Vehicle-Specific Emissions Modeling Based upon on-Road

Apr 8, 2010 - Vehicle-specific microscale fuel use and emissions rate models are developed based upon real-world hot-stabilized tailpipe measurements ...
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Environ. Sci. Technol. 2010, 44, 3594–3600

Vehicle-Specific Emissions Modeling Based upon on-Road Measurements H. CHRISTOPHER FREY,* KAISHAN ZHANG, AND NAGUI M. ROUPHAIL Department of Civil, Construction and Environmental Engineering, North Carolina State University, Campus Box 7908, Raleigh, North Carolina 27695-7908

Received September 18, 2009. Revised manuscript received March 7, 2010. Accepted March 24, 2010.

Vehicle-specific microscale fuel use and emissions rate models are developed based upon real-world hot-stabilized tailpipe measurements made using a portable emissions measurement system. Consecutive averaging periods of one to three multiples of the response time are used to compare two semiempirical physically based modeling schemes. One scheme is based on internally observable variables (IOVs), such as engine speed and manifold absolute pressure, while the other is based on externally observable variables (EOVs), such as speed, acceleration, and road grade. For NO, HC, and CO emission rates, the average R2 ranged from 0.41 to 0.66 for the former and from 0.17 to 0.30 for the latter. The EOV models have R2 for CO2 of 0.43 to 0.79 versus 0.99 for the IOV models. The models are sensitive to episodic events in driving cycles such as high acceleration. Intervehicle and fleet average modeling approaches are compared; the former account for microscale variations that might be useful for some types of assessments. EOV-based models have practical value for traffic management or simulation applications since IOVs usually are not available or not used for emission estimation.

Introduction The purpose of this paper is to develop an approach for microscale estimation of vehicle-specific emissions based on real-world data, in order to support long-term future development of more accurate and robust approaches for emissions estimation. An accurate assessment of highway vehicle emissions is essential for effective air-quality management, and emission estimates are needed at various spatial and temporal scales, including macro-, meso-, and microscale (1). Macroscale refers to urban or regional emission inventories based on aggregated data. Mesoscale refers to subregional estimates, such as for urban corridors. Microscale refers to nearly instantaneous vehicle emissions at specific locations, such as an intersection or segment of roadway. These different scales support different types of analyses. For example, many existing traffic demand models produce mesoscale estimates of average vehicle speeds for roadway links (2). However, because vehicle emissions are highly episodic, there is a critical need to better quantify the local effect of traffic control measures and other factors that contribute to variability in vehicle speed and acceleration (1). For example, microscopic simulation models such as AIMSUN (3) need to be calibrated using microscale fuel and emissions data from real-world measurements. * Corresponding author e-mail: [email protected]. 3594

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Emissions factor models should quantify the relationship between emissions, vehicle dynamics (e.g., speed and acceleration), and roadway infrastructure (e.g., road grade) at multiple scales (1). Since microscale emissions estimates can be aggregated over space and time to produce mesoor macroscale estimates, an ability to accurately estimate microscale emission factors is a key step toward development of a highly flexible vehicle emissions estimation system. Currently, the most widely used emission factor model, MOBILE6 (1) in the U.S. and COPERT (4) in Europe, is appropriate for macro- and mesoscale estimates of vehicle fleet emissions but is not applicable at the microscale or to individual vehicles. Alternative methods for emissions estimation applicable to the meso- and microscale have been explored for a number of years, including stratification of empirical data, statistical regression, neural network, and physically based approaches. Modal-based approaches involve stratification of data based on speed and acceleration, vehicle specific power (VSP), or other factors and are derived either based on a priori definitions of modes or from a statistical analysis of data using methods such as hierarchical tree-based regression (5). Examples of these types of models include HBEFA (6), ARTEMIS (7), Ecogest (8) in Europe, and CORSIM (9) in the U.S. Modal-based approaches are the foundation of the MOVES model that is under development to replace MOBILE6 (10). Statistically based approaches include least-squares linear regressions and time series modeling, among others (11-14). A neural network attempts to predict emissions by training the network with known emissions and vehicle activity data sets (15). Physically based approaches typically attempt to explicitly model the physics and chemistry of pollutant formation and control taking into account detailed characteristics of the vehicle and its operation (16-18). Examples include the Comprehensive Modal Emissions Model (CMEM) and Physical Emission Rate Estimator (PERE) models (17, 18). The advantage of the modal approaches is that they do not require fitting of an analytical model and thus do not introduce errors that might occur if the model is not a good fit to the data. However, such models inherently involve a significant amount of averaging of data, since a mode typically represents the average emissions for a significant proportion of the vehicle activity pattern. This may be adequate for mesoscale purposes but can reduce the model’s explanatory power and potentially limit its usefulness for microscale applications. Statistically based approaches typically involve fitting a model to empirical data. For some types of models, such as higher order polynomials, the terms in the model may or may not have any physical interpretation. For example, the product of speed (v) and acceleration (a) is a surrogate for power demand (av), while a3v3 does not have an explicit physical interpretation or relevance. However, if properly formulated, statistically based models can be both physically plausible while offering a useful degree of explanatory power. A key challenge, however, is whether such models can be developed appropriately for use in microscale emissions estimation. The physically based approaches typically have substantial requirements for input data that limit their practicality for general application. However, simplified models that have a physical basis may offer a substantial degree of explanatory power. For example, VSP, which is a function of speed, acceleration, and road grade, is an excellent predictor of vehicle fuel use (16). Because 10.1021/es902835h

 2010 American Chemical Society

Published on Web 04/08/2010

emissions of many pollutants have a significant relationship to fuel use, VSP is also a useful explanatory variable for vehicle emissions (5). The objectives of this paper are to (1) characterize and account for autocorrelation in vehicle fuel use and emission rates; (2) compare and evaluate alternative microscale vehicle-specific models based on EOVs and IOVs; and (3) compare vehicle-specific versus fleet average models.

