Regression-Based Oxides of Nitrogen Predictors for Three Diesel Engine Technologies

Regression-Based Oxides of Nitrogen Predictors for ThreeDiesel Engine Technologies

Xiaohan Chen and Natalia A. SchmidLane Department of Computer Science and Electrical Engineering, West Virginia University,Morgantown, WV

Lijuan Wang and Nigel N. ClarkDepartment of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, WV

ABSTRACTModels of diesel engine emissions such as oxides of nitro-gen (NOx) are valuable when they can predict instanta-neous values because they can be incorporated into wholevehicle models, support inventory predictions, and assistin developing superior engine and aftertreatment controlstrategies. Recent model-year diesel engines using multi-ple injection strategies, exhaust gas recirculation, andvariable geometry turbocharging may have more tran-sient sensitivity and demand more sophisticated model-ing than for legacy engines. Emissions data from 1992,1999, and 2004 model-year U.S. truck engines were mod-eled separately using a linear approach (with transientterms) and multivariate adaptive regression splines(MARS), an adaptive piece-wise regression approach thathas limited prior use for emissions prediction. Six inputvariables based on torque, speed, power, and their deriv-atives were used for MARS. Emissions time delay wasconsidered for both models. Manifold air temperature(MAT) and manifold air pressure (MAP) were further used

in NOx modeling to build a plug-in model. The predictiveperformance for instantaneous NOx on part of the certi-fication transient test procedure (Federal Test Procedure[FTP]) of the 2004 engine MARS was lower (R2 � 0.949)than the performance for the 1992 (R2 � 0.981) and 1999(R2 � 0.988) engines. Linear regression performed simi-larly for the 1992 and 1999 engines but performed poorly(R2 � 0.896) for the 2004 engine. The MARS performancevaried substantially when data from different cycles wereused. Overall, the MAP and MAT plug-in model trained byMARS was the best, but the performance differences be-tween LR and MARS were not substantial.

INTRODUCTIONDiesel engines are the most efficient internal combustionengines,1 in part because they operate in an unthrottledmode under lean burn conditions. However, inhomoge-neous compression ignition combustion produces highconcentrations of oxides of nitrogen (NOx), and the un-throttled operation makes NOx abatement using conven-tional aftertreatment impossible. NOx is implicated in theproduction of low-level ozone, which is in turn impli-cated in human health effects. Quantifying NOx fromdiesel engines is a central environmental objective for tworeasons. First, NOx production models would prove valu-able in preparing accurate emissions source terms for in-ventories and atmospheric quality modeling, particularlywhen incorporated into a whole vehicle model such asthe Powertrain Advanced Simulation Toolkit (PSAT)2,3 orthe Advanced Vehicle Simulator (ADVISOR).4–6 Second,control of advanced aftertreatment for NOx productionand verification of NOx sensor health relies in part onmodels that predict the engine-out NOx in real time.

The formation of NOx in the cylinders of diesel en-gines has been described in a large body of literature (e.g.,see refs 7–10). Fundamental combustion models with in-cylinder spatial and temporal variability are computation-ally intensive and differ from the models presented in thispaper, which rely on direct engine NOx measurements. Inthe past 2 decades, several models were proposed to linkengine and environmental physical processes with mea-sured NOx values. Some models are based on chemicalrate and equilibrium calculations under constraint of thein-cylinder physics, fluid motion, and composition. Theother models are “black-box” models, or a combination of

IMPLICATIONSHistorically engine emissions were viewed in cycle-aver-aged, brake-specific terms, and the adoption of the not-to-exceed (NTE) zone has only limited emissions in terms of30-sec (or larger interval) time averages. However, instan-taneous emissions are valuable for predictive inventorymodels, such as the emerging U.S. Environmental Protec-tion Agency Motor Vehicle Emissions Simulator (MOVES),and are essential for accurate local hotspot and conformityanalyses when considering transportation facility changes.Also, accurate engine models are needed for incorporationinto whole vehicle models, such as the Powertrain Ad-vanced Simulation Toolkit (PSAT), a whole vehicle modelingtool from Argonne National Laboratory, to predict vehicletailpipe emissions. A third application of an accurate modelis in developing superior controls for emissions aftertreat-ment; in particular, selective catalytic reduction. The LR andMARS models explored in this paper reveal that the emis-sions from a late model-year on-road diesel engines aremore difficult to predict than from earlier engines, but thatsufficiently accurate prediction of instantaneous NOx emis-sions is possible to satisfy the needs discussed above. Thispaper also supports continued use of MARS in emissionsmodeling.

TECHNICAL PAPER ISSN:1047-3289 J. Air & Waste Manage. Assoc. 60:72–90DOI:10.3155/1047-3289.60.1.72Copyright 2010 Air & Waste Management Association

72 Journal of the Air & Waste Management Association Volume 60 January 2010

both. Modeling using physical and chemical principlesrequires precise knowledge of reaction rates for manycompounds and detailed knowledge of the turbulent fluidbehavior. These models often are too complex to be usefulto predict emissions in real time.

Linear and nonlinear methods have been extensivelystudied as a means to predict diesel engine emissions. Thelinear model is simple and easy to train using collecteddata. However, it may fail as the number of inputs in-creases. For example, diesel engine NOx emissions havebeen successfully related to engine power (POW) outputwithout separate reference to torque and speed,11,12 butthe data used in these papers were for engines withoutexhaust gas recirculation (EGR) and represented technol-ogy that produced approximately 5 g/bhp � hr (6.7g/kW � hr) of NOx. NOx production from these engineswas influenced primarily by injected fuel quantity andinjection timing. The fuel quantity was dictated mainlyby the engine load, and the manufacturer would config-ure timing to match the 5-g/bph � hr emissions standardobjective over much of the operation envelope. Late mod-el-year U.S. on-road diesel engines that use multiple in-jections, sophisticated air management, and cooled EGRare not readily modeled using a simple linear approach. In

particular, the EGR rate control adds transient depen-dence of NOx not encountered in earlier engines. A non-linear model provides a more flexible way to model thistype of engine. For example, neural networks (NNs) havebeen applied in the past as a powerful tool to predict NOx

in engines and boilers and have even included fuel prop-erty effects as inputs.7,13–17

The goal of this work is to compare performance oflinear and nonlinear regression predictors in terms oftheir ability to predict NOx as a function of two funda-mental input parameters. Two input parameters are essen-tial for defining engine operation and are selected fromthe set of torque, speed, and power. Note that these twoinput parameters (or a predictive surrogate, such as fuelrate) must always be known, regardless of engine type, todefine the engine operation. Linear regression (LR) mod-els represent the output of function, NOx, as a linearcombination of input parameters. The nonlinear regres-sion model is based on the multivariate adaptive regres-sion splines (MARS) technique.18 MARS is an adaptivepiece-wise regression approach that builds a responsefunction in terms of nonlinear component functions andtheir products. MARS is completely data-driven in select-ing the model order; that is, in solving the problem ofoverfitting and underfitting. The main disadvantage ofMARS is its limiting ability to extrapolate results beyondthe range of the trained model. MARS has been used fordiverse applications in forecasting and data mining inrecent years.19–21 The first two authors have previouslyengaged in applying MARS to on-road truck emissionsdata.22 Additional information on the use of MARS topredict emissions is presented by Krishnamurthy.23 Thelast two authors have recently examined modelingthrough LR.24 In the study presented here, NOx predic-tion has been examined for engine dynamometer dataand would be useful for incorporation into inventorymodels, or for applications in engine control in whichcostly NOx sensors are not an option.

