There have been significant improvements in recent years in transporta-tion and emissions modeling to allow better evaluations of transportationoperational effects and associated vehicle emissions. In particular, instan-taneous or modal emissions models have been developed for a variety oflight-duty vehicles. To date, most of the effort has focused primarily ondeveloping these models for light-duty vehicles with less effort devotedto heavy-duty diesel (HDD) vehicles. Although HDD vehicles currentlymake up only a fraction of the total vehicle population, they are majorcontributors to the emissions inventory. A description is provided of anHDD truck model that is part of a larger comprehensive modal emissionsmodeling (CMEM) program developed at the University of California(UC), Riverside. Several HDD truck submodels have been developedin the CMEM framework, each corresponding to a distinctive vehicle–technology category. The developed models use a parameterized physi-cal approach in which the entire emission process is broken down intodifferent components that correspond to physical phenomena associatedwith vehicle operation and emission production. A variety of trucks wereextensively tested under a wide range of operating conditions at UCRiverside’s Mobile Emissions Research Laboratory. The collected datawere then used to calibrate the HDD models. Particular care was takento investigate and implement the effects of varying grade and the use ofvariable fuel injection strategies. Results show good estimates for fueluse and the regulated emission species including nitrogen oxides, one ofthe key targets for HDD vehicles.

In the past decade there has been a good deal of activity in devel-oping instantaneous or modal emissions models to better predictmobile-source emission inventories, primarily at the microscale level.In the past conventional mobile-source emission models were devel-oped for calculating regional inventories using aggregated vehicleemissions data and estimates of vehicle activity in the form of vehi-cle miles traveled and average speed (i.e., at the macroscale level).To better capture emissions effects associated with a wide range ofdriving dynamics, instantaneous (i.e., second-by-second) modelsare used; they are better suited for evaluating traffic operational strate-gies that improve traffic flow (e.g., ramp metering, signal coordina-tion, additional lanes, etc.). These instantaneous emission modelscan be used in conjunction with detailed vehicle activity data or withmicroscale traffic simulation tools to better predict the emissionsimpact of different traffic scenarios (1).

A variety of instantaneous emission models have been developedfor a wide range of light-duty vehicles (LDVs); however, only a fewhave been developed for heavy-duty diesel (HDD) trucks. Although

HDD vehicles currently make up only a fraction of the total vehiclepopulation, they are major contributors to the emissions inventory,accounting for more than 50% of nitrogen oxides (NOx) and particu-late matter (PM) in many locations (2, 3). These vehicles will continueto play a major emissions inventory role with their high durabilityand reliability and with increases in movement of goods.

One of the main reasons that HDD vehicle emission models areless developed than their LDV counterparts is that there is a largebody of LDV emissions data, and only a relatively small amount ofHDD emissions data. In fact, before 1997 the regulatory emissionsmodels developed by the U.S. Environmental Protection Agency(EPA) and California Air Resources Board relied primarily on 23 HDD vehicles (3). To be fair, there is a large amount of HDDengine certification data from laboratory test stands; however, it isfelt that these engine data from certification tests do not properlyrepresent real-world on-road emissions when placed in a variety ofvehicles operated under real-world driving conditions. Recently, anumber of investigators have developed tools to measure emissionsfrom engine–vehicle combinations driven over standard cycles onstationary or portable chassis dynamometers (4–6 ). The numberof these facilities is quite limited because of their expense, and usingthem still does not provide information on vehicles driven in the realworld (7, 8). Accordingly, some investigators are developing meth-ods based on a minidilution tunnel with onboard instruments (9–12).Others trail a moving vehicle and sample the plume after dilutionby ambient air (13).

To measure on-road real-world emissions more realistically, theUniversity of California (UC), Riverside, has developed a uniquemobile emissions research laboratory (MERL) consisting of a 53-fttrailer loaded with a full dilution tunnel and instrumentation that iscapable of measuring total emissions from the HDD truck that ispulling MERL. This is the first mobile laboratory capable of measur-ing HDD emissions at the quality level specified in the U.S. CongressCode of Federal Regulations (MERL is described in more detail ina later section.)

Data from MERL and supplementary HDD truck emissions datafrom Coordinating Research Council Project E-55 were used todevelop a power-demand, physical instantaneous HDD emissionsmodel that is part of a larger research program for modeling instan-taneous emissions for a wide set of vehicles (14). This comprehen-sive modal emissions modeling (CMEM) program began in 1995and continues today with support from EPA and other sponsors(CMEM is described in more detail in a later section.)

Other instantaneous HDD emissions models have been developedin recent years, most notably the work being carried out at WestVirginia University (15). Data from the university’s transportableheavy-duty chassis dynamometer systems were used to create aninstantaneous emissions model using a speed-acceleration binningtechnique (15). As discussed in Modeling Mobile-Source Emis-sions (1), the speed-acceleration binning technique is very conve-

Modal Emissions Model for Heavy-Duty Diesel Vehicles

Matthew Barth, George Scora, and Theodore Younglove

Transportation Research Record: Journal of the Transportation Research Board,No. 1880, TRB, National Research Council, Washington, D.C., 2004, pp. 10–20.

College of Engineering, Center for Environmental Research and Technology, Uni-versity of California, Riverside, CA 92521.

10

nient for interfacing with activity data or traffic simulation models;however, it does have some downfalls. For example, a wide rangeof vehicle-operating conditions are necessary when filling bins inthe lookup tables, which usually requires a good deal of testing time.Also, the use of instantaneous lookup tables assumes that there is notime dependence in the emissions response to the vehicle operation.For many vehicle types, operating history (i.e., the last several sec-onds of vehicle operation) can play a significant role in an instanta-neous emission value. For example, that assumption would nothold true for vehicle types incorporating variable fuel injectiontiming strategies (such as many of the vehicles tested in this study)or for vehicle types incorporating after-treatment devices involv-ing oxygen storage or timers that are likely to become prevalent inthe future. Last, there is no convenient method to introduce otherload-producing effects on emissions such as road grade or accessoryuse (e.g., air-conditioning), other than introducing numerous otherlookup tables or perhaps applying a set of corrections. In addition,HDD trucks have a wide range of weights (depending on the cargothey are carrying) that will have a significant effect on emissions,which is not easily modeled using a lookup table method.