Experimental Section This section describes methodologies for (1) on-road data collection; (2) development of data sets for model building and validation; (3) selection of vehicle-specific fuel use and emissions modeling approaches; and (4) model evaluation. On-Road Data Collection. In order to capture a substantial range of intravehicle variability, data were collected extensively for three “primary” vehicles using a portable emissions measurement system (PEMS) and were supplemented with fewer data on each of seven additional secondary vehicles (19). The measurements were made using the Montana system PEMS manufactured by Clean Air Technology International, Inc. The primary vehicles were operated by three drivers on three alternative routes between each of two origin/destination (O/D) pairs. On average, there were 65 h of secondby-second data collected over a three week period for each primary vehicle, involving an average of 14 runs on each route and travel direction. The routes included a variety of roadway facility types (i.e., feeder/collector street, minor arterial, major arterial, freeway) and road grades (varying between approximately plus or minus eight percent). Data were collected in both travel directions on each route for both morning and afternoon weekday time periods, thereby capturing both peak and off-peak traffic flow. Based on analysis of data collected for the primary vehicles, an estimate was made of the minimum field data requirement necessary to adequately quantify intravehicle variability in emissions. For each secondary vehicle, data collection occurred on preferred routes typically during one day by one driver. Development of Data Sets for Model Building and Validation. The field data were stratified into two data sets. One was used to build models, and the other was used to validate the models. In order for both data sets to have similar vehicle dynamics, trips from the same route were randomly but proportionally selected form each data set. Approximately 75% of all trips on a route were selected to populate the modeling data set, and the other 25% were included in the validation data set. A Kolmogorov-Smirnov (K-S) two sample test (20) was used to confirm that the two data sets had nonsignificant differences in vehicle speed and acceleration distributions. Selection of Vehicle-Specific Fuel Use and Emissions Modeling Approaches. Model specification takes into account the selection of a regression methodology, averaging time, and explanatory variables. Regression Approach. Both nonparametric and parametric regression approaches can be used for emissions modeling. However, nonparametric regression (NPR) models do not provide an explicit mathematical equation for model interpretation (21-24) and thus were not used. A linear regression model can be a linear combination of “basis functions” which may be nonlinear. In order to have confidence in the predictive ability of a regression model, each variable in the model should have a physical interpretation. In order to produce unbiased estimates of the model parameters, the model residuals should have constant variance with a zero mean and be independently and identically distributed (iid).

In some cases, a model with a physically based interpretation cannot be simplified to a linear combination of basis functions and may be inherently nonlinear. In these cases, nonlinear regression is used. Nonlinear regression is more sensitive to outliers (25). An assessment was made of the use of the Box-Cox transformation (BCT) in order to eliminate heteroscedasticity in the residuals. However, when variables are backtransformed, predictions of the model are biased and have to be corrected. The bias-corrected back-transformed models were found to perform more poorly than models fit directly to the data without the BCT. Therefore, BCT was not further applied. Averaging Time. The assumption of iid residuals is often not valid for models fit to raw second-by-second emissions data, since the vehicle activity and emissions in one second is dependent on activity and emissions in recent seconds. For example, an engine typically does not run at high RPM in one second unless it had been run at moderate to high RPM in the previous second. The response time of the PEMS emissions sensors are longer than the rate at which data are reported (26, 27), which imposes a correlation in the measured values even if the true emissions are changing independently every second. A technique for reducing the influence of autocorrelation and accounting for response time is to stratify the data and work with average, rather than continuous, values in each strata. Therefore, models were developed based on consecutive averages of vehicle activity and emission data that were equal to or greater than the response time of the emissions sensors and that include the most significant autocorrelated lags. Modeling Schemes. The vehicle-specific microscale emissions models were developed taking into consideration their potential applications. One possible future application is to couple such models with transportation microsimulation models that estimate externally (to the vehicle) observable information such as speed and acceleration of individual vehicles on a roadway network as well as characterize infrastructure features such as road grade. Another is to use the models as part of an in-vehicle information system that could report to a driver or a traffic management facility realtime fuel use and emissions. Such information could guide real-time decision making regarding driver behavior, traffic control, or routing. An in-vehicle model could access internally observable data from the on-board diagnostic (OBD) system, such as engine speed (ES), intake air temperature (IAT), and manifold absolute pressure (MAP). A key question is whether a model based on internally observable variables (IOVs) is more accurate or precise than one based on externally observable variables (EOVs). Internally Observable Variables Model (IOVM). ES and MAP were used as explanatory variables because they are significant factors in fuel injection control (28) and are strongly influenced by vehicle dynamics such as speed and acceleration. The formation of CO and HC are intimately coupled with the fuel combustion process whereas NO formation is assumed to occur as part of postflame processes (28). These processes account for engine-out emissions prior to the catalytic converter. One modeling approach is used to estimate fuel use and emission rates of HC and CO, while another is used to model NO emissions. The former were modeled as (model 1 in Table 1) ¯∆t ¯ mapS¯engine∆t ) aiP m i

