Cam-Phasing Optimization Using Artificial Neural Networks

8/7/2019 Cam-Phasing Optimization Using Artificial Neural Networks

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2005-01-3757

Cam-Phasing Optimization Using Artificial Neural Networks asSurrogate ModelsMaximizing Torque Output

Bin Wu, Robert G. Prucka and Zoran S. FilipThe University of Michigan

Denise M. Kramer and Gregory L. OhDaimlerChrysler Corporation

Copyright 2005 SAE International

ABSTRACT

Variable Valve Actuation (VVA) technology provideshigh potential in achieving high performance, low fuelconsumption and pollutant reduction. However, moredegrees of freedom impose a big challenge for enginecharacterization and calibration. In this study, asimulation based approach and optimization frameworkis proposed to optimize the setpoints of multipleindependent control variables. Since solving anoptimization problem typically requires hundreds offunction evaluations, a direct use of the high-fidelitysimulation tool leads to the unbearably longcomputational time. Hence, the Artificial NeuralNetworks (ANN) are trained with high-fidelity simulationresults and used as surrogate models, representingengines response to different control variable

combinations with greatly reduced computational time.To demonstrate the proposed methodology, the cam-phasing strategy at Wide Open Throttle (WOT) isoptimized for a dual-independent Variable Valve Timing(VVT) engine. The optimality of the cam-phasingstrategy is validated with engine dynamometer tests.

INTRODUCTION

Conventional Spark Ignition (SI) engines have a limitednumber of independent variables requiring propercontrol, such as spark timing, fuel injection amount andexternal Exhaust Gas Recirculation (EGR) [1]. However,

ever increasing market and regulatory pressures createan incentive to utilize additional devices allowingimproved performance. Recently, Variable ValveActuation (VVA) technology is being increasingly utilizedfor production due to its advantages in adjusting the gasexchange process to optimize engine performance for awide range of conditions experienced by the engineduring realistic driving conditions, and hence increasingtorque generation, improving fuel economy and reducingpollutant emissions [2-11]. With VVA technology, valvetiming, lift and duration become independent control

variables. Other technologies, such as Swirl ControValves (SCV) [12, 13] and cylinder deactivation [14]increase the total number of degrees of freedom furtherThe evolution of diesel engines has the same tendencyFor example, EGR [15, 16], Variable Geometry Turbo-charging (VGT) [17] and multiple injections [18, 19] alintroduce extra independent control variables.

While advanced hardware with additional degrees ofreedom provides more flexibility for improving engineperformance, achieving the full potential of the hardwareis a big challenge. The goal of engine calibration is tosearch for the optimal setpoint combination of alindependent control variables. In the case of aconventional engine, this is typically determined throughsystematic experimentation in the test cell. Howeverwith the increased number of variables the size of the

problem increases exponentially. Hence, techniqueshave been proposed to automate and expedite enginedata acquisition [20-24]. In addition, Design oExperiments (DOE) algorithms [25] are widely used toreduce the total number of experiments, andconsequently the cost and time devoted to enginemapping [26-30]. Nevertheless, searching for theoptimum in the test cell might be impractical and veryexpensive in the case of the large number of degrees offreedom, and a simulation based methodology couldgreatly facilitate the process.

As the number of independent control variables

increases, algorithms based on parametric studies andsimple interpolation do not provide any means folocating the optimum, especially when complexnonlinear constraints are applied. Numerical optimizationis necessary for calibrating high-degree-of-freedomengines. Gradient-based numerical algorithms [31require continuous predictions instead of discreteexperimental points. Hence, a suitable engine model isa prerequisite for developing an optimization frameworkfor engine calibration.


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In the past, empirical models were often generated torepresent the engine response. Statistical regressionanalysis was most commonly used to build the empiricalmodels [26, 27, 32]. Statistical regression was also usedto model the effect of local variables (e.g. spark timing)in a two-stage empirical model [28, 29, 33]. Two-stageempirical models split independent control variables intotwo different groups to reduce the number ofindependent variables in each stage. Although thesplitting eases the problem, the exponentially increasingtrend accompanying any data-driven algorithm is notchanged fundamentally and further increase ofindependent variables would present a challenge.