Other HDD emissions modeling techniques include vehicle-specific power binning (16, 17 ), load-based modeling using enginetest data (18), and neural network models (19, 20).

In this paper a description is given of the CMEM-based HDD emis-sions model, outlining several advantages in the way it inherentlyhandles issues of grade, variable weight, and variable fuel injectiontiming strategies. Background material is first provided on the CMEMprogram and the way this latest HDD emissions modeling fits in. Abrief description of MERL is then provided, followed by a descrip-tion of the data collection process. The modeling methodology isdescribed, followed by validation results for a variety of scenariosillustrating the flexibility of this model.

BACKGROUND

CMEM Program

CMEM was originally developed at the University of California,Riverside, along with researchers from the University of Michiganand Lawrence Berkeley National Laboratory, through an NCHRPresearch project that originally started in August 1995. The overallobjective of CMEM is to develop and verify a modal emissionsmodel that accurately reflects mobile-source emissions produced asa function of the vehicle’s operating mode. The model is compre-hensive in the sense that it is able to predict emissions for a widevariety of vehicles in various conditions (e.g., properly functioning,deteriorated, malfunctioning). The model is capable of predictingsecond-by-second tailpipe (and engine-out) emissions and fuel con-sumption for a wide range of vehicle–technology categories. Origi-nally, CMEM was targeted at LDVs (i.e., cars and small trucks) buthas since been expanded to include medium- and heavy-duty trucks.The focus of this paper is on HDD vehicles.

CMEM uses a physical power-demand modal modeling approachbased on a parameterized analytical representation of emissions pro-duction. In such a physical model the entire emissions process isbroken down into different components that correspond to physicalphenomena associated with vehicle operation and emissions pro-duction. Each component is then modeled as an analytical repre-sentation consisting of various parameters that are characteristic ofthe process. These parameters typically vary according to the vehi-cle type, engine, and emissions technology. Many of these param-

Barth, Scora, and Younglove 11

eters are stated as specifications by the vehicle manufacturers and arereadily available (e.g., vehicle mass, engine size, and transmissiontype). Other key parameters relating to vehicle operation and emis-sions production must be deduced from actual second-by-secondmeasured emissions data. The basic components found in the modelinstances include a power demand component, engine speed esti-mator, fuel rate model, engine-out emission component, and anafter-treatment component (21). Also part of the model are spe-cific components that mimic engine strategies that control fuel–airequivalency ratios or fuel injection timing.

This type of modeling is considered deterministic rather thandescriptive. Such a deterministic model is based on causal parametersor variables, rather than on simply observing the effects (i.e., emis-sions) and assigning them to statistical bins (i.e., a descriptive model).This approach provides understanding, or explanation, for the vari-ation in emissions among vehicles, types of driving, and other con-ditions. Using this type of model, analysts can gain insight into thephysical and chemical reasons behind this model of emissions pro-duction. The physical modal emissions modeling approach has sev-eral attractive attributes including the fact that (a) it inherently handlesall factors in the vehicle-operating environment that affect emis-sions, such as vehicle technology, fuel type, operating modes, main-tenance, accessory use, and road grade; (b) it is applicable to allvehicle and technology types such that when a heterogeneous vehi-cle population is modeled, separate sets of parameters can be usedin the model to represent all vehicle and technology types; the totalemissions outputs of the different classes can then be integrated withtheir correctly weighted proportions to create an entire emissionsinventory; and (c) it is not restricted to pure steady-state emissionsevents, as is an emissions map approach. Emissions events relatedto the transient operation of the vehicle can be appropriately mod-eled. Further, it can easily handle time dependence in the emissionsresponse to the vehicle operation. As stated previously, the operat-ing history (i.e., the last few seconds of vehicle operation) can playa significant role in an instantaneous emissions value. More detaileddiscussions about modal emissions modeling and CMEM can befound in the literature (21–24).

UC Riverside’s MERL

To measure on-road real-world emissions more realistically, UCRiverside has developed a unique mobile emissions research labora-tory (MERL). This laboratory contains all the instrumentation nor-mally found in a conventional vehicle emissions laboratory, but theequipment is mounted inside a 53-ft over-the-road truck trailer. Adilution tunnel inside the trailer mixes the truck’s exhaust (sampleddirectly from the exhaust pipe) with dilution air, and the samples aremeasured just as they would be in a stationary laboratory using theprocedures prescribed in the Code of Federal Regulations Parts 86and 89 (25). Both gaseous and PM emissions are measured with thesame levels of accuracy as are measurements made in a stationaryfacility. The laboratory weighs approximately 45,000 lb and servesas the truck’s load. Thus, it is possible to sample a truck’s emis-sions under real-world operating conditions with the accuracy andprecision normally restricted to a stationary laboratory. Any Class 8tractor can pull this trailer, and the lab has gone through extensivecalibration and testing to ensure accuracy and repeatability (26 ).MERL serves as an important tool for understanding how truckspollute and for quantifying the effects of different fuels (reformu-lated diesel, etc.), alternative power trains, different control strate-gies, and a variety of emissions control equipment. Further detailson MERL can be found elsewhere (26 ).

DATA COLLECTION

To create the HDD instantaneous emission model, a test programwas developed with a vehicle recruitment process, testing of thevehicles over a wide set of operating conditions on the road, andpostprocessing of the resulting data (e.g., time alignment) so thatthey could be used for calibrating the model.