(1)

j i∆t ) average mass flow rate for specie i (fuel, CO, where m HC) for a consecutive averaging period ∆t, g/s, Pmap ) Manifold Absolute Pressure (MAP), kPa, Sengine ) Engine Speed (ES) in revolutions per minute, rpm, PjmapSengine∆t ) average of the product of Pmap and Sengine for a consecutive, averaging VOL. 44, NO. 9, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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period ∆t, ai ) model coefficient for specie i, and ∆t ) duration of the averaging period (seconds). The NO formation rate in the engine is assumed to be based on a simplified Zeldovich mechanism (28) d[NO] -69090 6 × 1016 exp [O2]e0.5[N2]e ) dt T T0.5

(

)

(2)

where (d[NO])/(dt) ) NO formation rate (mol/cm3-s), T ) gas temperature in the cylinder (K), [O2]e ) equilibrium concentration of O2 (mol/cm3), and [N2]e ) equilibrium concentration of N2 (mol/cm3). However, T, [O2]e, and [N2]e are not measured by PEMS or reported by OBD system, these are not observable. [O2]e and [N2]e are a function of the cylinder gas temperature and pressure. An assumption is made that the engine gas temperature is proportional to fuel use. The resultant functional form is (model 2 in Table 1) aNO

_∆t

mNO )

¯ mapS¯engine∆t)0.5 (P

exp

(

-bNO _∆t

PmapSengine

)

VSP ) v{a(1 + ε) + gr + gCR} +

j NO∆t ) average mass emission rate for NO for a where m consecutive averaging period ∆t, g/s, and aNO, bNO ) model coefficients. The “R” statistical package (29) was used to fit eqs 1 and 3 to PEMS data for each vehicle. Externally Observable Variables Model (EOVM). VSP is a measure of load on a vehicle and is defined as the power per unit mass to overcome inertial acceleration (power demand), rolling resistance, road grade, and aerodynamic drag (16)

(4)

where a ) vehicle acceleration (m/s2), A ) vehicle frontal area (m2), CD ) aerodynamic drag coefficient (dimensionless), CR ) rolling resistance coefficient (dimensionless, ∼ 0.0135), g ) acceleration of gravity (9.8 m/s2), m ) vehicle mass (in metric tons), r ) road grade, v ) vehicle speed (m/s), VSP ) Vehicle Specific Power (kw/ton), ε ) mass factor accounting for the rotational masses (∼ 0.1), and F ) ambient air density (1.207 kg/m3 at 20 °C). The aerodynamic drag term in eq 4 varies by vehicle. For example, the difference could be a factor of 2 between a compact car and a full size passenger car (18). However, the aerodynamic drag term is relatively small for urban driving compared to the other terms and does not significantly effect the estimates of VSP. For each vehicle, individual terms in eq 4 were used as basis functions in a linear regression model (model 12 in Table 1) _

(3)

( )

1 3 CDA Fv 2 m

_

_

_

_

mj∆t ) A0,j + Ajav∆t + Bjv∆t + Cjvr∆t + Djv3∆t + εj

(5)

j ∆t ) average of the product av, for a consecutive where av averaging, period of duration ∆t (km2/h2s), εj ) model residual for specie j, j ) specie (i.e., NO, HC, CO, CO2, and fuel use), j j∆t ) average of mass emission rate specie j for a consecutive, m averaging period of duration ∆t (g/s), vj∆t ) average of v for j ∆t a consecutive averaging period of duration ∆t (km/h), vr ) average of vr for a consecutive averaging period of duration ∆t (km/h), vj3∆t ) average of v3 for a consecutive averaging period of duration ∆t (km3/h3), and A0, j, A j, B j, C j, D j ) model coefficients for specie j. The model intercept A0,j represents the fuel use or emissions rate when the vehicle is idling.

TABLE 1. Comparison of Goodness-of-Fit for Alternative Modeling Approachese coefficient of determination (R2) model P¯ mapSengine

a

1

aNO _

(PmapSengine)

exp 0.5

(

-bNO _

PmapSengine

2a

3b 4 5 6 7 8 9 10 11c 12a 13a 14

type of inputsd

explanatory variables

MERi,(i)1 to 14) v,a,r VSP ¯ VSP v, v3,av,r ¯ v¯3, av, ¯ r¯ v, viaj(i,j)1,2,3) VSPt, VSPt-1,VSPt-2,VSPt-3 VSPt,εt ¯ vr ¯ ¯ v¯3, av, v, ¯ vr ¯ ¯ v¯3, av, v, v,a,r, Pmap,Sengine,CT,TP,IAT

)