In this study, a simulation-based optimization frameworkis developed to calibrate high-degree-of-freedomengines. The key component in the framework is themapping relationship from independent control variablesto engine performance. This relationship should berepresented by engine models capable of providing ahigh degree of predictiveness combined with fastexecution speed. These two requirements are typicallyopposing each other. A two-step process is proposed to

satisfy the conflicting demands. Firstly, we develop ahigh-fidelity simulation tool with a full predictivecapability of quantifying the trends of engineperformance in response to different control variablecombinations. The full simulation tool relies on detailedphysical models and requires relatively long computationtime. However, a typical optimization procedurerequires hundreds of function evaluations, thus a muchfaster model needs to be developed as a replacement ora surrogate. We propose using Artificial NeuralNetworks (ANN) [34] for that purpose. ANNs are verycomputationally efficient models capable of learningfrom training samples, and subsequently approximating

the desired input/output relationship. Thus, a high-fidelity engine simulation tool, and a set of high-speedANN surrogate models trained with simulation resultsare key enablers of the simulation-based optimizationframework.

High-fidelity simulations have been considered as a toolfacilitating engine calibration in the past, but in contextsdifferent than proposed here. Fu et al. [35] used anengine simulation tool to investigate intake and exhaustcam-phasing at part load, but relied on parametricstudies and iso-contour plots to determine desirablesettings. Bozza et al [36, 37] used a one dimensional

engine model for comparing VVA strategies and defineda generic optimization problem with up to nine variables.However, only reduced problems with one to threeindependent variables were solved. Sellnau and Rask[38, 39] developed a simulation-based engine calibrationprocedure and conducted optimization of intake valveopening and switching between low- and high- lift lobes,but did not consider the exhaust cam-phasing. As thenumber of degrees of freedom increases, its thecombination of high-fidelity and surrogate models thatcan unlock the full potential of simulation-basedoptimization.

As fast and compact surrogate models, ANNs havebeen used to replace time-consuming computationatasks and expedite complicated simulationsPapadimitriou et al used ANNs to replacecomputationally intensive components, such as intakeand exhaust manifold, of a one-dimensional enginesimulation tool [40]. High-speed ANN models were alsoused for On-Board Diagnostics (OBD) fault detection[41, 42]. Hardware-in-the-Loop (HIL) simulation isanother suitable application exploiting the computationefficiency of ANN models [43, 44, 45]. The application ofANN models for real-time estimation of mass air flowrates through the engine with a dual-independent camphasing system has been demonstrated in previousstudies [63, 64].

To demonstrate the proposed algorithm, we select adual independent VVT engine as an example of high-degree-of-freedom engines. For this engine, the primaryindependent control variables include intake cam-phasing, exhaust cam-phasing, spark timing and fuel airequivalence ratio (Phi), while engine speed and torquecommand are determined by interaction with the driver

transmission and other torque consumers. The scope othis paper is limited to Wide Open Throttle (WOT) onlyfor which the engine torque is maximized at selectedengine speeds by ensuring minimum inlet restrictionAlthough all four independent variables are optimizedsimultaneously, more emphasis is placed on cam-phasing optimization, since camshaft positions affecfilling of the cylinder in a very direct way.

The paper is organized as follows. The optimizationframework is proposed and described first. Next, thehigh-fidelity simulation tool is built and used for pre-optimality studies. The high-fidelity simulation results

enable establishing benchmarks for subsequenvalidation of ANN predictions and optimization resultsThe procedure for training the ANN surrogate modelsand determining the best network structure and sizefollows. Then, the optimization problems are formulatedand solved to maximize wide-open throttle torqueFinally, the optimization results are validated with enginedynamometer tests. Further discussions are presentedto address practical issues before offering conclusions.

OPTIMIZATION FRAMEWORK

Figure 1 illustrates the optimization framework proposed

for calibrating high-degree-of-freedom engines. Thegraph consists of two parts. The top part shows steps forbuilding computationally efficient ANN surrogate modelsand the bottom part shows the use of ANN surrogatemodels in optimization. Developing fast ANN models is aprerequisite for optimization application, since the latteoften requires a large number of predictions in theirsearch for the optimum of the objective function.

The first step in building the ANN surrogate models is toacquire hardware specifications and geometricinformation for the target engine from componen


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High-FidelitySimulation

Componentgeometry

High-speed ANNSurrogateModels for boththe optimizationobjective andconstraints

DOESampling

UpdateSetpoints (SQP)

Satisfied?N

Y

ControlVariable

Setpoints

Engine Responses

ANNs for

Objective

ANNs forConstraint 1


Optimizationobjective &constraints

Speed & Load

OptimizedSetpoints

Operatingpoint

Optimizer

Hardwaretests

High-FidelitySimulation

Componentgeometry

High-speed ANNSurrogateModels for boththe optimizationobjective andconstraints

DOESampling

UpdateSetpoints (SQP)