Three diesel engine emission datasets were analyzedseparately using MARS and a LR model. No attempt wasmade to model emissions from one engine on the basis ofemissions from another. The emission datasets were avail-able from engines that were operated in a fully transient

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Figure 1. Hockey stick spline basis function and its image.

Table 1. Summary of available data.

Year Cycle Sample Size SPD (rpm) �mean�TQE (lb � ft)

�mean�MAP (kPa(g))

�mean� MAT (�C) �mean� NOx (g/sec) �mean�

1992 FTP 1199 583–1949 �1105� �278–1331 �245� 0–137 �22� 27–55 �32� 0–0.340 �0.0940�TRANS 687 577–1811 �1142� �647–1197 �111� 0–130 �10� 28–55 �29� 0–0.323 �0.0663�CRUISE 2083 583–1833 �1295� �579–1310 �351� 0–125 �21� 28–40 �32� 0–0.709 �0.2363�HHDDTS 759 581–1809 �1288� �486–1353 �551� 0–138 �36� 29–58 �33� 0–0.558 �0.2816�CREEP 1032 576–1776 �722� �736–539 �7.6� 0–8 �0.234� 27–57 �28� 0–0.203 �0.0260�

1999 FTP 1199 668–1937 �1165� �287–1285 �251� 0–182 �35� 27–43 �31� 0–0.353 �0.0777�2004 FTP 1199 650–2259 �1287� �338–1361 �206� 0–209 �51� 27–49 �32� 0–0.199 �0.0518�

TRANS 687 645–2097 �1328� �605–1284 �135� 0–190 �40� 25–40 �30� 0–0.176 �0.0383�CRUISE 2086 647–2121 �1506� �599–1183 �299� 0–199 �75� 24–42 �33� 0–0.213 �0.0607�HHDDTS 759 645–2097 �1497� �549–1352 �497� 0–218 �108� 28–44 �36� 0–0.213 �0.0784�CREEP 1031 644–2091 �842� �620–816 �17� 0–115 �2.5� 26–40 �27� 0–0.146 �0.0166�

Notes: NO � nitric oxide.

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Volume 60 January 2010 Journal of the Air & Waste Management Association 73

test cell with a full-scale dilution tunnel and research-grade analyzers. NOx was measured using the chemilumi-nescent principle and was expressed as mass of NO2. Thefirst engine was a 1992 model-year Detroit Diesel Corpo-ration (DDC) series 60 12.7-L engine, rated at 365 hp. Thesecond engine was a 1999 model-year Cummins ISMheavy-duty on-road engine with a wastegated turbo-charger and electronically managed injection, but with arelatively simple control philosophy. The third enginewas a 2004 model-year Cummins ISM heavy-duty on-roadengine incorporating cooled EGR and a variable geometryturbocharger. Both Cummins engines were rated at 370hp and all three engines were electronically managed.Federal Test Procedure (FTP) transient data were availablefor all three engines. For the 1992 and 2004 engines, fourmodes of engine operation were recorded: creep, tran-sient, cruise, and high-speed cruise. These four modesdefined speed and torque of the engine as a function oftime and were recently developed25,26 for the Coordinat-ing Research Council Advanced Collaborative EmissionsStudy (ACES) program on the basis of a previously devel-oped truck chassis test cycle.27,28 FTP transient data fromthe 1992 and 2004 engines were also used. Engine speed(SPD) and torque (TQE) were recorded for all engines.Manifold air pressure (MAP) and manifold air temperature(MAT) were accessible in experiments as two additionalinput parameters using broadcast information from theengine’s controller.

In this paper, NOx forecasting was performed usingthe FTP data. Linear and nonlinear models for each en-gine (1992, 1999, and 2004) were trained and validatedseparately. NOx was first modeled using SPD and TQE.Because MAP and MAT measurements were available,they were then added to input parameters to increase theprecision of the models. MAP and MAT are closely tied toTQE at a specified SPD during steady-state operation,whereas MAP typically lags TQE during transients wherePOW is rising. The authors then explored the scenario inwhich MAP and MAT were predicted from the SPD andTQE data and were used as input parameters together withthe SPD and TQE (plug-in model). For the 1992 and 2004engines, both models for prediction of NOx trained usingthe FTP data were further tested with the data from thefour ACES modes.

The choice of the input parameters can be justified asfollows. Most heavy-duty vehicles have manual transmis-sions, and so the SPD during active vehicle operation isdetermined by the vehicle speed and the selected gear,except during idle and shifting periods when the trans-mission is in neutral. The TQE is then determined by thedriver’s pedal position and the history of the pedal posi-tion. In this way torque and speed can be considered asprimary independent variables. MAP and MAT are vari-ables that depend largely on SPD and TQE, and theirhistory, and to a lesser extent on altitude and weatherconditions. Although MAP and MAT contain some inde-pendent information, they are also strongly dependenton the primary variables. It is true that a pair of variablessuch as SPD and MAP may reasonably define engine op-erating condition, but the authors prefer to consider MAPas dependent on TQE history (for a given SPD).

This paper first describes the LR model and the MARStechnique. The MARS models were developed using SPDand TQE; the plug-in models using SPD, TQE, and theestimated values of MAP and MAT. In this paper theplug-in model is defined as a regression model with a fewparameters in the model replaced by their estimated val-ues. The numerical results obtained using MARS werecompared against the results of the LR model. These twomodels were further trained on the FTP data and testedusing the data from the other four modes.

REGRESSION METHODSIn this work, the modeling problem is stated as a multi-variate regression problem. A general model can be ex-pressed as

Y � f�X�, (1)

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Figure 2. Cross-correlation results between (a) SPD, (b) TQE, and(c) POW and the NOx emissions for the 2004 model-year engine.The squares indicate the highest correlation coefficients.

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74 Journal of the Air & Waste Management Association Volume 60 January 2010

where Y is the dependent variable, in this case NOx, and“hat” stands for an approximation to the output Y, X �{X1, X2,…, Xp} is a vector of predictive variables, such astorque and speed.