averaging time (s) a

intercept included

NO

HC

CO

fuel

IOV

12/18

N

0.40

0.55

0.60

0.99

IOV EOV EOV EOV EOV EOV EOV EOV EOV EOV EOV EOV IOV and EOV

12/18a 1 1 1 5 1 5 1 1 1 12/18a 12/18a 1

N NA Y Y Y Y Y Y Y Y Y N Y

0.43 0.06 0.06 0.04 0.08 0.06 0.10 0.07 0.01 0.72 0.16 0.35 0.17

n/a 0.18 0.21 0.21 0.26 0.24 0.28 0.18 0.25 0.86 0.22 0.48 0.46

n/a 0.14 0.14 0.10 0.17 0.16 0.22 0.16 0.15 0.73 0.32 0.58 0.22

n/a 0.56 0.48 0.46 0.60 0.54 0.65 0.56 0.46 0.87 0.71 0.89 0.95

a Consecutive averages of both dependent and independent variables were used for modeling. The averaging time interval is 18 s for NO and is 12 s for the others. b MER - modal emission rates. In this model, measured values were compared with VSP-based modal emission rates, which are very similar to the MOVES model. The MOVES model uses VSP-based modes that are also stratified by speed. The modal modeling approach in MOVES is based in part on a comparison of modal modeling approaches evaluated by Frey et al. (5) that included the same VSP modal method as used here, along with a method based on binning by both VSP and speed. The results for estimates of cycle average emission rates are very similar for these two modal binning approaches. c This model is time series regression with serial errors (TSRSE). The second term (vt) in this model is further modeled as a 5th order autoregressive (AR) model. Higher order AR model did not significantly improve the explanatory power. d IOV - internal observable variables; EOV - external observable j ” in this variables. e Models were fit to PEMS data from a 2005 Chevrolet Cavalier using linear regression unless noted. “X table indicates that consecutive averages of both dependent and independent variables are used for modeling.

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Model Evaluation. The purpose of model evaluation is to (1) compare and select from among several alternative averaging times; (2) demonstrate the sensitivity of the model predictions to microscale features of driving cycles such as idle, acceleration, cruise, and deceleration; and (3) demonstrate the application of the models to predict fuel use and emissions. Both IOVM and EOVM were developed from modeling data sets for each vehicle. These models were used to predict emissions and fuel use for comparison to validation values. The model development and comparisons were done for various averaging times. In order to evaluate the sensitivity of the models to different driving cycles (intercycle variability) and to assess the ability of the models to make microscale predictions for a given cycle (intracycle variability), the models were used to predict fuel use and emissions for a selected set of standard and empirical driving cycles. These cycles included four chassis dynamometer cycles and four representative realworld cycles from field data collection. The four dynamometer cycles include Bags 1, 2, and 3 of the Federal Test Procedure (FTP), US06, New York City Cycle (NYCC), and California LA92. For the EOVMs, the model inputs are second-by-second speed profiles, from which acceleration can be inferred. Road grade was assumed to be zero. Average emissions for the various cycles were estimated using the EOVMs. Emissions from the FTP cycle were selected as the benchmark for cycle comparisons. Similar assessments for intercycle comparisons were done using MOBILE6. For the IOVMs, only real world driving cycles could be used for assessment because vehicle-specific engine data were available for these but not for the dynamometer cycles.

Results and Discussion Results are presented for (a) choice of averaging time; (b) selection of modeling approach; (c) model evaluation; (d) sensitivity of models to microscale events; and (e) comparison of fleet-average models and vehicle-specific models. Averaging Time. The effect of averaging time on model performance and model response to changes in driving conditions was evaluated. An increase in averaging time leads to an increase in R2, reduced influence of autocorrelation, and a decrease in residual variance. However, a long averaging time will smear out the effect on emissions of microscale events. Three multiples of the gas analyzer response time was selected for the averaging time. Hence, the averaging time for NO is 18 s, and for the other pollutants and fuel use it is 12 s (26). Modeling Approaches. Several modeling schemes were compared with respect to goodness-of-fit using data for a 2005 Chevrolet Cavalier with 2.2 L engine. As shown in Table 1, these include a VSP binning approach (model 3), linear and polynomial regression (models 4-10, 14), time series approaches such as moving averages (MA) and time series regression with serial errors (TSRSE) (30) (models 9 and 10, respectively), and physically based approaches (models 1 and 2). In nearly all cases, the best goodness-of-fit for fuel use or a given pollutant emission rate was produced by models 1, 2, 11, and 13. The lowest R2 among these four models for a given pollutant is typically higher than the R2 values for any other model (except model 14 applied to fuel use). The highest R2 values for NO, HC, and CO were obtained with the TSRSE model. However, because this model requires knowledge of prior model residuals, it cannot be used to make predictions. It illustrates, however, that there is autocorrelation in the residuals of model predictions. This motivates the use of methods that either account for or reduce the effect of autocorrelation. The attempt to account for autocorrelation

