment-to-segment speed match criterion is crucial when
transition matrix is used, and the accuracy highly depends
on the sample size [5]. The research presented in Shi et al.
[9] shows that only under the condition of small time in-
tervals does certain probability state transfer exist between
the current state and the next one.
Authors founded a theory for developing driving cycles
in Shi et al. [9]. The authors proved that a driving cycle has
the Markov property and that the application of transition
matrix is an appropriate method of developing driving cy-
cles. Considering that micro-trip-based driving cycles could
not fit the dynamometer test, developing driving cycles by
following its essential characteristics could be a more
appropriate method.
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3. SELECTION OF THE APPROPRIATE DRIVING
CYCLE CONSTRUCTION METHOD
3.1. Description of Markov chain method
Markov chain is a mathematical tool used to model a
random process, where the so-called Markov property,
which can be expressed by
PðXnþ1¼xjX1¼x1;X2¼x2;...;Xn¼xnÞ¼PðXnþ1
¼xjXn¼xnÞ;
(1)
that is, the next state depends on the current state only.
We can write the one-step transition probability from
state x
i
to state x
j
as
pij ¼PXnþ1¼xjjXn¼xi;i;j¼1;...;N;(2)
where Ndenotes the number of the states. The one-step state
probabilities constitute the so-called transition probability
matrix.
3.2. Data processing
In this method, the states can be characterized by the
average speed and the acceleration values calculated from
the speed change measured at the same time interval. Since
the instantaneous speed value was read every second during
the measurement, the average speed shall be determined by
the following formula
vi¼viþvi−1
2:(3)
Acceleration values are also available from the measure-
ment, but they are also instantaneous values, and the values
calculated from the actual speed change are required for the
calculation. The speed is measured in km/h unit and the
time interval is 1 s, so the acceleration value can be calcu-
lated with this formula
ai¼vivi−1
3:6:(4)
The data were discretized in step of 1 km/h in speed and
0.2 m/s
2
in acceleration following the method used e.g., in
Torp and €
Onnegren [10]. Figure 1 shows the speed-accel-
eration distribution of discretized points gained from the full
dataset.
3.3. Calculation of the transition probability matrix
To determine the number of states we have to consider the
measured maximum speed and absolute maximum accel-
eration values and have to fix the resolution of speed and
acceleration. In our investigations the resolutions followed
from the discretization steps a
res
50.2 m/s
2
and v
res
51
km/h, respectively.
We checked many pairs and (a
res
,v
res
)5(0.2 m/s
2
,1km/h)
was found to be the most appropriate one from the point
of view of the accuracy of the final driving cycle. Although
the application of larger discretization steps (coarser res-
olution) results a smaller matrix, and consequently shorter
computation time, the accuracy of the result is much
worse. This resolution is used in several literatures as well.
The number of the rows and columns were calculated by
equations
nr¼2$
jamaxj
ares
þ1;nc¼vmax
vres
þ1:(5)
Each speed-acceleration pair represents a state, so we have
nr$ncdifferent states.
3.4. Generating the candidate driving cycles
The duration of the desired driving cycle is determined by
the needs of the simulation. According to Huang et al. [1]
the length of the representative driving cycle should be be-
tween 500 and 3,000 s. Based on the requirements of the
simulation and the recommendations in the literature, we
used 1,200 s as the length of the driving cycle.
The driving cycle has to start with the idle state where
the speed and the acceleration are zero. The transition
probability matrix is used to determine the next state. A
random number ris generated in interval (0, 1), and if r
satisfies the inequality
X
k−1
j¼1
pij<r ≤X
k
j¼1
pij ð1≤k≤NÞ;(6)
then the next state is set to state k.
In the new state the speed and acceleration are given by
the discretized dataset. Repeat this method until the dura-
tion of the driving cycle reaches or leaves the desired length
and the actual state is the idle state. We generated 10
candidate driving cycles using this method.
Fig. 1. Discretized dataset
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4. RESULTS
4.1. Selection and analysis of representative driving
cycle
To validate each generated driving cycle the following var-
iables were used:
Average speed (v
total
in km/h): Average value of the speed
during a driving segment.
Average cruising speed (v
cruise
in km/h): Average value of
the non-zero speeds.
Average acceleration (ain m/s
2
): Average value of the
positive accelerations.
Average deceleration (din m/s
2
): Average value of the
negative accelerations.
Root mean square acceleration (a
RMS
in m/s
2
): root mean
square of the positive and negative accelerations, calcu-
lated as
aRMS ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
n
i¼1xixi
xi2
s:(7)
Idle time percentage (t
idle
in %): the quotient of the idle
time and the total time in percentage.
To select the most representative driving cycle we used
the root mean square (RMS) error. All of the parameters
were calculated for each candidate driving cycle and were
compared to the parameters of the full dataset. Table 1
shows the characteristic parameters of the candidate driving
cycles.