Satisfied?N

Y

ControlVariable

Setpoints

Engine Responses

ANNs for

Objective



Optimizationobjective &constraints

Speed & Load

OptimizedSetpoints

Operatingpoint

Optimizer

Hardwaretests

Figure 1 Optimization framework for calibrating independent control variables in high-degree-of-freedom engines

drawings and other design documentation. Secondly, ahigh-fidelity simulation tool is developed to model thetarget engine. The simulation tool is based on physicalprinciples, real engine geometry and phenomenologicalmodels. The model constants are determined with the

aid of experimental data. The advantage of using thehigh-fidelity tool is that only a limited number of engineexperiments can provide sufficient data for determiningmodel coefficients. It can also enable inclusion ofdesign features that might not be available in hardware.Depending on specific goals of the calibration problem,the simulation tool can be tailored to include details atdifferent levels and retain proper fidelity. After the high-fidelity simulation tool is built and validated, it is used topredict the engines response under various operatingconditions. Benchmarks of high-fidelity simulation resultsare built to check and validate ANN behavior in thesubsequent steps.

In the third step, the input combinations of high-fidelityruns are determined with a Design-Of-Experiments(DOE) algorithm - Latin Hypercube Sampling (LHS) [46,47]. LHS generates input combinations by assuminguniform distribution of all independent variables withintheir respective ranges. The assumption of uniformdistribution leads to input combinations covering theentire operating space evenly, which improves theefficiency of sampling process. The full simulationresults are then used for training ANN surrogate modelsthat are capable of predicting engine responses. Several

multi-input-single-output ANNs are used instead of usingone multi-input-multi-output ANN. Each ANN modelsone variable formulated as a part of the optimizationobjective or constraints. This has proven to be beneficiafor overall accuracy of ANN models. It also provides

more flexibility for adding or removing engineperformance variables from the formulation ooptimization problems.

Once the ANN surrogate models are trained andvalidated against full simulation benchmarks, they areemployed to optimize independent control variables, asshown in the bottom part of Figure 1. We use enginespeed and torque command to define the enginesoperating point. Hence, the setpoints of independencontrol variables are optimized at any given combinationof engine speed and torque command. The optimizecalls ANN surrogate models to obtain engine responses

The engines responses are then used to evaluate theobjective function and constraints. If the convergencecriteria are not satisfied, the optimizer will update thevalues of independent control variables and the ANNsurrogate models will be called again. The processiterates until the optimization objective is achieved andall constraints are satisfied. To solve a typicaoptimization problem, the ANN surrogate models arecalled and evaluated hundreds of times, thus precludingthe use of high-fidelity full simulations directly and

justifying the up-front effort of developing surrogatmodels.


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Figure 2 Definition of intake and exhaust camshaftpositions

HIGH-FIDELITY SIMULATION TOOL

The engine used in this study is a production-style 2.4liter, in-line four cylinder dual overhead camshaft(DOHC) engine manufactured by DaimlerChrysler. Eachcylinder has two intake valves and two exhaust valves.The engine was originally designed as a conventionalfixed-cam engine. However, the prototype VVT versionis equipped with intake and exhaust cam-phasers.

Intake and exhaust camshaft positions areindependently controlled with vane type hydraulicactuators. Its worth noting that all other parts, such asintake/exhaust manifolds, ports, camshaft lobe profiles,cylinder head and pistons, are not redesigned andoptimized for VVT operation. Therefore, demonstratingor evaluating the maximum potential of VVT is not theintention of this study, rather the methodology tomaximize the torque output of the given configuration.

For the VVT engine, we use Intake Centerline Location(ICL) and Exhaust Centerline Location (ECL) torepresent the intake and exhaust camshaft positionsrespectively. As shown in Figure 2, ICL is defined as the

distance between the top dead center (TDC) and thecenterline of intake camshaft lobe; and ECL is definedas the distance between TDC and the centerline ofexhaust camshaft lobe. They both are measured incrank angle (CA) degrees. Before adding the cam-phasers, the default camshaft positions were: ICL0=115degrees ATDC and ECL0=111 degrees BTDC. The cam-phasing range with the prototype VVT system is 15degrees for both intake and exhaust. The mainspecifications of the target engine are listed in Table 1.

The effects of cam-phasing on engine performance stemprimarily from the change of engine breathing behavior.