by considering lag effects in the explanatory variables, as embodied in model 10, produces a fairly poor goodnessof-fit for all pollutants and thus is not an effective approach. An alternative is to use consecutive averaging times in an attempt to “average out” autocorrelation effects. Models 1, 2, and 13 use consecutive averages and produce R2 values that are quite high for fuel use (and CO2 emissions) and imply that approximately 35 to 60% of the variability in the emissions of the other pollutants can be explained. Overall, for IOVMs, models 1 and 2 are the most practical basis for more extensive exploration; for EOVMs, the approach of model 12 is chosen instead of model 13 because (1) both have the same modeling structure except model 13 does not include an intercept and (2) excluding an intercept in a linear regression model provides a better goodness-of-fit but results in biased estimates of model coefficients. However, an intercept is not included in model 1 because ES and MAP cannot be zero if the engine is on, whereas vehicle speed can be zero. For model 2, an intercept is not necessary because nonlinear regression is used. Model Evaluation. IOVMs and EOVMs were developed for each of the three primary and seven secondary vehicles. Each model was fit to the modeling data set. The goodnessof-fit is assessed based on the slope and R2 of a parity plot of predicted versus actual average mass rates for each consecutive averaging time period. The slope is an indicator of model accuracy, while the R2 is an indicator of model precision. Furthermore, the models were applied to the validation data sets to make independent predictions of emissions and fuel use. The model predictions for the validation data were plotted versus the actual values and a slope, and R2 for the trend line was assessed. Ideally, the goodness-of-fit for the validation data set should be similar to that of the modeling data set. The results of goodness-of-fit for the IOVMs are given in Table 2. As expected, the slope in the modeling domain is unity for all vehicles. The slope in the validation domain varies depending on the robustness of the model in explaining variability in the validation data. In most cases, the slope in the validation domain is close to one, with average values among the 10 vehicles for each pollutant ranging from 1.00 to 1.05. In only four cases does the slope differ from unity by more than 20%, primarily for HC (in three cases) and CO (in one case). For each pollutant, the average of the slopes among all 10 vehicles does not differ significantly from unity. Thus, the IOVM approach is robust with respect to intervehicle differences. However, the portion of intravehicle variability explained by the models varies among the vehicles. On average, 40 to 99% of the variability can be explained for a given pollutant or for fuel use. However, there are isolated cases in which the R2 values are very low. For example, R2 values of less than 0.3 occur for 6 cases in Table 2, of which 4 are for CO, 1 is for HC, and 1 is for NO. The low R2 values for CO are likely to be associated with vehicles that have highly pronounced fuel enrichment characteristics, which in turn are associated with short episodes of high CO emissions. The data were not further stratified to attempt to isolate possible enrichment episodes because the average duration of fuel enrichment is less than 2 s, which is much shorter than the averaging time used in the models. Furthermore, enrichment events are sensitive to the response of the catalytic converter, whose performance (in terms of second-by-second control efficiency by pollutant) is mostly unobservable even when OBD data are available. The goodness-of-fit is excellent for fuel use for both modeling and validation data sets for all 10 vehicles, with an average R2 of 0.99 and an average slope of 1. Furthermore, there is little variability in either of these values among the 10 vehicles. VOL. 44, NO. 9, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 2. Goodness-of-Fit of Vehicle-Specific Internally-Observable Variable Models (IOVM) for NO, HC, CO, and Fuel Use for Ten Vehicles Using Time-Averaged Engine Speed and Manifold Absolute Pressurea NO modeling b

vehicles

2

Rm

2005 Chevrolet Cavalier 2.2 L 2005 Dodge Caravan 3.3 L 2005 Chevrolet Tahoe 5.3 L 1997 Honda Accord 2.2 L 1998 Plymouth Breeze 2.4 L 2004 Dodge Stratus 2.7 L 1997 Dodge Caravan 3.3 L 2000 Dodge Caravan 3.3 L 2002 Dodge Caravan 3.3 L 2000 Ford Crown Victoria 4.6 Lc average

0.43 0.10 0.50 0.75 0.75 0.75 0.92 0.84 0.72 0.86 0.66 0.10 0.92

range a

HC

validation

Slm

2

Rv

1 1 1 1 1 1 1 1 1 1 1

0.43 0.10 0.50 0.75 0.74 0.75 0.90 0.84 0.68 0.84 0.65 0.10 0.90

1

modeling

Slv

2

Rm

1.02 1.16e 1.02 1.18e 0.99 1.19e 1.01 1.00 1.00 0.96e 1.05 0.99 1.19

0.54 0.67 0.59 0.70 0.44 0.70 0.88 0.06 0.74 0.82 0.60 0.060 0.88

CO validation

Slm

2

Rv

1 1 1 1 1 1 1 1 1 1 1

0.56 0.67 0.59 0.69 0.43 0.69 0.88 0.10 0.81 0.83 0.62 0.10 0.88

1

modeling

Slv

2

Rm

0.99 1.04 1.20e 0.78e 1.00 0.78e 1.05 1.07 1.49e 1.01 1.04 0.78 1.49

0.61 0.03 0.60 0.62 0.48 0.62 0.67 0.05 0.26 0.12 0.41 0.03 0.67

Fuel

validation

Slm

2

Rv

1 1 1 1 1 1 1 1 1 1 1

0.59 0.03 0.60 0.61 0.49 0.61 0.67 0.05 0.29 0.12 0.41 0.03 0.77

1

modeling

validation

Slv

2

Rm

Slm

R2v

Slv

1.05 0.69e 1.04 1.03 1.02 1.03 1.00 1.09e 1.04 1.08 1.01 0.69 1.09

>0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99

1 1 1 1 1 1 1 1 1 1 1

>0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99

1.00 1.01 1.00 1.00 0.99 0.99 1.00 1.00 1.00 1.00 1

>0.99

1

>0.99 1

Unless otherwise noted, the functional forms of the models (model 2 for NO, and model 1 for HC, CO, and Fuel) are aNO

_∆t

NO:mNO )

_∆t

(

exp 0.5

(PmapSengine)

-bNO _∆t

PmapSengine

)

¯∆t HC, CO, Fuel:m ) aiP¯ mapS¯ engine∆t i

where aNO, bNO, and ai are fitted constants; m¯ i and m¯ NO are average mass rate, g/s Pmap is manifold absolute pressure, kPa; Sengine is engine speed, rpm; P¯ mapSengine is average of the product of Pmap and Sengine for a consecutive averaging period; and ∆t is the duration for the averaging period (seconds). b Year, manufacturer, model, and engine size are indicated. c For this vehicle, Pmap was not available from the on-board diagnostics (OBD) link. However, intake mass air flow, mIAF (g/s) is reported by the OBD link. Hence, the model used here is aNO

_∆t

NO:mNO )

_∆t

( )

exp

(mIAF)0.5

-bNO _∆t

mIAF

¯∆t HC, CO, Fuel:m ¯ IAF∆t ) a im i

The averaging time for NO is 18 s and 12 s for other pollutants and fuel use. R2 and slope are based upon the model of actual measurements vs model predicting values. R2m and Slm -R2 and slope using data from modeling databases; R2v and Slv - R2 and slope using data from validation databases. e The numbers in italics indicate that the slope is significantly different from unity.