An alternative tool to describe driving patterns is based
on the Speed-Acceleration Probability Distribution (SAPD)
[11]. This method classifies the average speed and average
acceleration of the vehicles into speed-acceleration bins. The
similarity between the SAPD of a candidate driving cycle
and the SAPD of the full dataset is another useful indicator
of the representativeness. We used the Quality of Fit (QoF)
value
QoF ¼X
n
i¼1X
m
j¼1Pij;candidate Pij;fulldataset 2(8)
to evaluate the degree of similarity between SAPDs, where
P
ij
is the probability that the vehicle travels within the bin i
of speed and the bin jof acceleration, nis the total number
of the bins of speed, and mis the total number of the bins of
acceleration. To define the number of bins we used v
int
5
5 km/h and a
int
50.5 m/s
2
as the length of speed and
acceleration intervals, respectively.
As Table 1 shows, cycles DC6 and DC7 have the lowest
RMS value. The QoF value of DC7 is 0.008, while that of
DC6 is only 0.002, which indicates very good accuracy, that
is, this driving cycle represents better the full dataset than
the others. Figure 2 shows the constructed driving cycle as a
speed-time chart. It has total time of 1,208 s.
4.2. Comparison with driving cycle based on the
micro-trip method
In V
amosi et al. [2] a Bus Driving Cycle was constructed for
Debrecen using the micro-trip method. There the total time
of the cycle was 747 s, the further parameters of the driving
cycle are collected in Table 2.
As we can see from the results in Table 2,bothdriving
cycles have similar RMS error, but the driving cycle
constructed with the Markov chain method has lower QoF
value than the driving cycle constructed with the micro-
trip method. Figure 3 shows the SAPD of the driving
pattern and the SAPDs of the two driving cycles obtained
with the micro-trip method and the Markov chain
method, respectively. It can be seen that both SAPDs look
similar to the SAPD of the driving pattern, but level of
similarity is higher in the case of the Markov chain
method.
Table 1. Characteristic parameters of the candidate driving cycles
Parameter Full dataset DC1 DC2 DC3 DC4 DC5 DC6 DC7 DC8 DC9 DC10
v
total
(km/h) 13.837 11.705 15.172 15.542 13.810 10.478 12.793 14.034 8.943 16.268 15.634
v
cruise
(km/h) 22.659 20.925 22.561 24.334 21.177 20.385 21.754 22.764 20.521 23.844 22.891
a(m/s
2
) 0.773 0.762 0.828 0.768 0.698 0.760 0.817 0.718 0.797 0.804 0.794
d(m/s
2
)0.648 0.641 0.659 0.656 0.592 0.623 0.651 0.668 0.615 0.660 0.556
a
RMS
(m/s
2
) 0.602 0.566 0.647 0.621 0.573 0.539 0.613 0.574 0.497 0.665 0.592
t
idle
(%) 38.935 44.059 32.750 36.130 34.786 48.598 41.191 38.350 56.421 31.776 31.703
RMS error 0.225 0.214 0.165 0.186 0.378 0.120 0.092 0.608 0.284 0.270
Fig. 2. Proposed driving cycle
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5. CONCLUSIONS
In this paper we compared two Bus Driving Cycles for
Debrecen constructed with two common techniques of
driving cycle development, namely the micro-trip-based
approach and the Markov-chain approach. We introduced
the application of Markov chain approach, then we
compared it to the driving cycle developed using the micro-
trip method focusing on the requirements of a dynamic
simulation, which is a crucial tool of research project aiming
at the analysis and optimization of emission and fuel con-
sumption of various vehicles. As a result of our research it
can be stated that both driving cycles have similar RMS error
values based on certain kinematic parameters, but the
driving cycle developed with the help of the Markov chain
method shows better correspondence to the original dataset
on the basis of the SAPD, thus it has better relation to energy
consumption. This driving cycle has a time duration of 1,208
s and an average speed of 12.793 km/h, the degree of sim-
ilarity between SAPDs, in terms of the Quality of Fit value, is
0.002, which means very good accuracy. The new repre-
sentative Bus Driving Cycle for Debrecen will be applied in a
dynamic vehicle simulation-based development process
aiming at the improvement of fuel economy of vehicles, the
Fig. 3. Speed-Acceleration Probability Distributions (a) full dataset, (b) micro-trip method, (c) Markov chain method
Table 2. Driving cycle characteristic parameters
Parameter Full dataset Micro-trip method Markov chain method
Total time (s) 15,658 747 1,208
Cruise time (s) 9,561 450 710
Idle time (s) 6,097 297 498
Idle time percentage (%) 38.939 36.142 41.191
Average speed (km/h) 13.837 13.025 12.793
Average cruise speed (km/h) 22.659 19.197 21.754
Maximum speed (km/h) 59.0 56.8 59.0
Average acceleration (m/s
2
) 0.773 0.295 0.817
Average deceleration (m/s
2
)0.648 0.314 0.651
Root mean square acceleration (m/s
2
) 0.602 0.571 0.613
Maximum acceleration (m/s
2
) 1.8 1.57 1.6
Maximum deceleration (m/s
2
)2.8 1.62 2.4
RMS error 0.082 0.122
Quality of Fit 0.028 0.002
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proper selection of the power source for various applications
and the optimization of the powertrain and energy con-
sumption.
ACKNOWLEDGMENT
The research was financed by the Thematic Excellence
Programme of the Ministry for Innovation and Technology
in Hungary (ED_18-1-2019-0028), within the framework of
the (Automotive Industry) thematic programme of the
University of Debrecen.
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