LR MethodAs a baseline for performance analysis, the authors con-sidered a LR method that models emissions as a linearcombination of POW, TQE, SPD, and their time deriva-tives. The LR model is described by

fL�x� � �0 � �i � 1

p

�ixi, (2)

where xi, i � 1,…,p, represents POW, SPD, TQE, and theirderivatives and �i are the coefficients estimated by mini-mizing the mean squared error between actual and pre-dicted values in a time sequence. For N observed values{xj j � 1,…, N} and {yj j � 1,…, N}, when N � p � 1, thefollowing matrix is formed:

�y1

y2···yN

� � �1 x11 · · · xp1

1 x12 · · · xp2······

···1 x1N · · · xpN

� ��0

�1···�p

� (3)

or in matrix form, Y � X�. In matrix form the estimatedparameters are then given by � � (XTX)�1XTY. Simple

linear models have been used previously to describe emis-sions from diesel engines that used less sophisticated con-trols than the present-day U.S. engines.

MARSThe MARS model used a special set of spline functionscalled “hockey stick” basis functions.18 These two-sidedtruncated functions (see Figure 1 for illustration) mappedvariable X to a new variable X* by using eq 4 (for solidline) or by using eq 5 (for dashed line).

X* � �X � t� � � �X � t X � t0 X � t , (4)

X* � �t � X� � � �t � X X � t0 X � t, (5)

where t is the knot of the basis function. In Figure 1, t isset to 0.5.

Suppose that for each input variable Xi, i � 1,2,…,p,there are N observed values {xij� j � 1,…,N}. A pair of basisfunctions is knotted at each of the observed values andlinked as a reflected pair. These 2Np basis functions forman initial collection of basis functions C,

C � �Xi � t� � , �t � Xi� � �t � xi1, . . . , xiN;

i � 1, . . . , p}. (6)

MARS uses the combination of basis functions to approx-imate model 1. Let fM( � ) be a MARS approximation tomodel 1; that is,

Table 2. Average performance of NOx modeling using MARS and LR in the model with and without plug-ins.

Engine Model Methods

Train Test

R 2 RMSE RTD R 2 RMSE RTD

1992 FTP LR 1 sec 0.967 0.0188 0 0.959 0.0191 0.04295 sec 0.980 0.0141 0.977 0.0146

LR plug-in 1 sec 0.967 0.0188 0 0.959 0.0191 0.04135 sec 0.979 0.0142 0.977 0.0147

MARS 1 sec 0.979 0.0149 0 0.966 0.0161 0.02325 sec 0.990 0.0099 0.981 0.0115

MARS plug-in 1 sec 0.982 0.0141 0.001 0.969 0.0154 0.02845 sec 0.991 0.0092 0.984 0.0109

1999 FTP LR 1 sec 0.985 0.0121 0 0.977 0.0133 0.03835 sec 0.991 0.0089 0.987 0.0104

LR plug-in 1 sec 0.985 0.0122 0 0.976 0.0134 0.03855 sec 0.991 0.0090 0.987 0.0104

MARS 1 sec 0.990 0.0099 0 0.978 0.0119 0.03745 sec 0.995 0.0068 0.988 0.0090

MARS plug-in 1 sec 0.990 0.0098 0.006 0.977 0.0130 0.03695 sec 0.996 0.0064 0.990 0.0092

2004 FTP LR 1 sec 0.900 0.0183 0 0.856 0.0187 0.02145 sec 0.928 0.0147 0.896 0.0150

LR plug-in 1 sec 0.900 0.0182 0 0.856 0.0186 0.02685 sec 0.929 0.0146 0.897 0.0149

MARS 1 sec 0.937 0.0144 0 0.896 0.0157 0.02835 sec 0.965 0.0102 0.940 0.0113

MARS plug-in 1 sec 0.940 0.0135 0.015 0.904 0.0153 0.02865 sec 0.969 0.0098 0.949 0.0108

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Volume 60 January 2010 Journal of the Air & Waste Management Association 75

fM�x)��0� �m�1

M

�mBm(x), (7)

where Bm(x) is the mth basis function, which is either afunction in the collection C or a product of two or moresuch functions. Given a choice for Bm(x), the coefficients{�m�m � 0,…,M} are estimated by minimizing the sum ofsquared residuals. Basis functions can be highly nonlinearfunctions of X, but the mapping Y � fM( � ) is a linearfunction of the basis functions. By analogy with fM( � ), Yis an approximation to the output Y. The advantage ofMARS is in its ability estimate in an adaptive fashion thelocation and number of basis functions to guarantee localand global fit of approximation function fM ( � ) into a setof output measurements. The output points that undergoabrupt changes in their values are described by manyclosely spaced basis functions to achieve good fit. Con-versely, if the output function is smooth and slowly varieswithin some regions of support, the number of support-ing basis functions selected by the MARS is small andsparsely located. In general, MARS trades off complexity

of the model and the accuracy of representation, whichmakes the approach economical and robust.

MARS operates in two steps: forward selection andbackward deletion. In the first step, MARS selects a pair ofbasis functions that fit the model best at the current stage.To prevent the final model from being overfitted, a back-ward deletion step is processed to prune basis functions. Amodified form of the generalized crossvalidation criterion(MGCV) is used as the lack-of-fit criterion

MGCV �1N

�i � 1

N

�yi � f�xi��2

�1 �C�M�

N �2 , (8)

where significant. �1 �C�M�

N �2

is a complexity function,

C (M) is defined as C (M) � C (M) � d � M, C(M) is thenumber of parameters being fit, and d is set to the defaultvalue of 3 as suggested in refs 18 and 29.

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Figure 3. Parity plots of the estimated NOx and measured NOx emissions using (a and b) LR and (c and d) MARS for (a and c) training and(b and d) testing data of the 2004 model-year engine. The linear fit lines are included.

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As a result of these operations, MARS automaticallydetermines the most important independent variablesand the most significant interactions among them. Fur-ther details on MARS modeling are given in refs 18 and29.

DATASETSData from 1992, 1999, and 2004 model-year U.S. truckengines were acquired following the same procedures andusing the same experimental settings. Emissions weremeasured using full flow exhaust dilution and research-grade analyzers, whereas SPD and TQE were controlledand measured in a transient test cell that has been de-scribed elsewhere.24,26 An Ecophysics CDL 822 CMhchemiluminescence analyzer was used for NOx concen-tration. It was fed by a heated probe and line from thedilution tunnel sample plane. The 1992 engine (DDC,Series 60, 12.7 L) used electronically managed fuel injec-tion and was turbocharged with no wastegate. This en-gine met U.S. 5-g/bhp � hr (6.7 g/kW � hr) NOx and 0.25-g/lb � hr (0.33 g/kW � hr) particulate matter (PM)standards. The 1999 engine (Cummins, ISM 370, 10.8 L)was electronically managed but did not have EGR. Itsturbocharger was equipped with a wastegate and it metU.S. 4-g/bhp � hr (5.3 g/kW � hr) NOx and 0.1-g/bhp � hr(0.13 g/kW � hr) PM standards. The 2004 engine (Cum-mins ISM370, 10.8 L) was the same engine used to verify

the operation of the test modes in reference.26 MAP andMAT were broadcast by the engine controller. The engineused cooled EGR and a variable geometry turbochargerand complied with U.S. 2.4-g/bhp � hr (3.2 g/kW � hr)NOx and 0.1-g/bhp � hr (0.13 g/kW � hr) PM standards.