Vehicle–Technology Categorization and Vehicle Recruitment

Similar to the CMEM approach for LDVs, HDD vehicle technol-ogy and existing emissions data were examined closely and severalvehicle–technology categories were derived. For each category, adifferent model “instance” has been developed, described in anothersection of this paper. The vehicle–technology categories were derivedbased on differences in emissions behavior, which were given pri-ority over factors that were more likely to affect emission levels. Forexample, technology factors such as fuel injection type that couldresult in emissions differences that were not consistent by operatingmode were given priority over factors that were more likely to affectemissions level (e.g., engine displacement), but not modal behavior.The reason for this is that a composite vehicle that averages the dif-ferent levels of vehicles having the same modal behavior will havelower vehicle-to-vehicle error rates across driving modes than a com-posite vehicle that averages trucks having different modal behaviors.Also playing a major role in selection of the vehicle–technologygroups are the California state and federal emissions standards forHDD vehicles. Manufacturers have met these increasingly stringentstandards through basic improvements to the combustion process(e.g., electronic fuel injection, quiescent combustion chambers,increased injection pressure, etc.) rather than through addition ofexhaust after-treatment or add-on controls (27 ).

After several iterations in balancing the number of vehicle–technology groups with the potential number of testing samples,the final HDD categories were chosen and are shown in Table 1.Fewer samples were allocated to the mechanical injection groupsbecause of the lack of multiple operating modes made possible byelectronic ignition systems. Manufacturer-to-manufacturer as wellas model-year-to-model-year differences in timing strategies wereexpected to lead to higher vehicle-to-vehicle variability within theelectronic injection categories, so more samples were allocated tothe electronic injection groups. Vehicles were recruited from usedvehicle fleets in Southern California for testing using MERL. Thusfar, a total of 11 vehicles were recruited and tested, all in Technol-ogy Groups 5, 6, and 7. One vehicle was eliminated from the modeldevelopment fleet because it was found to have mechanical prob-lems with the engine. The test fleet was augmented with 23 addi-

12 Transportation Research Record 1880

tional vehicles from an HDD dynamometer test program (14). Thetarget sample size and actual sample size including the dynamometertest vehicles are listed in Table 1. Vehicles were recruited randomlywithin test categories by engine model year, and a balance betweenhorsepower and between manufacturers was attempted.

Testing Procedure

As part of the data collection effort, a vehicle-testing procedure wasdeveloped and applied to the recruited vehicles. This vehicle-testingprocedure includes the following test cycles:

1. Complete California Air Resources Board HDD (CARB-HDD)test, including creep mode, transient mode, and freeway mode (28);

2. Urban dynamometer driving schedule (UDDS) test cycleadapted for on-road use;

3. Real-world driving with the flow of highway traffic; and4. Set of modal emission cycles developed by the research team.

A complete CARB-HDD test is necessary for two reasons. First,it is the standard testing procedure used by CARB in testing HDDvehicles and provides baseline information about a vehicle’s emis-sions that can be used as a reference to compare with existing testsof other vehicles. Second, the cycle provides a structured set ofdriving to be compared with unstructured “real-world” driving.The primary reason for including the freeway driving without atest cycle in the test protocol is that the emissions under this drivingare directly representative of in-use emissions. The UDDS cyclewas included to provide a common baseline driving cycle that hasbeen commonly used in emissions testing in the lab. The UDDScycle is also used primarily as an independent cycle for validationpurposes (see section on results).

To capture specific modal emission events, a specific set of modalemissions cycles was designed and applied. The two general objec-tives of constructing these cycles were to (a) cover the majority ofspeed, acceleration, and specific power ranges that span the perfor-mance envelope of most heavy-duty vehicles and (b) cover a seriesof modal events such as various levels of accelerations and deceler-ations, a set of constant cruise speeds, speed-fluctuation driving, andconstant power driving. In addition to these criteria, the cycles hadto conform to the lengths of the road segments, speed limits, andotherwise safe driving practices of the testing area. On the basis offeedback from the initial tests and simulation runs, the modal cycleswere iteratively refined before any substantial vehicle testing. Theresulting three modal cycles are illustrated in Figure 1.

A total of 11 HDD vehicles were tested thus far by the College ofEngineering, Center for Environmental Research and Technology,using this test schedule. A total of 442 individual cycles were col-

TABLE 1 Vehicle–Technology Categories for HDD Vehicles

Model Year (Group) Engine Injection Target Vehicle Count

(Model Development Count)

Pre 1991 (1) 2-stroke Mechanical FI 3 (0) Pre 1991 (2) 4-stroke Mechanical FI 3 (11)

1991-1993 (3) 4-stroke Mechanical FI 3 (1) 1991-1993 (4) 4-stroke Electronic FI 5 (4)

1994-1997 (5) 4-stroke Electronic FI 5 (8)

1998 (6) 4-stroke Electronic FI 5 (4)

1999-2002 (7) 4-stroke Electronic FI 5 (6)

Barth, Scora, and Younglove 13

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120 140 160 180 200 220 240 260

Vel

oci

ty (

mp

h)

0

10

20

30

40

50

60

0 20 40 60

Vel

oci

ty (

mp

h)

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400 450 500 550

Time (s)

Vel

oci

ty (

mp

h)

(a)

(b)

(c)

FIGURE 1 Derived modal cycles for HDD testing: (a) “three hills” of acceleration/deceleration, (b) “one hill” of constantspeed events, and (c) power mode events.

Recruiting of older vehicles proved to be more difficult thananticipated, so the test data were augmented with additional second-by-second data collected on 23 additional HDD vehicles in theCoordinating Research Council E-55 dynamometer study (14 ).

Data Conversion and Time Alignment

Emission concentrations and mass flow rates are recorded secondby second during the testing and are stored in a database. The raw

lected on the vehicles with a total of 376,371 s of data. Ambient tem-perature and humidity were measured continuously during testing,and local hourly wind measurements were obtained. All vehicleswere tested using standard fuel obtained from the same source, withspot testing to ensure consistency.

