&EPA
United States
Environmental Protection
Agency
Air and Radiation EPA420-R-03-018
August 2003
Roadway-Specific Driving
Schedules for Heavy-Duty
Vehicles
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EPA420-R-03-018
August 2003
Roadway-Specific Driving Schedules for
Heavy-Duty Vehicles
Assessment and Standards Division
Office of Transportation and Air Quality
U.S. Environmental Protection Agency
Prepared for EPA by
Eastern Research Group, Inc.
EPA Contract No. 68-C-OO-l 12
Work Assignment No. 3-07
NOTICE
This technical report does not necessarily represent final EPA decisions or positions.
It is intended to present technical analysis of issues using data that are currently available.
The purpose in the release of such reports is to facilitate the exchange of
technical information and to inform the public of technical developments which
may form the basis for a final EPA decision, position, or regulatory action.
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Table of Contents
1.0 Introduction 1-1
2.0 Data Sources 2-1
3.0 Preparation of Raw Data for Cycle Building 3-1
3.1 Timestamp Corrections 3-3
3.2 Speed Value Flags and Vehicle Deletions 3-5
3.3 Idle Designations 3-6
3.4 Trip and Micro-Trip Designations 3-8
4.0 Selection of Cycles to be Developed 4-1
4.1 Vehicle Type/Usage Designations 4-1
4.2 Freeway Micro-Trip Designations 4-1
4.3 Micro-Trip Average Speed Bins 4-2
5.0 Cycle Development 5-1
5.1 General Methodology 5-1
5.2 Generation of Alternative Candidate Cycles 5-6
5.3 Specific Details of Cycle Generation 5-9
5.3.1 Estimation of Vehicle Specific Power 5-9
5.3.2 Binning of Continuous Variables 5-10
5.3.3 Criteria for Skipping Micro-Trips for a Cycle 5-11
5.3.4 Criteria for Judging Candidate Cycles 5-14
5.3.5 Evaluation of Observations in Micro-Trips after Selection
for a Cycle 5-14
6.0 Heavy-Duty Vehicle Operating Characteristics 6-1
7.0 Comparison of Dataset and Cycle Statistics 7-1
8.0 Recommendations for Development of Final Cycles 7-1
List of Tables
Table 3-1. Missing Value Flag Definitions 3-9
Table 4-1. Distribution of Binned Average Micro-Trip Speeds 4-3
Table 4-2. Final Descriptions of Cases 4-4
Table 5-1. Comparison of Cycle and Target Vectors for a Hypothetical One-Dimensional
Example 5-4
Table 5-2. Comparison of Cycle and Target Matrices for a Hypothetical Two-Dimensional
Example 5-7
Table 5-4. Road Load Coefficients for the VSP Equation 5-10
Table 5-5. Distribution of Binned Speeds in the Edited Dataset 5-12
Table 5-6. Distribution of Binned Accelerations in the Edited Dataset 5-12
Table 5-7. Distribution of Binned VSP in the Edited Dataset 5-13
Table 7-1. Comparison of Dataset and Cycle Operation Characteristics 7-2
Table 7-2. Comparison of Dataset and Cycle Operation Modes 7-3
Table 7-3. Comparison of Data and Cycle Extreme Values 7-4
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List of Figures
Figure 5-1. Vector Description of Comparing Target and Cycle Activity 5-3
Figure 5-2. Visual Comparison of Vector Elements 5-5
Figure 5-3. Square of the Length of T_C as Micro-Trips are Added for Case H_l_50 5-15
Figure 5-4. Speed vs. Time for the Candidate Cycle for CaseH_l_50 5-15
Figure 5-5. Acceleration vs. Speed for Case H_l_50 5-16
Figure 5-6. VSP vs. Speed for Case H_l_50 5-17
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1.0 Introduction
EPA is currently beginning development of a new mobile source emissions model that
will replace MOBILE6. As part of that development, modules are being written to calculate
emission factors from typical driving traces of different kinds of vehicles under different
operating conditions. For this work assignment, EPA has asked ERG to use existing heavy-duty
vehicle activity data to develop representative speed versus time driving cycles for heavy-duty
vehicles. Once these driving cycles are developed, they can be incorporated into the code of the
new mobile source model where they can be used by simulation programs to estimate the
emissions of vehicles as they might be produced by heavy-duty vehicles actually driving the
particular schedules.
In this study, we construct cycles from so called micro-trips in an effort to match the
speed, acceleration, and vehicle specific power characteristics of the non-idle driving portions of
the dataset. These three particular activity variables are chosen for matching purposes because
they largely influence the emissions behavior of a given vehicle. The effects of vehicle weight
and road grade are not included in developing these cycles even though they are known to have
important effects on emissions because those parameters were not available in the existing
dataset. Accordingly, the cycles developed in this study should be regarded as a temporary
solution to describing heavy-duty vehicle driving behavior. When data becomes available that
has vehicles weights and road grade in addition to speed, acceleration, and vehicle specific
power on a second-by-second basis, then improved driving schedules can be developed.
Another reason that these cycles should be regarded as temporary is that the mix of
vehicle types and vehicle usage was not planned during data collection. This means that the data
represents operation of the vehicles that just happened to be instrumented rather then a
representation of the mix of different types of vehicles and usage that occurs in the fleet.
To meet the particular needs of the new mobile source emissions model, EPA requested
that a set of separate driving cycles be developed for different combinations of vehicle
type/usage, freeway/non-freeway driving, and different average speeds. A separate, although
related, analysis of the activity data was performed to identify the speed bins for which an
adequate amount of existing data was available.
The cycles developed in this study are not intended to be used to test vehicle emissions
on a dynamometer but are solely to be used in the new model. As a result, the duration of the
individual schedules did not need to be limited although EPA did want to have the duration of
the cycles be reasonable so that a large amount of computer memory would not be required for
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them. In addition, we were also instructed to consider all of the existing data to be driving under
warmed-up, running operating conditions. In other words, we were not to build different "bags"
that characterized vehicle operation during cold starts and hot starts, for example.
Section 2 describes the sources of existing data. Section 3 describes the preparation of
the raw data for cycle building. It includes a discussion of the numerous quality checks and edits
that were made to the millions of second-by-second observations in the datasets. Section 4
describes the analysis of the datasets for the purposes of identifying the different cases for which
cycles would be built. Section 5 describes the general methodology and the specific details of
building the cycles. The results of an analysis that characterized the heavy-duty operating
characteristics of the vehicles are presented in Section 6. A comparison of statistics for the
cycles and the datasets on which they were built is presented in Section 7. Finally, in Section 8,
we make recommendations for the development of final cycles using these datasets.
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2.0 Data Sources
Three sources of data were used to develop the cycles in this study.
Second-by-second driving data on four Texas Department of Transportation dump trucks
were provided by TxDOT. The data was collected using dataloggers based on the Cummins
QuickCheck that attached to the vehicle's serial data communication port following the SAE
J1587/J1708 protocol.
Heavy-duty truck activity data from the Battelle study was collected using data logged
from global positioning system (GPS) units installed on 140 vehicles. Data from 120 of those
vehicles were used to help develop the cycles in the study. The collection of this data is
described in "Heavy-Duty Truck Activity Data," Battelle, Columbus, Ohio, April 30, 1999.
Activity data on heavy-duty trucks was also collected using GPS units by Jack Faucett
and Associates. Second-by-second data from 31 trucks were available and data from 30 of the
trucks were used to help build driving cycles in this study.
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3.0 Preparation of Raw Data for Cycle Building
The raw data taken in the TxDOT, Faucett, and Battelle heavy-duty vehicle studies
required varying amounts of preparation before the data could be used to develop heavy-duty
cycles. The TxDOT data on the four dump trucks had already been quality checked and
corrected by ERG prior to its use in this study. While the Faucett and Battelle data had been
used previously in other studies, that data was reviewed for quality in this study to ensure a
consistent level of quality throughout the datasets and to identify any specific issues that needed
to be addressed during cycle development.
An initial examination of the quality of the Faucett and Battelle second-by-second data,
which were collected from GPS units, revealed that a substantial effort beyond the cost limits of
the project would be required to detect and repair problems in the millions of observations in
those datasets. Accordingly, as far as quality control was concerned, we took the following
approach:
1) Faucett and Battelle timestamps were repaired to the degree possible to provide a
continuous flow of 1-second time steps when vehicle engines were believed to be running.
2) Faucett and Battelle speed values that we could reliably determine to be suspect
were changed to missing values.
3) Faucett and Battelle idle observations were detected as well as could be and the
corresponding speed values were set to 0.00 mph.
4) For all three datasets, all trips were divided into micro-trips based on idles
assigned to observations. Micro-trips from Faucett and Battelle data were "ragged" because they
contained some missing speed values, some remnant GPS dither, some uncertainty about what
was idle, and some uncertainty about the location of the beginning and end of micro-trips.
Micro-trips from TxDOT had none of these problems; they were "clean."
5) For all three datasets, micro-trips were categorized into cases according to vehicle
type/usage, freeway/non-freeway, and average micro-trip speed.
6) For each case, cycles were built using micro-trips to describe all of the operation
for the case. Note that both "clean" and "ragged" micro-trips were in the operation dataset and
were considered for use in the cycle.
7) After the micro-trips for each cycle were selected, the missing values, remnant
dither, remnant high accelerations and decelerations, and any other suspect features were to be
repaired in the cycles.
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By changing suspect speed values in the dataset to missing values so that they not affect
micro-trip selection, and by repairing the micro-trips only as they are selected, we believe that
representative cycles can be developed by this approach, without embarking on the huge job of
repairing every suspect observation in the entire dataset.
The several subsections that follow describe the major steps in quality checking the
Faucett and Battelle data and the steps used to mark special second-by-second observations in
the vehicles from all three studies. The first two subsections describe the methods used to
correct the timestamps in the raw datasets and to flag second-by-second speed values that were
suspect. SAS programs (Battelle/qc_bl.sas and Faucett/qc_bl.sas) were written to automate the
timestamp insertion and speed value flag process. This was done so that hand editing of the
millions of observations in these datasets could be avoided.
The approach for development of the cycles is based on a process of building up cycles
from individual micro-trips selected from the database. For this to work, the trips for all vehicles
must be separated into micro-trips. In this study we define the beginning of a micro-trip as the
point at which the vehicle speed moves from a non-idle speed to an idle speed. For a dataset
such as that collected by TxDOT, which used dataloggers from a speed transducer on the
vehicle, the distinction between non-idle and idle speeds is clear-cut. That is, when the speed is
0.00 mph, the vehicle is idling. Unfortunately, the vehicle speeds from the GPS units in the
Faucett and Battelle studies were almost never observed to be 0.00 mph - probably because of
the effects of dithering. Dithering is the term we use in this study to describe the effects of
Selective Availability (SA)1. The speeds from the Battelle and Faucett datasets showed low
speeds that moved up and down in the vicinity of 0 to 5 mph when the vehicle was not moving.