Table 1 presents a summary of the data available foranalysis. The first two columns of the table characterizethe model year of engines and types of cycles involved.The third column indicates the number of data samplesavailable per cycle. Columns 4–8 provide ranges of mea-surements; for example, the minimum and maximumvalues of the SPD achieved by a truck equipped with 1992engine in FTP cycle are 583 and 1949 revolutions perminute (rpm), respectively. The arithmetic average ofeach measurement is shown in square brackets.

NOX MODELING BASED ON SPEED ANDTORQUE

Input ParametersIn this section, TQE and SPD are two primary indepen-dent variables used to model NOx response. However,because the combination of SPD and TQE results in an-other physically meaningful variable, which is often in-cluded in emissions analyses, the dependence of NOx onPOW was also analyzed. The model for NOx should alsobe based on the samples of inputs taken at previous time

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Figure 4. Comparison of predicted and measured NOx emissionsfor the 2004 model-year engine using (a) LR method and (b) MARSmethod (over a selected 180-sec increment).

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Figure 5. Cross-correlation results between (a) MAP and (b) MATand the NOx mass emissions rate for the 2004 model-year engine.The squares indicate the highest correlation coefficients.

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Volume 60 January 2010 Journal of the Air & Waste Management Association 77

instances to account for any dependence of NOx on tran-sient engine operation. The transient response of NOx

may be attributed to turbocharger lag, as well as turbo-charger geometry control and EGR valve control on re-cent model-year engines. As an example, the instanta-neous MAP during transient operation depends not onlyon SPD and TQE, but also on the recent history of thosetwo variables, largely because of the response time of theturbocharger. Additional delay is due to the separate issueof emissions sampling system and analyzer behavior.Therefore, before training and validating the MARSmodel, the authors performed selection of input parame-ters. The relative time delays of input variables were esti-mated by performing cross-correlation between an indi-vidual input variable and the NOx data. A detaileddescription of the procedure for evaluation of delay canbe found in the paper by Messer and Clark30 and theconcept of delay is also discussed in refs 31 and 32.

Figure 2 demonstrates the results of performing cross-correlation for the 2004 model-year engine. The box is

used to mark the peak of cross-correlation. Note that thecross-correlation curves for TQE and POW are very simi-lar. From Figure 2, TQE and POW have 7-sec delays withrespect to NOx, whereas SPD only has a 2-sec time delay.The peaks in cross-correlation plots for TQE and POWdelays are more pronounced than the peak in the cross-correlation plot for SPD, which is expected becauseSPD varies by only a factor of 3, whereas TRQ and POWvary widely. The cross-correlation results indicate whichvariables and corresponding time delays should beconsidered in the model. The authors imposed a 7-secdelay for all input variables for the 2004 engine. It is alsoappropriate that SPD and TQE, which were measuredsimultaneously and have no known measurement delayrelative to one another, preceded the measured NOx bythe same time period for modeling purposes. The timedelays for the 1992 and 1999 model-year engines werealso set to be 7 sec, and values close to 7 sec have beenfound in prior studies conducted by West Virginia Uni-versity (WVU).

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y = 0.952*x + 0.00291

(c)

0 0.05 0.1 0.150

0.05

0.1

0.15

Actual NOx (g/sec)

Ees

timat

ed N

Ox

(g/s

ec)

2004 FTP_Test_MARS_Plug−in

y = 0.955*x + 0.00226

(d)

Figure 6. Parity plots of the estimated and measured NOx using (a and b) LR and (c and d) MARS for (a and c) training and (b and d) testingdata of the 2004 model-year engine assuming plug-in models. The lines of the linear fit are included.

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78 Journal of the Air & Waste Management Association Volume 60 January 2010

Instead of involving several individual input vari-ables at different time delays (historic values) to establisha rate of change of the variable, the authors used thederivatives of POW, SPD, and TQE with respect to time asadditional inputs to further aid NOx modeling. Eitherderivatives or historic data are essential for the quantifi-cation of engine transient behavior.

In summary, to estimate the NOx at time t, six inputvariables were used: SPD, TQE, POW, dTQE/dt, dPOW/dt,and the product of dSPD/dt and dTQE/dt all at time t � 7for all three engines. Note that dPOW/dt is equivalent tothe sum of SPD(dTQE/dt) and TQE(dSPD/dt).

Experiments and ResultsThe last part of the FTP cycle is a repeat of the first part, andso only the first 900 sec of the 1199-sec cycle data were usedfor crossvalidation. In 5-fold crossvalidation, the first 900samples of the FTP data from each engine were partitionedinto five subsamples. A single subsample was retained as thevalidation dataset for testing the model, and the remainingfour subsamples were used as training data. The crossvalida-tion process was then repeated five times for each engine,with each of the five subsamples used exactly once as thevalidation data. The results were averaged to produce a sin-gle evaluation metric.

The goodness of fit between the predicted emissionsand the measured data was evaluated using two criteria:(1) the root mean square error (RMSE) and (2) the squareof correlation coefficients (R2). Equations 9 and 10 are themathematical definitions of the criteria.

RMSE � �1N �

i � 1

N

�yi � yi�2, (9)

R2 � �i � 1

N

�yi � y� ��yi � y� �

�N � 1�sysy

2

, (10)

where yi is the estimated NOx and y� i is its sample mean, sy

and sy are the sample standard deviations of y and y, andN is the number of samples.

To eliminate poor prediction because of tiny time align-ment and diffusion problems, a 5-sec average window wasfurther applied to measured and estimated NOx to evaluateprediction performance during this short period. The 5-secaverage NOx also serves to deal with a feedback to thecontrol units that need an average emissions value in a shortperiod rather than an instantaneous value. Selective cata-lysts used with urea injection are one example in which a5-sec averaged signal would often suffice for control pur-poses. The criteria introduced in eqs 9 and 10 were alsoapplied to the 5-sec average NOx and its estimates. Theoverall emissions during the whole sampling period werealso compared against the overall estimated values. To com-pare the results of different cycles, a relative total difference(RTD) was used. The definition of RTD is as follows:

RTD �

� �i � 1

N

yi � �i � 1

N

yi��

i � 1

N

yi

. (11)

During the training of MARS, several scenarios for select-ing the number of basis functions, M, (see eq 6) as afunction of the involved input variables were examined.The goal at this stage was to find a relatively simple andeffective model. As mentioned in the description of theMARS method, each basis function was selected from theset C of functions. In this work, the functions wereformed either as a single basis function or as a product oftwo basis functions. To control the complexity of themodel, the authors did not appeal to a set of more com-plex functions. For the 1992 engine, the best model wasobtained when the number of basis functions was set toM � 20 and only single-basis functions were used. For the1999 engine, MARS selected a more complex model withM set to 20 and double-basis functions. For the 2004engine, the best selected by MARS model had M � 15 andwas based on single-basis functions. An example of theMARS models for the data describing the 1999 engine isdemonstrated in Appendix A.

