A Simulation-Based Approach for Developing Optimal Calibrations for Engines with Variable Valve Actuation

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Oil & Gas Science and Technology – Rev. IFP, Vol. 62 (2007), No. 4, pp. 539-553 Copyright © 2007, Institut français du pétrole DOI: 10.2516/ogst: 2007047 IFP International Conference Rencontres Scientifiques de l’IFP

New Trends on Engine Control, Simulation and Modelling Avancées dans le contrôle et la simulation des systèmes Groupe Moto-Propulseur

B. Wu1, Z. Filipi1, R. Prucka1, D. Kramer2 and G. Ohl2

1 University of Michigan, 2031 W. E. Lay Automotive Lab, 1231 Beal Ave., Ann Arbor, MI 48109-2133, USA 2 DaimlerChrysler Corporation, 800 Chrysler Drive, Auburn Hills, MI 48326-2757, USA e-mail: [email protected] - [email protected] - [email protected] - [email protected] - [email protected]

Résumé — Une approche basée sur la simulation pour le développement de réglages optimaux des moteurs avec système d’actionnement variable de soupape — La technologie d’actionnement variable de soupape (Variable Valve Actuation, VVA) présente un fort potentiel pour augmenter les performances et réduire consommation et pollution. Les avantages du VVA proviennent d’une meilleure aération et de la possibilité de contrôler les résidus internes. Par contre, l’addition de variables de contrôle supplémentaires dans un moteur VVA augmente la complexité du système, ce qui nécessite la mise au point d’une stratégie de contrôle optimale afin d’en tirer tous les bénéfices. L’approche traditionnelle reposant sur l’expérimentation s’avère trop onéreuse dans ce cas du fait de l’augmentation exponentielle du nombre de tests. Ce projet propose comme alternative de définir le réglage des soupapes comme un problème d’optimisation. Il identifie les simulations nécessaires au développement d’une méthode générique capable d’intégrer un nombre croissant de degrés de liberté afin de développer un outil de grande fidélité pour la prédiction des effets de différents dispositifs. Puisque la résolution d’un problème d’optimisation requiert l’évaluation de centaines de fonctions, l’utilisation directe d’une simulation haute- fidélité demande des temps de calculs beaucoup trop longs. En remplacement, un réseau artificiel de neurones est entraîné avec des résultats de simulation haute-fidélité et utilisé pour représenter la réponse du moteur à différentes combinaisons de variables de contrôle, et ce avec des temps de calcul beaucoup plus courts. Cet article décrit une méthode basée sur la simulation, apporte des détails sur les techniques de modélisation haute-fidélité et démontre une application à un prototype de moteur à essence à quatre cylindres et double arbre à cames indépendant.

Abstract — A Simulation-Based Approach for Developing Optimal Calibrations for Engines with Variable Valve Actuation — Variable Valve Actuation (VVA) technology provides high potential for achieving improved performance, fuel economy and pollutant reduction. Benefits of VVA stem from better breathing and the ability to control internal residual. However, additional independent control variables in a VVA engine increase the complexity of the system, and achieving its full benefit depends critically on devising an optimum control strategy. The traditional approach relying on experimentation is in this case prohibitively costly, since the number of tests increases exponentially. Instead, this work formulates the task of defining actuator set-points as an optimization problem. It identifies simulation needs for supporting development of a generic methodology, capable of handling increased number of degrees of freedom. A high-fidelity tool predicts effects of various devices being considered. Since solving 06108_O_Wu 13/11/07 15:10 Page 540

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an optimization problem requires hundreds of function evaluations, direct use of the high-fidelity simulation leads to unacceptably long computational times. Instead, the Artificial Neural Networks (ANN) are trained with high-fidelity simulation results and used to represent engine’s response to different control variable combinations with greatly reduced computational time. The paper describes a comprehensive simulation-based methodology, provides details of high-fidelity and surrogate modeling techniques, and then demonstrates application on a prototype four-cylinder spark-ignition engine with dual independent cam-phasers.

INTRODUCTION A high-fidelity engine simulation is used to characterize the effects of cam-phasing on engine performance, fuel con- Passenger car engines experience a very wide range of operat- sumption and, to some degree, emissions. After calibrating ing conditions. Flexible systems have thus become increas- the model constants with a limited number of experimental ingly attractive as means of achieving optimal engine-in-vehi- data, the simulation tool is able to predict engine behavior cle operation. Advanced Variable Valve Actuation (VVA) with sufficient fidelity for generating a robust calibration technologies are particularly promising in saving fuel, reduc- [18]. The predictiveness of physics-based models used in a ing emissions and increasing Spark-Ignition (SI) engine out- high-fidelity simulation allows investigations of new system put [1-5]. Among various VVA options, cam-phasing is gain- configurations, even those that have not been built yet. Given ing broad acceptance, due to its ease of implementation and the fact that running a high-fidelity simulation takes a signifi- tangible advantages over conventional fixed-cam engines [6- cant amount of computation time and solving an optimization 11]. The continuous, dual independent cam-phasing, i.e. inde- problem requires hundreds of function evaluations, a faster pendent phasing of intake and exhaust cams — offers signifi- engine model is required to enable optimizations at many cant flexibility in optimizing engine breathing and internal operating points. Artificial Neural Networks (ANN) [19] are residual gas fraction, while preserving the relative simplicity very computationally efficient, and are therefore considered of Variable Valve Timing (VVT) concept. as fast surrogate models suitable for optimization exercises. The extra flexibility enabled with intake and exhaust cam- Previous applications of ANNs in the automotive field phasers increases the overall system complexity by introduc- encourage their use here. He et al. [20, 21] have demon- ing more degrees of freedom. For any arbitrary operating strated ANN’s capability of modeling a turbo-charged diesel point, the set-points of intake and exhaust cam-phasers need engine. Brahma et al. [22] used the ANN models to optimize to be defined during calibration development. This creates a control variables of the diesel engine, although with some challenge for the traditional calibration approach relying on challenges regarding noise in optimization results. On-Board experimentation in the dynamometer test-cell. The increase Diagnostics (OBD) [23, 24] and Hardware-in-the-Loop in the number of independent variables leads to an exponen- (HIL) simulation [25-27] exploited ANNs computational tial increase of the number of tests required. This easily efficiency. Using ANN’s for estimating mass air flow rate becomes unmanageable and prohibitive in terms of cost and through the VVT engine has been demonstrated by Wu et al. development time. Novel approaches are needed for address- in [28]. ing the problem of set-point calibration in high degree-of- With the goal of either maximizing performance or mini- freedom (DOF) engines. Hence, attempts have been made to mizing fuel consumption, the set-point calibration is formu- reduce the effort and address cam-phasing optimization using lated and solved as a series of optimization problems with computer simulations and design-of-experiments approaches objectives and constraints defined at individual operating [12-17]. However, these approaches are suitable only for sys- points. Constraints include functional limits of cam phasers tems with a moderate increase of DOF. This work presents and critical engine output variables, such as exhaust tempera- development of a comprehensive methodology utilizing ture or knock intensity. Selection of independent variables advanced modeling techniques and an optimization frame- and constraints changes depending on the particular task, e.g. work to determine the best combination of actuator set-points F/A ratio is an independent variable when maximizing WOT for a given objective. Relying on predictive models and performance, while stoichiometric mixture composition multi-variable optimization makes the methodology generic, becomes a prescribed parameter when minimizing fuel con- as it allows handling any number of independent variables sumption at part load. The optimality of intake and exhaust within reasonable limits. The methodology is demonstrated cam phasing determined using the proposed simulation-based through a case study of an SI engine with two additional methodology is verified with experiments in the test cell. DOF enabled by dual-independent cam phasing. Potential challenges related to practical implementation, such 06108_O_Wu 13/11/07 15:10 Page 541