We developed a probabilistic method of detecting idle speeds using SAS programs (stats/fid, sas
and stats/vid.sas) for the Faucett and Battelle datasets.
As an aside, there may be a question of whether dithering in the GPS speed values of the
Faucett and Battelle data introduces a positive bias in the reported speed values. We believe that
the reported speeds above about 10 mph are not biased on the average, but the speeds below 5
mph have a substantial positive bias. At high speeds dither causes the length and direction of the
velocity vector to be uncertain. However, since the magnitude of the velocity vector is much less
than the magnitude of the velocity vector, fluctuations in the length of the velocity vector
average out to be zero over several seconds. On the other hand, at low vehicle velocities, when
1 According to www.garmin.com, "SA is an intentional degradation of the GPS signal once imposed by the U.S. Department of
Defense. SA was intended to prevent military adversaries from using the highly accurate GPS signals. The government turned
off SA in May 2000," which was after all of the data in the Faucett and Battelle data used in this study were collected.
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the magnitude of the dither is comparable or greater than to the magnitude of the velocity vector,
fluctuations in the length of the velocity vector will not average to zero. The extreme case is
when the vehicle is not moving. In this situation, the average speed is zero but because of the
dither the velocity vector points from second to second in different directions. The length of the
vector is not zero and a vector cannot have a negative length. Therefore, the average speed is
biased positive.
Once the Battelle and Faucett datasets had timestamp corrections, flags to designate
suspect speed values, and a flag variable to mark observations believed to be idles, the three
datasets were combined into a master dataset. Then, the idle flags were used to separate trips
into individual micro-trips. The entire dataset was then written to a final SAS dataset. This was
done using the program stats/prep.sas.
3.1 Timestamp Corrections
The qc_bl.sas programs were used to make timestamp corrections to the raw Faucett and
Battelle datasets. In general, each timestamp was compared to the previous and subsequent
timestamps to determine if each timestamp was consistent with those around it. Examination of
the data indicated that some timestamps were skipped, duplicated, or otherwise incorrect. The
SAS programs detected timestamp errors by calculating the size of the time steps, which is the
time difference between adjacent observations in the datasets. Except at the beginning of trips,
all time steps should be one second. The following discussion describes the general approach for
detecting timestamp problems and describes how the timestamps were modified. In most
instances, the time step was found to be one second. However, other time step values were also
found.
The first step was to look for duplicate adjacent records in the datasets. These were
records where the timestamp, speed, latitude, and longitude for a given vehicle were the same on
two or more consecutive observations. For these instances the duplicated records were removed
from the dataset. Occasionally, the same timestamp was found on consecutive observations but
the speed values were different. In these cases, we incremented the timestamp on consecutive
seconds to provide a continuous flow of time.
In the Battelle dataset, a large number of timestamps were found to be 01JAN04 which
was the value that was logged when the GPS unit had not yet found its satellite signal. In these
cases, we looked at the timestamps before and after these and entered a corrected timestamp.
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Some time steps were found to be greater than one second during a trip. This indicated
that records were missing. In these instances, in the Faucett dataset we inserted observations in
the dataset with timestamps that would make the set of timestamps continuous during the trip
and assigned missing speed values to those timestamps. In the Battelle dataset, we found time
steps that were negative followed several observations later where the time step was positive to
bring the following observations back to the correct time. In these instances we hand corrected
this "drop out" period to have correct timestamps to which the speed values were assumed to be
correctly assigned.
In the Battelle dataset we examined the frequency distribution of the time steps and found
that there were a large number of time steps of exactly 30 seconds. This corresponded to the
Battelle datalogging system going "dormant" during a perceived idle of the vehicle. During
these periods, the Battelle datalogger recorded vehicle speed for one second every 30 seconds
until the datalogger found the vehicle to be no longer idling. For these 30-second dormant
periods, if the logged speed at the end of the dormant period was 0.00 mph, then we assigned the
previous 29 seconds to have a speed of 0.00 mph and inserted the 29 observations with the
appropriate timestamps. However, if the speed following the 30-second time step was greater
then 0.00 mph we inserted the previous 29 observations with timestamps but assigned them to
have missing speeds.
In the Battelle dataset, the distribution of time steps indicated a moderately large number
of time steps with durations between 2 and 29 seconds. We believe these instances were from
cases where the datalogger awoke from its dormancy during which the vehicle had already
started moving. Since we could not tell from the data which seconds of those periods were idles
and which were not idles, we had to assign all speed observations in those periods to missing
values. We took the same approach for the relatively small number of periods with time steps
greater then 30 seconds.
In both the Faucett and Battelle datasets, the insertion of timestamps for time steps that
were greater then one second caused a large increase in the total number of observations in the
datasets. In the Faucett dataset, the number of observations increased from 2.0 million to 3.6
million and for the Battelle dataset, it increased from 8.0 million to 13.7 million. In the Battelle
dataset, the majority of the increased time was caused by the large number of 30 second
dormancy periods during idles. However, in the Faucett dataset, the large increase in number of
observations was caused by the insertion of a large number of timestamps for a relatively few
large time steps. The largest time step was around 90,000 seconds.
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As best we can determine, the beginning of trips (key on) was detected by the
datalogging system by monitoring increases in noise and small changes in voltage levels of the
12-volt vehicle auxiliary power outlet. If an engine-on or engine-off event was not detected by
the datalogging system, then the system could incorrectly assign a trip number to a portion of the
data. The result could be a period of missing timestamps for a trip when actually the vehicle was
between trips.
Accordingly, we compared the speeds before and after time steps greater than one
second. We found two types of behavior. As the duration of time steps increased, the speeds
just before and just after the time gap were more likely to be idle speeds. However, for short
time steps greater then one second, the speeds before and after the time gap tended to be in good
agreement and tended to not be idle speeds. Accordingly, for the Faucett data if the before speed
was less than 12 miles per hour and the after speed was less then 15 miles per hour, we removed
the observations with missing timestamps. This broke the trip designated by the datalogging
system into two separate trips. If the before or after speeds were longer than these limits, then
we left the inserted timestamps with missing speeds and the single trip remained as we had
already corrected it. We, therefore, assumed that the missing time gap represented a continuing
trip that simply had speed values missing. In the case of the Battelle dataset, the criteria were
speeds before of less than 5 miles per hour and speeds after of less than 35 miles per hour.
3.2 Speed Value Flags and Vehicle Deletions
The data quality checking programs for the Faucett and Battelle datasets also were
written to set suspect speed values to missing values. This was done individually for each of the
vehicles in the datasets by examining the speed values on a plot of acceleration versus speed for
each individual vehicle.
In the Faucett and Battelle datasets, we made plots of acceleration versus speed for each
of the individual 171 vehicles. Usually, the plots showed high accelerations at low speeds and
low accelerations at high speeds in the familiar triangular shape seen for light-duty vehicles. We
arbitrarily drew upper and lower limit lines on these plots for each vehicle to help designate the
points that appeared to be outliers. Observations where the speed and acceleration values were
outside of these upper and lower limits were given a flag designation of A for acceleration that
was too high or D for a deceleration that was too low.
However, for 20 of the 140 vehicles in the Battelle dataset, the acceleration versus speed
plots indicated a large amount of noise in the speed values as shown by many extremely large
accelerations and decelerations in the dataset. An examination of the speed versus time plots for
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portions of these vehicles indicated that the data from these vehicles was not useful for the
purpose of generating cycles. Accordingly, these 20 vehicles were eliminated from further
consideration in this project. In the case of the Faucett dataset, one vehicle (Vehicle 143) was
found to have speed values that were excessively noisy. This vehicle was dropped from the
Faucett dataset.
In the Faucett dataset, in addition to the flagging of certain observations with A and D,
we noticed that observations adjacent to these flagged observations were sometimes "stuck" at
constant speed values. Thus, the Faucett dataset exhibited periods of datalogging failure that
were made up of different combinations and orders of high acceleration, high deceleration, and
stuck speeds. Therefore, in the Faucett dataset, we also included a flag of Z for accelerations of
exactly 0.00 mph/s when the speed was not equal to 0 mph. When we examined the groups of
observations that were contiguous in flags of A, D, and Z we found these to be periods in which
the speed values were unquestionably erroneous. We set the speed values during these identified
periods to missing.
We also found a large number of periods in the Battelle data with "stuck" speeds, but we
did not change speeds of the affected observations to be missing since such a large portion of the
Battelle data had 0.00 mph/s arising from the lower speed resolution (0.11 mph) of the
datalogging system. In the case of the Battelle dataset, any observation that had an A or D flag
had its speed changed from its reported value to a missing value, but the periods of stuck speed
were left as reported.
After the timestamp insertions and vehicle deletions, the Faucett dataset had 2,125,097
observations and the Battelle dataset had 10,714,023 observations. The TxDOT dataset had
709,581 observations. The combined data from these three datasets were used to build the cycles
for this study.
3.3 Idle Designations
Because the cycle development process is based on building up candidate cycles from
micro-trips, which are defined by idle periods, it is important to correctly designate what
observations are idles. Because of the presence of dithering in the GPS speed values, non-zero
speeds are almost always reported in the Battelle and Faucett datasets - even when the vehicles
are not moving. Consequently, we had to develop a method for designating when a vehicle was
at idle. Our examination of the Faucett and Battelle data on an acceleration versus speed plot
showed that a large peak in observations occurred at 0.6 mph and 0.00 mph/s which is near the
expected idle values of 0.00 mph and 0.00 mph/s. This finding caused us to develop a
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probabilistic method of estimating whether an individual observation represented an idle or a
non-idle condition for the vehicle.
The method is based on the frequency of observations that occur in speed/acceleration
bins for each individual vehicle in the vicinity of idle conditions. The vicinity that we used was
for speeds between 0 and 10 mph and for accelerations between -0.5 and +0.5 mph/s. (The 10
mph value was used for all vehicles in the Faucett dataset. Different values were used for
different vehicles in the Battelle dataset.) In this region, we counted the number of observations
in bins that were 0.2 mph wide and 0.02 mph/s wide. The bin with the maximum frequency was
assigned a probability value of 1.00. Other bins in this vicinity were given probabilities in
proportion to their frequencies relative to the maximum frequency. Speeds that were greater
than 10 mph or accelerations greater than +0.5 mph/s acceleration or less than -0.5 mph/s were
assigned probabilities of zero. All observations in the dataset were assigned individual
probabilities (variable name: p_i) that corresponded to the probability assigned to the speed
acceleration bin into which that observation fell. This resulted in observations having
probabilities assigned to them of being an idle observation.
