Selection and Tuning of a Reduced Parameter Setfor a Turbocharged Diesel Engine Model

Rasoul Salehi1, Anna G. Stefanopoulou1, Dejan Kihas2 and Michael Uchanski2

Abstract— This paper presents an approach for systematicreduced-parameter-set adaption applicable to internal com-bustion engine models. The presented idea is to detect themost influential parameters in an engine air-charge path modeland then use them as a reduced-parameter-set for furthercalibration to improve the model accuracy. Since only mostinfluential parameters (in comparison with a complete set ofparameters) are tuned at the final calibration process, thisapproach helps reducing over-parameterization associated withtuning highly nonlinear engine models. Detection of the influ-ential parameters is done using the sensitivity analysis followedby the principle component analysis. Accuracy of the reduced-parameter-set tuned model is compared to a model with a tunedfull-parameter-set developed following commercially availableOnRAMP Design Suite [1] methodology. Results from experi-ments on a heavy duty diesel (HDD) engine show that althoughtuning the full-parameter-set (with over 70 parameters) createshigher accuracy, an average of 50% improvement of the modelaccuracy is attained using the proposed reduced-parameter-setapproach (which tunes only 2 parameters).

I. INTRODUCTION

Models for simulation of the gas exchange process in aninternal combustion engine have found many applicationsfor monitoring and control in modern engine control units(ECUs)[2], [3]. Having a simple structure and low computa-tional burden, the Mean Value Modeling (MVM) is the mainconcept used in commercialized ECUs which, on the otherhand, requires extensive calibration efforts to ensure accuratetracking of variables.

Physics-based modeling and automatic calibration usingsoftware tools such as OnRAMP used in this work, aresolutions to reduce calibration work on an engine model.In this paper a new approach is proposed and elaborated inwhich, while doing physics-based modeling, only the mainaffecting parameters of a complete engine model is detectedand tuned. To detect the most influential parameters, the sen-sitivity analysis followed by the principle component analysisis utilized. Since only the main influencing parameters go tothe final tuning process, it is computationally much easierand is realized here using a Kalman filter. The implementeddiscrete Kalman filter identifies the influential parameters,which are mapped as functions of speed and load, at differentengine operating points over drive cycles. Finally, a similarengine model is developed in OnRAMP design suite wherethe model is with a full set of tunable parameters. The

1 R. Salehi and and A. Stefanopoulou are with the Department of Me-chanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA.Email: rsalehi@umich.edu and annastef@umich.edu

2 D. Kihas and M. Uchanski are with Honeywell AutomotiveSoftware. Email: Dejan.Kihas@honeywell.com andMichael.Uchanski@honeywell.com

“fully parameterized” highly accurate model developed inOnRAMP is used by industry for offline development andcalibration of controllers and is utilized in this work asthe reference showing the expected level of accuracy foran engine model. Both reduced-parameter (approach of thispaper) and full-parameter (approach of OnRAMP) tunedmodels are compared to experimental data from a heavy-duty diesel (HDD) engine. The reduced-parameter-set tuningtechnique is shown to halve the estimation error of theengine model and approach the accuracy of the highlyaccurate reference model developed in OnRAMP. In additionto [12], this paper presents complete parameterization of thecomponent models, results of a realized discrete Kalmanfilter for online parameters tuning and a comparison to thereference OnRAMP model.

In section II, the engine model is described both atcomponent and engine levels. In section III, an assessmentof the parameter’s importance is presented using sensitivityand principle component analysis. Then, results of reduced-parameter-set and full-parameter-set tuning are compared insection IV. Finally, the conclusion comes in section V.

II. HDD DIESEL ENGINE MODEL

A 13 liters 6-cylinder heavy duty diesel (HDD) enginewith high pressure cooled exhaust gas recirculation (EGR)and a wastegate controlled asymmetric twin-scroll turbine isstudied in this paper. The asymmetric twin-scroll turbine hasbenefit in increasing EGR while keeping low back pressureand smoke [4]. The engine is also equipped with a wastegatevalve, which bypasses the large scroll avoiding over-boostingand reducing the pumping loss.

The model development presented for this engine hastwo steps. The first step is a component-level modelingwhere parameters for individual models of components areestimated. At the engine level, which is the second step,all components are connected and the final complete enginemodel is formed. The following subsections describe eachstep respectively.