The goodness-of-fit for the validation data is very similar to that for the modeling data, indicating consistent performance of the models. MAP for the Ford vehicle was not reported by the OBD system; however, air intake flow rate was reported. Thus, for this vehicle only, intake flow rate was used as an IOV. The R2 for fuel use and CO2 emissions is greater than 0.99 and ranges from 0.10 to 0.86 for other pollutants. The goodness-of-fit and model evaluation results for EOVMs are given in Table 3. For a given vehicle and pollutant the R2 values are typically lower for the EOVM than for the IOVM. The average EOVM R2 values for a given pollutant are 0.17 to 0.59. Compared to IOVMs, the average decrease in the R2 values for EOVMs is -0.36, -0.37, -0.24, and -0.40 for NO, HC, and CO emissions and fuel use, respectively. The R2 values for EOVMs are similar for the validation and calibration data. The slope of the validation cases is between 0.9 to 1.1 for 30 of the 40 pollutant/fuel and vehicle combinations. The average of the slopes does not significantly differ from unity. Both IOVMs and EOVMs were developed based on tailpipe emissions. The tailpipe emissions are also influenced by the catalytic conversion efficiency (CCE). However, this influence cannot be quantified because needed data such as engine out emissions and exhaust temperature are not observable with OBD and PEMS data. One reason that R2 for fuel use is better than for NO, CO, and HC is that the latter three are significantly influenced by CCE, whereas the former is not. 3598

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Sensitivity of Models to Microscale Events. The sensitivity of cycle average gram per mile emission rates to eight selected driving cycles, including five standardized and four empirical cycles, was evaluated for both the EOVMs and MOBILE6. Relative trends in these normalized emission rates versus average cycle speeds were compared between the EOVMs and MOBILE6. In the EOVMs, second-by-second speed profiles with corresponding average speeds are used as input. For MOBILE6, average speed is specified as an input. For CO, HC, and NO, the qualitative trends for the EOVM and MOBILE6 were similar for cycles with average speeds lower than that of the FTP: typically, the emission rate increases as the average cycle speed decreases. The EOVMs predicted larger increases in emissions rates as cycle average speed was reduced. For example, for CO, the emission rate at an average speed of 7 mph is a factor of 1.4 greater than for the FTP based on MOBILE6 and a factor of 2.1 greater based on the average of the EOVMs for the 10 vehicles. At average speeds higher than that of the FTP up to 65 mph, MOBILE6 predicts an increase in average emission rate for NOx and CO and a decrease for HC. On average over the 10 vehicles, the EOVMs predict a decrease in average emission rate for all three of these pollutants, but there is substantial intervehicle variability in which some vehicles have higher average emission rates at the higher speeds. For CO2, MOBILE6 uses a constant emission rate and therefore a comparison was not made. The EOVMs predict that the CO2 emission rate decreases significantly as average cycle speed increases up

TABLE 3. Goodness-of-Fit of Vehicle-Specific Externally-Observable Variable Models (EOVM) for NO, HC, CO, and Fuel Use for Ten Vehicles Using Time-Averaged Speed, Acceleration, and Road Gradea NO modeling vehicle

2

Rm

Slm

2005 Chevrolet Cavalier2.2 L 0.16 2005 Dodge Caravan 3.3 L 0.05 2005 Chevrolet Tahoe 5.3 L 0.24 1997 Honda Accord 2.2 L 0.11 1998 Plymouth Breeze 2.4 L 0.56 2004 Dodge Stratus 2.7 L 0.44 1997 Dodge Caravan 3.3 L 0.31 2000 Dodge Caravan 3.3 L 0.52 2002 Dodge Caravan 3.3 L 0.36 2000 Ford Crown Victoria 4.6 L 0.27 average 0.30 0.05 range 0.56