Since the ultimate goal in this study is cam-phasingoptimization, it is essential to accurately model theengines intake and exhaust process. A high-fidelitysimulation tool is based on a co-simulation approachthat combines the strength of the commercial codeRicardo WAVE

in gas dynamics modeling and the

strength of the quasi-dimensional Spark IgnitionSimulation (SIS) in combustion modeling. WAVE [48, 49]has been widely used and validated for engineperformance predictions [50-52]. In this study, it is usedto model gas dynamics in the intake and exhaustsystems from air filter to tailpipe. SIS is a research codewritten in FORTRAN language that has been refined

over time and used routinely at the University ofMichigan for a variety of simulation studies. Availabilityof its source code provides flexibility to revise and tailorthe program as needed [53, 60, 61].

Quasi-dimensional SI simulation (SIS) is based on themass and energy conservation and thephenomenological models for turbulence, combustionand heat transfer in the cylinder, represented with a setof first-order, simultaneous ordinary differentialequations. The details have been described previouslyby Filipi and Assanis [53]. The combustion sub-model is

based on the turbulent flame entrainment mode

proposed by Tabaczynski [54,55] and further refined byPoulos and Heywood [56]. The combustion model iscomplemented by a single-zone turbulence model [57-59], which calculates crank-angle resolved globaturbulent flow field parameters throughout the wholecycle. The interaction between the spherical flame fronand the combustion chamber walls defines the flamearea, and the geometric information about thecombustion chamber is taken into account within theframework of a time-based code. The effect of air/fueratio and residual on the rate of entrainment and burn-upis accounted for by the laminar flame speed term, whichis particularly important in case of potentially increased

overlap leading to large quantities of residual. In itsvarious evolutions, the simulation has been used in 2and 4-valve SI engine turbocharger matching studies[53], in valve event optimization [60], and in optimizingstroke-to-bore ratio for SI engine design [61].

In SI engines, knock is an important factor limitingengine torque at low speeds. Spark timing is oftenretarded and/or mixture is enriched to suppress knockIn order to be able to consider knock as a constraint, thisstudy uses WAVEs knock model for predicting knockintensity [62]. The knock intensity is defined as the

Table 1 Critical parameters of the target VVT engine

Displacement 2.4 liters

Bore/Stoke 87.5/101.0 mm

Compression Ratio 9.4:1

Max. Intake Valve Lift 8.25 mm

Max. Exhaust Valve Lift 6.52 mm

Default Intake Valve TimingCloses/Opens/ Centerline

51oABDC/ 1

o

BTDC/ 115oATDC

Default Exhaust Valve TimingCloses/Opens/ Centerline

9oATDC/ 51

o

BBDC/ 111oBTDC

Default Valve Overlap 10o

@ 0.5 mm liftAllowed Intake Cam-phasingRange

15o

Crank Angle

Allowed Exhaust Cam-phasingRange

15o

Crank Angle


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(a) (b)Figure 3 High-fidelity simulation benchmark of WOT torque at 2000rpm: (a) plotted as a function of intake and

exhaust camshaft ositions b lotted as a function of s ark timin and fuel/air e uivalence ratio

mass fraction of unburned mixture when auto-ignitionhappens. The effects of cam-phasing on knock in a VVTengine can be magnified due to the possibility of runningwith increased amounts of hot internal residual.

The WAVE and SIS models are coupled at intake andexhaust valves as interfaces. A top level program isdeveloped in C++ to integrate the WAVE and SISmodels by feeding WAVE results of valve mass flowrates to SIS, and SIS results for burning rate back toWAVE. Limited experimental data are acquired toidentify model coefficients such as flow coefficients (Cd)of intake and exhaust valves, turbulence dissipationconstant, heat transfer correlation coefficient, andengine friction model coefficients. Previous studies havedemonstrated that the high-fidelity simulation tool iscapable of capturing air flow rate accurately [63, 64].More details about the high-fidelity simulation tool for the2.4 L engine are available in the previous publication[63] and references therein.

The effort and cost associated with development of thehigh-fidelity code is more than offset by savings in the

subsequent optimization process, as well as by its abilityto provide a wealthof information even beyond what theexperimental setup can deliver. For example, internalEGR is hard to measure directly, and yet it plays acritical role in explaining the VVT engines capability ofincreasing WOT torque and fuel economy, and reducingNOx emissions.

Figures 3 to 5 show examples of high-fidelity simulationresults at 2000 rpm, WOT. In Fig 3(a), the torquecontours are plotted with respect to intake and exhaustcamshaft positions, with spark timing and fuel/airequivalence ratio (Phi) being fixed. In Fig 3(b), the

torque contours are plotted with respect to spark timingand Phi for fixed ICL and ECL at default valuerespectively. The equivalence ratio is varied fromstoichiometric to rich, due to the focus of this study onWOT. To generate each graph, high-fidelity simulations

are run in a 7 x 7 grid. Further investigation shows thaWOT torque is primarily determined by the amount otrapped air, when other operating parameters are fixedat desired values or within normal range. The amount oftrapped air directly depends on intake and exhauscamshaft positions, as illustrated by Figures 4 and 5.