A. Component Models

For the HDD engine, all components (namely: engineblock, turbocharger, intercooler, EGR and wastegate) aremodeled individually. Inputs and outputs of each componentare measured explicitly (except for the wastegate whichits output flow is estimated). The modeling approach forcomponents is similar to the work presented in [4] with re-estimation of parameters given that the engine consideredhere is a different model year and has a smaller level of

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asymmetry in the turbine scroll. Since the turbocharger,EGR and wastegate are discussed in later sections of thepaper, their detailed equations are described here. The reasonfor selecting these three components is higher uncertaintyassociated with their modeling equations compared to otherengine sub-models. The EGR and turbine uncertainties comefrom flow pulsations, the compressor is effected by the heattransfer from the turbine and the WG flow model is uncertainsince it is not measured but estimated [5].

Turbocharger speed, Ntc, comes from its rotational dy-namics written by:

ItcNtcNtc = ηtηmmtTemCp,t(1− Pex

Pem

(1−1/γt))−

˜mcTinCp,c(Pim

Pin

(1−1/γc) − 1)/ηc(1a)

ηt = θT ∗ ηt (1b)˜mc = θC ∗ mc (1c)

in which ηm and ηc are mechanical and compressor ef-ficiency, mt is the turbine flow, Tem and Pem are thetemperature and pressure in the exhaust manifold, Pex ispressure in the exhaust pipe, Cp is specific heat, Tin andPin are the compressor inlet temperature and pressure, Pimis the intake manifold pressure, γ is the ratio of specificheats of the gas and rc is the impeller radius. θT and θC aremathematical parameters included in the turbocharger modelto scale the turbine efficiency, ηt, and the compressor flow,mc, and are used for the sensitivity analysis described inSection 3.

The scaled EGR flow, ˙mEGR, is modeled using thestandard isentropic orifice flow model as:

˙mEGR = θEGR ∗AEGRPems√RTems

F (PimPems

) (2)

in which the parameter θEGR again is defined for implement-ing the sensitivity analysis within the simulation and Pemsis the exhaust manifold pressure at the turbine’s small scroll.The effective area in (2), AEGR = gEGR(uEGR, Ne, PR),is a function of ECU command (uEGR), the pressure ratio(PR = Pim/Pems) and the engine speed (Ne) which areincluded to account for the pulsation effects. The EGR flowmeasured on the engine test bench is used to tune parametersin (2). The same isentropic orifice model is used to simulatethe WG flow and scale it as:

˙mWG = θWG ∗AWG(xWG)Peml√RTeml

F (PimPeml

) (3)

where θWG is the scaling parameter for sensitivity analysisand Peml is the exhaust manifold pressure at the turbine’slarge scroll. xWG = gWG(uWG, Peml, Pex) is the wastegatedisplacement taken from the wastegate mechanism forcebalance which also depends on the ECU command to theWG valve, uWG[5].

B. Complete Engine Model

The complete engine model (shown schematically inFig. 1) is formed by connecting individual steady statecomponents models (three of them were reviewed in the

Fig. 1: Overview of the complete engine model, its inputsand selected outputs.

former subsection) along with dynamical models for pres-sures (Pim, Pems, Peml, Pex), air fractions (Fim, Fem) andthe turbocharger speed (Ntc) with details presented in [4].The final performance of the complete HDD engine modelis presented in Fig. 2 over three different drive cycles(DCs) in which different trajectories for the engine speed,torque, EGR and WG were used. As plotted the generaltrend of the engine model follows that of the measurementshowever, steady state errors clearly exist. The averaged rootmean square (RMSEavg) used in Fig. 2 is defined as theconventional RMSE divided by the average of measured dataover the entire time window at each test. A final tuning ofthe engine model parameters is a typical step to reduce theestimation error but, computationally, it is difficult to tuneall parameters in the complete engine model. In the nextsection, the sensitivity analysis is used to detect parametersin the complete HDD engine model whose tuning has themost improvement in a set of selected outputs.