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as smoothing of rapid high-amplitude excursions of opti- emissions target into the optimization formulation and ensur- mized cam-phaser positions, and limiting NOx emissions ing reduction of total emissions over a selected driving cycle. over a set of representative driving cycles, are addressed in The paper ends with summary and conclusions. the post-optimality study. The paper is organized as follows. The next section describes the optimization framework and outlines the com- 1 OVERALL METHODOLOGY plete methodology. Then, the high-fidelity simulation tool is – OPTIMIZATION FRAMEWORK introduced. The effects of cam-phasing on gas exchange and overall sensitivity of engine output to valve timing is ana- The overall methodology relies on a basic premise that a lyzed in a pre-optimality study. This is followed by a proce- multi-variable optimization algorithm can be utilized to dure for building ANN surrogate models. Next, two opti- determine the best combination of actuator set-points for any mization problems are formulated with different objectives operating condition. Simulation tools having appropriate and constraints: maximizing engine torque output is the level of fidelity are an essential part of the methodology. A objective at wide open throttle, while minimizing fuel con- high-fidelity, predictive tool is necessary for pre-optimality sumption becomes an objective at part load. Maps of optimal studies and for generating data required for building fast camshaft positions are generated by solving the optimization models. A fast model is needed for enabling computationally problem using ANN surrogate models. Benefits of optimiz- intensive optimization runs, since solving a single optimiza- ing valve timing are quantified through comparisons with tion problem might require hundreds of function evaluations. baseline fixed-cam engine. Finally, practical implementation In this work we propose neural network based fast surrogate issues are considered, including a technique for including models rather than a combination of empirical models or

Hardware tests

High-speed ANN Surrogate Models for both the optimization objective and constraints Component High -Fidelity DOE geometry Simulation Sampling

Optimizer Operating Speed & Load point Control Variable Setpoints . ANNsANNs forfor ANNsANNs AANNsNNs forfor … . ObjectiveObjective ConstraintConstraint 1 ConstraintConstraint 2 .

Engine Responses Optimization Update objective & Satisfied? constraints N Setpoints (SQP) Y Optimized Setpoints

Figure 1 Framework for calibrating independent control variables in high-degree-of-freedom engines. 06108_O_Wu 13/11/07 15:10 Page 542

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curve-fits. The motivation stems from the assessment that can be allowed to vary within certain limits. In contrast, max- input-output relationships in high degree-of-freedom engines imizing engine efficiency is the objective of the part load are too complex to be easily captured by a simplified empiri- optimization, while preserving a stoichiometric F/A ratio, cal model. In contrast, ANNs have been proven to be univer- staying within prescribed exhaust temperature, avoiding mis- sal function approximators [29, 30], capable of representing fires or excessive knock, and meeting emissions constraints. complex mapping relationship between multiple inputs and It is important to note that there are no apparent limits in the outputs. number of independent variables or the formulation of the A schematic illustrating the optimization framework and optimization objective function. Hence, the methodology is overall methodology is given in Figure 1. The upper branch generic and, while it will be demonstrated here through a in Figure 1 shows the steps required to build ANN surrogate case study of the SI engine with dual-independent cam phas- models. The high-fidelity simulation replaces experimenta- ing, it can easily be applied to very different engine or pow- tion that used to be a corner-stone of traditional calibration ertrain systems with more degrees of freedom. methodologies. The experiments are still required, but only to provide sufficient data for validating a baseline high fidelity simulation. A validated model can then be modified and used 2 ENGINE SPECIFICATIONS AND EXPERIMENTAL to explore design options that might not exist in hardware. As SETUP an example, an engineer might desire investigating the effects of valve lift using a simulation tool adapted from a The engine used in this study is a production-style 2.4 liter, baseline model that has already been validated on an engine in-line four cylinder dual overhead camshaft (DOHC) engine with cam-phasing. In addition, a simulation can characterize manufactured by DaimlerChrysler Corp. Each cylinder has engine behavior under different environmental conditions, two intake valves and two exhaust valves. The engine was such as high altitude or extreme temperatures if a test cell originally designed as a conventional fixed-cam engine. with full climate control is not available. Even if the hard- However, the prototype VVT version is equipped with intake ware exists, a simulation-based approach offers significantly and exhaust cam-phasers. Intake and exhaust camshaft posi- reduced time and cost provided that up-front modeling effort tions are independently controlled with vane type hydraulic is done. Design of Experiments (DOE) is used to additionally actuators. Cam lobe profiles, cylinder head and pistons, were streamline the process of creating a data base for training not redesigned for VVT operation. Therefore, demonstrating ANNs. A set of ANN surrogate models is generated to repre- or evaluating the ultimate potential of VVT is not the inten- sent the engine’s response to different combinations of inde- tion of this study; rather the focus is on the methodology for pendent control variables. Each ANN represents one engine maximizing torque output or efficiency of a given configura- variable that is included in the optimization objectives or tion. The main engine specifications are listed in Table 1. constraints. The optimization objective function and con- The phasing of camshafts is described with the Intake straints can change depending on operating conditions. As an Centerline Location (ICL) and Exhaust Centerline Location example, maximum output is an obvious objective of opti- (ECL). As shown in Figure 2, ICL is defined as the crank- mization at wide open throttle, while F/A ratio and emissions angle interval between the top dead center (TDC) and the centerline of intake camshaft lobe; and ECL is defined as the crank-angle interval between TDC and the centerline of exhaust camshaft lobe. The default camshaft positions in the fixed-cam baseline engine are: ICL0 = 115 degrees ATDC ECL ICL and ECL0 = 111 degrees BTDC. The range of varying cam- phasing with a prototype VVT system is ±15 degrees for both intake and exhaust. The prototype VVT 2.4 L engine is setup for testing in the University of Michigan W. E. Lay Automotive Laboratory. The engine is coupled to an electric DC dynamometer and instrumented for detailed diagnostics of in-cylinder processes and engine system variables. In particular, cylinder pressure is measured with a Kistler 6125B piezoelectric sensor mounted -270 -180 -90 090180 270 flush with the combustion chamber wall. Intake and exhaust manifold pressures are measured with piezo-resistive trans- BDCTDC BDC ducers Kistler 4045A2, and a cooling adapter is used to pro- Figure 2 tect the transducer from overheating on the exhaust side. Defining intake and exhaust camshaft phasing with positions Pressure signals are sampled with one crank angle degree res- of their respective centerlines. olution using a VXI-bus data acquisition system with 16-bit 06108_O_Wu 13/11/07 15:10 Page 543