0 20 40 60 80 100 120 140 160 180−0.05

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NO

x (g

/sec

)

2004 FTP_Test_LR_Plug−in

ACTUAL NOxESTIMATED NOx

(a)

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0.05

0.1

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0.25

Time (sec)

NO

x (g

/sec

)

2004 FTP_Test_MARS_Plug−in

ACTUAL NOxESTIMATED NOx

(b)

Figure 7. Comparison of predicted and measured NOx emissionsof the 2004 model-year engine using (a) LR and (b) MARS in theplug-in model (over a selected 180-sec increment).

Chen, Schmid, Wang, and Clark

Volume 60 January 2010 Journal of the Air & Waste Management Association 79

Table 2 summarizes the results of validation usingMARS and LR methods. From the results it can be seen thatMARS outperforms LR for all engines on the basis of mostcriteria. The improvement using MARS rather than LR forthe 2004 engine is greater than for the 1992 and 1999engines. The NOx emissions of the 1992 and 1999 engineswere predicted more accurately than the emissions of the2004 engine when comparing the results for (R2). Anothervery important observation is that LR and MARS demon-strate a relatively similar performance on the 1992 and 1999engines compared with the performance of the 2004 engine,which has more complex controls and a greater number ofcontrol variables. The performance in the 5-sec window ismuch better than the performance evaluated using 1-secdata, which may in part be due to diffusion of the 1-secemissions data in time.33,34

The parity plots of actual NOx and estimated NOx forthe 2004 model-year engine and their linear fit are shownin Figure 3. MARS provides a better fit in training and

testing procedures. The parity plots for the 1992 and 1999model-year engines are presented in Appendix B.

The comparisons of predicted and measured NOx of the2004 engine in the time domain are shown in Figure 4a forLR and in Figure 4b for the MARS method. The predictedNOx emissions follow relatively well the measured valuesfor both methods. The only regions that require a morecareful fit are the flat (piecewise constant) intervals of themeasured NOx. The results obtained for the 1992 and 1999engines are summarized in Appendix B.

PLUG-IN MODELSMAP and MAT also have an important impact on emis-sions because they may add information on atmosphericconditions, altitude (barometric pressure), and short- andlong-term transient engine behavior. High combustiontemperatures promote reactions between available nitro-gen and oxygen that lead to NOx formation. An increasein MAT, which is affected by ambient temperature, boost,

Table 3. Training and testing performance for five cycles of the 1992 engine using four NOx models.

Method Cycle Average R2 RMSE RTD

LR FTP (training) 1 sec 0.968 0.0181 05 sec 0.980 0.0136

Transient 1 sec 0.839 0.0319 0.0925 sec 0.903 0.0227

Cruise 1 sec 0.867 0.1493 0.4735 sec 0.877 0.1478

HHDDTS 1 sec 0.789 0.1427 0.3945 sec 0.783 0.1423

Creep 1 sec 0.365 0.0213 0.0465 sec 0.688 0.0145

MARS FTP (training) 1 sec 0.979 0.0145 05 sec 0.990 0.0098

Transient 1 sec 0.858 0.0296 0.0615 sec 0.912 0.0205

Cruise 1 sec 0.890 0.1401 0.4385 sec 0.902 0.1387

HHDDTS 1 sec 0.833 0.1359 0.3745 sec 0.831 0.1354

Creep 1 sec 0.504 0.0190 0.0295 sec 0.753 0.0135

LR plug-in FTP (training) 1 sec 0.968 0.0181 05 sec 0.980 0.0136

Transient 1 sec 0.838 0.0321 0.1005 sec 0.900 0.0231

Cruise 1 sec 0.869 0.1491 0.4735 sec 0.879 0.1476

HHDDTS 1 sec 0.789 0.1422 0.3925 sec 0.783 0.1417

Creep 1 sec 0.348 0.0216 0.0535 sec 0.666 0.0148

MARS plug-in FTP (training) 1 sec 0.981 0.0138 0.0055 sec 0.991 0.0092

Transient 1 sec 0.885 0.0267 0.0565 sec 0.937 0.0178

Cruise 1 sec 0.891 0.1388 0.4315 sec 0.902 0.1374

HHDDTS 1 sec 0.837 0.1369 0.3775 sec 0.838 0.1364

Creep 1 sec 0.622 0.0172 0.0955 sec 0.854 0.0125

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80 Journal of the Air & Waste Management Association Volume 60 January 2010

and aftercooler operation, is likely to imply an increase inthe in-cylinder temperature and is likely to promote NOx

formation. Also, a reduction in MAP or increase in MATfor the same fuel quantity is likely to increase NOx pro-duction because the in-cylinder mass is lowered and theresulting in-cylinder temperature is higher. Therefore, ifMAP and MAT can be included in NOx modeling, the fitof the predicted NOx may be improved. A serious draw-back is that MAP and MAT are usually not measured andare not variables under direct independent driver com-mand. They are more a consequence of SPD and TQE andtheir histories. Unfortunately, because MAP and TQE arestrongly correlated there is a danger that they may beindividually used in an inappropriate fashion by a fittedmodel in transient operation. In this work the authorshave explored the possibility of replacing the true (butusually unknown) measurements of MAP and MAT withtheir estimates. This resulted in a plug-in model. Submod-els 12 and 13 were first generated using SPD and TQE topredict MAP and MAT. Then a complex model (model 14)

was built with SPD, TQE, MAP, and MAT as inputs topredict NOx. By substituting the estimated values into thecomplex model 14, a plug-in model (model 15) wasformed. The unknown parameters, MAP and MAT, andthe output NOx are estimated as follows:

MAP � fp�SPD, TQE�, (12)

MAT � fT�SPD, TQE�, (13)

NOx � fN�SPD, TQE, MAP, MAT�, (14)

NOx � fN�SPD, TQE, MAP, MAT�, (15)

where fp( � ), fT( � ), and fN( � ) are three distinct functionsestablishing relationships between their arguments and thevalues they take. The correlation between MAP, MAT, andNOx emissions for the 2004 engine are shown in Figure 5.

Table 4. Training and testing performance for five cycles of the 2004 engine using four models.