The HDD testing with MERL was carried out on seldom-usedroadways in California’s Coachella Valley, approximately 2 h fromUC Riverside. This area was chosen for its relative proximity to UCRiverside and its long, uninterrupted stretches of road at zero grade,approximately at sea level.

emission gas concentrations are then converted from concentrationsin parts per million to mass emission rates in grams per second, usingalgorithms for the gas analyzers that account for parameters suchas emission densities, exhaust flow rates, and differences in dryand wet gas measurements. This is carried out for carbon dioxide(CO2), carbon monoxide (CO), hydrocarbon (HC), and NOx. This isthen followed by a comparison between the cumulative modal dataand integrated bag results as part of the quality assurance/qualitycontrol procedures.

Further, an important part of postprocessing is to time-align allnecessary second-by-second emission data. This step is crucialbecause there is a time delay inherent in each of the gas analyzerresponse times and between data from the analyzer and the vehicle’sengine control unit (ECU). Data obtained from the ECU, such asengine speed, vehicle speed, and fuel use, either are obtained byfeedback from vehicle sensors or are calculated by the ECU itselfand for the authors’ purposes are essentially time-aligned and rep-resentative of real time.

The proper time shift for the emission data is determined throughseveral steps. An initial time shift for each pollutant emission is pro-vided by MERL as part of the validation and calibration of the emis-sion benches. The second step is to analyze the time shifts for eachpollutant emission relative to the ECU data. Because the ECU fueldata show a strong relationship with the emission data and are thebasis for much of the later regression work, they are used to deter-mine alignment between the ECU and emission data sets. Alignmentof these two data sets is done via a cross-correlation analysis usinga cross-correlation estimate function to calculate correlation valuesfor a range of lag times between the emission and the ECU fuel data.The lag times with the highest correlations are then compared withMERL’s expected time shifts and with the optimal lag times ofother tests in the series to determine the proper lag times for a rangeof tests.

MODEL STRUCTURE

The HDD truck emissions model has been developed using princi-ples that are very similar to those of other models in the CMEM pro-gram. As discussed earlier, the emissions process is broken downinto different components or modules that correspond to physicalphenomena associated with vehicle operation and emissions pro-duction. With heavy-duty vehicles, similar to light-duty vehicles,each component is then modeled as an analytical representationconsisting of various parameters characteristic of the process. Theseparameters vary because of several factors such as vehicle–technologytype, vehicle age, and so on. Because these parameters typicallycorrespond to physical values, many of the parameters are statedas specifications by the vehicle manufacturers and are readily avail-able (e.g., vehicle mass, engine size, gear ratios, etc.). Other keyparameters relating to vehicle operation and emissions productionmust be determined from a testing program as part of the modelcalibration procedure.

The physics-based emissions model uses a bottom-up approach;the basic building block is the individual truck operating on a fine timescale (i.e., second by second). However, the HDD model, similar tothe light-duty CMEM models, does not focus on modeling specificmakes and models of trucks. The primary goal is the prediction ofemissions in several-second modes for average composite trucks foreach of the truck categories specified in the section on data collection.Thus, separate submodels for each composite truck category have

14 Transportation Research Record 1880

been created. These submodels are similar in structure; however, theparameters used to calibrate each submodel are different.

General Structure of the Model

In the developed HDD emissions model, second-by-second tailpipeemissions are modeled as the product of three components (fuel rate(FR), engine-out emission indices (gemissions/gfuel), and an emissionafter-treatment pass fraction):

Here FR is fuel use rate in grams per second, engine-out emissionindex is grams of engine-out emissions per gram of fuel consumed,and the after-treatment pass fraction is defined as the ratio of tail-pipe to engine-out emissions. To date, no HDD vehicles with after-treatment devices have been tested or are commonly available, sothe after-treatment pass fraction for all current truck categories isbeing modeled as 100%. (A variety of after-treatment devices can bemodeled separately and integrated into this model structure withoutextensive retesting.)

The complete HDD emissions model is composed of six modules,as indicated by the six square boxes in Figure 2: (a) engine powerdemand, (b) engine speed, (c) fuel rate, (d ) engine control unit,(e) engine-out emissions, and ( f ) after-treatment pass fraction. Themodel as a whole requires two groups of input (rounded boxes inFigure 2): (g) input operating variables and (h) model parameters.The output of the model is tailpipe emissions and fuel consumption.The vehicle power demand (a) is determined based on operatingvariables (g) and specific vehicle parameters (h). All other modulesrequire the input of additional vehicle parameters determined on thebasis of on-road measurements, as well as the engine power demandcalculated by the model. The core of the model is the fuel rate calcu-lation (c). It is a function of power demand (a) and engine speed (b).Engine speed is determined on the basis of vehicle velocity, gear shiftschedule, and power demand.

Engine Power Demand Module

Establishing a power demand function for each truck is straight-forward. The total tractive power requirements (in kW) placed onthe truck (at the wheels) are given as follows:

where

M = truck mass with appropriate inertial correction for rotatingand reciprocating parts (kg),

v = speed (m/s),a = acceleration (m/s2),g = gravitational constant (9.81 m/s2),θ = road grade angle in degrees,

Cd = coefficient of drag,A = frontal surface area (m2),ρ = air density (kg/m3), and

Cr = coefficient of rolling resistance.

P M a M g Cd A v

M g Cr v

tract = + +

+ )� � � � � �

� � � �

sin

cos ( )

θ ρ

θ

1

2

1000 2

tailpipe emissions

treatment pass fraction

emissions

fuel

=

−FRg

gafter� �

( )1

The terms in parentheses represent resistance due to acceleration,grade, wind, and rolling friction. To translate the tractive powerrequirement to demanded engine power requirements, the followingrelationship applies:

where

P = second-by-second engine power output in kW,� = vehicle drivetrain efficiency, and

Pacc = engine power demand associated with running losses ofthe engine and the operation of vehicle accessories such asair-conditioning use.