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Integration program Geometry of 1-D gas dynamics components model

Hardware experiments

Geometry of Quasi-D combustion chamber combustion model

Figure 3 Co-simulation methodology for generating a high-fidelity tool.

vertical resolution. Other signals such as intake air flow rate, amount of trapped fresh charge at the end of intake process. air/fuel ratio, intake air and coolant temperatures are recorded In addition, large variations of valve events may cause signif- using a separate data acquisition system sampling at 10 Hz. icant variations of turbulence levels and internal residual in the cylinder. This in turn will affect burn rates and emission TABLE 1 formation during a particular cycle. Consequently, a truly Specifications of the 2.4 L VVT engine predictive simulation tools needs to be able to represent these phenomena and capture their effect on engine output. Hence, Displacement 2.4 liters a high-fidelity simulation tool is developed using a co-simu- Bore/Stroke 87.5/101.0 mm lation approach that integrates a one-dimensional gas dynam- Compression Ratio 9.4:1 ics model and a quasi-dimensional combustion model – see illustration in Figure 3. The strength of the commercial code Max. Intake Valve Lift 8.25 mm Ricardo WAVE® in gas dynamics modeling is combined Max. Exhaust Valve Lift 6.52 mm with the strength of the quasi-dimensional Spark Ignition Default Intake Valve Timing Simulation (SIS) in combustion modeling to produce a 51° ABDC/1° BTDC/115° ATDC Close/Open/ Centerline desired level of fidelity. Default Exhaust Valve Timing WAVE [32] has been widely used and validated for 9° ATDC/51° BBDC/111° BTDC Close/Open/ Centerline engine performance predictions [33-35]. In this study, the simulation includes the entire flow path comprised of the Default Valve Overlap 10° @ 0.5 mm lift air-box (filter), intake manifold/runners, intake valves/ports, Allowed Intake Cam-phasing Range ±15° Crank Angle cylinder block, exhaust valves/ports, exhaust manifold/run- Allowed Exhaust Cam-phasing Range ±15° Crank Angle ners, catalyst, muffler/resonator and a tail-pipe. SIS is a research code that has been refined over time and used rou- tinely at the University of Michigan for a variety of simula- 3 HIGH-FIDELITY SIMULATION TOOL tion studies [36]. In its various evolutions, the simulation has been used by Filipi et al. [36] for 2- and 4-valve SI The effects of cam-phasing on engine performance stem pri- engine turbocharger matching studies, in valve event opti- marily from variations of the engine gas exchange process. mization in [37], and for optimizing stroke-to-bore ratio for SI Valve opening/closing affect gas dynamics and determine the engine deign [38]. The combustion sub-model is based on the 06108_O_Wu 13/11/07 15:10 Page 544

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turbulent flame entrainment model proposed by Tabaczynski 2000 rpm, PHI-1.11, ICL = 100 [39] and further refined by Poulos and Heywood [40]. The 190 entrainment rate is a function of the instantaneous flame front Experiments Simulations area, charge density, turbulence intensity and laminar flame 180 speed. Calibration of the combustion model amounts to 170 adjustments of two constants, a dissipation constant in the turbulence model and a constant in the heat transfer correla- 160 tion [36]. Physics-based models of important phenomena ensure validity of the simulation across the wide operating 150 range. Variations of flow parameters with VVT are captured