In Fig. 4(a) and (b), engine torque and air flow rate areplotted as a function of intake camshaft position. Thedirect correlation between torque and air flow rate isshown clearly. Both air flow and torque are verysensitive to variations of intake cam phasing. Thisemphasizes the fact that maximum performancedepends on both the throttle position and camshaftposition; hence, a wide open throttle is only aprerequisite for reaching maximum performance. In Fig4(c) and (d), the mass flow rate through intake andexhaust valves are plotted at three different intakecamshaft positions. Advancing intake timing at lowengine speed traps more air in the cylinder since lessfresh charge is pushed back before intake valve closes(IVC), as shown in Fig. 4(c). Although early intake valveopening (IVO) leads to longer valve overlap and large

reverse flows through both intake and exhaust valvesduring valve overlap, the effect on total air intake is lessthan the advantage of early IVC. Thus, engine torque atthis speed is maximized with the most advanced intakecamshaft position of ICL=100 degrees ATDC.

Similar graphs are plotted in Figure 5 as exhauscamshaft position is changed, while intake camshaftposition and other independent variables are fixedHowever, Figs. 5(a) and (b) show that engine torque andair flow rate are much less sensitive to variations of ECLthan ICL, at least at the given speed of 2000 rpm. Therelatively flat lines make it hard to pinpoint the optima

value of exhaust camshaft position. The mass flow ratesplotted in Fig. 5(c) and (d) confirm above observationRetarding exhaust timing results in re-induction ofexhaust gas when exhaust valve closing (EVC) issubstantially after TDC. In contrast, advancing exhaus


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Figure 4 High-fidelity simulation results at 2000rpm, WOT: (a) torque vs. intake camshaft position; (b) air flow ratevs. intake camshaft position; (c) intake mass flow rate vs. crank angle at selected intake camshaft positions; (d)

exhaust mass flow rate vs. crank angle at selected intake camshaft positions

Figure 5 High-fidelity simulation results at 2000rpm, WOT: (a) torque vs. exhaust camshaft position; (b) air flow ratevs. exhaust camshaft position; (c) intake mass flow rate vs. crank angle at selected exhaust camshaft positions; (d)

exhaust mass flow rate vs. crank angle at selected exhaust camshaft positions

timing and closing exhaust valves before TDC results inre-compression of residual gas and larger reverse flowthrough intake valves. Both retarding and advancingexhaust timing lead to larger residual fraction. This inturn displaces fresh air and reduces engine torque. Inaddition, early exhaust valve opening (EVO) reducesexpansion stroke length and expansion work.Consequently, the optimal tradeoff is achieved inbetween, for ECL=116 degrees after top dead center.Although the effects of exhaust camshaft position onengine torque seem negligible at 2000 rpm, it is notnecessarily true at other speeds. Retarding the exhaustevent at higher speeds proved to be beneficial due torelatively longer expansion stroke and less significant re-induction of exhaust gas.

After examining and validating the behavior of the high-fidelity simulation tool, the tool is used to buildbenchmarks similar with the contour graphs in Figure 3.

A series of high-fidelity simulation benchmarks are builfor different engine performance variables as functionsof different combinations of independent variablesTogether with other criteria, these benchmarks are usedto determine the best ANN network structure in thefollowing section.

ANN SURROGATE MODELS

For the target VVT engine, we identify four independentcontrol variables at WOT for any given engine speedintake cam-phasing, exhaust cam-phasing, spark timingand Phi. Hence, the WOT torque is fundamentally afunction of five independent variables when enginespeed is taken into account. Figure 6 illustrates theinput/output relationship that the ANN surrogate modewill approximate.


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Using Latin Hypercube Sampling technique, a set of1025 different input combinations are generated, forwhich high-fidelity simulations are run. The samplingprocess is automated by using iSIGHT

. iSIGHT parses

input files, runs simulations, and saves results desired.The sampling ranges of all inputs are listed in Table 2.We intentionally select relatively large ranges to ensurethat all applicable input combinations are encompassed.The high-fidelity simulation results are split randomly intotwo subsets: one subset (95% of all samples) for trainingANNs and the other subset (the remaining 5%) fortesting generalization during training. The training

procedure determines the values of weights and biasesfor all neurons in the network. All ANNs are trained withthe trainbr function in Matlab Neural Network Toolbox,which exploits Bayesian regularization to reduceoverfitting [65]. The overfitting can be described as theoccurrence of undesirable fluctuations of output data forinputs different than those used in training. It oftenhappens as the consequence of imposing too severeaccuracy limits.