When we examined speed versus time plots for these assigned probabilities, we found
that there was a lot of noise in the assigned probabilities from second-to-second because of small
changes in accelerations from point to point. Consequently, we calculated a rolling average
probability (variable name: p_i7) for each observation by calculating the joint probabilities for
the current observation and the three probabilities in the previous three observations and the
three probabilities in the following three observations. This provided a smoothing of
probabilities. Special code was written for calculating the joint probabilities at the beginning and
end of trips since, in those locations, three seconds before and three seconds after the current
observation do not always exist.
Our examination of the joint probabilities and speed as a function of time indicated that it
was quite possible to make a reasonable separation of observations into non-idle and idle
observations. To determine the value of the threshold that should be used to separate the
probabilities into idle and non-idle, we made a frequency distribution of the joint probabilities
for each vehicle in the two datasets. We found that a minimum in the distribution was observed
near a joint probability of 0.45 for all of the vehicles. Accordingly, we used this value to
separate the idle from non-idle observations. This separation was manifested as a flag variable
called idle_mark that had a value of one when the observation was believed to be an idle
condition and zero when the observation was believed to be a non-idle condition.
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3.4 Trip and Micro-Trip Designations
The edited data from the TxDOT, Faucett, and Battelle datasets were next combined and
prepared for use in cycle development. This preparation was done by the prep.sas program.
First, the data from all three sets were put into one dataset. Next, the reported speeds that were
believed by the qc_bl.sas program to be idles (idle_mark=l) were changed to have values of 0.00
mph. This was done only for the Faucett and Battelle data since the TxDOT data already had
measured speeds of zero for idle periods.
Once the speeds at idle were set to zero, the designation of trips and micro-trips could be
done. The beginning of trips occurred:
• At the first observation of the dataset;
• When the vehicle changed; or
• When the time step between sequential time stamps was greater than 1 second or
less than -1 second.
Whenever the program detected the start of a new trip using these criteria, the trip
number was incremented. Trip numbers for the entire dataset were unique.
The observations were marked for the beginning of a micro-trip:
• If a new trip began;
• If the current speed was zero and the previous second's speed was non-zero.
Whenever a new micro-trip was detected, the micro-trip number was incremented.
Micro-trip numbers for the entire dataset were unique.
Finally, the data from all three datasets with the new flags were written to a permanent
dataset for use by the cycle development programs. The dataset variables included study, vehicle
ID, trip number, trip seconds, trip start flag, micro-trip number, micro-trip seconds, micro-trip
start flag, the date/time stamp, the corrected speed to be used for cycle building, the original raw
speed from the original datasets, and a flag that gave the reason that the original speed was
changed. Table 3-1 provides a list of the different flag values and their meanings.
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Table 3-1. Missing Value Flag Definitions
Value of Flag
FIX1
FIX10
FIX13
FIX2*
A
D
P
JAN04
SPN
Action Taken
Inserted a missing observation. Provided the appropriate timestamp value.
Speed value was set to missing.
Corrected the timestamp and left the reported speed as is. Occurred when the
raw timestamp value was duplicated, but the raw speed value was not
duplicated.
For Battelle data only where the time step was 30 seconds. Inserted 29 seconds
with appropriate timestamps. If the reported speed on the thirtieth second was
0.00 mph, then the previous 29 1-second inserted speed values were set to 0.00
mph. Otherwise, the inserted speed values were set to missing.
Same explanation as for the FIX1* values above, but the action was taken on
the second pass through the dataset.
The indicated acceleration was greater than the high acceleration limit for that
vehicle. The speed value was set to missing.
The indicated acceleration was less then the low acceleration limit for that
vehicle. The speed value was set to missing.
For Faucett data only. Suspect observations near A and D flag values that were
part of a pattern of speed value excursions associated with "stuck" speed values.
The speed values were set to missing.
For Battelle data only. When the reported timestamp was 01 JAN04 (GPS unit
lost satellite signal). The timestamp was set to an appropriate value and the
speed was set to missing.
A time step was negative and then several seconds later it was positive by just
an amount that put the timestamp back where it should have been. All
timestamps during this period were hand edited and speed values were left as
reported.
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4.0 Selection of Cycles to be Developed
In this study, the heavy-duty vehicle activity data was used to develop individual cycles
for the operation of vehicles for different combinations of vehicle type/usage, freeway/non-
freeway operation, and average micro-trip speeds. In this study these different combinations are
called cases. The following subsections describe the analysis of the edited heavy-duty activity
dataset to arrive at descriptions of the different cycles that were developed. The vehicle
type/usage designations and freeway/non-freeway trip designations were arrived at based on
definitions suggested by EPA. The selection of micro-trip average speed bins was based on an
analysis of the heavy-duty vehicle activity dataset.
4.1 Vehicle Type/Usage Designations
As specified by EPA, the 154 heavy-duty vehicles in the activity dataset were divided
into three categories:
• Heavy heavy-duty vehicles - these vehicles had gross vehicle weight ratings of
33,001 Ibs. and greater;
• Non-parcel medium heavy-duty vehicles - these vehicles had gross vehicle
weight ratings from 19,501 to 33,000 Ibs. and the vehicles were those that were
not used for postal/parcel service;
• Parcel medium heavy-duty vehicles - these vehicles had gross vehicle weight
ratings from 19,501 to 33,000 Ibs. and were specifically designated as being used
for postal/parcel service. The only vehicles that fell into this category were a
portion of those in the Battelle dataset.
The vehicle type designations for all 154 vehicles that were used to develop cycles in this
study are shown in Appendix A.
4.2 Freeway Micro-Trip Designations
Micro-trips were designated as freeway or non-freeway micro-trips. EPA had decided to
designate micro-trips with regard to freeway use based on the distance of the micro-trip. Micro-
trips that had a total distance of greater than or equal to 3 miles were designated as freeway
micro-trips. The freeway designation is more a designation of whether a micro-trip was involved
in stop-and-go driving rather than an actual verification that a given micro-trip occurred on a
freeway. While the GPS latitude and longitude information could be used to determine which
observations were associated with the presence of a vehicle on a freeway, this approach was not
taken in this study.
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4.3 Micro-Trip Average Speed Bins
The heavy-duty vehicle activity dataset was analyzed to arrive at several speed bins for
the six different combinations of vehicle type/usage and freeway/non-freeway designations.
First, all of the micro-trips in a dataset were designated for vehicle type/usage and freeway/non-
freeway operation. Then, the average vehicle speed for all of the micro-trips in each of the six
combinations of vehicle type/usage and freeway/non-freeway operation were calculated. The
micro-trip average vehicle speeds were then binned into the average speed bins that will be used
for the new MOBILE model. These speed bins were created by rounding the average speed to
the nearest 5 mph. Table 4-1 shows the distributions of the binned average micro-trip speeds for
the six different combinations of vehicle type and freeway/non-freeway operation. From these
distributions, the final description of cycles to be developed in terms of combinations of vehicle
type/usage, freeway/non-freeway operation, and micro-trip average speed are shown in Table 4-
2.
The goal in creating the different cases was to combine adjacent average speed bins such
that each combination of vehicle type and freeway/non-freeway operation had five or six speed
bins associated with it. In addition, each of the cases needed to have a relatively large number of
micro-trips so that the typical operation was well defined and so that the cycle development
software had a sufficiently large number of micro-trips to choose from to build the cycle.
4-2
-------
Table 4-1. Distribution of Binned Average Micro-Trip Speeds
Vehicle Type
Operation
Rounded Average
Micro-Trip Speed (mph)
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
Total
HHDV
Non-Freeway
16993
4561
2461
1610
1317
944
510
167
62
16
3
1
2
0
0
28647
HHDV
Freeway
0
2
2
12
29
66
129
208
291
429
616
534
172
20
0
2510
MHDV Non-
Parcel
Non-Freeway
3926
1362
887
829
758
497
224
53
14
3
0
0
0
0
0
8553
MHDV Non-
Parcel
Freeway
0
0
1
2
5
13
40
41
67
94
87
74
34
2
1
461
MHDV
Parcel
Non-Freeway
9318
4712
3942
3370
2320
1239
586
227
112
36
7
1
0
0
0
25870
MHDV
Parcel
Freeway
0
0
0
0
2
9
18
70
71
88
95
61
39
7
0
460
Total
30237
10637
7293
5823
4431
2768
1507
766
617
666
808
671
247
29
1
66501
4-3
-------
Table 4-2. Final Descriptions of Cases
Case Name
H_0_5
H_0_10
H_0_15
H_0_20
H_0_25
H 0 30
H_l_30
H_l_40
H_l_50
H 1 60
N_0_5
N_0_10
N_0_15
N_0_20
N_0_25
N 0 30
N_l_30
N_l_40
N_l_50
N 1 60
P_0_5
P_0_10
P_0_15
P_0_20
P_0_25
P 0 30
P_l_30
P_l_40
P_l_50
P 1 60
Vehicle
Type/Usage
HHDV
MHDV Non-Parcel
MHDV Parcel
Operation
Non-Freeway
Freeway
Non-Freeway
Freeway
Non-Freeway
Freeway
Micro-Trip Average Speed Bin
5
10
15
20
25
30
30
40
50
60
5
10
15
20
25
30
30
40
50
60
5
10
15
30
30
40
50
60
Speed (niph) Bin Definition
Avg Micro-Trip Speed < 7.5
7 - < Avg Micro-Trip Speed < 12.5
12.5 < Avg Micro-Trip Speed < 17.5
17.5 < Avg Micro-Trip Speed < 22.5
22.5 < Avg Micro-Trip Speed < 27.5
27.5 < Avg Micro-Trip Speed
Avg Micro-Trip Speed < 35
35 < Avg Micro-Trip Speed < 45
45 < Avg Micro-Trip Speed < 55
55 < Avg Micro-Trip Speed
Avg Micro-Trip Speed < 7.5
? 5 < Avg Micro-Trip Speed < 12.5
12.5 < Avg Micro-Trip Speed < 17.5
17.5 < Avg Micro-Trip Speed < 22.5
22.5 < Avg Micro-Trip Speed < 27.5
27.5 < Avg Micro-Trip Speed
Avg Micro-Trip Speed < 35
35 < Avg Micro-Trip Speed < 45
45 < Avg Micro-Trip Speed < 55
55 < Avg Micro-Trip Speed
Avg Micro-Trip Speed < 7.5
7 - < Avg Micro-Trip Speed < 12.5
12.5 < Avg Micro-Trip Speed < 17.5
17.5 < Avg Micro-Trip Speed < 22.5
22.5 < Avg Micro-Trip Speed < 27.5
27.5 < Avg Micro-Trip Speed
Avg Micro-Trip Speed < 35
35 < Avg Micro-Trip Speed < 45
45 < Avg Micro-Trip Speed < 55
55 < Avg Micro-Trip Speed
Number of Micro-Trips
14911
2461
1610
1317
944
761
337
595
1157
421
4571
887
829
758
497
294
81
136
171
73
10127
3941
3370
2318
1239
968
50
165
175
70
Total 55234
4-4
-------
5.0 Cycle Development
The cycles to be built for heavy-duty vehicle operation will ultimately be used in EPA's
new MOBILE model of vehicle emissions for heavy-duty vehicles. The idea of a cycle is that it
contain the essence of heavy-duty vehicle driving behavior. To make a representative cycle
practical, the cycle should be relatively short so that it does not take up a large amount of
memory in the model. Since the heavy-duty vehicle activity database contains second-by-second
data for 154 vehicles over a considerable amount of time, the key challenge for the cycle builder
is to compress the dataset to produce a reasonably short cycle while maintaining the essence of
the heavy-duty vehicle driving behavior. Such a short cycle can then be used by the model to
calculate emissions of a heavy-duty vehicle.