III. PARAMETER IMPORTANCE DETECTION

Importance of the defined scaling parameters θT ,θC , θEGR and θWG is calculated by detecting their influenceon a set of the engine model outputs which is selected here asY = [Ntc, Pim, Pems, Peml]. The influence is detected usingparameter sensitivity analysis which uses the normalizedoutput-to-parameter sensitivity matrix ,S, defined to containinformation about the effect of a system parameters onits outputs. The elements of the sensitivity matrix, Sij aredefined as:

Sij =θjyi.∂yi

∂θj(4)

In (4) yi is the nominal value for ith output calculatedby using the nominal value for the jth parameter, θj , at aspecific operating point. The normalization introduced in (4)eliminates the effects of magnitude and unit of outputs andparameters. Different approaches can be used to computethe partial derivative ∂yi/∂θj from the model equations [6].For highly nonlinear dynamic models (as in our case) anefficient technique is to use the finite difference formulation

5088

0 500 1000 15001000

1400

1800

Ne (

RP

M)

0 500 1000 1500

1.5

2

2.5

3

3.5x 10

5

Pim

(P

a)

RMSE

avg = 5.45%

0 500 1000 1500

1.5

2

2.5

3

3.5x 10

5

Pem

l Pa)

RMSEavg

= 5.77%

0 500 1000 1500

1.5

2

2.5

3

3.5

4x 10

5

Pem

s (P

a)

RMSEavg

= 7.08%

0 500 1000 1500

6

7

8

9

10

11x 10

4

Ntc

(R

PM

)

RMSEavg

= 8.11%

0 500 1000 15001000

1400

1800

Ne (

RP

M)

0 500 1000 1500

1.5

2

2.5

3x 10

5

Pim

(P

a)

RMSE

avg = 9.9%Meas.

Model

0 500 1000 1500

1.5

2

2.5

3x 10

5

Pem

l (P

a)

RMSEavg

= 9.1%

0 500 1000 1500

1.5

2

2.5

3x 10

5

Pem

s (P

a)

RMSEavg

= 9.86%

0 500 1000 1500

4

6

8

10

x 104

Ntc

(R

PM

)

RMSEavg

= 10.5%

0 2000 4000950

1150

1350

Time (sec)

Ne (

RP

M)

0 2000 4000

1.5

2

2.5x 10

5

Pim

(P

ar)

Time (sec)

RMSE

avg = 4.76%

0 2000 4000

1.5

2

2.5x 10

5

Pem

l (P

a)

RMSEavg

= 5.17%

Time (sec)0 2000 4000

1.5

2

2.5

3x 10

5

Pem

s (P

a)

RMSEavg

= 7.12%

Time (sec)0 2000 4000

4

6

8

10x 10

4

Ntc

(R

PM

)

RMSEavg

= 8.61%

Time (sec)

DC2

DC1

DC3

Fig. 2: Simulated outputs of the complete HDD engine model compared to measured data for three drive cycles (DC).

as: ∂yi/∂θj ≈ ∆yi/∆θj with proper selection of the stepsize ∆θj . Although, small values for ∆θj make the finite dif-ference assumption more accurate, but computational noisewould affect the final results [7]. Moreover, the locality inthe sensitivity analysis (small value for ∆θj) is acceptablein this work since the case is that at the fine-tuning stage ofa modeling work, the range of all parameters is known andsmall changes in the parameters are desired.

The sensitivity of the selected output vector to the scalingparameters vector Θ = [θT , θC , θEGR, θWG] is calculatedand results are shown in Fig. 3 for all variables in the selectedoutput vector. As observed, θT has the most influence in alloutputs. But for other three parameters, based on the selectedoutput, each parameter has different level of influence. Forexample, θC is the main parameter influencing the turbospeed (Fig. 3-a) while θEGR effects Pems more than theother two parameters (Fig. 3-c). This output-based influencerequires a metric which utilizes all sensitivities and makesa decision on the importance of a parameter on an outputvector. As an example, in [8] the average of all outputssensitivities to each parameter in the sensitivity matrix isused as a measure of importance. Another technique tocalculate a quantitative measure for importance is to lookat the direction (in the parameter space) at which data fromthe sensitivity matrix is distributed and selecting a parameterwhich has affected the distribution more than others. This canbe done by applying Principle Component Analysis (PCA) tothe sensitivity matrix S which calculates eigenvalues (maindirections of data distribution) and eigenvectors (variations ateach main direction) of the covariance matrix X = Cov(S).For a n ×m matrix S (n outputs and m parameters in ourSA case study) PCA calculates (maximum) n orthonormaleigenvectors in a m-dimensional space. The first eigen-