A procedure for determining the optimal networkstructure has been developed in our previous studies[63, 64]. The same procedure is followed in this paper.

We train networks with one, two and three hidden layers,and consider different number of neurons in hiddenlayers. The prediction accuracy of any ANN model isthen evaluated using the mean squared errors (mse).However, before the decision about the ANNarchitecture is made, the risk of overfitting and thedeterioration of generalization quality are considered.

The following ANNs are trained and shown in Figure 7:one hidden layer networks 5-4-1, 5-6-1, 5-28-1; twohidden layer networks 5-3-3-1, 5-4-4-1, 5-10-10-1; andthree hidden layer networks 5-3-3-3-1, 5-4-4-4-1, 5-8-8-8-1. The convention allowing description of networkstructure with a sequence of numbers is that the first andlast numbers represent the number of inputs and outputsrespectively. Each number in the middle represents thenumber of hidden neurons in a corresponding hiddenlayer. The mean squared errors for training samples andtesting samples are plotted against network size inFigure 7(a) and (b), respectively. The training andtesting mse are largely regarded as indicators of fittingaccuracy and generalization accuracy of the ANN.Figure 7 displays how mses vary with architecture andnetwork size, which is quantified by the total number ofconnecting weights and neuron biases.

The following criteria are used to select the besnetwork:

Small training msefor good fitting accuracy;

Small testing msefor good generalization accuracy;

Good match with high-fidelity simulationbenchmarks;

No overfitting assessed based on high-fidelitypredictions.

The first two criteria are quantitative and easy toimplement utilizing plots like those given in Fig. 7Overall, both fitting accuracy and generalizationaccuracy are improved by increasing network size, asindicated by decreasing mses plotted in Figure 7(a) and(b). However, the decreasing rate diminishes and it is

hard to distinguish two networks with negligibledifference in mses if only the msecriteria are used.

The third and fourth criteria are somewhat subjectivebut important for making the final selection. ComparingANN predictions with high-fidelity simulation results canbe of great help in assessing overall features of thesurrogate model. As network size grows, we keepchecking ANN predictions against high-fidelitybenchmarks until we get a satisfying match, bothqualitatively and quantitatively. In other words, weensure that there is no local anomaly at any given point

Figure 6 ANN surrogate model for engine torque atwide-open-throttle

Figure 7 Training neural networks with differentnetwork structures and sizes: (a) mean squared errorfor training samples vs. network size; (b) meansquared error for testing samples vs. network size.

Table 2 Ranges of inputs to ANN surrogate models

Variable

Lower

bound

Upper

bound Unit

ICl 95 135degreeATDC

ECL 91 131degreeBTDC

Spark -60 10degreeATDC

Phi 1.0 1.5 -

Speed 600 6500 rpm


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Figure 8 compares the predictions of ANN 5-10-10-1 forWOT torque with the high-fidelity simulation resultsshown previously in Figure 3. Obviously, the operatingconditions were exactly the same. Clearly, ANNpredictions match high-fidelity benchmarks very well anddemonstrate features important for optimization, such asthe same locations of maximum torque points.Comparison with other benchmarks confirmedadvantageous behavior of ANN 5-10-10-1. Smoothsurfaces as those shown in Figure 8 indicate that thereis no overfitting. Overfitting is usually accompanied withrandom, un-explained fluctuations. Hence, the 5-10-10-1network is selected as the preferred network for WOTtorque. Please see reference [64] for the example ofoverfitting and measures to reduce it.

OPTIMIZATION USING ANN SURROGATEMODELS

For WOT operation, engine performance is assigned thehighest priority. Therefore, the optimization objective isto maximize torque generation, within given constraintssuch as exhaust temperature limit or prevention ofknock. The optimization problem is formulated asfollows:

1.0);(

850);(

3.10.1

ATDCdegree050

BTDCdegree12696

ATDCdegree130100

:Subject to

),,,(

);(:Maximize

=

=

SpeedxK

CSpeedxT

Phi

Spark

ECL

ICL

PhiSparkECLICLx

SpeedxTorqueObj

i

o

exh

(1)

In above equation, exhT represents exhaust temperature

iK represents knock intensity; x represents fou

independent variables, while engine speed is regardedas a given parameter. The first four constraintsrepresent the allowed ranges for all four independenvariables. The constraint on exhaust temperature isintroduced to protect the catalyst from overheating. Thelast constraint prevents unrealistic spark timing thaleads to excessive knock.