with the turbulence intensity term. The laminar flame speed torque (N-m) Brake 140 term accounts for the effect of fuel/air ratio and residual, which is particularly important in the case of potentially 130 increased overlap leading to large quantities of residual. The 120 formation of NO is governed by extended Zeldovich mecha- 95 100 105 110 115 120 125 130 nisms, a practice commonly used in engine cycle simulations ECL (deg CA BTDC) [36, 40, 46]. In order to enable considering knock as a constraint, an autoignition model is utilized for predicting knock Figure 4 intensity [41]. The knock model is calibrated based on test Comparison of predicted and measured engine torque as a cell experiments to ensure its accuracy in capturing behavior function of exhaust cam phasing. of the 2.4 L engine. The WAVE and SIS models are coupled at intake and exhaust valves as interfaces. A top level program is developed in C++ to integrate the WAVE and SIS models by feed- 4 PRE-OPTIMALITY STUDIES – ENGINE SENSITIVITY ing WAVE results of valve mass flow rates to SIS, and SIS TO CAM PHASING results for burning rate back to WAVE. Limited experimental data are acquired in the test cell to identify model coeffi- The effort and cost associated with development of the high- cients such as turbulence dissipation constant, heat transfer fidelity code is more than offset by savings in the subsequent correlation coefficient, and engine friction model coeffi- optimization process, as well as by its ability to provide a cients. Previous studies have demonstrated that the high- wealth of information beyond what the experimental setup fidelity simulation tool is capable of capturing air flow rate can deliver. For example, internal EGR is hard to measure accurately [28, 42]. directly, yet it plays a critical role in VVT engine’s perfor- Simulation predictiveness is illustrated in Figure 4 and mance, fuel economy and NOx emissions. The high-fidelity Figure 5. The comparison between predicted and measured code is utilized to generate insight about engine sensitivity to engine peak torque as a function of exhaust cam phasing main control/operating parameters prior to commencing opti- demonstrates the ability of the code to accurately predict the mization runs. The pre-optimality results are used as bench- behavior of the complete engine system (see Fig. 4). Graphs marks for evaluating the behavior of ANN surrogate models in Figures 5a and b show details of the in-cylinder process described in the next section. In addition, the information will and demonstrate the effect of exhaust valve timing on gas be useful for subsequent interpretation of optimization exchange. The relatively low speed (2000 rpm) and low load results. Due to the limited length of the paper, this section (35 N-m) represents conditions where substantial efficiency only briefly highlights some of the findings. improvements can be expected from improved valve timing. Figure 6 illustrates variations of engine maximum The spark timing is set to maximum brake torque (MBT) torque as a function of intake and exhaust cam phasing. timing. The late exhaust valve opening (EVO) prolongs the Not unexpectedly, the sensitivity to variations of intake expansion stroke, while late exhaust valve closing (EVC) cam phasing is much greater. The torque production is leads to higher intake manifold pressure due to large valve directly correlated with air flow rate trend. Detailed analy- overlap and residual backflow. Both are favorable for sis of intake valve flow rates revealed that advancing increasing engine efficiency at a given level of output torque. intake timing at low engine speed traps more air in the Comparing the high-fidelity predictions shown in Figure 5a cylinder since less fresh charge is pushed back before and experimental measurements shown in Figure 5b con- intake valve closes (IVC). Valve overlap and reverse flows firms the ability of the physics-based models to precisely during that period were found to be less important at WOT capture the effects of valve timing on gas exchange and in- conditions. Lower sensitivity of maximum torque to varia- cylinder processes. tions of ECL means that it will be harder to pinpoint the 06108_O_Wu 13/11/07 15:10 Page 545

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2000 rpm, 35 N-m, MBT Spark, Stoichiometry 2000 rpm, 35 N-m, MBT Spark, Stoichiometry 3.0 3.0 ICL = 100, ECL = 96 ICL = 100, ECL = 96 Measured ICL = 100, ECL = 111 ICL = 100, ECL = 111 2.5 ICL = 100, ECL = 126 2.5 ICL = 100, ECL = 126

EVO 2.0 EVO 2.0

1.5 1.5 IVO IVO 1.0 1.0 Cylinder pressure (bar) IVC Cylinder pressure (bar) IVC 0.5 0.5

EVC EVC 0 0 012345678910 012345678910 a) Volume ratio (-) b) Volume ratio (-)

Figure 5 Comparison of high-fidelity simulation results and experimental measurements — engine P-V diagrams with three different exhaust camshaft positions: (a) high-fidelity simulation results; (b) experimental measurements.

optimal value of exhaust camshaft position. Early exhaust Another local minimum of BSFC is observed at the lower valve opening (EVO) reduces expansion stroke length and right corner of Figure 7a, where both exhaust and intake cam expansion work. In addition, advancing exhaust timing and timings are retarded. The main effect responsible for this is closing exhaust valves before TDC results in re-compres- late IVC causing a significant fraction of intake gas to be sion of residual gas and larger reverse flow through intake pushed back from the cylinder into the intake manifold. valves. Retarding exhaust timing results in re-induction of exhaust gas when exhaust valve closing (EVC) is substan- Again, MAP has to be raised to meet the torque requirement tially after TDC. Both retarding and advancing exhaust timing lead to larger residual fraction, less fresh charge and reduced torque output. Consequently, the optimal tradeoff is achieved in between, at roughly ECL = 116 deg. before TDC. Although the effects of exhaust camshaft position on Speed = 2000 rpm, Spark = -17 deg ATDC, Phi = 1.1, WOT engine torque seem negligible at 2000 rpm, they can be 190 ICL sweep at fixed ECL = 116 deg BTDC more significant at higher speeds due to relatively larger 185 ECL sweep at fixed ICL = 100 deg ATDC benefits of longer expansion and reduced impact of re- 180 induction of exhaust. 175 Engine part load operation is explored in Figure 7, show- 170 ing complete maps of relevant engine parameters obtained 165 when intake and exhaust cam timings are allowed to vary within the complete cam-phasing range. Engine operates at 160 2000 rpm, 35 N-m of torque, with F/A equivalence ratio Torque (N-m) 155 (Phi) of one and fixed spark timing. The brake specific fuel 150 consumption (BSFC) contours are plotted in Figure 7a, and 145 residual gas fraction in the cylinder is shown in Figure 7b. 140 The minimum BSFC point is in the lower left corner of 95 100 105 110 115 120 125 130 Figure 7a. This is where the valve overlap and the residual ICL (deg CA ATDC), ECL (deg CA BTDC) gas fraction are maximized. Increased internal exhaust gas recirculation (EGR) requires higher average intake manifold Figure 6 absolute pressure (MAP) for desired torque level and hence Sensitivity of engine torque to variations of intake (solid line) leads to reduced pumping losses. and exhaust phasing (dotted line). 06108_O_Wu 13/11/07 15:10 Page 546

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BSFC contours in (g/kW-h) Residual fraction contours (%) 125 125

120 120

115 115

110 110

105 105 ECL (deg CA BTDC) ECL (deg CA BTDC) 100 100

100 105 110 115 120 125 130 100 105 110 115 120 125 130 a) ICL (deg CA ATDC) b) ICL (deg CA ATDC)

Figure 7 High-fidelity simulation predictions of cam phasing effects on: (a) brake specific fuel consumption; and (b) residual fraction (35 N-m, 2000 rpm, Spark 20 deg BTDC, Phi = 1).