Method Cycle Average R2 RMSE RTD

LR FTP (training) 1 sec 0.892 0.0185 05 sec 0.926 0.0144

Transient 1 sec 0.794 0.0181 0.0575 sec 0.881 0.0125

Cruise 1 sec 0.895 0.0158 0.1335 sec 0.919 0.0140

HHDDTS 1 sec 0.690 0.0347 0.2015 sec 0.703 0.0332

Creep 1 sec 0.638 0.0110 0.0095 sec 0.866 0.0074

MARS FTP (training) 1 sec 0.921 0.0158 05 sec 0.953 0.0115

Transient 1 sec 0.794 0.0181 0.0335 sec 0.865 0.0133

Cruise 1 sec 0.861 0.0153 0.0035 sec 0.887 0.0131

HHDDTS 1 sec 0.707 0.0293 0.0585 sec 0.728 0.0274

Creep 1 sec 0.659 0.0106 0.0425 sec 0.812 0.0070

FTP (training) FTP (training) 1 sec 0.892 0.0185 05 sec 0.927 0.0143

Transient 1 sec 0.808 0.0181 0.0805 sec 0.895 0.0120

Cruise 1 sec 0.899 0.0151 0.1305 sec 0.923 0.0135

HHDDTS 1 sec 0.685 0.0336 0.1835 sec 0.702 0.0323

Creep 1 sec 0.712 0.0100 0.0085 sec 0.898 0.0068

MARS plug-in

FTP (training) 1 sec 0.925 0.0154 0.0025 sec 0.961 0.0105

Transient 1 sec 0.807 0.0182 0.0035 sec 0.891 0.0121

Cruise 1 sec 0.875 0.0147 0.0275 sec 0.906 0.0120

HHDDTS 1 sec 0.723 0.0292 0.0485 sec 0.731 0.0270

Creep 1 sec 0.717 0.0097 0.0445 sec 0.873 0.0069

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Volume 60 January 2010 Journal of the Air & Waste Management Association 81

0 0.05 0.1 0.150

0.05

0.1

0.15

Actual NOx (g/sec)

Ees

timat

ed N

Ox

(g/s

ec)

FTP_Train_MARS_Plug−in

y = 0.929*x + 0.00381

(a)

0 0.05 0.1 0.150

0.02

0.04

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0.08

0.1

0.12

0.14

0.16

Actual NOx (g/sec)

Ees

timat

ed N

Ox

(g/s

ec)

Transient_Test_MARS_Plug−in

y = 1.05*x − 0.00186

(b)

0 0.05 0.1 0.15 0.20

0.05

0.1

0.15

0.2

Actual NOx (g/sec)

Ees

timat

ed N

Ox

(g/s

ec)

Cruise_Test_MARS_Plug−in

y = 0.954*x + 0.00441

(c)

0 0.05 0.1 0.15 0.20

0.05

0.1

0.15

0.2

Actual NOx (g/sec)

Ees

timat

ed N

Ox

(g/s

ec)

HHDDTS_Test_MARS_Plug−in

y = 0.741*x + 0.0242

(d)

0 0.05 0.10

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Actual NOx (g/sec)

Ees

timat

ed N

Ox

(g/s

ec)

Creep_Test_MARS_Plug−in

y = 0.645*x + 0.00519

(e)

Figure 8. Parity plots of the estimated and measured NOx of the 2004 model-year engine using the plug-in model trained by MARS from (a)the FTP cycle and tested on the (b) transient, (c) cruise, (d) HHDDTS, and (e) creep cycles. The linear fit lines are included.

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82 Journal of the Air & Waste Management Association Volume 60 January 2010

The time delays of MAP and MAT for both engines were setto be 7 sec to align with emissions, similar to other cases.MAP and MAT may not be fully aligned with TQE because ofreal transient engine behavior, but the 7-sec delay was con-sidered most appropriate.

Because variations of the ambient temperature do notsubstantially alter input and output functions, only the dif-ferentiation of MAP with respect to time was considered.Thus, for the models 12 and 13, six input functions—SPD,TQE, POW, dPOW/dt, dTQE/dt and the product of dSPD/dtand dTQE/dt—were involved. To model NOx using complex

model 14, the six input variables mentioned above aug-mented with MAP, MAT, and dMAP/dt were utilized. Allinputs were subject to 7-sec time delay.

Similar to the experiments for the models with twoinputs, the first 900 samples of the FTP data from threeengines were processed using 5-fold crossvalidation. Models12–14 were trained using the four-fifths fraction of the dataand tested on the remaining one-fifth of the data. The finalpredicted NOx was obtained using plug-in model 15. Theexperiment was repeated five times and the results wereaveraged. The average performance using the criteria

0 200 400 600 800 1000 1200−0.05

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0.05

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NO

x (g

/sec

)

FTP_Train_MARS_Plug−in

ACTUAL NOxESTIMATED NOx

(a)

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0

0.05

0.1

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Time (s)

NO

x (g

/s)

Transient_Test_MARS_Plug−in

ACTUAL NOxESTIMATED NOx

(b)

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0.05

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Time (sec)

NO

x (g

/sec

)

Cruise_Test_MARS_Plug−in

ACTUAL NOxESTIMATED NOx

(c)

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0.05

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Time (s)

NO

x (g

/s)

HHDDTS_Test_MARS_Plug−in

ACTUAL NOxESTIMATED NOx

(d)

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−0.02

0

0.02

0.04

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0.08

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0.14

0.16

Time (s)

NO

x (g

/s)

Creep_Test_MARS_Plug−in

ACTUAL NOxESTIMATED NOx

(e)

Figure 9. Comparison of predicted and measured NOx emissions of the 2004 model-year engine from the (a) FTP, (b) transient, (c) cruise,(d) HHDDTS, and (e) creep cycles using the plug-in MARS model.

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Volume 60 January 2010 Journal of the Air & Waste Management Association 83

defined in the previous section is shown in Table 2. TheMARS method provides a better fit than the LR model.Compared with the results in the previous section, theplug-in model trained using the LR method did not signifi-cantly improve the performance; however, the plug-inmodel trained using the MARS method improved the per-formance. The improvement is limited because the estima-tion error propagates when the estimated parameters MAPand MAT are substituted into the complex model. The re-sults may be improved if the parameters MAP and MAT andthe mapping function f( � ) are jointly estimated.

The parity plots of actual NOx and estimated NOx forthe plug-in model and their linear fits are shown in Figure 6.The comparisons of predicted and measured NOx in thetime domain for the 2004 engine are shown in Figure 7, aand b, for LR and MARS models, respectively. Comparedwith the fitting results in Figure 4, the plug-in models addvalue by improving the fit relative to the case when pressureand temperature are not taken into account. This is espe-cially noticeable in the regions where NOx is close to zero.

NOX PREDICTION MODEL TRAINED USING FTPDATAThe previous two sections have discussed the case where theNOx models were trained to predict the emissions of thesame cycle. In this section, the regression models trainedusing data from one cycle were tested to predict the emis-sions of the other cycles. These engine emission cycles(termed also “modes”) include creep, transient, cruise, andhigh-speed cruise (HHDDTS).24–26 These four modes eachcontain distinct types of engine operation, and no singlemode accounts for all types of engine operation. In contrast,the FTP was derived from vehicles operating under freewayand non-freeway conditions and provides a broad operatingenvelope for an engine. The four modes, if composited,would also cover a broad operating range.