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

a

HC validation 2

Rv

0.16 0.05 0.23 0.15 0.55 0.41 0.35 0.53 0.36 0.20 0.30 0.05 1.00 0.55

modeling

Slv

2

Rm

Slm

0.99 1.04 0.98 1.26b 0.98 1.00 0.88b 1.01 0.93b 1.16b 1.02 0.36 1.16

0.22 0.32 0.20 0.03 0.29 0.46 0.21 0.02 0.28 0.24 0.23 0.02 0.46

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

CO validation 2

Rv

0.20 0.33 0.19 0.08 0.24 0.47 0.25 0.03 0.29 0.16 0.22 0.03 1.00 0.47

modeling

Slv

2

Rm

0.94b 1.01 0.98 1.09b 0.97b 1.02 0.91b 1.09b 0.85b 0.87b 0.97 0.85 1.09

0.32 0.02 0.24 0.06 0.33 0.41 0.14 0.04 0.14 0.02 0.17 0.02 0.41

Fuel validation

Slm

2

Rv

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1

0.31 0.02 0.24 0.07 0.32 0.42 0.12 0.04 0.13 0.03 0.17 0.02 0.42

1

modeling

validation

Slv

2

Rm

Slm

R2v

Slv

1.00 0.94b 1.00 1.56b 0.98 1.15b 0.90b 1.19b 0.97b 1.25b 1.09 0.94 1.25

0.71 0.77 0.62 0.17 0.79 0.46 0.43 0.79 0.71 0.46 0.59 0.43 0.79

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1

0.70 0.77 0.61 0.26 0.80 0.42 0.47 0.80 0.74 0.42 0.60 0.35 0.80

0.99 1.00 1.00 1.45b 1.00 0.97b 0.99 1.01 1.00 0.97b 1.04 0.97 1.45

1

The model form (model 12) is _

_

_

_

_

mj∆t ) A0,j + Ajav∆t + Bjv∆t + Cjvr∆t + Djv3∆t + εj The averaging time period for NO is 18 s and 12 s for the others with nonzero corresponding average speed. R2 and slope are based upon the model of actual measurements vs model predicting values. R2m and Slm -R2 and slope using data from modeling databases; R2v and Slv - R2 and slope using data from validation databases. b The numbers in italics indicate that the slope is significantly different from unity.

to approximately 50 mph. At speeds higher than approximately 60 to 65 mph, the CO2 emission rate increases with average speed. MOBILE6 does not explicitly account for microscale variation in acceleration. However, since both microscale acceleration and speed are explicit inputs for EOVMs, EOVMs are sensitive to microscale events in vehicle dynamics. For example, as shown in Figure 1, a peak in the speed profile corresponds to a peak in emissions. Although a longer averaging time leads to lower spatial resolution, the NOx EOVM with 18 s averaging time is still able to capture episodic emissions events. A shorter averaging time produces a larger shorter duration peak in emissions. Fleet-Average versus Vehicle-Specific Models. Emissions hotspots at specific locations identified for one vehicle were not hotspots for another, and the trend in variation of emissions over distance is not the same for each vehicle (31). Thus, it is worthwhile to develop vehicle-specific models for a variety of applications, such as near roadside human exposure assessment. Vehicle-specific models were compared to a “fleet” model to assess the benefits of the former. Data collected from all vehicles for this study were combined to form a “fleet” data set from which fleet-based models similar to model 12 of Table 1 were fit. Emission rates estimated by the fleet models were compared to the weighted averages of emissions predicted by vehicle-specific models for selected driving cycles and for the same set of vehicles. The weighting was based upon the amount of data for individual vehicles used to develop the fleet model. Comparing the EOV fleet model with the weighted average of vehicle-specific models, the differences in average NO, HC, and CO emission rates ranged from -37 to 83% depending on the pollutant and driving cycle. For fuel use, the differences were relatively small, ranging from -5 to 7%. These differences indicate that there is substantial intervehicle variability in emissions that is averaged out in the fleet model. For a large flow of vehicles, this is appropriate. However, in order to capture episodic emissions at high spatial and temporal resolution, vehiclespecific models may be useful. The details are given in the SI.

FIGURE 1. Microscale prediction of NO and HC emissions using externally observable variables models (EOVMs) (model 12) for a 2005 Chevrolet Cavalier with 2.2 L engine. In general, IOVMs have higher explanatory power than EOVMs. When IOVs are available, IOVMs are preferred. However, EOVMs may have more practical value for traffic management such as arterial signalization and level of service determination (32) and simulation since IOVs usually are not available or not used for emission estimation. Over the VOL. 44, NO. 9, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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entire trip, total fuel use and emissions estimated by IOVMs and EOVMs are comparable. For example, for HC and fuel use, the relative difference between IOVMs and EOVMs is approximately 10% for all three primary vehicles over all trips. For NO and CO, depending on averaging time and vehicle, the difference varied from 9 to 65%. IOVMs predict more fuel use and emissions than EOVMs, except for NO.

Supporting Information Available Texts, figures, and tables pertinent to this paper. These materials include (1) summary of data collection activities; (2) exploratory analysis of PEMS data; (3) documentation of model parameters; (4) comparison of IOVMs and EOVMs; (5) evaluation of application of an EOVM model for microscale prediction of emissions; (6) evaluation of Box-Cox transformation; (7) identification and comparison of statistical summaries for alternative average time intervals of activities and emissions; (8) time series regression with serial errors; (9) evaluation of vehicle-specific models for multiple averaging times, vehicles, driving cycles, and comparisons to MOBILE6; (10) assessment of intervehicle variability in model parameters and predictions; (11) assessment of “Open loop” fuel enrichment; (12) relationship between fuel use and CO2 emissions; (13) VSP-based modal approach for emissions modeling, and (14) minimum data requirement. This material is available free of charge via the Internet at http:// pubs.acs.org.

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Acknowledgments This material is based upon research supported by the National Science Foundation under Grant No. CMS-0230506. Any opinions, findings, conclusions, or recommendations expressed in this document are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Drs. Bibhuti Bhattacharyya, David Dickey, and Jerome Sacks provided advice on statistical procedures.