Representative cycles can be built using different methodologies. The methodology we
have chosen for this study's cycles is to use pieces of real driving, called micro-trips, from the
heavy-duty activity database, which when connected together can be expected to have similar
emissions behavior to heavy-duty vehicles driving on the road. However, the emissions behavior
of different vehicles with different technologies - even future technologies - will differ.
Accordingly, we cannot create cycles based directly on emissions behavior. Instead, the cycles
will be built around parameters of vehicle operation and usage that are known or expected to be
important to exhaust emissions of heavy-duty vehicles. By using this approach of matching
vehicle operation between measured driving behavior and candidate cycles, it can be inferred
that the emissions behavior of vehicles over the cycles will be similar to the emissions behavior
of heavy-duty vehicles on the road.
In the creation of these heavy-duty cycles, we have chosen vehicle speed, acceleration,
and vehicle specific power (VSP) as the variables that are important to the exhaust emissions of
heavy-duty vehicles. All three of these variables together provide a measure of the load on the
engine, which is an important variable associated with exhaust emissions. In this study, we are
building cycles only for warmed up operation of heavy-duty vehicles. That is, we are not
building special cycles for cold starts and warm starts. We assume that all data in the datasets
represent warmed-up driving.
5.1 General Methodology
The cycles were created by combining micro-trips of actual driving. Each cycle should
be a good representation of the driving behavior in the dataset. The three critical variables
(speed, acceleration, vehicle specific power) were used for selection of micro-trips. The speed of
each vehicle was measured directly in the TxDOT, Faucett, and Battelle datasets. The
5-1
-------
acceleration of the vehicle for each second was estimated as the derivative of the speed. The
vehicle specific power for each second was estimated from the speed and acceleration as
described in Section 5.3.1.
To identify specific segments of vehicle driving for inclusion in the cycle, the entire
activity dataset was converted to a set of micro-trips. A micro-trip is defined as a contiguous
speed trace of vehicle driving and is made up of an idle followed by all non-idle driving until the
next idle begins. A single vehicle trip may be composed of numerous micro-trips.
A strategy based on a minimizing the difference between a cycle vector C representing
the driving in the candidate cycle and a target vector T representing the driving in the activity
database for the case was used to select micro-trips from the database for inclusion in the cycle.
As micro-trips are used to build-up a candidate cycle, the difference between the two vectors
tends to become smaller and smaller. The build-up process ends when the cycle developer
decides that the two vectors are substantially the same and the duration of the cycle that has been
built up is acceptable. The multi-dimensional space that these vectors are in will be described
shortly, but first let us consider how the build-up process works for developing a cycle.
The goal of building the cycle is to select micro-trips such that when their vectors MI are
added together, the vector C of the resulting cycle is as similar as possible to the target vector T
of the activity database. Figure 5-1 shows the hypothetical situation of the vectors after two
micro-trips have been used to create a cycle. In this hypothetical example, the first micro-trip
was selected from the activity database for the case as the one whose vector MI was closest to
the target vector T for the database. Then, a second micro-trip is searched for such that when its
vector M2 is added to MI to create the resultant vector C shown in Figure 6-1, the distance
between the tips of C and T is minimized. This distance is the length of the vector T-C as
denoted in the figure by the dashed vector. As micro-trips are added to create the built-up cycle
represented by C, the length of T-C is calculated after each additional micro-trip is added to the
cycle to follow the progress of the build-up process. It should be noted that the order of the
micro-trips in the final cycle is unimportant from the point of view of the selection of the micro-
trips. The reason for this is that the resultant C is independent of the order in which the micro-
trip vectors MI are added together.
5-2
-------
Figure 5-1. Vector Description of Comparing Target and Cycle Activity
T
T-C
It should also be noted that we are forcing micro-trips to be added to the candidate cycle.
This is done even if the addition of the best incremental micro-trip causes the length of T-C to
increase in some instances. Generally, as the cycle is built up there will be a decrease in the
length of T-C. After several micro-trips have been added, the length of T-C may increase
slightly. Later, with the addition of more micro-trips, a "discovery" will be made that will
produce a relatively abrupt decrease in the length of T-C so that the accumulated cycle will be
substantially better than the cycle was much earlier in the build-up process.
All of the vectors used above to describe the build-up process are based on
representations of the frequency distributions of observations in cumulative speed, acceleration,
vehicle specific power space. This statement requires some explanation. A segment of driving,
whether it is a micro-trip, a piece of a driving cycle, or the entire activity database can be
described as a frequency distribution. The distribution consists of combinations of the three
variables: speed, acceleration, and vehicle specific power. The continuous values for each of
these variables were converted into frequency distributions through the use of bins. Each
observation in the database was placed in a particular speed/acceleration/VSP bin. The
cumulative frequency distribution is made up of the number of observations that fall "below" the
5-3
-------
current bin for each of the three-binned variables. The binning criteria for each of the three
variables are described in Section 5.3.2. To help the reader understand the process, we will
present a numerical example in one dimension and another example in two dimensions to
demonstrate how the comparison of the vectors T and C works.
Suppose we wanted to compare a candidate cycle with the database using a single vehicle
operation variable that was monitored second-by-second in the collection of data for the activity
database. The single variable might be engine load. In this hypothetical example, we have
35,900 one-second observations of engine load in the target activity database and 68 one-second
observations in the cycle. The first step in comparing T and C is to bin the observations of load
in the target data and in the cycle data. Table 5-1 shows the binning of the hypothetical data in
Columns 2 and 3. Note that the number of observations in the target data in Column 2 is much
higher then the number of observations in the cycle data in Column 3. This is a consequence of
the activity database containing all of the observations for all micro-trips but the cycle has just
one micro-trip. The frequency counts in Columns 2 and 3 are then converted to cumulative
frequency counts in Columns 4 and 5. This is done to provide proximity information for the
micro-trip searching algorithm. In other words, we wanted to the algorithm to be able to select a
micro-trip even if the observations for a given micro-trip were not in exactly the same bins as the
target but did have observations at least in a nearby bin. The use of the cumulative distributions
helps ensure that proximity information is available.
Table 5-1. Comparison of Cycle and Target Vectors
for a Hypothetical One-Dimensional Example
Bin
1
2
3
4
5
6
7
8
9
10
Counts
Target
1000
11000
7000
6000
4500
2800
1500
800
600
700
Cycle
0
30
10
7
5
1
4
6
1
4
Cumulative Counts
Target
1000
12000
19000
25000
29500
32300
33800
34600
35200
35900
Cycle
0
30
40
47
52
53
57
63
64
68
Vector
(Normalized Cumulative Counts)
Target
0.028
0.334
0.529
0.696
0.822
0.900
0.942
0.964
0.981
1.000
Cycle
0.000
0.441
0.588
0.691
0.765
0.779
0.838
0.926
0.941
1.000
Vector Length
T C T-C
1.246 1.2660.138
A comparison of the cumulative counts for the target and cycle information in Columns 4
and 5 shows that if we used these counts to create the T and C vectors, the lengths of the vectors
5-4
-------
would be greatly different simply because the target vector, which is made up of the 10 elements
in Column 4, would be a much longer vector then the cycle vector, which is made up of the 10
elements in Column 5. Accordingly, we normalize the target and cycle cumulative counts in 4
and 5 to produce the target vector elements and the cycle vector elements as the fractional values
between 0 and 1 shown in Columns 6 and 7.
The values in Columns 6 and 7 become the elements of the T and C vectors, which are in
10-dimensional space. A visualization of the elements of these vectors is provided in Figure 5-2.
This figure shows the normalized cumulative counts of the target and cycle from Columns 6 and
7 as a function of the bin number. What we want to do in developing the cycle is select micro-
trips so that the curve for the cycle is as close as possible to the curve for the target in this figure.
The way we do this is to minimize the sums of the squares of the differences between the value
for the corresponding elements of the target and cycle vectors. This corresponds to the square of
the length of T-C. Table 5-1 shows the calculated length of T, C, and T-C. These lengths can
be determined from the values of the elements for T and C in Columns 6 and 7 using the
standard relationship for determining the length of a vector if its elements are known.
Figure 5-2. Visual Comparison of Vector Elements
1
7
8
10
23456
Bin
Extension of the one-dimensional example shown in Table 5-1 and Figure 5-2 to multiple
dimensions is demonstrated by the spreadsheet calculations shown in Table 5-2. In this example,
5-5
-------
100 matrix elements are used. The table shows 10 rows which might be accelerations and 10
columns which might be speeds. The left side of Table 5-2 shows the calculations for the target
matrix and the right side shows the calculations for the cycle matrix. In Tables a) and b), the
second-by-second observations of the target and cycle data are binned. The numbers in each bin
represent the frequency of observations that meet the criteria for those bins. In Tables c) and d),
the counts in the Tables a) and b) are accumulated across each row. Then, in Tables e) and f),
the accumulated frequencies in Tables c) and d) are accumulated down each column. This
produces a field of frequencies on a cumulative basis that run from a low value in the upper left
corner of each matrix to a high number in the lower right corner of each matrix. The value in the
lower right hand corner of Tables e) and f) is equal to the total number of observations in the
target or cycle matrix. These total observation numbers in the lower right hand corner of e) and
f) are used to normalize all of the frequencies in Tables e) and f) to arrive at the normalized
cumulative matrices in g) and h). The values in g) and h) are then used to calculate the square of
the differences in each corresponding matrix element to produce the values in Table i). The
value in Tablej) is just the summation of all of the elements of Table i) and represents the square
of the length of the T-C vector. This is the value that we attempt to minimize when selecting
micro-trips for the cycle.
Note that the counts in a) and b) did not need to be in corresponding bins for this
comparison process to work. The use of cumulative distributions permitted the two matrices to
be compared successfully.
Extension of the technique to the third dimension for vehicle specific power or any
number of higher dimensions is made by analogy.