The simple models and the plug-in models, reported inthe previous two sections, using MARS and LR were consid-ered. All of the FTP cycle data were first used to train a modeland then the ability of the model to predict emissions forthe other four cycles was assessed. Tables 3 and 4 list all ofthe training and testing results for the 1992 and 2004 en-gines, respectively. From the tables it can be concluded thatthe prediction capabilities of the proposed models vary sub-stantially. Compared with the original two input parametermodels, the plug-in model was able to improve the perfor-mance for some cycles, especially for the creep cycle. How-ever, the overall improvement was limited, which rein-forced the fact that MAP and MAT are not sufficientlyinformative when estimated from TQE and SPD data com-pared with TQE and SPD themselves. The MARS methodprovides significantly better training results than the LRmethod, but MARS performs merely the same as the LRmodel when applied to testing data. Note that the fivecriteria do not exhibit similar trends when used to evaluatedifferent models. For the 1992 engine, the MARS and MARSplug-in models perform best in the sense of R2; however,the improvements compared against the LR method in thesense of RTD are limited. For the 2004 engine, from R2, theMARS and MARS plug-in models do not perform best for allcycles. However, they perform much better according toRTD, especially for the cruise and HHDDTS cycles. Overall,

the plug-in model using MARS performs best but is the mostcomplex model.

The parity plots of the estimated and measured NOx

emissions for all five cycles of the 2004 engine usingMARS plug-in model are shown in Figure 8. The compar-isons in time domain are shown in Figure 9, a–e. From thefigures it can be seen that although R2 for the creep cycleis low, the predicted results in the time domain follow thetrue value of NOx relatively well. The main gap is in theprediction of the HHDDTS mode. The authors carefullyexamined the NOx data for HHDDTS mode from the 2004engine and found that NOx emissions during a steadyportion in the middle of the cycle were anomalous. Theseemissions are most likely associated with failure of theEGR valve to move, perhaps because of a wiring testharness fault, and resulted in low NOx emissions and thenhigh NOx emissions, each for approximately 90 sec ofoperation. These anomalous emissions provide a seren-dipitous opportunity to show how comparison of mod-eled and actual data can reveal a system malfunction. Ona more general note, certain engine protection modes canalso result in reduced EGR and would result in emissionsthat could not be anticipated by a simple model usingTQE and SPD as independent variables; emissions discon-tinuities of this kind are usually not reliably modeled. Theresults for the 1992 engine are in Appendix C for refer-ence. For the cruise and HHDDTS modes, it was evidentthat the 1992 engine was able to produce two differentlevels of NOx at the same POW rating. These bifurcationshave usually been associated with injection timingchanges under cruise conditions11,12 and are also difficultto model with the variables used in this paper.

CONCLUSIONSIn this study, the LR method and MARS were used tomodel NOx emissions of three types of engines—1992,1999, and 2004 model-year engines—with a time delay of7 sec between the power and resulting emissions. Five-fold crossvalidation was performed using the FTP data forall engines. Application of the MARS model leads to abetter fit, in the sense of R2, RMSE of 1- and 5-sec averagedata, and RTD when compared with the LR model.

MAP and MAT were further used in NOx modeling tobuild a plug-in model. Although the performance of theplug-in models is better than the performance of the simplemodels without MAP and MAT parameters as inputs, theimprovement is limited because of the propagation of esti-mation errors of MAP and MAT. For example, for the threeengines, plug-in use improved R2 on the FTP 1-sec predic-tion by �0.001 to 0 for LR, and �0.001 to 0.008 for MARS.

The 2004 engine with a variable geometry turbo-charger and active cooled EGR rate control is expected toyield NOx levels that are sensitive to transient behavior,therefore it is harder to find a linear model that fits thedata well. The fitting performance (R2) of the 2004 engineusing LR and MARS methods is lower than the perfor-mance of the 1992 and 1999 engines. This is not surpris-ing because the 2004 engine has a more complex controlstrategy, with EGR and variable turbine geometry. Theimprovements of prediction performance for the 1992

Chen, Schmid, Wang, and Clark

84 Journal of the Air & Waste Management Association Volume 60 January 2010

and 1999 engines using the plug-in model are more lim-ited than the improvement for the 2004 engine because ofthe higher dependence of MAP on the torque history.

For the 1992 and 2004 engines, the simple model andthe plug-in LR and MARS models were further trained usingthe whole FTP cycle dataset. Then the trained models weretested on the data from the other four cycles: transient,cruise, HHDDTS, and creep. The predicted NOx values ineach cycle were compared with the true value. The perfor-mance varies substantially when data from different cycles

were used. Creep cycle (which contains much idle) was notwell predicted, the 1992 HHDDT prediction was difficultbecause of “off-cycle” emissions, and the 2004 HHDDT pre-diction was marred by an anomaly in measured emissions.However, the transient and cruise modes were well pre-dicted by MARS even at the 1-sec level, with R2 at 0.858 and0.890 for the 1992 engine and 0.794 and 0.861 for the 2004engine. Overall, the plug-in model trained by MARS is thebest; however, the performance differences between LR andMARS are not significant.

APPENDIX A

An example of the MARS model for the data describing the 1999 model year engine:NOx � a0 � a1 (POW � 510.741)� � a2 (510.741 � POW)� � a3 (dPOW/dt � 233729.2)� � a4 (233729.2 � dPOW/dt)�

� a5 (dTQE/dt � 369.974)� � a6 (369.974 � dTQE/dt)� � a7 (POW � 510.741)�(SPD � 1447)� � a8 (POW �510.741)�(1447 � SPD)� � a9 (POW � 510.741)�(TQE � 801.119)� � a10 (POW � 510.741)�(801.119 � TQE)� � a11

(POW � 510.741)�(dPOW/dt � 702852.6)�

where [a0, a1, . . . a11] � [�1.881E � 02, 1.534E � 07, �5.65E �08, 8.11E �08, �7.510E � 08, �2.2E � 04, 1.317E �04, �5.462E � 11, 4.142E � 011, 1.996E � 14, 1.133E � 14, 5.184E � 08].

APPENDIX B

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Time (sec)

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ACTUAL NOxESTIMATED NOx

(a)

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x (g

/sec

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ACTUAL NOxESTIMATED NOx

(b)

Figure 10. Comparison of predicted and measured NOx emissions of the 1992 model-year engine using (a) LR and (b) MARS (over a selected180-sec increment).

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Volume 60 January 2010 Journal of the Air & Waste Management Association 85

0 0.1 0.2 0.30

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0.3

Actual NOx (g/sec)

Est

imat

ed N

Ox

(g/s

ec)

1992 FTP_Train_LR

y = 0.976*x + 0.00264

(a)

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Est

imat

ed N

Ox

(g/s

ec)

1992 FTP_Test_LR

y = 0.853*x + 0.0156

(b)

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Est

imat

ed N

Ox

(g/s

ec)

1992 FTP_Train_MARS

y = 0.987*x + 0.00146

(c)

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Est

imat

ed N

Ox

(g/s

ec)

1992 FTP_Test_MARS

y = 0.898*x + 0.00999

(d)

Figure 11. Parity plot of the estimated and measured NOx emissions using (a and b) LR and (c and d) MARS for (a and c) training and (b andd) testing data of the 1992 model-year engine. The linear fit lines are included.