As the model was developed, intermediate engine power validationwas performed with actual “load” values provided by the ECU.

Engine Speed Module

Engine speed is approximated in regard to vehicle speed:

where

N(t) = engine speed (rpm) at time t,S = engine speed–vehicle speed ratio in top gear Lg (known as

N/v in units rpm/mph),R(L) = gear ratio in Lth gear,

L = 1, . . . , Lg, andv(t) = vehicle speed (mph) at time t.

Gear ratio is selected from a given set of shift schedules. Under cer-tain circumstances, especially for high-power events, down shift-ing is required as determined by a wide-open-throttle (WOT) torquecurve. The general relationship between torque and power output ofthe engine is as follows:

N t SR L

R Lv t

g

( ) =( )

( )( )� � ( )4

PP

P= +tractacc

�( )3

Barth, Scora, and Younglove 15

where Q(t) is engine torque in ft-lb at time t and P(t) is enginepower in horsepower. The engine torque at any engine speed must notexceed the WOT torque [QWOT(t)]. The latter is based on an approxi-mation of the manufacturer’s supplied torque curve. When the calcu-lated Q(t) is greater than QWOT(t), the vehicle down shifts to the nextlower gear. New values of engine speed, torque, and WOT torque arecalculated on the basis of the equations above and a representationof the vehicle’s torque curve. If necessary, this process is repeated(i.e., a second downshift is considered) to satisfy operating conditions.

Fuel Rate Module

Modeling the fuel rate in any driving cycle for any vehicle was pre-viously developed by An and Ross (29, 30). The basic diesel fuelconsumption module is as follows:

where

FR = fuel use rate in g/s,P = engine power output in kW,K = engine friction factor,N = engine speed (revolutions per s),V = engine displacement (L),

η ≈ 0.45 = measure of indicated efficiency fordiesel engines,

b1 ≈ 10−4 and C ≈ 0.00125 = coefficients, and 43.2 kJ/g = lower heating value of a typical diesel

fuel.

NV

0 303 0

8≈ �.

( )

K K C N N= + −( )[ ]0 01 7� � ( )

FR K N VP

b N N≈ +

+ −( )[ ]� � � �η

1

43 21 60

2

.( )1

Q tP t

N t( ) =

( )

( )� 5252

5( )

(b)EngineSpeed

(a) Power

Demand

(e)Engine-

OutEmissions

(f)Exhaust

After-Treatment

(h) ModelParameters

(g) InputOperatingVariables

(c)Fuel Rate

(d)Engine

Control Unit

Operating Time

TailpipeEmissions& Fuel Use

FIGURE 2 HDD emissions model structure.

As described in the section on the engine-out emissions module,often alternate fuel injection timing strategies are used to improvefuel economy at the expense of NOx emissions. For modeling pur-poses, a fuel-use reduction factor has been introduced to account forthese alternative fuel injection timing strategies:

where FRoff is the off-cycle fuel rate in grams per second and fRed isthe fuel use reduction factor associated with off-cycle fuel injectiontiming strategies.

Engine-Out Emissions Module

CO emissions are a product of incomplete combustion and are greatlydependent on the air–fuel ratios occurring during combustion. Sincefuel-rich combustion leads to increased CO, diesel engines, whichrun lean, typically have extremely low CO emissions, unlike sparkignition engines. This analysis shows that there is a linear correlationbetween fuel use and engine-out CO; however, it is not a particularlystrong one. The following equation is used for modeling CO:

where ECO is the engine-out emission rate in grams per second andaCO and rCO are the CO emission index coefficients.

HC emissions from diesel engines are unburned hydrocarbonsresulting primarily from combustion inefficiencies. Incomplete fuel–air mixing in the combustion chamber results in portions of the com-bustion mixture not supporting combustion. Similar to the correla-tion between fuel use and CO, this analysis shows that there is alinear correlation between fuel use and engine-out HC:

where EHC is expressed in grams per second and aHC and rHC are theHC emission index coefficients.

NOx emissions along with particulates are the diesel pollutants ofprimary concern. The formation of NOx emissions in diesel enginesis well understood and is dependent mainly on the presence of suffi-cient oxygen and high temperatures. NOx emissions exhibit a stronglinear relationship with load or fuel use. The following equation isused for basic NOx emissions modeling:

where

FR = fuel rate,aNO = NOx emission index coefficient in grams emission/grams

fuel, andrNO = small residual value.

NOx emissions may be controlled by reducing in-cylinder tem-peratures, which can be accomplished with retarded fuel injectiontiming at the expense of increased particulate emissions and reducedfuel economy. That is commonly referred to as the NOx, particulate,fuel “trade-off.” For that reason fuel injection timing strategies arecritical to the formation of NOx.

It has also been noted that the fuel injection timing strategies ofmany existing electronic controlled HDD vehicles do not alwaysremain consistent with those used during engine certification test-ing. It has been determined that under certain modes of operation,

NOx NO NO= +a FR r� ( )12

EHC a FR r= +HC HC� ( )11

ECO a FR r= +CO CO� ( )10

FR FR foff Red= −( )� 1 9( )

16 Transportation Research Record 1880

many of the HDD vehicles found in today’s vehicle fleet use off-cycle fuel injection timing strategies, resulting in higher NOx emis-sion rates in favor of increased fuel economy. Figure 3 illustratesdual NOx/fuel emission rates as a result of off-cycle fuel injectiontiming strategies.