In Equation 1, Torque , exhT , and iK are functions o

independent variables and speed. Three ANN surrogatemodels are constructed to model these functions. Thepreferred network structures are 5-10-10-1, 5-11-11-1and 5-11-11-1 respectively. The ANN surrogate modelsare inserted into the optimization framework shown inFigure 1. The optimization problem is solved at 100equally spaced speeds between 1000 and 6000rpmThe optimized results of all four independent variablesare subsequently plotted as dotted lines in Figure 9. InFig. 9(b) and (d), the lines of ECL and Phi show a sharp

fluctuation around 2000 rpm, which is obviouslyundesirable from the point of view of driveability. Havingaccess to the high-fidelity simulation allowed detailedanalysis of the anomaly. It is found that the fluctuation ismainly due to the insensitivity of engine torque withrespect to ECL and Phi. As shown in Figure 3(a) and(b), as well as Figure 5(a), the gradients along ECL andPhi axes are very small in the area surrounding themaximum torque point. This causes difficulty for theoptimizer to locate the optimum.

To overcome the problem, two extra terms are added topenalize the sudden drastic changes of ECL and Ph

between two adjacent speeds. The optimizationobjective is revised as follows:

(a) (b)

Figure 8 Comparison of high-fidelity simulation and ANN model predictions of WOT torque at 2000 rpm, plotted as afunction of: (a) intake and exhaust camshaft positions; (b) spark timing and fuel/air equivalence ratio


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1211

);(

+

+=

kkkk

kk

PhiPhiCECLECLC

SpeedxTorqueObj(2)

Where, subscript k indicates the index of optimizationproblem in the speed sequence. Depending on whetherthe optimization problems are solved in ascending ordescending order of speed, the sign in the penalty termscan be either - or +. In this study, the optimizationproblems are solved in both directions and the average

of the two results is reported in Figure 9 (solid lines).

The constant coefficients 1C and 2C are tuned to

generate smooth ECL and Phiresults without noticeabledeterioration of WOT torque. The lower range constrainton ICL is active at low engine speeds, as shown in Fig.9(a). Relaxing the lower range constraint of ICL couldtherefore increase WOT torque further at low enginespeed. The optimized results of other three independentvariables are well within the allowed range.

The VVT engines performance with the optimizedcontrol variables is given in Figure 10. For comparisonpurposes, we optimize spark timing and Phi for the fixed-camshaft baseline engine using the same ANNsurrogate models and optimization algorithm, while fixingintake and exhaust camshaft position at default values.In Figure 10, we use solid lines to represent the VVTengine with optimized camshaft positions and dottedlines to represent the baseline engine with defaultcamshaft positions. As shown in Fig. 10(a), VVT

increases WOT torque at low and medium speeds. Thedifference in WOT torque diminishes around 4900 rpmwhere the optimized camshaft positions are very close totheir default values. Fig. 10(b) compares the powegenerated by the two engine configurations. In Fig10(c), the constraint on exhaust temperature becomesactive at speeds above 4500 rpm for both engineconfigurations. In contrast, the constraint on knockintensity is active at low speeds, as shown in Fig. 10(d)Compared with the fixed-cam engine, the VVT engine ismore likely to knock because early intake valve closingincreases the engines effective compression ratio. Asshown in Fig. 9(d), the combustion is enriched at lowspeeds to reduce knock sensitivity and at high speeds tocool down the exhaust. As a result, both constraints arefully satisfied.

EXPERIMENTAL VALIDATION AND PRACTICALIMPLEMENTATION

Engine dynamometer tests are carried out in the W.ELay Automotive Laboratory at the University of Michiganto validate the optimization results. All experiments aredone at steady state after the engine is well warmedThe first part of the experimental work compares engineperformance with the optimized and default camshaftpositions and quantifies the gain in performance. Therelative fuel/air equivalence ratio is fixed at Phi=1.11, thespark timing corresponds to the optimized value, and thespeed is varied up to 3600 rpm due to hardware

Figure 9 Optimized independent variables at different engine speeds: (a) intake camshaft position; (b) exhaustcamshaft position; (c) spark timing; (d) fuel/air equivalence ratio


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limitations. The tests cover the speed range wheretangible torque improvement is achievable. Theexperimentally determined torque increase with theoptimized camshaft is compared to correspondingpredicted values in Figure 11. The overall measuredmagnitude of the increase is very much in line withsimulation results, as well as the overall shape of linesas a function of speed. The latter confirms the ability ofthe model to accurately predict relative effects of cam-phasing on engine torque a critical feature given itsintended use within the optimization framework.