5.2 Generation of Alternative Candidate Cycles
The implementation of the cycle development methodology is provided by three
computer programs: makemicro.sas, fmdcycle.f, and makecycle.sas, which are run sequentially.
The important details of what the three programs do are described in the following subsections.
However, what they do in general is described here.
5-6
-------
Table 5-2. Comparison of Cycle and Target Matrices for a Hypothetical Two-
Dimensional Example
Target Activity Matrix
a) Count the second-by-second observations in each bin.
ABCDEFGH
1
2
3
4
5
6
7
8
9
10
2
1
2
5
1
5
2
6
5
9
3
1
4
1
2
1
1
2
9
3
c) Accumulate the above frequencies across each row
1
2
3
4
5
6
7
8
9
10
2
0
0
0
0
0
0
0
0
0
2
1
2
0
5
0
0
0
1
0
2
1
2
5
5
2
0
6
1
0
2
1
7
5
14
2
0
6
1
0
2
1
7
8
15
2
0
6
1
0
2
1
7
8
15
6
0
7
1
0
2
1
7
10
15
7
0
7
1
0
2
1
7
11
17
7
0
7
1
0
2
1
7
11
26
7
0
7
1
0
2
1
7
11
29
7
0
7
1
0
e) Accumulate the above frequencies down each column.
1
2
3
4
5
6
7
8
9
10
2
2
2
2
2
2
2
2
2
2
2
3
5
5
10
10
10
10
11
11
2
3
5
10
15
17
17
23
24
24
2
3
10
15
29
31
31
37
38
38
2
3
10
18
33
35
35
41
42
42
2
3
10
18
33
39
39
46
47
47
2
3
10
20
35
42
42
49
50
50
2
3
10
21
38
45
45
52
53
53
2
3
10
21
47
54
54
61
62
62
2
3
10
21
50
57
57
64
65
65
g) Normalize the elements in the above matrix.
1
2
3
4
5
6
7
8
9
10
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.031
0.046
0.077
0.077
0.154
0.154
0.154
0.154
0.169
0.169
0.031
0.046
0.077
0.154
0.231
0.262
0.262
0.354
0.369
0.369
0.031
0.046
0.154
0.231
0.446
0.477
0.477
0.569
0.585
0.585
0.031
0.046
0.154
0.277
0.508
0.538
0.538
0.631
0.646
0.646
0.031
0.046
0.154
0.277
0.508
0.600
0.600
0.708
0.723
0.723
0.031
0.046
0.154
0.308
0.538
0.646
0.646
0.754
0.769
0.769
0.031
0.046
0.154
0.323
0.585
0.692
0.692
0.800
0.815
0.815
0.031
0.046
0.154
0.323
0.723
0.831
0.831
0.938
0.954
0.954
0.031
0.046
0.154
0.323
0.769
0.877
0.877
0.985
1.000
1.000
Cycle Activity Matrix
b) Count the second-by-second observations in each bin.
A BCDEFGH I
1
1
4
5
4
8
3
3
1
1
4
1
2
d) Accumulate the above frequencies across each row
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
6
0
0
1
0
4
0
0
0
0
6
0
0
1
4
4
0
8
0
0
6
0
0
1
4
4
0
8
3
0
6
0
0
1
4
7
0
8
3
0
6
0
0
1
4
7
0
8
3
1
6
0
0
1
4
8
4
8
3
1
6
0
0
1
4
8
5
8
3
1
6
0
0
1
4
8
5
10
3
1
6
0
f) Accumulate the above frequencies down each column.
0
0
0
0
0
0
0
0
1
1
0
1
1
5
5
5
5
5
11
11
0
1
1
5
5
5
5
5
11
11
0
1
5
9
9
17
17
17
23
23
0
1
5
9
9
17
20
20
26
26
0
1
5
12
12
20
23
23
29
29
0
1
5
12
12
20
23
24
30
30
0
1
5
13
17
25
28
29
35
35
0
1
5
13
18
26
29
30
36
36
0
1
5
13
18
28
31
32
38
38
h) Normalize the elements in the above matrix.
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.026
0.026
0.000
0.026
0.026
0.132
0.132
0.132
0.132
0.132
0.289
0.289
0.000
0.026
0.026
0.132
0.132
0.132
0.132
0.132
0.289
0.289
0.000
0.026
0.132
0.237
0.237
0.447
0.447
0.447
0.605
0.605
0.000
0.026
0.132
0.237
0.237
0.447
0.526
0.526
0.684
0.684
0.000
0.026
0.132
0.316
0.316
0.526
0.605
0.605
0.763
0.763
0.000
0.026
0.132
0.316
0.316
0.526
0.605
0.632
0.789
0.789
0.000
0.026
0.132
0.342
0.447
0.658
0.737
0.763
0.921
0.921
0.000
0.026
0.132
0.342
0.474
0.684
0.763
0.789
0.947
0.947
0.000
0.026
0.132
0.342
0.474
0.737
0.816
0.842
1.000
1.000
i) Calculate the squares of the differences in corresponding elements of the above two matrices.
C
D
H
I
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.000
0.000
0.001
0.000
0.003
0.003
0.000
0.000
0.000
0.000
0.014
0.014
0.001
0.000
0.003
0.000
0.010
0.017
0.017
0.049
0.006
0.006
0.001
0.000
0.000
0.000
0.044
0.001
0.001
0.015
0.000
0.000
0.001
0.000
0.000
0.002
0.073
0.008
0.000
0.011
0.001
0.001
0.001
0.000
0.000
0.002
0.037
0.005
0.000
0.010
0.002
0.002
0.001
0.000
0.000
0.000
0.050
0.014
0.002
0.015
0.000
0.000
0.001
0.000
0.000
0.000
0.019
0.001
0.002
0.001
0.011
0.011
0.001
0.000
0.000
0.000
0.062
0.021
0.005
0.022
0.000
0.000
0.001
0.000
0.000
0.000
0.087
0.020
0.004
0.020
0.000
0.000
j) Sum the squares of the differences.
5-7
-------
The first program, makemicro.sas, reads in the edited second-by-second data that is to be
used to generate cycles. The data that is read in has already had the micro-trips designated by
prep.sas. Each micro-trip is assigned to one of the 30 cases for which an individual cycle will be
produced. Then, makemicro.sas estimates the vehicle specific power for every observation in the
database based on the database values for speed and acceleration and the coefficients provided
by EPA to estimate the effects of aerodynamic drag and rolling resistance on the vehicle specific
power. Next, the continuous values for speed, acceleration, and VSP are binned through a
rounding process. For each of the micro-trips in a case and for all micro-trips in a case taken
together, the program counts the number of one-second observations that are spent in each
speed/acceleration/VSP bin. At this point, makemicro.sas outputs the following variables for use
by fmdcycle.f:
• Case ID;
• Micro-trip number;
• Speed bin;
• Acceleration bin;
• VSP bin; and
• Count, which is the number of observations in the speed/acceleration/VSP bin.
The next program, fmdcycle.f, picks up the dataset produced by makemicro.sas which
contains the counts of observations in each speed/acceleration/VSP bin for all micro-trips in all
of the 30 cases. The job of findcycle.sas is to use the micro-trip information to find those micro-
trips which when concatenated best describe the activity for each case. In this study, we match
the non-idle portions of the cycles to the non-idle driving in the activity dataset as the process of
selecting micro-trips to build cycles. For each case, the overall activity is described by the sum
of the counts in the speed/acceleration/VSP bins for all micro-trips that fall in that case.
However, the micro-trips that are eligible for being used in the cycle to describe that target
activity are selected from a subset of the micro-trips in the case.
The program works like this. Each case is considered separately and no micro-trips for
one case are used to provide a cycle for another case. First, the program finds the best micro-trip
whose sum of the squares difference between the cumulative normalized elements of the micro-
trip with the corresponding elements of the target is the smallest. This corresponds to finding the
micro-trip such that the T-C vector is the smallest. This becomes the first micro-trip in the
cycle. Then, the program looks through all remaining micro-trips to find the best second micro-
trip such that when it is added to the first micro-trip the new vector T-C has a minimum length.
5-8
-------
This process is repeated until the developer wants to stop searching. In this project, we stopped
searching after 25 micro-trips were added to the cycle.
The program, findcycle.f, outputs a list of the 25 selected micro-trips in the order in
which they were selected for each of the 30 cases. In addition, the program provides a square of
the length of T-C vector, the number of seconds in each of the micro-trips, and an accumulated
total of the number of seconds in the cycle as the micro-trips were selected and added to the
candidate cycle being built up.
The third program, makecycle.sas, uses the output of findcycle.f for each case to
visualize each cycle using plots of cycle speed versus time, acceleration versus speed for the
target and cycle, VSP versus speed for the target and cycle, and various statistics on the
individual micro-trips in each cycle. One of these statistics is the number of missing values in
each of the selected micro-trips. Micro-trips that have a large number of missing speed,
acceleration, or VSP values may be difficult to repair. Accordingly, we arbitrarily decided to
accept no micro-trips that had more then 10 to 15 missing speed values. When micro-trips with
large numbers of missing values were selected by the program, we edited findcycle.f so that
those particular micro-trips would be skipped. Then, findcycle.f and makecycle.sas were run
again iteratively until all micro-trips that were selected by makecycle.sas contained less then 10
to 15 missing values in each micro-trip.
5.3 Specific Details of Cycle Generation
There are several areas of generating the cycles that need to be explained in some
additional detail. These areas are described in more detail in the following subsections.
5.3.1 Estimation of Vehicle Specific Power
Before all three continuous variables (speed, acceleration, and VSP) can be binned, the
vehicle specific power variable needed to be calculated. This calculation was done in
makemicro.sas based on input from EPA. EPA provided the following VSP equation to be used
with the coefficients in Table 5-4. The first term in the equation is for the rolling resistance, the
second term is a correction for rolling friction and rotational inertia at higher speeds, the third
term is for aerodynamic drag, the fourth term is for accelerating the mass of the vehicle, and the
fifth term is for changing the potential energy of the vehicle as it moves up and down road
grades. The road load coefficients given in Table 5-4 are provided for three different vehicle
weight ranges. Since all the vehicles in the dataset are medium and heavy heavy-duty vehicles,
only the coefficients for the two upper vehicle weight ranges were used. Note that the
5-9
-------
coefficient for B/M is zero. This causes the second term of the VSP equation to provide no
contribution to the calculated VSP values. In addition, all VSP calculations assume that the road
grade was level. This causes the last term in the equation to be zero so that it also does not
contribute to the calculated VSP values.
where:
VSP =
v =
a =
g =
6 =
vehicle specific power (kW/Mg or W/kg)
vehicle speed (m/s)
vehicle acceleration (m/s2)
acceleration of gravity (9.8 m/s2)
road grade
Table 5-4. Road Load Coefficients for the VSP Equation
A(kW*s/m)/M(tonne)
B(kW*s2/m2) /M(tonne)
C(kW*s3/m3)/M(tonne)
Vehicle Weight Range
8500 to 14000 Ibs
(3. 855 to 6.350 tonne)
(0.4777/5.1 =)
0.094
0
(2.037 xlQ-3/5.1=)
0.40 x ID'3
14000 to 33000 Ibs
(6.350 to 14.968 tonne)
(0.7652/10.7=)
0.072
0
(3.52xlQ-3/10.7=)
0.33 x ID'3
>33000 Ibs
(>14.968 tonne)
(1.188/15=)
0.08
0
(4.93xlQ-3/5.1=)
0.97 x ID'3
Since the actual weight of the vehicles as they were loaded during the TxDOT, Faucett,
and Battelle studies were unknown, EPA assumed that for the purposes of calculating the road
load coefficients A/M and C/M that the average weight of the vehicles during data collection was
near the middle of the gross vehicle weight range. This assumption is demonstrated by the
parenthetical calculations shown in the cells of Table 5-4.