These off-cycle strategies are not publicly documented and are tobe eliminated in the future. Nevertheless, it is important to modelthis effect when dealing with the current (short-term) and futurevehicle fleet. In an effort to model these off-cycle fuel injectionstrategies, an off-cycle NOx–fuel relationship is used:

where aNOh is the off-cycle NOx emission index coefficient in gramsemission/grams fuel and rNOh is a small residual value associated withoff-cycle NOx emissions. Determining NOx emission factors for usewith normal injection timing strategies and off-cycle fuel injectionstrategies is relatively straightforward and usually results in strongleast squares fits (see Figure 3). The difficulty lies in determiningwhen in a given cycle each strategy is used. It was observed that theoff-cycle timing strategies appear to have a history effect and in somecases show a moderately predictable pattern across similar cycles. Formodeling purposes, off-cycle fuel injection strategies are being char-acterized as a function of time and velocity; these strategies occurafter 80 s above 30 mph, and then normal operation resumes once thevehicle speed drops below 30 mph. The off-cycle timing strategiesappear to vary by manufacturer, model year, and sometimes from testcycle to test cycle during a single day of testing. Determining the bestoverall model formulation of the off-cycle strategy is therefore highlydependent on the vehicle test fleet. Because of the difficulty in deter-mining the best overall strategy with the current data set, a genericspeed and time method was used for this initial version of the model,pending collection of more data. (The model strategy is not intendedto represent a particular manufacturer’s truck, but rather to give a goodapproximation of the fleet behavior.)

Model Calibration and Vehicle Compositing Procedures

As discussed previously, separate submodels for each truck categoryhave been created. The submodels have similar structure (as describedin a previous section); however, they differ primarily in their param-eters. Each submodel uses three dynamic operating variables as input.These variables include second-by-second vehicle speed (from whichacceleration can be derived; acceleration can be input as a separateinput variable), grade, and accessory use (such as air-conditioning). Inmany cases, grade and accessory use may be specified as static inputsor parameters. In addition to these operating variables, each sub-model uses a total of 31 static parameters to characterize the vehicletailpipe emissions for the appropriate vehicle–technology category.As the submodels were developed, each test vehicle was individuallymodeled by determining all parameters. Readily available param-eters of test vehicles (e.g., mass, engine displacement, etc.) have beenobtained for each vehicle. Next, a set of calibration parameters wasdetermined through estimation procedures using the measured emis-sions results for each test vehicle. Depending on the specific param-eter, the values are determined either (a) directly from measurementsor (b) on the basis of several regression equations.

Each test vehicle has been individually modeled; however, theprimary modeling goal is to predict detailed emissions for each aver-age composite vehicle that represents the vehicle–technology cate-gories described in the section on data collection. Thus, a compositingprocedure has been developed to construct a composite vehicle to

NOx NOh NOh= +a FR r� ( )13

represent each of the different HDD vehicle–technology modeledcategories. The compositing procedure is relatively straightforward.In previous CMEM work, compositing LDVs involved first aver-aging second-by-second emission values in time across all vehiclesin the category. The modeling procedure was then carried out onthe averaged emission traces (23). This was possible because everyvehicle was tested very closely following the prescribed drivingcycles. For the on-road HDD testing, it was impossible to followeach target trace exactly because of wide differences in the vehicle’spower–weight ratio. Therefore, the previous emission trace aver-aging technique does not work. Instead, each test vehicle is indi-vidually modeled, resulting in an individual vehicle parameter set.The parameter sets from all vehicles in the category are then averagedappropriately to provide a representation of a composite vehicle.Influential factors such as emissions rate and vehicle weight haveroughly symmetric distributions so that the mean is a good estimatorof the central value of the distribution. For parameters such as num-ber of gears, in which the mean value does not make physical sense,the mode was used.

RESULTS

On the basis of the methods described in the section on results, sep-arate modal emissions submodels were developed for the vehiclecategories described in the section on data collection. A number ofintermediate validation exercises took place during the develop-ment examining the output from the different components of each

Barth, Scora, and Younglove 17

submodel. With the models complete, a more rigorous validationprocedure took place by application of independent driving cycles(i.e., driving patterns not used in the model calibration process) tothe models and a comparison of results with real-world measure-ments. Validation on independent vehicles and independent testcycles will be conducted in the future, but at this time all vehicleswere used in the development of the model.

Example results using the independent test cycles are shown in Fig-ure 4, in which a composite 94-97 four-stroke electronic fuel injectionHDD truck was modeled and compared against a real truck in thatclass. A number of independent cycles were applied, including seg-ments of the UDDS as well as various driving patterns recorded onthe local freeways and arterials. The validation plots are simplyregressions with the measured data in units of grams per mile for thecycle segment along the x-axis and the modeled data on the y-axis.Remember that the model in this case represents a composite vehi-cle in that class and not the specific vehicle. If the model were per-fect, all of the data would fall on the (green) line with slope = 1. It canbe seen that fuel use is modeled well, with the linear regression slopeclose to 1 with an r2 of 0.86. NOx is also modeled well with a slope of0.923 and r2 of 0.78. CO is not quite as good with a slope of 0.78 andr2 of 0.58. The slope for the HC regression is 0.88 with an r2 of 0.77.These example results are representative of the other validation regres-sions that were performed for the other submodels. (Results of othersubmodels are not shown here due to space limitations.)

These results are thought to be fairly good when considering thateach submodel represents a composite of all vehicles tested in thatcategory.

60

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b: y = 0.0544x + –0.0168, Rsq = 0.94

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0 2 4 6 8 10

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NO

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FIGURE 3 (a) Velocity (mph) versus time (s) and (b) NOx (g) versus fuel rate (g) with correspondingsymbols and associated regression lines. High-speed cruise, off-cycle activity has higher NOx and lowerfuel compared with on-cycle activity.

y = 1.0722x + 20.753R2 = 0.855

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y = 0.9233x + 3.6329

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y = 0.7853x + 1.2308

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y = 0.8836x + 0.0492

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(a) (b)

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FIGURE 4 Example of validation results for the 94-97 HDD category with independent cycles; regressions of the modeled composite vehicleagainst example vehicle in class: (a) fuel, (b) NOx, (c) CO, and (d ) HC.