0 200 400 600 800 1000 1200 1400 16000

0.5

1

|S2j

| y=

Pim

0 200 400 600 800 1000 1200 1400 16000

0.5

1

|S1j

| y=

Ntc

θT

θC

θEGR

θWG

0 200 400 600 800 1000 1200 1400 16000

0.5

1

|S3j

| y=

Pem

s

0 200 400 600 800 1000 1200 1400 16000

0.2

0.4

0.6

Time (sec)

|S4j

| y=

Pem

l

(a)

(b)

(c)

(d)

Fig. 3: Sensitivity of air-charge path variables to differentparameters

vector is the main direction (in the m-dimensional space)at which data of S are distributed. Therefore the weightof each element in an eigenvector shows how much thecorresponding parameter has contributed to data alignment inthat direction[9]. The eigenvectors, [C1i, ..., Cji, ..., Cmi]

T ,and eigenvalues, λi, from PCA of S are used to calculate thefollowing importance measure for the j th parameter[10]:

µj =

n∑i=1

|λiCji|n∑i=1

|λi|(5)

5089

(a)- DC1

θT

θC

θEGR

θWG

Imp.

Mea

s., µ

(-)

0

0.2

0.4

0.6

0.8

1

(b)- DC3

θT

θC

θEGR

θWG

Imp.

Mea

s., µ

(-)

0

0.2

0.4

0.6

0.8

1

Fig. 4: Importance measure for different parameters from theoff-line analysis

with 0 ≤ µj ≤ 1. As the numerator in (5) suggests, theimportance of each parameter in a principle direction, Cji, ismultiplied by the direction’s importance, λi. Since elementsof S represent deviation of outputs due to perturbation in pa-rameters, thus the measure, µj , shows how much perturbingthe jth parameter has contributed to deviation in the vectorof outputs, Y [11].

The importance measure introduced in (5) for parameteranalysis is applied here to detect effectiveness of eachparameter on the engine model outputs with details describedin [12]. Two different test procedures were selected, onewith major changes in the engine torque and engine speedand the other with major changes in the wastegate and EGRpositions (DC1 and DC3 in Fig. 2 respectively). To calculatethe importance measures, the sensitivity matrices calculatedfrom (4) at each step time are stacked over a test procedureand then PCA is applied to the final matrix. Fig. 4 shows theresults for the two drive cycles. As observed, at both DC1 andDC3, θT (as is expected) has the main effect on the outputs(though µθT is lower in DC3 which has trajectories withhigh variations in engine EGR and WG). The parameter θCcomes as the second influential parameter of the air-chargepath model, θEGR as the third and the wastegate shows theleast influence on the model. One reason for higher EGRinfluence (compared to WG) is that changing the EGR effectsboth the turbine flow and the engine air-fuel-ratio while theWG only effects the turbine flow. Another interesting resultfrom Fig 4 is that when the wastegate and EGR are swept(i.e. in DC3) their effect is relatively higher compared to thetest (DC1) at which there is no specific pattern for actuating(exciting) these two components. Thus, depending on the testcycle, each parameter may have different importance for themodel designer.

IV. PARAMETER TUNING AND RESULTSA. Reduced-Parameter-set Tuning

Having θT and θC selected as the most influential param-eters, a discrete Kalman filter is realized for identificationof the parameters over drive cycles DC1 and DC2 withmeasured Ntc and Pim as feedback variables. The identifiedparameters (mapped as functions of speed and load) areshown in Fig. 5. As shown, θT (ranges in [1.01− 1.12]) haslower variation than θC (ranges in [0.77−0.96]) which agreeswith µθT > µθC . This is explained using (1) as, a θT > 1increases Ntc and (from the compressor map and the intake

(a) Parameter θT

(b) Parameter θC

Fig. 5: Contour plots of estimated θT and θC estimated overDC1 and DC2.

manifold filling dynamics) mc and Pim consequently. Thismonotonic effect helps to decrease estimation errors in theKalman filter quickly since the original model underestimatesboth Ntc and Pim (Fig. 2). But θC does not effect Ntc andPim monotonically since a θC > 1 increases the compressorflow which in turn could be balanced by slowing down Ntc.Fig. 5 also shows smooth change of parameters over theengine speed and load range. This is required for linearinterpolation inside the maps to calculate θT and θC foroperating points not visited during the identification step.