and pumping losses are reduced. In addition, the expansion ing training samples. Assuming uniform distribution of inde- work is increased due to late EVO. The existence of two pendent variables, the operating points selected with LHS local BSFC minima indicates that a global optimum may method populate the entire operating space evenly. High- shift abruptly from ICLmin to ICLmax when operating condi- fidelity simulations are carried out for a set of 2000 operating tions change. Examination of NOx predictions showed a points at Part Load and 1025 points at WOT. Majority of strong correlation with residual fraction. Residual gas lowers data are subsequently used for ANN training, while 5% of combustion temperature and reduces NOx generation. points are randomly selected for testing of ANNs. The com- Therefore, conditions corresponding to maximum residual plete process is illustrated in Figure 8. In a general case, fraction produce the least NOx. either the simulation or experiments could be used to generate data for training, assuming that the hardware prototype exists. However, high-fidelity simulation was used here due 5 ANN SURROGATE MODELS to advantages discussed in the section on Overall Methodology. The VVT engine has five independent actuators, namely the The procedure for determining the optimal structure of an throttle, intake cam-phaser, exhaust cam-phaser, spark and ANN model has been developed in previous studies [28, 42]. fuel injector. Engine speed is an additional input required to Networks with one, two and three hidden layers are trained determine any engine output. However, to facilitate exhaust first. The number of neurons in hidden layers is increased aftertreatment with a three-way-catalyst (TWC), the air fuel gradually until the decreasing rate of the mean squared error ratio at part load is normally fixed at stoichiometry. Therefore, the fuel injection pulse width at every point is TABLE 2 determined by the mass of trapped air at IVC. In case of WOT operation, this constraint is removed and fuel-air Ranges of input data used for ANN training equivalence ratio becomes an additional independent vari- Variable Lower bound Upper bound Unit able. Ranges of all independent variables are given in ICL 95 135 deg ATDC Table 2. To avoid extrapolation, the ranges covered by training samples extend beyond what is expected in practi- ECL 91 131 deg BTDC cal situations. Spark – 60 10 deg ATDC The ANN surrogate models are trained on a set of high- PHIWOT 1 1.5 - fidelity simulation results. A Design of Experiments algo- TorquePartLoad – 40 175 N-m rithm – Latin Hypercube Sampling (LHS) [43, 44] – is used to choose a representative set of operating points for generat- Speed 600 6500 rpm 06108_O_Wu 13/11/07 15:10 Page 547

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Hardware TABLE 3 experiments Preferred structure of ANN models ANN Design Models ANN model Unit Network structure of Full ANN Factorial Experi- or Latin Training Fuel flow rate g/s 5-15-15-1 ments Hypercube Samples (DOE) NOx emission rate g/s 5-15-15-1 High-fidelity TorqueWOT N-m 5-10-10-1 simulations Residual fraction - 5-15-15-1 Knock intensityWOT % (unburned mixture) 5-11-11-1 Knock intensityPartLoad % (unburned mixture) 5-10-10-10-1 Tests & Exhaust temperatureWOT K 5-11-11-1 validation Exhaust temperaturePartLoad K 5-15-15-1 Combustion duration degree 5-12-12-1

Figure 8 6 MAXIMIZING ENGINE PERFORMANCE Process of generating engine ANN surrogate models. In the case of maximum driver demand or WOT, the optimization objective is to maximize torque generation. The constraints are set by the exhaust temperature limit, preven- tion of knock and physical ranges for independent variables. (mse) diminishes. The mse of training samples is used to The constraint on exhaust temperature is introduced to pro- tect the catalyst from overheating. Thus, the optimization measure fitting accuracy, and the mse of testing samples is problem is formulated as follows [18]: used to evaluate generalization accuracy, i.e. accuracy in = zones away from training points. The network that attains Maximize: Obj Torque(; x Speed ) small training and testing mse, close to the point of diminish- x= (, ICL ECL , Sparrk,) Phi ing returns, with no signs of overfitting, is selected as the pre- Subject to: ferred network. Training ANNs using Bayesian 100≤≤ICL 130 degree ATDC Regularization technique, available in MATLAB® Neural 96 ≤≤ECL 126 degree BTDC Network Toolbox [45], minimizes the risk of overfitting. (1) −≤ ≤ Comparison of ANN predictions and high-fidelity simulation 50Spark 0 degree ATDDC benchmarks provides a qualitative verification of good ANN 10..≤≤Phi 13 ≤° behavior without overfitting. It should be noted that using Texh (; x Speed ) 850 C simulation results for training reduces the risk of ANN over- ≤ Ki (; x Speed)).01 fitting, since there is no noise in the data. Table 3 lists the structure of the preferred networks for all where Texh is exhaust temperature; Ki is knock intensity; and ANN surrogate models used in this work. The network struc- x represents four independent variables. Engine speed is ture is represented by a series of numbers. The first and last regarded as an input parameter determined by the numbers represent the number of inputs and outputs, respec- engine/vehicle interaction. tively. Each numbers in the middle represents the number of In Equation (1), Torque, Texh, and Ki are functions of independent variables and RPM, represented by separate ANNs. hidden neurons in a corresponding hidden layer. The optimization framework is setup using fmincon from the The fidelity of ANN surrogate models is verified by com- Matlab™ Optimization Toolbox to perform a constrained paring the predictions of ANN models with high-fidelity sim- nonlinear optimization of a multivariable function. The opti- ulation output. Figures 9 and 10 illustrate excellent agree- mization problem is solved at 100 equally spaced steps ment of both WOT and part load results. Peak torque between 1000 and 6000 rpm, and results are shown in predictions as a function of ICL and ECL are given in Figure 11. While all four variables display a clear trend in the Figure 9, and fuel flow rate for 35 N-m, 2000 rpm are shown most of the speed range, ECL and Phi show an undesirable in Figure 10. In particular, the shape of surfaces and the loca- sharp fluctuation around 2000 rpm. This is mainly due to the tions of minima are aligned precisely in high-fidelity simula- insensitivity of engine torque with respect to ECL and Phi, tion benchmarks and ANN predictions. e.g. gradients along the ECL axis in Figure 6 are very small 06108_O_Wu 13/11/07 15:10 Page 548

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Speed = 2000 rpm, Spark = -20 deg ATDC, Phi = 1, WOT 35 N-m, 2000 rpm, Spark = -20 degree ATDC 125 High-fidelity 125 High-fidelity ANN ANN 120 120 Fuel Consumption