5.3.2 Binning of Continuous Variables
To use the cycle development approach discussed above, all of the micro-trips in the
edited dataset needed to have all of their second-by-second observations binned in terms of
speed, acceleration, and vehicle specific power. While the size of the bins is arbitrary, bins in
general need to be narrow enough to resolve important emissions effects. In addition, bins need
to be sufficiently narrow to distinguish different micro-trips for low speed, low acceleration, and
low VSP micro-trips where those variables do not vary over a large range. On the other hand,
from a practical perspective, the number of bins needs to be small so that the program that selects
micro-trips can run in a reasonable amount of time.
5-10
-------
For the cycle development in this project, we used the following binning schemes:
• Speed - the continuous speed values in miles per hour were ceilinged up to the
next whole number. For example, 5.6 miles per hour was assigned to bin 6, 5.2
miles per hour was assigned to bin 6, 5.001 miles per hour was assigned to bin 6,
5.000 miles per hour was assigned to bin 5.
• Acceleration - Acceleration values in miles per hour per second were ceilinged
just as the speed values were.
• Vehicle Specific Power - VSP values in kW/Mg were rounded to the nearest 5
kW/Mg.
When these bin definitions were used, the counts of observations for the entire edited
dataset were found to be distributed for speed, acceleration, and vehicle specific power as shown
in Tables 5-5, 5-6, and 5-7.
5.3.3 Criteria for Skipping Micro-Trips for a Cycle
In general, the cycle development programs were run for each of the 30 cases to allow
selection of micro-trips that best described the operation of vehicles for all operation in the case.
However, some types of micro-trips were not considered for inclusion in the candidate cycle.
Some micro-trips were entirely idle operation. These micro-trips were not assigned to
any cases since a dedicated idle cycle is not needed.
For the purposes of selecting micro-trips for cycles, observations with extreme
acceleration values or extreme VSP values were not considered in the dataset or in the cycle.
But they also were not deleted from the dataset or cycles. Specifically, observations with
accelerations greater then 14 mph/s or less then -10 mph/s or with VSPs greater than 62.5
kW/Mg or less then -47.5 kW/Mg were not considered.
5-11
-------
Table 5-5. Distribution of Binned Speeds in the Edited Dataset
Wffl
iTkri^
Table 5-6. Distribution of Binned Accelerations in the Edited Dataset
5-12
-------
Table 5-7. Distribution of Binned VSP in the Edited Dataset
Any micro-trips less then 20 seconds in duration were not considered for inclusion in a
cycle. The reason for not including these is that many short micro-trips can be produced by
common, but non-representative, operation of the vehicle. One example is when a vehicle starts
moving from a standstill but the engine dies because the clutch is let out too quickly. Another
reason that short micro-trips are present in the dataset is because of the algorithm used to divide
trips into micro-trips and the presence of dither in the raw data. We believe that the criteria that
we used to divide trips into micro-trips erred on the side of making more micro-trips than were
actually performed by the vehicles. Accordingly, in some situations very short micro-trips were
created that really represent different pieces of dither in the raw data. In any case, we have found
in this study as well as in past studies that the micro-trips longer than 20 seconds are adequate to
describe the vehicle driving behavior of the entire dataset taken as a whole.
Another reason for deleting some micro-trips after they were selected for a cycle was
when the micro-trip contained 10 to 15 or more missing values for speed, acceleration, or VSP.
Missing values in micro-trips represent instances where we would be required to manufacture
numerical values to produce a complete cycle. Micro-trips that contained too many missing
values and especially long strings of consecutive values would be difficult or impossible for us to
replace with values that were close to the actual, but unmeasured, speeds that the vehicles drove.
5-13
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5.3.4 Criteria for Judging Candidate Cycles
For each case the cycle development software built-up a candidate cycle using 25 micro-
trips. In each instance, the plot of the square of the length of T-C vector as micro-trips were
added to the cycle was examined. A sample plot is shown in Figure 5-3. The figure shows that
as micro-trips were added, the square of the length of the vector drops substantially at first and
then reached a plateau and then dropped again. This drop-following-plateau behavior was
commonly seen in many of the cycles generated for the different cases.
Next, we examined a speed versus time plot of the 25 micro-trips that made up the cycle.
An example of this is shown in Figure 5-4. The small circles on the plot indicate the beginning
of each micro-trip. This candidate cycle plot was used to examine the overall appearance of the
cycle and to show the duration of the cycle. At this point, the cycle development analyst decided
where the cycle could be ended and still achieve a substantial agreement between the driving
behavior in the cycle and the driving behavior in the entire dataset for the case. Typically the
cycle was terminated using as few micro-trips as possible but for which the length of the T-C
vector was quite short and where the addition of more micro-trips caused the length of the vector
to increase slightly or be on a plateau.
Finally, we examined scatter plots of acceleration versus speed and VSP versus speed for
the candidate cycle and for a random subset of the data in the case under consideration.
Examples of these plots are shown in Figures 5-5 and 5-6.
5.3.5 Evaluation of Observations in Micro-Trips after Selection for a Cycle
Once the final set of micro-trips for the cycle of each case was selected, repairs needed
by the individual observations in the cycles were identified. A data file for each cycle was
created to aid in visual examination by the developer. Each file included the case ID, the micro-
trip ID, the edited speed that was used to select the micro-trip, the raw speed that was present in
the original dataset, the test vehicle number, the probability that an individual observation was an
idle observation, and the flag that indicated the reason for any change of the raw speed to a
missing speed value. Plots of edited speed and raw speed versus time for each of the micro-trips
selected for a cycle were examined to look for abnormal behavior. Specifically, abnormal
behavior would be for portions of speed traces that reflected more the artifacts of the data
collection and editing process than the manner in which heavy-duty vehicles are driven.
5-14
-------
Figure 5-3. Square of the Length of T_C as Micro-Trips
are Added for Case H 1 50
Figure 5-4. Speed vs. Time for the Candidate Cycle for Case H_1_50
5-15
-------
a) Target
b) Cycle
Figure 5-5. Acceleration vs. Speed for Case H_1_50
30 40 50
Speed (mph)
30 40 50 60
Speed (mph)
80 90
80 90
5-16
-------
a) Target
b) Cycle
Figure 5-6. VSP vs. Speed for Case H_1_50
50 60
5-17
-------
Several types of problems were identified in the micro-trips of the cycles:
• Missing values - While during cycle development micro-trips were selected only
if they had less then 10 to 15 missing values, many of the micro-trips did have
some missing values. In most cases, missing values were isolated to a one-second
period.
• Jumps in speed from idle to non-idle segments - Because of the algorithm used
to detect idles in the raw data, we frequently saw jumps in speed from zero
speeds, which were the idles at the beginning of micro-trips, to significantly larger
speeds than might really be expected in normal driving behavior when the vehicle
started moving. Jumps in speed as large as 7 miles per hour were seen. However,
when we examined the raw speed for those observations, in many instances we
saw that the raw speed values were quite reasonable.
• Speed shoulders at the end of micro-trips - At the end of most micro-trips
derived from the Battelle and Faucett datasets the speed traces displayed a
shoulder where the speed was decreasing and almost came to a plateau and then
abruptly dropped to zero. We believe this behavior was a result of the dither in
the speed values being clipped by the idle detection algorithm when trips were
converted to micro-trips. In other words, as the speeds got low, the influences of
dither became more obvious in a speed trace and produced these shoulders, which
are not at all typical of normal vehicle driving behavior.
• "Stuck" speeds in the Battelle micro-trips - Both the Faucett and Battelle
datasets had many periods during which the reported vehicle speed was constant
for periods of consecutive observations. We believe these periods were a result of
the GPS units temporarily losing contact with the satellite during vehicle driving.
In these instances, the datalogger retained the most recent vehicle speed until the
GPS unit reacquired the satellite signal. Because the Faucett datalogging system
reported vehicle speeds to much higher resolution (0.02 mph) than did the Battelle
datalogging system (0.11 mph), the SAS quality checking program was able to
successfully distinguish most periods of stuck speeds in the Faucett datasets but it
could not do so in the Battelle datasets. In the Faucett dataset, stuck speeds were
changed to missing values but in the Battelle dataset, the stuck speeds were left
unedited and contained no edit flags. Examination of the cycles show numerous
instances of stuck speed segment for up to perhaps 20 seconds. Replacement of
these stuck speed values with realistic vehicle operating speeds becomes more
difficult as the duration of the stuck speed segment increases. At some point,
micro-trips containing stuck speeds probably should be deleted from
consideration in cycle development.
• Dither in micro-trips - In spite of our efforts to detect dither during the quality
checking of the entire dataset, periods of speed observations that are clearly dither
remain in some micro-trips and are present in the final cycles. Whether a
particular segment of observations is dither or not is not always clear-cut but, in
most cases, the cycle developer can make reasonable guesses.
5-18
-------
At the point in the project where we wanted to start making edits to the final micro-trips,
we ran short on approved labor hours and budget. Therefore, the selected micro-trips could not
be edited to solve most of the problems discussed above. Instead of performing detailed
corrections on all of the observations in the 30 cycles where problems existed, we simply linearly
interpolated values for missing speeds from the speed values before and after missing speed
segments. This produced cycles that had all observations with non-missing speed values.
However, the speed behavior during interpolated segments is not always representative of the
manner in which heavy-duty vehicles are driven. The statistical results that are calculated for the
tables in Section 7 and for the plots that are shown in Appendix F are all based on these final
cycles with interpolated values replacing missing values. Section 8 presents recommendations
for revisiting the development and editing of the 30 heavy-duty vehicle cycles to produce much
improved cycles.