B. Full-Parameter-Set Tuning in OnRAMP

The OnRAMP Design Suite [13], [1], [14], [15] providesa systematic approach to control design process startingfrom system modeling. It makes the modeling process moreefficient and less dependent on the skill level of the engineer.The tool provides environments for building engine schemeout of engine elements library, design of experiment, datamanagement, data analysis and fully automated model cali-

5090

bration based on experimental data and component data suchas turbocharger maps. Further, the tool has model validationfeatures and both the local performance of the individualcomponents and the global input-output behavior of overallconnected model can be evaluated.

The followings are three main steps carried out to developand calibrate a reference model in OnRAMP:

1- Setting up the model structure by using the elementslibrary. Also the same data sets as those used forcomponent modeling (Section II-A) are included formodel identification.

2- Steady state identification of the model in two steps.At first, a component-level identification is performedthat provides reasonable starting points for a globalidentification. Then, the global identification is done thatreconciles the tuning of components in order to achievevery high accuracy of the overall input-output modelwith interconnected components.

3- Transient identification of the engine model. Parameterssuch as time constants of actuators and rotational inertiaof the turbocharger are identified in this step.

It is recommended to collected data based on a design ofexperiment (DoE) which is implemented in OnRAMP ifa user desires it. However even data collected without aDoE (as done in this work), can be used for modelingin OnRAMP. The 3-step identification scheme has shownsuccessful results for optimally solving complex model iden-tification problems. In the case of the HDD engine modeldeveloped in OnRAMP, 79 parameters were taken to thefinal (global) identification stage which include pressure,temperature, speed and emission models. Out of this 79parameters, 47 of them are associated with turbocharger andother sub-models with pressure outputs. The optimizationproblem for the identification is to reduce a quadratic costfunction from estimation errors subjected to both dynamicand static constraints which OnRAMP solves it by employingan optimization algorithm based on nonlinear least squaresfor model identification [13]. OnRAMP can be used onengines of displacements from 1.2L to 15L and consequentlyit is important to get component local parameters in a feasibleinitial range so that good performance of the identificationprocedure is achieved and unnecessary user interventionavoided [13]. This initial range is calculated at the componentlevel identification stage.

C. Comparing Reduced and Full-Parameter-Set Tuning

The final tuned models are tested in the three DCs usedto test the original HDD engine model (shown in Fig. 2). Itis worth noticing that DC3 is not used during the parameteridentification process. Results are shown in Fig. 6 in whichexperimental measurements and OnRAMP simulated dataare also included. Compared to Fig. 2, the averaged RMSEis reduced in all drive cycles for the model with tunedreduced-parameter-set (indicated as “Reduced” in Fig. 6).Moreover, as shown, the full-parameter-set model identifiedby OnRAMP has better accuracy for all variables except thesmall exhaust manifold pressure (Pems). A reason for this

Fig. 7: Comparison of models accuracy in three differentdrive cycles (DCs).

problem is that EGR valve position was not swept enough inthe dataset used for setting up the engine model in OnRAMP.

Fig. 7 shows a summary of accuracy of the three modelsdiscussed in this paper. As shown, by reduced-parameter-set tuning, accuracy of estimation for all variables hasimproved noticeably, with Ntc attaining the highest im-provement. Predictive ability of the “Reduced” model isalso good as for DC3 (which has not been used duringparameter tuning) accuracy has improved, even with lowerfinal values compared to DC1 and DC2. However, as shownin Fig. 7, the OnRAMP model has the highest accuracy forall variables (except Pems) which is attained through full-parameter-set tuning. Therefore, the reduced-parameter-settuning approach is recommended in applications requiringon-line model tuning where moderate accuracy along withsimplicity is mandatory and where the high accuracy needsto be sacrificed due to heavy computational load.