115 115 Torque 110 110

105 105 ECL (CA degree) ECL (degree BTDC) ECL (degree

100 100

100 105 110 115 120 125 130 100 105 110 115 120 125 130 ICL (degree ATDC) ICL (CA degree) Figure 9 Figure 10 Comparing ANN predictions with high-fidelity simulation Comparing ANN predictions with high-fidelity simulation benchmarks to validate ANN models: WOT torque (N-m). benchmarks to validate ANN models: fuel flow rate (g/s).

in the vicinity of the peak torque. To overcome the problem, where subscript k indicates the index in a speed sequence. two extra terms are added to penalize sudden changes of ECL Depending on whether the optimization problems are solved and Phi between two adjacent speed steps. The optimization in ascending or descending order of speed, the sign in the objective is revised as follows: penalty terms can be either “–” or “+”. We solve the optimization problems in both directions and report the average Obj=+ Torque(; x Speed ) in Figure 11 with solid lines. Constants C and C are kk (2) 1 2 − +− adjusted to generate smooth ECL and Phi without a notice- CECL1 k ECLkkkk±±12 C Phi Phi 1 able torque penalty.

135 130 0 125 Without penalty -10 120 Penalty averaged Constraint -20 115 110 -30 105 -40 ICL (deg ATDC) (deg ICL Spark (deg ATDC) Spark (deg 100 -50 95 a) 1000 2000 3000 4000 5000 6000 c) 1000 2000 3000 4000 5000 6000

130 125 1.3 120 1.2 115 110 Phi (-) 1.1 105 ECL (deg BTDC) ECL 100 1.0 95 b)) 1000 2000 3000 4000 5000 6000 d) 1000 2000 3000 4000 5000 6000 Engine speed (rpm) Engine speed (rpm)

Figure 11 Independent variables optimized for maximum output: (a) ICL; (b) ECL; (c) Spark timing; and (d) F/A equivalence. 06108_O_Wu 13/11/07 15:10 Page 549

B Wu et al. / A Simulation-Based Approach for Developing Optimal Calibrations for Engines with Variable Valve Actuation 549

210 Given the torque request by the driver and current engine Optimized cam speed, the optimization problem is formulated as follows: 200 Default cam = Minimize Obj mfuel (; x Speed , Torque ) 190 xICLE= (,CCL,) Spark

180 Subject to: 100≤≤ICL 130 degree ATDDC 170 96≤≤ECL 126 degree BTDC (3) Torque (N-m) 160 −≤60Spark ≤ 10 degreee ATDC ≤° Texh 900 C 150 ≤ t0− 50% 60 degree 140 K ≤ 10%n (unburned mass) 1000 2000 3000 4000 5000 6000 i Engine speed (rpm)

Figure 12 Phi-1.11, WOT Peak torque improvement due to optimized cam phasing. 210 1200 rpm, ECL = 120 deg BTDC, Spark = -8 deg ATDC 2000 rpm, ECL = 115 deg BTDC, Spark = -24 deg ATDC 200 3600 rpm, ECL = 113 deg BTDC, Spark = -30 deg ATDC

190 Figure 11a indicates significant benefits of advancing ICL at lower engine speeds. Indeed, Figure 12 shows maximum torque 180 improvements between 5% and 10% in the 1000–3500 rpm range when compared to the fixed-cam baseline engine. Since 170

ICL is at the lower limit in this range, relaxing of the limit or (N-m) Torque redesigning of the cam profile could bring additional improve- 160 ments. Examination of other constraints showed that knock 150 intensity is active at low speeds (up to 2800 rpm), while maxi-

mum exhaust temperature becomes active above 4500 rpm. 140 The optimality of the camshaft positions was validated 95 100 105 110 115 120 125 130 135 with experiments in the test cell. Complete sweeps of ICL a) ICL (degree ATDC) and ECL were performed while keeping engine speed, spark timing and A/F ratio constant. Tests were performed at three 210 1200 rpm, ICL = 100 deg BTDC, Spark = -8 deg ATDC engine speeds: 1200, 2000 and 3600 rpm and results are dis- 2000 rpm, ICL = 100 deg BTDC, Spark = -24 deg ATDC played in Figure 13. The optimum ICL and ECL positions are 200 3600 rpm, ICL = 102 deg BTDC, Spark = -30 deg ATDC marked with vertical solid bars. The optimized positions 190 coincide with, or are extremely close to the best positions suggested by the experimental curves, and this effectively 180 verifies the optimality. 170 Torque (N-m) Torque 7 MINIMIZING FUEL CONSUMPTION AT PART LOAD 160

During most driving the engine is operating at part load and 150 fuel economy is the priority. At part load, the fuel-air equivalence ratio is kept at stoichiometric to enable efficient opera- 140 95 100 105 110 115 120 125 130 tion of the three-way catalyst. Therefore, minimizing the fuel b) ICL (degree ATDC) consumption without considering emission constraints is dis- Figure 13 cussed first. Since engine-out emission can be a concern given the ultra-low tailpipe emissions mandated by current Experimental validation of the optimality of cam positions: (a) intake cam-phasing sweep; (b) exhaust cam-phasing and future regulations, an approach for including emissions sweep. Optimized camshaft positions are marked with thick into the optimization is discussed in the subsequent section solid bars. 06108_O_Wu 13/11/07 15:10 Page 550

550 Oil & Gas Science and Technology – Rev. IFP, Vol. 62 (2007), No. 4

. In the above equation, mfuel represents fuel flow rate, and obtained at one grid node are used as the initial values for X are independent variables, such as ICL, ECL and Spark optimization at the next grid node. Multiple initial values are timing. All three independent control variables are con- used for the first node on each grid line. Computational effi- strained by corresponding upper and lower limits. The con- ciency of ANN surrogate models enables solving a total of straint on Texh protects catalyst from overheating. An interval 1000 optimization problems within four hours on a desktop between ignition and phasing of the 50% mass burned point personal computer.