The second part of the experimental plan is designed tovalidate the optimality of the optimized camshaftpositions. In this part, the intake and exhaust camshafpositions are swept in turn, while air/fuel ratio and sparktiming were kept fixed. Tests are performed at threeengine speeds: 1200, 2000 and 3600 rpm. Figure 12displays the test results. In the top graph (Fig. 12(a))intake camshaft position varies within the allowed rangeand exhaust camshaft position is fixed at the optimizedvalue. In the bottom graph (Fig. 12(b)), exhaustcamshaft position changes while intake camshaft isfixed. In both graphs, the optimized positions ointake/exhaust camshaft are marked with thick solidbars. The optimized positions coincide with, or are veryclose to the best positions suggested by theexperimental curves. Considering the 1% tolerance intorque measurement, this effectively verifies theoptimality. In addition, it confirms the ability of the fulsimulation model to reliably predict the relative effects o

cam-phasing, irrespective of possible smaldiscrepancies in absolute values.

While the simulation-based approach allows optimizingcamshaft positions, a practical implementation will stilrequire follow-up experiments to account for modelinginaccuracy. The emphasis in this study is on modelingthe gas exchange process accurately, and simulationshave demonstrated sufficient fidelity for optimizing thecam-phasing strategy. However, careful validation othe combustion or the knock sub-models might not

Figure 11 Comparison of measured and predictedtorque increases with the optimized cam phasing at

wide open throttle.

Figure 10 Comparison of engine performance with optimized and default camshaft positions: (a) engine torque; (b)engine power; (c) exhaust temperature; (d) knock intensity


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always be possible due to development time constraintsand unavailability of test data. In that case, the absolutevalues of spark timing are not directly applicable. Once

the optimized camshaft positions are validated and fixed,follow-up experiments could easily fine-tune the tworemaining independent variables. This coincides withthe current practice for conventional, fixed camshaftengines, and hence would not require changes ofexisting calibration procedure.

SUMMARY AND CONCLUSIONS

This paper proposes an optimization framework and asimulation-based approach for calibrating high-degree-of-freedom engines. The high-fidelity simulation tool isdeveloped first as a virtual engine, capable of modeling

the relationship between independent variable setpointsand engine performance. After identifying modelcoefficients with a limited set of experimentalmeasurements, the tool can be used to create anydesired set of data and simulate new designs not yetavailable in hardware. However, the prospect ofexecuting the simulation hundreds of times within theoptimization framework imposes a need for much fasterand yet accurate surrogate models. The artificial neuralnetworks (ANN) are used to create such computationallyefficient models. The ANNs are trained on operating

points chosen by a design-ofexperiments techniqueand produced by high-fidelity simulations.

The computational speed of neural networks allowssolving optimization problems with various formulationsof optimization objectives and constraints. This studydemonstrates the use of the proposed algorithm fomaximizing the WOT torque of the prototype VVT enginewith dual-independent cam-phasers. The independenvariables are: intake cam-phasing, exhaust cam-phasing, spark timing and fuel-air equivalence ratio. Thefollowing steps are demonstrated:

Pre-optimality studies to illustrate sensitivities of thesystem to changes of main parameters.

Generating benchmarks with high fidelity simulations

and using them to determine optimal networkstructures for ANN surrogate models.

Formulating the objective function and solving theoptimization problem for the WOT operation with theaid of ANN surrogate models.

The optimality of cam-phasing results is subsequentlyverified using hardware experiments. The magnitudesof predicted relative engine torque improvements in thelow- to medium-speed range are confirmed as well. Themain effect comes from optimized intake valve closingtime.

Figure 12 Experimental validation of the optimality of intake and exhaust camshaft positions: (a) intake cam-phasing sweep; (b) exhaust cam-phasing sweep. Optimized camshaft positions are marked with thick solid bars.


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The application of the proposed algorithm to part loadconditions, using fuel efficiency as an objective functionand emissions asconstraintsispursued as the next step.

ACKNOWLEDGMENTS

The authors appreciate the contribution of Roger Vick,Fadi Kanafani, Michael Prucka, Eugenio DiValentin, of

Daimler Chrysler in developing the component modulesfor the engine simulation tool and other technicalsupport.

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CONTACT

Prof. Zoran FilipiDepartment of Mechanical Engineering,University of Michigan2031 W. E. Lay Automotive Lab1231 Beal Ave., Ann Arbor, MI [email protected]

Documents

Cam-Phasing Optimization Using Artificial Neural Networks