V. CONCLUSIONS

Reduced-parameter-set tuning was addressed in this paperfor the gas exchange path model of a HDD engine. To makethe reduced-parameter-set adaption possible, the main ideawas to tune only parameters with the highest influence on themodel. The influential parameters were detected using fourparameters added to the engine model such that the sensi-tivity of selected outputs was analyzed to flow of the EGR,wastegate and compressor as well as the turbine efficiency.Since the outputs were not showing a unique sensitivity toall parameters, a metric to quantify the overall sensitivityof all outputs to a parameter was used based on principlecomponent analysis. After the turbine efficiency and thecompressor flow were detected to be the most influential,their scaling parameters were tuned in a final identification

5091

0 500 1000 15001000

1400

1800

Ne (

RP

M)

0 500 1000 15000.1

2.1

3x 10

5

RMSEavg,UM

= 4.7%

Pim

(P

a)

RMSEavg,OR

= 3.9%

0 500 1000 15000.1

2.1

3x 10

5

RMSEavg,UM

= 5.4%

Pem

l (P

a)

RMSEavg,OR

= 4.8%

0 500 1000 15000.1

2.1

3x 10

5

RMSEavg,UM

= 5.9%Pem

s (P

a)

RMSEavg,OR

= 4.4%

0 500 1000 1500

2

4

6

8

x 104

Ntc

(R

PM

)

RMSEavg,UM

= 4.9%

RMSEavg,OR

= 4.4%

0 500 1000 15001000

1400

1800

Ne (

RP

M)

0 500 1000 15000.1

2.1

3.5x 10

5

RMSEavg,UM

= 2.4%

Pim

(P

a)

RMSEavg,OR

= 2.7%

0 500 1000 15000.1

2.1

3.5x 10

5

RMSEavg,UM

= 3.6%Pem

l (P

a)

RMSEavg,OR

= 2.2%

0 500 1000 15000.1

2.1

4x 10

5

RMSEavg,UM

= 2.2%Pem

s (P

a)

RMSEavg,OR

= 7%

0 500 1000 1500

2

4

6

8

10x 10

4

Ntc

(R

PM

)

RMSEavg,UM

= 3.1%

RMSEavg,OR

= 2.2%

0 2000 4000950

1150

1350

Ne (

RP

M)

Time (sec)0 1000 2000 3000 4000 5000

0.1

1.6

2.5x 10

5

RMSEavg,UM

= 4.6%

Time (sec)

Pim

(P

a)

RMSEavg,OR

= 1.7%

0 1000 2000 3000 4000 50000.1

1.6

2.5x 10

5

RMSEavg,UM

= 2.9%

Time (sec)

Pem

l (P

a)

RMSEavg,OR

= 2.7%

0 1000 2000 3000 4000 50000.1

1.6

3x 10

5

RMSEavg,UM

= 5.8%

Time (sec)

Pem

s (P

a)

RMSEavg,OR

= 8%

0 1000 2000 3000 4000 5000

2

4

6

8x 10

4

Ntc

(R

PM

)

RMSEavg,UM

= 3.9%

Time (sec)

RMSEavg,OR

= 3.9%

Meas.ReducedOnRAMP

DC2

DC1

DC3

Fig. 6: Measured outputs compared to those simulated by the tuned model and by the model developed in OnRAMP

step. A discrete Kalman filter was implemented and theparameters (mapped as functions of speed and load) wereidentified over two drive cycles. The reduced-parameter-settuned model was tested against experimental measurementson a HDD engine as well as a model developed in OnRAMPDesign Suite which tunes a full set of parameters in an enginemodel. Results from different test drive cycles showed tuningreduced number of parameters (only 2 parameters in theturbocharger model) improves the model accuracy more than50% in average. This made the tuned model to successfullyapproach to the highly accurate model tuned by OnRAMP.

ACKNOWLEDGMENT

The authors would like to acknowledge the financialassistance provided by the U.S. Army Tank AutomotiveResearch, Development and Engineering Center (TARDEC)and the Automotive Research Center (ARC). Also thanks toDaniel Pachner and Greg Stewart from Honeywell Automo-tive Software team and Shankar Mohan and Youngki Kimfrom University of Michigan for their helpful discussions.

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