Literature Cited (1) National Research Council. Modeling Mobile Source Emissions; National Academy Press: Washington, DC, 2000. (2) Federal Highway Administration (FHWA). CORSIM User Guide; U.S. Department of Transportation: Washington, DC, 1996. (3) Transport Simulation Systems. AIMSUN Version 4.1 User Manual; 2002. (4) Cloke, J.; Boulter, P.; Davies, G. P.; Hickman, A. J.; Layeld, R. E.; McCrae, I. S.; Nelson, P. M. Traffic management and air quality research programme. TRL Report 327; 1998; p 70. (5) Frey, H. C.; Unal, A.; Chen, J.; Li, S.; Xuan, C. Methodology for Developing Modal Emission Rates for EPA’s Multi-scale Motor Vehicle & Equipment Emission System; EPA420-R-02-027; Prepared by North Carolina State University for Office of Transportation and Air Quality, U.S. Environmental Protection Agency: Ann Arbor, MI, 2002. (6) Colberga, C. A.; Tonab, B.; Stahelb, W. A.; Meierc, M.; Staehelina, J. Comparison of a road traffic emission model (HBEFA) with emissions derived from measurements in the Gubrist road tunnel, Switzerland. Atmos. Environ. 2005, 39, 4703–4714. (7) Andre´, M.; Keller, M.; Sjo¨din, A.; Gadrat, M.; Crae, I. C.; Dilara, P. the ARTEMIS European Tools for Estimating the Transport Pollutant Emissions, the 18th Annual International Emission Inventory Conference, “Comprehensive Inventories -Leveraging Technology and Resources”, Baltimore, Maryland,April 14-17, 2009. (8) Silva, C. M.; Farias, T. L.; Frey, H. C.; Rouphail, N. M. Evaluation of numerical models for simulation of real-world hotstabilized fuel consumption and emissions of gasoline light-

3600

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 44, NO. 9, 2010

(19)

(20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31)

(32)

duty vehicles. Trans. Res. Part D: Transp. Environ. 2006, 11 (5), 377–385. Halati, A.; Lieu, H.; Walker, H. CORSIM-corridor traffic simulation model, Proceedings of the Traffic Congestion and Traffic Safety in the 21st century: Challenges, Innovations, and Opportunities, Chicago, IL,June 8-11, 1997. U.S. Environmental Protection Agency. A Roadmap to MOVES 2004; EPA420-S-05-002; Office of Transportation and Air Quality, U.S. Environmental Protection Agency: Ann Arbor, MI, 2005. Sturm, P. J.; Almbauer, R. A.; Sudy, C.; Pucher, K. Application of computational methods for the determination of traffic emissions. J. Air Waste Manage. Assoc. 1997, 47 (11), 1204–1210. West, B.; McGill, R.; Hodgson, J. W.; Sluder, S. Development of data-based, light-duty modal emissions and fuel consumption models; Paper 972910; Society of Automotive Engineers: Warrendale, PA, 1997. Joumard, R.; Jost, P.; Hickman, J.; Hassel, D. Hot passenger car emissions modeling as a function of instantaneous speed and acceleration. Sci. Total Environ. 1995, 169 (1-3), 167–174. Ahn, K.; Hesham, R.; Trani, A.; Aerde, M. V. Estimating vehicle fuel consumption and emissions based on instantaneous speed and acceleration level. Transp. Eng. 2002, 128 (2), 182–190. Thompson, G. J.; Atkinson, C. M.; Clark, N. N.; Long, T. W.; Hansevack, E. Neural network modeling of the emissions and performance of a heavy-duty diesel engine. J. Aut. 2000, 214 (2), 111–126. Jime´nez-Palacios, J. L. Ph.D. Dissertation, Massachusetts Institute of Technology: Cambridge, MA, 1999. Barth, M.; An, F.; Norbeck, J.; Ross, M. Modal emissions modeling: a physical approach. Transp. Res. Rec. 1996, 1520, 81–88. Nam, E. K. Proof of Concept Investigation for the Physical Estimation Rate Estimator (PERE) for MOVES; EPA 420-R-03005; Prepared by Ford Research and Advanced Engineering for Office of Transportation and Air Quality, U.S. Environmental Protection Agency: Ann Arbor, MI, 2003. Frey, H. C.; Zhang, K.; Rouphail, N. M. Fuel use and emissions comparisons for alternative routes, vehicles, road grade and time of day using in-use measurements. Environ. Sci. Technol. 2008, 42 (7), 2483–2489. Durbin, J. Distribution theory for tests based on the sample distribution function; SIAM: 1973. Hastie, T. J.; Tibshirani, R. J. Generalized Additive Models; Chapman and Hall: London, 1990. Simonoff, J. S. Smoothing Methods in Statistics; Springer-Verlag: New York, 1996. Bowman, A. W.; Azzalini, A. Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-plus Illustrations; Oxford: New York, 1997. Schimek, M. G. Smoothing and Regression; John Wiley and Sons: New York, 2000. Bates, D. M.; Watts, D. G. Nonlinear Regression Analysis and Its Applications; John Wiley & Sons: New York, 1988. Zhang, K.; Frey, H. C. Evaluation of response time of a portable system for in-use vehicle tailpipe emissions measurement. Environ. Sci. Technol. 2008, 42 (1), 221–227. Arieli, R.; Van Liew, H. D. Corrections for the response time and delay of mass spectrometers. J. Appl. Physiol. 1981, 51 (6), 1417– 1422. Heywood, J. B. Internal Combustion Engine Fundamentals; McGraw-Hill: New York, 1988. The R Foundation for Statistical Computing. R; 2005. http:// www.r-project.org (accessed December 16, 2005). Shumway, R. H.; Stoffer, D. S. Time Series Analysis and Its Applications; Springer-Verlag: New York, 2000. Frey, H. C.; Zhang, K. Spatial and Temporal Analysis of RealWorld Empirical Fuel Use and Emissions, Proceedings of the 100th Annual Exhibition & Conference of the Air & Waste Management Association, Pittsburgh, PA, June 2007. Unal, A.; Rouphail, N.; Frey, H. C. Effect of Arterial Signalization and Level of Service on Measured Vehicle Emissions. Transp. Res. Rec. 2003, 1842, 47–56.

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