18 Transportation Research Record 1880

with the measured emissions in Figure 6b for going both up- anddownhill. However, in Figure 6c, NOx emissions are grossly under-estimated when the truck is going uphill and grossly overestimatedwhen it is heading downhill (Figure 6c). Again grade is an importantparameter to consider when dealing with HDD trucks because thepower–weight ratios can vary widely. A physical modeling approachinherently handles grade better than methods that rely on speed andacceleration only.

CONCLUSIONS AND FUTURE WORK

HDD trucks play an increasingly important role in the overall emis-sions inventory because LDV emissions continue to decrease. Inmany microscopic transportation evaluations, it is important to havethe ability to model second-by-second emissions of all vehicles. Withthe HDD truck models now in place, UC Riverside’s CMEM programis now capable of simulating a wide variety of traffic scenarios.

The HDD truck models in CMEM are based primarily on test-ing carried out with UC Riverside’s MERL. Vehicles will continueto be tested with MERL, and the results will continually be added tothe models. In addition, other HDD truck data will be collected from

To show the value of modeling the fuel injection timing strategiesdescribed in the section on the engine-out emissions module (see Fig-ure 3), a comparison was made between the model with the timingstrategy software module turned on and the model with the timingstrategy module missing. Results are shown in Figure 5. Given theUDDS cycle (Figure 5a), second-by-second predicted NOx emis-sions are shown for both a measured truck and its modeled categorywith the timing strategy software module turned on (Figure 5b). Forthis cycle, the model predicted 23.57 g compared with a measured27.75 g, a 15% difference. If the timing strategy module was removedaltogether, it can be seen in Figure 5c that the model grossly under-predicts NOx when traveling at high-speed extended cruises. In thiscase, the model predicted 19.18 total grams, a difference of 31%.

Last, to show the advantage of a physics-based modal emissionsmodel in the way it inherently handles grade, another comparisonwas conducted for a driving pattern that traveled up and over a moun-tain pass. In this example the elevation of the roadway is shown inFigure 6a (measured by a differential Global Positioning System).The second-by-second measured and modeled NOx emissions arecompared for the case in which grade is used as input (Figure 6b)and in the case in which the grade is set to 0 for the entire run (Fig-ure 6c). It can be seen that the modeled emissions track pretty well

Barth, Scora, and Younglove 19

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FIGURE 5 Comparison of second-by-second NOx emissions for UDDS cycle: (a) UDDS velocityprofile, (b) modeled (dash) versus measured (solid) with timing strategy implemented, and (c) modeled (dash) versus measured (solid) with the timing strategy removed.

800

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FIGURE 6 Comparison of second-by-second NOx emissions for varying grade: (a) elevationprofile for a specific driving pattern, (b) modeled (dash) versus measured (solid) emissionswith grade as input, and (c) modeled (dash) versus measured (solid) emissions with gradeset equal to zero.

other programs and integrated into the CMEM models to providefurther breadth.

The HDD truck emissions model described herein is based on aphysical, power-demand approach. Because it is a physical model,it inherently handles fluctuations in power that may arise, such aschanging road grade. Further, by modeling individual componentsof the physical process, it is possible to include emissions and fueleffects that arise from different control strategies. In this paper theHDD model has been described in detail, and more recent resultsillustrating its effectiveness have been provided. The plan is to usethis model for evaluating a variety of traffic scenarios, in particular,those that are associated with HDD trucks, such as truck climbinglanes and restricted truck lanes.

ACKNOWLEDGMENTS

This work has been sponsored in part by EPA and the CaliforniaPATH Program. The authors acknowledge the people involved inthe testing and data-handling portion of this project: Wayne Miller,Kent Johnson, and Chan-Sueng Park. The authors also acknowledgeFeng An of Argonne National Lab for his insightful comments onemissions modeling.

REFERENCES

1. National Research Council. Modeling Mobile-Source Emissions. NationalAcademy of Science Press, 2000.

2. Yanowitz, J., R. L. McCormick, and M. S. Graboski. In-Use Emis-sions from Heavy-Duty Diesel Vehicles. Environmental Science andTechnology, Vol. 34, No. 5, 2000, pp. 729–740.

3. Lloyd, A. C., and T. A. Cackette. Diesel Engines: Environmental Impactand Control. Journal of the Air and Waste Management Association,Vol. 51, No. 6, 2001, pp. 809–847.

4. Yanowitz, J., M. S. Graboski, L. B. A. Ryan, T. L. Alleman, and R. L.McCormick. Chassis Dynamometer Study of Emissions from 21 In-UseHeavy-Duty Diesel Vehicles. Environmental Science and Technology,Vol. 33, No. 2, 1999, pp. 209–216.

5. McKain, D. L., N. Clark, T. McDaniel, and J. Hoppie. Chassis Test CycleDevelopment for Engine Test Compliance on Heavy Duty Engines. SAEPaper 980407. SAE, Warrendale, Pa., 1998.

6. Messer, J., and N. Clark. Measurement Delays and Modal Analysis for aTransportable Heavy Duty Vehicle Emissions Testing Laboratory. SAEPaper 950218. SAE, Warrendale, Pa., 1995.

7. Brown, J. E., M. J. Clayton, D. B. Harris, and F. G. King, Jr. Compari-son of Particle Size Distribution of Heavy-Duty Diesel Exhaust Using aDilution Tailpipe Sampler and In-Plume Sampler During On-Road Oper-ation. Journal of the Air and Waste Management Association, Vol. 50,No. 8, 2000, pp. 1407–1416.

8. McCormick, R. L., M. S. Graboski, A. W. Newlin, and J. D. Ross.Effect of Humidity on Heavy-Duty Transient Emissions from Dieseland Natural Gas Engines at High Altitude. Journal of the Air and WasteManagement Association, Vol. 47, No. 7, 1997, pp. 784–791.