(t0-50%) is checked to avoid extremely slow burning and The results of optimized ICL, ECL are plotted in Figures incomplete combustion. Knock intensity (Ki) is defined as 14a and b. As shown in Figure 14a, the optimal ICL changes the mass fraction of unburned mixture when auto-ignition suddenly from being most advanced to being most retarded happens, and more than 10% is deemed unacceptable to pre- when increasing either engine speed or load from the low vent possible damage to the engine or excessive noise. The speed and low load quadrant. The discontinuity is the conse- ANN models listed in Table 3 are used to evaluate indepen- quence of the abrupt transition from one local minimum point dent variables within the optimization framework. to the other one identified in Figure 7a. For a similar reason, The optimization problem is solved on a 50 × 20 grid of an additional discontinuity occurs when approaching the high engine speed and torque. Along each grid line of fixed engine speed and high load corner. This time, the optimal ICL reverts speed, optimization is carried out in sequence from high to being most advanced. In contrast, the optimal ECL surface torque to low torque. To facilitate optimization, the results is smooth, as shown in Figure 14b. Except at high speed and

Contours of fuel consumption reduction (%) 90

80 130 70 120 60 110 50 100

Load (%) 40 1000 80 2000 60 3000 30 Optimized ICL (degree ATDC) 40 Engine speed 4000 20 Load (%) 20 (rpm) 5000 a) 10 1000 1500 2000 2500 3000 3500 4000 4500 5000 a) Engine speed (rpm)

Contours of optimized residual fraction (%) 90

120 70 115 110 60 105 50 100

95 Load (%) 40 1000 80 2000 60 30 Optimized ICL (degree ATDC) 3000 40 d (%) Engine speed 4000 20 Loa 20 (rpm) 5000 10 1000 1500 2000 2500 3000 3500 4000 4500 5000 b) b) Engine speed (rpm) Figure 15 Figure 14 Results of optimizing valve and spark timing for best fuel Optimization results for minimizing fuel consumption: (a) economy: (a) relative fuel consumption reduction compared intake camshaft position; (b) exhaust camshaft position. to the baseline; and (b) residual fraction in the cylinder. 06108_O_Wu 13/11/07 15:10 Page 551

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load, the exhaust event is retarded to prolong the expansion operating in typical driving conditions. Special issues, such stroke, thus increasing gross specific work and thermal effi- as cold start and idle roughness should be treated separately, ciency. At high speed and load, advancing ECL reduces just like in the case of fixed-cam engines. Depending on the pumping loss, while the effect of interrupting expansion early design of cam-phasers, parasitic losses associated with actua- becomes less tangible. The optimal ECL surface represents tion can be a factor at near-idle conditions. This should be the best compromise between two competing effects. accounted for in the model or examined experimentally after Figures 15a and b show maps of relative fuel consumption the final refinement of component design. The outcome will reduction compared with the baseline fixed-cam engine, and determine whether the optimal strategy will be applied in a residual fraction obtained with the optimized ICL, ECL and complete speed range, or adjustments will be needed to offset Spark, respectively. While absolute benefits are highest at the impact of parasitic losses. higher loads, relative improvements are greater in the low load (<40 N-m) and low speed (<2000 rpm) corner, ranging from 4% to 11%. Figure 15b shows that optimal ICL leads to CONCLUSIONS large valve overlap and high residual faction in the low speed/low load corner, which helps reduce engine-out NOx This work proposes a systematic methodology for character- emissions. Indeed, subsequent close inspection of NOx pre- izing the behavior of a high-degree of freedom engine and dictions revealed up to eight times lower values of the NOx developing efficient calibration methods for handling emission index (g NOx/kg Fuel) in the low-speed, low-load increased number of independent variables. The approach part of the operating range. uses a multi-variable optimization framework for determining the best combination of actuator set-points for any operating condition. The methodology is simulation based, and it 8 CLOSING REMARKS – IMPLEMENTATION AND relies on two key enablers: (i) high-fidelity simulation capa- EMISSIONS ISSUES ble of predicting complex interactions in the high degree-of- freedom engine; and (ii) artificial neural networks suitable The setpoints obtained in the previous section represent a true for computationally intensive optimization runs. optimum with respect to corresponding objectives. However, The methodology is generic and can be applied to practical implementation might require additional considera- engine/powertrain system with a large number of indepen- tions. As an example, step changes of optimal ICL shown in dent variables. A case study demonstrates its application to a Figure 14 are not desirable due to potential issues with multi-cylinder spark-ignition engine with dual-independent dynamic actuator control and driveability. Excessive tran- cam phasing. The study addresses optimization of camshaft sients might also degrade efficiency and emissions benefits. positions, spark timing and F/A ratio for maximum torque The engine-out emissions constraint might need to be consid- output at WOT and minimum fuel consumption at part load. ered as well. In both cases realistic driving schedules have to The optimization problem is solved individually at many be analyzed in order to enable refinement of the optimal set- operating points covering the complete operating range. point maps. The essence of the approach is discussed here, Important constraints, such as knock, exhaust temperature but details are omitted for brevity and can be found in [31]. and excessive combustion duration (indication of incomplete Distribution of engine operating time over a set of rep- combustion and misfires) are included in the algorithm. resentative driving schedules provides a foundation for Practical implementation might require post-optimality global refinement of the VVA engine’s calibration. If the processing of optimized results to smooth discontinuities in goal is to make transients smother, slopes of surfaces in the intake camshaft phasing map and account for phenomena actuator maps should be limited in a way that causes the that may have not been modeled. NOx emissions could be least impact on real-world fuel economy. This is achieved included in the optimization formulation as well. Since emis- by moving the modified points in the direction of less fre- sions are regulated over a complete driving schedule, a quently visited regions [31]. If emissions are considered, promising approach is to determine relevant operating points the total driving time can be broken up and lumped into a through analysis of driving schedules and add a NOx penalty limited number of representative operating points. Then, term in the optimization objective. the NOx penalty term is included in the objective function in order to investigate the trade-off between fuel economy and NOx emission. Subsequently, the optimization prob- ACKNOWLEDGEMENTS lem can be formulated in a way that enables minimizing fuel consumption while constraining total NOx emissions The authors appreciate the contribution of Roger Vick, Fadi below the given target value [31]. Kanafani, Michael Prucka, Eugenio DiValentin, of In summary, our study is focused on the core calibration DaimlerChrysler in developing the component modules for problem, i.e. determining actuator set-points for an engine the engine simulation tool and other technical support. 06108_O_Wu 13/11/07 15:10 Page 552