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86 Journal of the Air & Waste Management Association Volume 60 January 2010

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(a)

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Time (sec)

NO

x (g

/sec

)

1999 FTP_Test_MARS

ACTUAL NOxESTIMATED NOx

(b)

Figure 13. Comparison of predicted and measured NOx emissions of the 1999 model-year engine using (a) LR and (b) MARS (over a selected180-sec increment).

0 0.1 0.2 0.30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Actual NOx (g/sec)

Est

imat

ed N

Ox

(g/s

ec)

1999 FTP_Train_LR

y = 0.989*x + 0.00107

(a)

0 0.1 0.2 0.30

0.05

0.1

0.15

0.2

0.25

0.3

Actual NOx (g/sec)

Est

imat

ed N

Ox

(g/s

ec)

1999 FTP_Test_LR

y = 1.06*x + 0.00212

(b)

0 0.1 0.2 0.30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Actual NOx (g/sec)

Est

imat

ed N

Ox

(g/s

ec)

1999 FTP_Train_MARS

y = 0.993*x + 0.000695

(c)

0 0.1 0.2 0.30

0.05

0.1

0.15

0.2

0.25

0.3

Actual NOx (g/sec)

Est

imat

ed N

Ox

(g/s

ec)

1999 FTP_Test_MARS

y = 1.04*x + 0.00297

(d)

Figure 12. Parity plot of the estimated and measured NOx emissions using (a and b) LR and (c and d) MARS for (a and c) training and (b andd) testing data of the 1999 model-year engine. The linear fit lines are included.

Chen, Schmid, Wang, and Clark

Volume 60 January 2010 Journal of the Air & Waste Management Association 87

APPENDIX C

0 0.1 0.2 0.30

0.05

0.1

0.15

0.2

0.25

0.3

Actual NOx (g/sec)

Est

imat

ed N

Ox

(g/s

ec)

1992 FTP_Train_MARS_Plug−in

y = 0.981*x + 0.00134

(a)

0 0.1 0.2 0.30

0.05

0.1

0.15

0.2

0.25

0.3

Actual NOx (g/sec)

Est

imat

ed N

Ox

(g/s

ec)

1992 Transient_Test_MARS_Plug−in

y = 0.884*x + 0.00401

(b)

0 0.2 0.4 0.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Actual NOx (g/sec)

Est

imat

ed N

Ox

(g/s

ec)

1992 Cruise_Test_MARS_Plug−in

y = 0.48*x + 0.021

(c)

0 0.1 0.2 0.3 0.4 0.50

0.1

0.2

0.3

0.4

0.5

Actual NOx (g/sec)

Est

imat

ed N

Ox

(g/s

ec)

1992 HHDDTS_Test_MARS_Plug−in

y = 0.546*x + 0.0218

(d)

0 0.05 0.1 0.15 0.20

0.05

0.1

0.15

0.2

Actual NOx (g/sec)

Est

imat

ed N

Ox

(g/s

ec)

1992 Creep_Test_MARS_Plug−in

y = 0.491*x + 0.0108

(e)

Figure 14. Parity plots of the estimated and measured NOx of the 1992 model-year engine using the plug-in model trained by the MARSmethod from (a) the FTP cycle and tested on the (b) transient, (c) cruise, (d) HHDDTS, and (e) creep cycles. The linear fit lines are included.

Chen, Schmid, Wang, and Clark

88 Journal of the Air & Waste Management Association Volume 60 January 2010

ACKNOWLEDGMENTSEngine data were acquired in the WVU transient test cell.The authors are grateful to Clint Bedick for providing the2004 engine data and to David McKain for providing the1992 and 1999 data. The contributions to transient emis-sions measurement capability of Dr. Gregory Thompson,Thomas Spencer, Brad Ralston, and WVU Center for Al-ternative Fuels, Engines, and Emissions (CAFFE) facultyand staff are gratefully acknowledged. The 2004 data wereacquired during the operation of the ACES test schedulewith funding from the Coordinating Research Council.

Student funding was provided by a Department of Trans-portation award and by the George B. Berry Chairendowment.

REFERENCES1. Heywood, J.B. Internal Combustion Engine Fundamentals; McGraw Hill:

New York, 1988.2. Rousseau, A.; Sharer, P.; Pasquier, M. Validation Process of a System

Analysis Model: PSAT. Presented at the Society of Automotive Engi-neers (SAE) World Congress; SAE Technical Paper 2001-01-0953; SAE:Warrendale, PA, 2001;

0 200 400 600 800 1000 1200−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Time (sec)

NO

x (g

/sec

)

1992 FTP_Train_MARS_Plug−in

ACTUAL NOxESTIMATED NOx

(a)

0 100 200 300 400 500 600 700−0.05

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NO

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/sec

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ACTUAL NOxESTIMATED NOx

(e)

Figure 15. Comparison of predicted and measured NOx emissions of the 1992 model-year engine from the (a) FTP, (b) transient, (c) cruise,(d) HHDDTS, and (e) creep cycles using the plug-in MARS model.

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Volume 60 January 2010 Journal of the Air & Waste Management Association 89

3. An, F.; Rousseau, A. Integration of a Modal Energy and EmissionsModel into a PNGV Vehicle Simulation Model, PSAT; Society of Au-tomotive Engineers (SAE) Paper 2001-01-0954; SAE: Warrendale, PA,2001.

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22. Krishnamurthy, M., Chen, X., Schmid, N. A., Gautam, M. Develop-ment of NOx Predictive Model Using Multiple Adaptive RegressionSplines. Paper 07-2847, Presented at the Transportation ResearchBoard Annual Meeting, Washington, DC, 2007.

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About the AuthorsXiaohan Chen received her Ph.D. in electrical engineeringfrom the Lane Department of Computer Science and Elec-trical Engineering at West Virginia University (WVU) in 2008.She is now a researcher at Texas Instruments. Natalia A.Schmid is an associate professor with the Lane Departmentof Computer Science and Electrical Engineering at WVU.Lijuan Wang is a Ph. D. student at the Department ofMechanical and Aerospace Engineering at WVU. Nigel N.Clark is a professor with the Department of Mechanical andAerospace Engineering, and Berry Chair in the College ofEngineering and Mineral Resources at WVU. Please ad-dress correspondence to: Natalia A. Schmid, Lane Depart-ment of Computer Science and Electrical Engineering,West Virginia University, Engineering Sciences Building,Evansdale Drive, Room G-70, Morgantown, WV 26506;phone: �1-304-293-0405 ext. 2557; e-mail: [email protected].

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90 Journal of the Air & Waste Management Association Volume 60 January 2010