9. Gautam, M., G. J. Thompson, D. K. Carder, N. N. Clark, B. C., Shade,W. C. Riddle, and D. W. Lyons. Measurement of In-Use, On-BoardEmissions from Heavy-Duty Diesel Vehicles: Mobile Emissions Mea-surement System. SAE 2001-01-3643. Society of Automotive Engineers,Warrendale, Pa., 2001.

10. Weaver, C. S., and M. V. Balam-Almanza. Development of the “RAVEM”Ride-Along Vehicle Emission Measurement System for Gaseous andParticulate Emissions. SAE 2001-01-3644. SAE, Warrendale, Pa., 2001.

11. Reading, A. R., G. Eden, and C. Ensfield. The Design and Implementa-tion of a Portable Analytical System (SEMTECH) for the Measurement

20 Transportation Research Record 1880

of In-Use Diesel Engine Emissions. Proc., 11th CRC On-Road VehicleEmissions Workshop. San Diego, Calif., 2001.

12. Spears, M. W. Advancing the Development of Portable EmissionMeasurement Systems. Proc., 12th CRC On-Road Vehicle EmissionsWorkshop. San Diego, Calif., 2002.

13. Brown, J. E., F. G. King, W. A. Mitchell, W. C. Squier, D. B. Harris,and J. S. Kinsey. On-Road Facility to Measure and CharacterizeEmissions from Heavy-Duty Diesel Vehicles. Journal of the Air andWaste Management Association, Vol. 52, No. 4, 2002, pp. 388–395.

14. Coordinating Research Council. Project E-55: Heavy-Duty Vehicle Chas-sis Dynamometer Testing for Remissions Inventory. www.crcao.com/annualreport/emission/e55.htm. Accessed Nov. 15, 2003.

15. Clark, N., P. Gajendran, and J. Kern. A Predictive Tool for Emissions fromHeavy-Duty Diesel Vehicles. Environmental Science and Technology,Vol. 37, No. 1, 2003. pp. 7–15.

16. Methodology for Developing Modal Emission Rates for EPA’s Multi-ScaleMotor Vehicle and Equipment Emission System. EPA420-R-02-027.Office of Transportation and Air Quality, U.S. Environmental ProtectionAgency, Ann Arbor Mich., Oct. 2002.

17. U.S. EPA’s On-Board Emission Analysis Shootout: Overview andResults. EPA420-R-02-026. U.S. Office of Transportation and AirQuality, Environmental Protection Agency, Ann Arbor Mich., April 2002.

18. Yanowitz, J., M. Graboski, and R. McCormick. Prediction of In-Use Emis-sions of Diesel Vehicles from Engine Testing. Environmental Science andTechnology, Vol. 36, No. 2, 2002, pp. 270–275.

19. Traver, M., C. Atkinson, and R. Atkinson. Neural Network-BasedDiesel Engine Emissions Prediction Using In-Cylinder CombustionPressure. SAE Paper 1999-01-1532. International Fuels and LubricantsMeeting and Exposition, SAE, Warrendale, Pa., 1999.

20. Gamo, O., M. Ouladrine, and A. Rachid. Diesel Engine Exhaust EmissionsModeling Using Artificial Neural Networks. SAE Paper 1999-01-1163.Society of Automotive Engineers, Warrendale, Pa., 1999.

21. An, F., M. Barth, J. Norbeck, and M. Ross. Development of Compre-hensive Modal Emissions Model: Operating Under Hot-StabilizedConditions. In Transportation Research Record 1587, TRB, NationalResearch Council, Washington D.C., 1997, pp. 52–62.

22. Barth, M., F. An, J. Norbeck, and M. Ross. Modal Emissions Modeling:A Physical Approach. In Transportation Research Record 1520, TRB,National Research Council, Washington, D.C., 1996, pp. 81–88.

23. Barth, M., T. Younglove, T. Wenzel, G. Scora, F. An, M. Ross, andJ. Norbeck. Analysis of Modal Emissions from Diverse In-Use Ve-hicle Fleet. In Transportation Research Record 1587, TRB, NationalResearch Council, Washington, D.C., 1997, pp. 73–84.

24. Barth, M., F. An, T. Younglove, C. Levine, G. Scora, M. Ross, andT. Wenzel. The Development of a Comprehensive Modal EmissionsModel. Final report submitted to the National Cooperative HighwayResearch Program, Nov. 1999, p. 255.

25. Code of Federal Regulations: Protection of the Environment. 40 C.F.R. 86.26. Cocker, D., K. Johnson, J. W. Miller, and J. N. Norbeck. Development

and Application of a Mobile Laboratory for Measuring Emissions fromDiesel Engines I. Regulated Gaseous Emissions. Environmental Science& Technology, Vol. 38, No. 7, pp. 2182–2189.

27. Fleet Characterization Data for Use in MOBILE6 Final Report.Office of Mobile Sources Technical Report #EPA420-P-98-016. U.S.Environmental Protection Agency, 1998.

28. Maldonado, H., A. Agrawal, and M. Carlock. Development of Heavy-DutyVehicle Chassis Dynamometer Driving Cycles. Proc., 12th CRC On-RoadVehicle Emissions Workshop Conference, San Diego, Calif., 2002.

29. An, F., and M. Ross. Model of Fuel Economy with Applications toDriving Cycles and Traffic Management. In Transportation ResearchRecord 1416, TRB, National Research Council, Washington, D.C., 1993,pp. 105–114.

30. Ross, M., and F. An. The Use of Fuel by Spark Ignition Engines. SAETechnical Paper 930329. SAE, Warrendale, Pa., 1993.

The contents of this paper reflect the views of the authors and do not necessarilyindicate acceptance by the sponsors.

Publication of this paper sponsored by Transportation and Air Quality Committee.