5-19
-------
6.0 Heavy-Duty Vehicle Operating Characteristics
EPA wanted us to evaluate the characteristics of the datasets from the perspective of
heavy-duty vehicle operation. This evaluation is really independent of the development of the
cycles. Several pages of SAS printouts and plots are provided in Appendices A, B, C, D, and E
to give an idea of the vehicle operation, trip characteristics, and micro-trip characteristics of the
combined TxDOT, Faucett, and Battelle datasets.
6-1
-------
7.0 Comparison of Dataset and Cycle Statistics
For each of the 30 cases, we produced a cycle from micro-trips selected from all micro-
trips that were assigned to the case. A number of statistics were calculated for each case so that
the characteristics of the cycle could be compared to the characteristics of the dataset, which we
call the target. For each of the statistics that was requested by EPA, we provide a value for target
and cycle. These statistics are shown in Tables 7-1, 7-2, and 7-3. It is important to remember
when comparing any of these statistics in the three tables that the micro-trips in the cycles were
selected only because their non-idle speed, VSP, and acceleration characteristics match those of
the target. Any other statistics that are calculated and compared were not the basis, or at least not
the direct basis, for choosing the micro-trips for each cycle. The fact that the micro-trip statistics
for the targets and cycles come as close as they do is noteworthy, but perhaps not critical, to the
applicability of the cycles for the calculation of emissions.
Table 7-1 shows that the average second-by-second speeds of the cases for the targeted
cycle data agree well with each other. Probably the only exception to this statement is that for
the lowest speed cases, the cycle had a substantially larger average speed then the target did.
The reason for this is that the cycles were selected based only on the non-idle portion of the
micro-trips in the target set. Therefore, differences in the fraction of idling can have an influence
on the average speed and this influence is most easily seen in the micro-trips that have the lowest
average speed. The influence of the difference of idles in the target and cycle can also be seen in
Table 7-2 by comparing the percentages in the idle mode. The lowest speed cases have much
larger percentages of idle in the target data then in the cycle data. Distributions for speed,
acceleration, and VSP are provided in plots in Appendix F.
Table 7-1 also shows that the average micro-trip distance for cycles is usually smaller
then the average micro-trip distance for the target. We have not determined why this appears to
be the case.
7-1
-------
Table 7-1. Comparison of Dataset and Cycle Operation Characteristics
Case Code
Name
N 0 5
N 0 10
N 0 15
N 0 20
N 0 25
N 0 30
N 1 30
N 1 40
N 1 50
N 1 60
P 0 5
P 0 10
P 0 15
P 0 20
P 0 25
P 0 30
P 1 30
P 1 40
P 1 50
P 1 60
H 0 5
H 0 10
H 0 15
H 0 20
H 0 25
H 0 30
H 1 30
H 1 40
H 1 50
H 1 60
Total Time (s)
Target
493,816
84,840
97,070
111,862
83,014
55,621
63,189
117,229
226,562
168,786
726,990
227,431
242,596
220,948
147,958
148,539
25,741
79,901
108,965
97,217
4,215,612
239,821
201,255
208,233
177,071
153,756
303,878
580,763
2,391,077
1,550,245
Cycle
638
883
1,100
2,336
1,536
1,702
5,905
5,646
8,618
8,157
988
856
988
896
1,109
1,657
2,600
6,196
5,282
8,586
1,441
1,997
1,251
1,797
2,166
1,967
6,670
7,350
6,898
16,685
Average sxs
Speed (mph)
Target
1.3
10.0
15.1
19.9
24.7
31.1
28.2
41.0
50.4
58.0
1.7
10.0
15.0
19.9
24.8
33.1
29.9
39.9
50.1
59.9
0.5
9.9
15.0
20.0
24.8
32.1
27.4
41.0
51.1
58.2
Cycle
4.9
10.5
15.6
20.4
24.4
30.8
29.9
41.2
50.2
57.1
5.3
10.7
15.5
19.7
25.5
32.5
31.9
41.2
49.4
59.5
4.7
10.8
15.2
19.8
24.9
30.8
31.9
41.2
50.6
58.0
Total Distance
(mile)
Target
161.86
217.66
382.21
588.22
550.31
464.13
469.96
1276.51
3030.66
2496.70
283.08
560.45
921.11
1148.56
963.77
1309.57
204.29
871.14
1498.06
1606.31
520.18
619.07
798.01
1113.85
1185.85
1304.50
2192.32
6248.94
32489.53
24616.30
Cycle
0.87
2.58
4.75
13.22
10.39
14.58
48.27
64.59
120.17
129.49
1.45
2.55
4.25
4.91
7.87
14.97
23.03
70.87
72.48
141.94
1.87
5.96
5.29
9.89
14.96
16.84
59.17
84.15
97.03
268.60
Average Micro-
Trip Time
(s)
Target
93
96
117
148
167
189
780
862
1325
2312
52
58
72
95
119
153
515
484
623
1389
196
97
125
158
188
202
902
976
2067
3682
Cycle
58
63
79
117
96
142
484
706
718
1360
47
61
82
75
92
127
433
443
440
1227
63
80
104
106
155
164
513
613
985
2781
Average Micro-
Trip Distance
(mile)
Target
0.031
0.245
0.461
0.776
1.107
1.579
5.802
9.386
17.723
34.201
0.020
0.142
0.273
0.495
0.778
1.351
4.086
5.280
8.560
22.947
0.024
0.252
0.496
0.846
1.256
1.714
6.505
10.502
28.081
58.471
Cycle
0.079
0.185
0.340
0.661
0.650
1.215
4.022
8.075
10.014
21.582
0.069
0.182
0.354
0.409
0.656
1.151
3.838
5.062
6.040
20.278
0.081
0.239
0.441
0.582
1.069
1.403
4.551
7.012
13.862
44.770
Micro-Trips
(count)
Target
5288
887
829
758
497
294
81
136
171
73
14030
3942
3370
2320
1239
969
50
165
175
70
21554
2461
1610
1317
944
761
337
595
1157
421
Cycle
11
14
14
20
16
12
12
8
12
6
21
14
12
12
12
13
6
14
12
7
23
25
12
17
14
12
13
12
7
6
7-2
-------
Table 7-2 shows a comparison of the dataset and cycle operation modes. The operation
modes were set by the program utrip_comp.sas. An observation was assigned to "Cruise" if the
average difference between the previous observation and the following observation was less than
0.5 mph and the speed of the observation was greater then 0.00 mph. The observation was called
a "Decel" if the average difference between the previous and the following observations was less
then or equal to -0.5 mph and the observation had a speed greater then 0.00 mph. The
observation was called an "Accel" if the average difference between the previous and following
observation was greater then or equal to 0.5 mph and the speed of the observation was greater
then 0.00 mph. If the difference between the previous and the following observation could not
be determined because one or both were missing or the observation speed itself was missing,
then the mode was determined to be "Missing." All other observations were assigned to the
"Idle" mode.
Table 7-2. Comparison of Dataset and Cycle Operation Modes
Case Code Name
N 0 5
N 0 10
N 0 15
N 0 20
N 0 25
N 0 30
N 1 30
N 1 40
N 1 50
N 1 60
P 0 5
P 0 10
P 0 15
P 0 20
P 0 25
P 0 30
P 1 30
P 1 40
P 1 50
P 1 60
H 0 5
H 0 10
H 0 15
H 0 20
H 0 25
H 0 30
H 1 30
H 1 40
H 1 50
H 1 60
Accel (%)
Target
3.23
20.46
26.57
27.16
27.50
26.66
17.87
17.93
12.46
7.22
4.34
20.91
27.04
30.34
30.32
28.39
25.67
23.10
17.91
9.10
0.98
17.38
24.08
25.54
25.94
24.35
15.29
13.40
7.95
4.95
Cycle
17.55
26.61
33.00
33.26
32.42
30.85
24.03
19.85
14.96
10.09
18.83
26.29
33.30
33.71
35.17
32.47
30.92
26.15
19.42
10.97
14.92
23.23
29.10
31.27
29.69
28.11
21.53
18.30
11.00
6.08
Cruise (%)
Target
9.26
25.08
26.52
30.13
34.23
38.01
42.65
55.06
66.87
73.70
5.00
18.28
21.08
24.65
28.69
35.66
39.84
49.15
62.68
79.63
3.84
37.02
34.01
37.26
41.56
44.24
47.78
62.27
76.99
85.99
Cycle
35.11
24.46
25.09
29.11
29.88
36.90
45.99
60.64
69.38
78.53
16.70
22.43
21.86
23.55
29.67
32.71
41.85
48.29
60.89
77.98
36.36
40.51
32.05
34.45
39.47
42.60
59.04
64.83
77.76
87.19
Decel (%)
Target
3.34
18.10
21.93
21.91
22.45
21.09
15.00
15.45
11.22
6.82
4.83
20.39
24.38
25.93
25.36
23.19
21.17
18.83
14.68
8.60
1.04
14.84
18.04
18.58
18.72
17.80
12.30
10.88
7.05
4.68
Cycle
17.87
24.24
27.36
26.41
26.24
24.32
18.95
16.44
13.38
9.46
18.83
24.42
27.63
28.01
27.95
25.65
24.04
21.45
15.68
9.34
14.23
17.88
22.06
19.87
20.96
18.05
16.69
13.48
8.84
5.66
Idle (%)
Target
73.40
24.92
15.37
11.57
8.86
7.13
15.79
2.66
1.62
0.60
64.49
26.99
17.19
11.70
8.98
7.55
7.90
6.65
2.96
1.49
82.80
21.91
15.78
12.55
9.03
6.86
15.71
3.66
1.47
0.58
Cycle
27.74
23.10
13.27
10.36
10.42
7.23
10.82
2.92
2.15
1.84
43.52
25.23
15.99
13.39
6.13
8.39
2.96
3.89
3.79
1.63
32.89
17.13
15.83
13.47
9.23
10.63
2.55
3.22
2.29
1.04
Missing (%)
Target
10.76
11.44
9.60
9.22
6.96
7.11
8.69
8.89
7.83
11.67
21.34
13.43
10.30
7.38
6.65
5.21
5.42
2.27
1.78
1.18
11.35
8.86
8.10
6.07
4.75
6.75
8.92
9.79
6.54
3.80
Cycle
1.72
1.59
1.27
0.86
1.04
0.71
0.21
0.14
0.14
0.07
2.13
1.64
1.21
1.34
1.08
0.78
0.23
0.23
0.23
0.08
1.60
1.25
0.96
0.95
0.65
0.61
0.19
0.16
0.10
0.04
7-3
-------
EPA also requested certain maximum and minimum values for speed, acceleration, and
VSP. When we identified these values, we found that, as expected, they were highly variable
since they were the extreme values in the dataset. So rather than reporting these values, we
instead determined the 0.5 and 99.5 percentile values for the speed, acceleration, and VSP
quantities of interest. These are reported in Table 7-3 for the target and cycle datasets for each
case.
Table 7-3. Comparison of Data and Cycle Extreme Values
Hase Code
Name
N 0 5
N 0 10
N 0 15
N 0 20
N 0 25
N 0 30
N 1 30
N 1 40
N 1 50
N 1 60
P 0 5
P 0 10
P 0 15
P 0 20
P 0 25
P 0 30
P 1 30
P 1 40
P 1 50
P 1 60
H 0 5
H 0 10
H 0 15
H 0 20
H 0 25
H 0 30
H 1 30
H 1 40
H 1 50
H 1 60
99.5 %ile sxs
Speed
(mph)
Target
24.27
39.78
44.18
47.84
51.79
61.10
64.68
66.96
69.02
77.34
25.99
41.17
43.93
48.88
55.09
64.75
64.29
67.62
73.14
73.83
15.07
39.68
42.35
47.38
53.48
61.76
62.53
64.86
66.17
70.73
Cycle
28.21
35.28
41.30
44.45
48.42
55.88
61.41
67.28
68.31
67.39
27.95
34.39
39.45
46.12
52.56
61.30
64.52
67.51
71.53
72.34
26.87
34.00
41.28
43.70
50.72
64.06
60.49
63.02
64.63
69.69
0.5 %ile sxs
Acceleration
(mph/s)
Target
-2.99
-4.71
-4.95
-4.97
-5.06
-5.18
-3.91
-4.07
-3.55
-3.22
-6.10
-7.36
-7.36
-7.13
-7.02
-6.91
-5.98
-5.75
-5.29
-4.02
-1.61
-5.06
-5.40
-5.17
-5.06
-5.06
-3.80
-3.68
-2.88
-2.30
Cycle
-3.57
-4.60
-5.29
-5.40
-4.95
-5.63
-4.20
-4.37
-4.02
-3.50
-7.25
-7.36
-8.45
-6.79
-7.13
-7.13
-5.52
-5.52
-5.64
-4.60
-3.68
-5.29
-4.94
-5.52
-4.71
-4.14
-3.80
-4.37
-3.68
-2.42
99.5 %ile sxs
Acceleration
(mph/s)
Target
2.50
4.25
4.26
4.14
4.14
4.07
2.89
3.00
2.65
2.53
5.41
11.39
11.04
8.06
6.56
5.86
4.71
4.26
3.79
2.76
1.25
4.83
4.72
4.26
4.15
4.03
2.76
2.64
2.19
1.95
Cycle
3.57
5.01
5.99
4.71
6.62
4.50
3.17
3.00
2.87
2.76
7.94
12.77
13.57
13.23
9.89
7.07
4.72
4.37
4.14
2.88
5.06
7.59
6.79
4.49
5.06
4.25
3.10
2.88
2.65
2.18
0.5 %ile VSP
(kW/Mg)
Target
-3.86
-14.28
-18.41
-19.20
-21.46
-24.10
-18.17
-20.64
-19.55
-18.38
-8.36
-19.36
-22.74
-25.64
-28.64
-32.68
-28.40
-29.25
-28.48
-21.27
-0.87
-11.75
-16.25
-18.66
-20.78
-22.72
-17.40
-18.50
-15.72
-13.37
Cycle
-10.06
-15.10
-20.41
-19.71
-22.77
-24.73
-22.89
-24.82
-18.78
-22.33
-15.06
-22.04
-32.11
-26.22
-32.14
-37.65
-25.60
-31.01
-30.77
-23.61
-7.42
-13.62
-20.11
-22.05
-21.30
-21.14
-16.74
-20.70
-21.84
-13.36
99.5 %ile
VSP
(kW/Mg)
Target
6.24
15.11
18.63
19.34
21.86
23.74
18.87
23.76
26.00
27.50
12.87
29.73
31.89
31.84
32.27
33.50
28.75
30.36
31.30
31.11
2.50
13.82
17.34
19.05
21.30
24.21
19.27
22.32
24.69
26.10
Cycle
12.45
17.17
20.32
20.31
25.79
26.10
24.85
29.63
26.75
31.37
25.03
34.25
53.94
36.01
34.82
42.59
29.23
32.33
34.07
31.54
10.36
17.76
20.43
21.03
22.01
27.58
19.19
25.50
31.92
26.44
7-4
-------
For each of the cases, there are 20 plots in Appendix F. The plots in Appendix F will be
described, in general, here so that the reader can get an idea of what they show. On the first page
of the plots for each case, the top plot shows the final cycle speed trace. The small circles along
the trace denote the beginning of each micro-trip that makes up the cycle. By counting the
number of small circles on the speed trace, the number of cycles can be determined.
The second plot for each case shows the square of the length of the T-C vector as micro-
trips were built up to create the candidate cycle that contained 25 micro-trips. Usually the first
few micro-trips drop the sum of squares value substantially. Then, the addition of more micro-
trips may reduce it slightly more or, in some cases, may increase the length of the T-C vector to
a degree. The plot does not show the point at which the build up was truncated for the final
micro-trip shown in the previous plot.
The next nine pages in each series show plots on the top of the page that represent the
target data and plots on the bottom of the page that represent the same sort of plot but for the
cycle data. Therefore, by comparing the plot on the top with the plot on the bottom, the
representativeness of the cycle can be evaluated. Some judgment needs to be made in comparing
the horizontal bar plots because auto-scaling was used to make those histogram plots. In the case
of the scatter plots and the stair-step plots, the same scales were used for each pair of plots.
Horizontal bar plots are shown to denote the distributions of speeds, accelerations, and
VSPs on the next six plots. The four scatter plots show a comparison of acceleration versus
speed and VSP versus speed. In the case of the cycle data on the bottom of these plots, all of the
data points are plotted. However, because of the much larger number of data points in the target
data only a random subset of the data points are plotted for the target data.
The next several stair-step plots show distributions of micro-trip times, time in idle in the
micro-trips, running time in the micro-trips which is the time when the vehicle is not idling, and
micro-trip distance. Each of the stair-step plots shows the differential distribution with a solid
line and a cumulative distribution with a dotted line. The horizontal scale of the stair-step plots
is a log scale so that some of the detail at very low values and very high values can be seen at the
same time on one plot.
7-5
-------
8.0 Recommendations for Development of Final Cycles
As discussed above, the final cycles developed in this work assignment have minor
problems. However, now that we have gone completely through the development of the heavy-
duty cycles, we can look back on the development process to see where improvements can be
made. We know that much better heavy-duty cycles can be easily and quickly developed using
this same set of data and we think that a small follow-on work assignment can be used to
produce these cycles in a short amount of time.
There are two major and two minor problems that we see in the final cycles developed
here:
Major Problem 1: The Battelle dataset contains "stuck" speed values. Since these stuck
speed values are present not only in the developed cycles but also, more importantly, in the
dataset, they potentially cause a bias in the cycles because the cycles will try to simulate the
speed, accelerations, and VSPs that are associated with the stuck values. Solution: We think
that removal of the Battelle speeds that are associated with stuck speed values from the Battelle
dataset is worth doing. Stuck speed values could be changed to missing values and a stuck speed
value flag for those observations could be produced so that they could be quickly found in any
micro-trip chosen for a cycle. Changing the stuck speed values to missing values would
eliminate just those observations from consideration for comparison with the candidate micro-
trips under review for a given cycle.
Major Problem 2: In the 30 cycles developed in this work assignment, many of the
micro-trips have the minor problems that were presented in Section 5.3.5. However, fixing these
problems after all of the micro-trips have been chosen for a given cycle will result in a cycle that
does not match the dataset as well as the original cycle matched it before the edits were made.
Yet, it is important to make these edits so that the cycle that is produced is a reasonable
representation of the way heavy-duty vehicles are driven. Solution: If each micro-trip were
evaluated and edited for the detailed second-by-second observation problems listed in Section
5.3.5 before the micro-trip selection algorithm proceeded to select the subsequent micro-trip, this
problem would be avoided. If an iterative process of select-evaluate-edit for each micro-trip
were used, by the time all 25 micro-trips were selected, each of them would have already been
edited. In addition, if the edits on a selected micro-trip slightly degrade the ability of that micro-
trip to match the dataset, the subsequent micro-trips would be chosen by the program to converge
on the entire sequence of micro-trips that has a good match with the dataset.
8-1
-------
Minor Problem 3: The allocation of speed, acceleration, and VSP bins to the continuous
values of those variables does not reflect the importance of the variables on emissions. We used
too many speed bins (80) and too few acceleration bins (8) and VSP bins (10). Solution: Since
emissions are perhaps more closely associated with acceleration and VSP then with speed, the
binning scheme for acceleration and VSP should contain more bins and fewer bins should be
used for speed. This will produce cycles that better match the driving characteristics that are
important to emissions.
Minor Problem 4: In the micro-trip selection program we forbade the selection of any
given micro-trip more than once. This arbitrary rule provides a restriction, although perhaps
minor, on the micro-trips that are allowed to be selected for a cycle. We could envision that a
cycle could be made up of nine repeats of one micro-trip and one repeat of another micro-trip
perhaps because the bulk of the dataset behavior is represented by the first micro-trip but the
second kind of micro-trip is needed to a small degree. With the current restrictions on the micro-
trip selection this mixture of different micro-trip richnesses cannot be provided. Solution: The
only restriction we really need to make is that the second micro-trip cannot be the same micro-
trip as the first one. From the third micro-trip on, any micro-trip should be allowed to be
selected.
As far as the detailed second-by-second editing of selected micro-trips goes, the
following techniques can be used to edit micro-trips as each one is selected for addition to the
candidate cycle being built up:
• Missing values - Where missing values are present, hand editing can be used to
replace missing values with numeric values for speed by examining the speeds in
the seconds before and after the missing value segment.
• Jumps in speed from idle to non-idle segments - In many instances the decision
by the idle detection algorithm can be overridden and the reported raw speed
values can be used. This can produce reasonable speed transitions at the
beginning of the non-idle portion of micro-trips.
• Speed shoulders at the end of micro-trips - In these instances, hand edits can be
used to remove the shoulder by decreasing the speed values in two or three of the
seconds at the end of each micro-trip.
• Stuck speeds from Battelle data - If periods of stuck speeds are relatively short
(on the order of 5 seconds), manufactured speeds may be relatively easy to
produce. For periods of stuck speeds longer than this, it may be more reasonable
to eliminate the offending micro-trip from further consideration in building up the
candidate cycle.
8-2
-------
Dither in micro-trips - In most cases, the dither that may be present as part of
selected micro-trips may be simply changed to 0.00 mph speed values and one or
two seconds of speed transition values can be manufactured to avoid large jumps
in speed.
8-3
------- |