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REFERENCES 19 Mehrotra, K., Mohan, C.K., Ranka, S. (1997) Elements of Artificial Neural Networks, the MIT Press, Cambridge, Massachusetts, ISBN 0-262-13328-8. 1 Ahmad, T. and Theobald, M.A. (1989) A survey of variable- valve-actuation technology. SAE Technical Paper No. 891674. 20 He, Y. and Rutland, C.J. (2002) Modeling of a Turbocharged DI Diesel Engine Using Artificial Neural Networks. SAE Technical 2 Hannibal, W., Flierl, R., Stiegler, L. and Meyer, R. (2004) Paper No. 2002-01-2772. Overview of Current Continuously Variable Valve Lift Systems for Four-Stoke Spark-Ignition Engines and the Criteria for Their 21 He, Y. and Rutland, C.J. (2004) Application of Artificial Neural Design Ratings. SAE Technical Paper No. 2004-01-1263. Networks in Engine Modeling. Int. J. Engine Res., 5, 4, 281-296. 3 Flierl, R. and Fluting, M. (2000) The Third Generation of 22 Brahma, I. and Rutland, C.J. (2003) Optimization of Diesel Valvetrains – New Fully Variable Valvetrains for Throttle-Free Engine Operating Parameters Using Neural Networks. SAE Load Control. SAE Technical Paper No. 2000-01-1227. Technical Paper No. 2003-01-3228. 4 Nakamura, M., Hara, S., Yamada, Y., Takeda, K., Okamoto, N. 23 Grimaldi, C.N. and Mariani, F. (1997) On-board Diagnosis of and Hibi, T. (2001) A Continuous Variable Valve Event and Lift Internal Combustion Engines: a New Model Definition and Control Device (VEL) for Automotive Engines. SAE Technical Experimental Validation. SAE Technical Paper No. 970211. Paper No. 2001-01-0244. 24 Grimaldi, C.N. and Mariani, F. (2001) OBD Engine Fault 5 Nishizawa, K., Mitsuishi, S., Mori, K. and Yamamoto, S. (2001) Detection Using a Neural Approach. SAE Technical Paper No. Development of Second Generation of Gasline P-ZEV 2001-01-0559. Technology. SAE Technical Paper No. 2001-01-1310. 25 Krug, C., Liebl, J., Munk, F., Kammer, A. and Reuss, H.-C. (2004) 6 Hong, H., Parvate-Patil, G.B. and Gordon, B. (2004) Review and Physical Modelling and Use of Modern System Identification for Analysis of Variable Valve Timing Strategies-Eight Ways to Real-Time Simulation of Spark Ignition Engines in All Phases of Approach. Proceedings of the Institution of Mechanical Engine Development. SAE Technical Paper No. 2004-01-0421. Engineers, Part D. J. Automobile Eng., 218, 1179-1200. 26 Winsel, T., Ayeb, M., Theuerkauf, H.J., Pischinger, S., Schernus, 7 Gray, C. (1988) A review of variable engine valve timing. SAE C. and Lutkemeyer, G. (2004) HiL-Calibration of SI Engine Technical Paper No. 880386. Cold Start and Warm-up Using Neural Real-Time Model. SAE Technical Paper No. 2004-01-1362. 8 Dresner, T. and Barkan, P. (1989) A review of variable valve 27 Ayeb, M., Lichtenthäler, D., Winsel, T. and Theuerkauf, H.J. timing benefits and modes of operation. SAE Technical Paper (1998) SI engine modeling using neural networks. SAE No. 891676. Technical Paper No. 980790. 9 Asmus, T.W. (1991) Perspectives on applications of variable 28 Wu, B., Filipi, Z.S., Assanis, D.A., Kramer, D.M., Ohl, G.L., valve timing. SAE Technical Paper No. 910445. Prucka, M.J. and DiValentin, E. (2004) Using artificial neural 10 Ma, T.H. (1988) Effect of variable engine valve timing on fuel networks for representing the air flow rate through a 2.4 liter economy. SAE Technical Paper No. 880390. VVT engine. SAE Technical Paper No. 2004-01-3054. SAE Trans. – J. Engines. 11 Bohac, S. and Assanis, D. (2004) Effects of Exhaust Valve Timing on Gasoline Engine Performance and Hydrocarbon 29 Hornik, K., Stinchcombe, M., and White, H. (1989) Multilayer Emissions. SAE Technical Paper No. 2004-01-3058. feedforward networks are universal approximators. Neural Networks, 2, 5, 359-366. 12 Roepke, K. and Fischer, M. (2001) Efficient Layout and Calibration of Variable Valve Trains. SAE Technical Paper 30 Hornik, K. (1991) Approximation capabilities of multilayer feed- 2001-01-0668. forward networks. Neural Networks, 4, 2, 251-257. 13 Flint, S. and Causey, P. (2003) Use of Experimental Design and 31 Wu, B., Filipi, Z.S., Prucka, R.G., Kramer, D.M. and Ohl, G.L. Two Stage Modeling in Calibration Generation for Variable (2006) Cam-phasing Optimization Using Artificial Neural Camshaft Timing Engines, Design of Experiments (DOE), in der Networks as Surrogate Model – Fuel Consumption and NOx Motorenentwicklung, Expert Verlag, ISBN 3-8169-2271-6, Emissions, SAE paper 2006-01-1512. SAE Trans., J. Engines, pp. 57-77. presented at the 2006 SAE World Congress in Detroit. 14 Morton, T., Connors, R., Maloney, P. and Sampson, D. (2003) 32 WAVE V5 Engine Reference Manual (2002) Ricardo Software, Model-Based Optimal Calibration of a Dual Independent Ricardo, Inc., November. Variable Valve-Timing Engine, Design of Experiments (DOE), 33 Morel, T., Flemming, M. and LaPointe, L.A. (1990) in der Motorenentwicklung, Expert Verlag, ISBN 3-8169-2271- Characterization of Manifold Dynamics in the Chrysler 2.2l S.I. 6, pp. 77-85. Engine by Measurements and Simulation. SAE Technical Paper 15 Rask, E. and Sellnau, M. (2004) Simulation-Based Engine No. 900679. Calibration: Tools, Techniques, and Applications. SAE 34 Wren, C.S. and Johnson, O. (1995) Gas Dynamics Simulation Technical Paper No. 2004-01-1264. for the Design of Intake and Exhaust Systems – Latest 16 Fu, H., Chen, X., Mustafa, E., Trigui, N., Richardson, S. and Techniques. SAE Technical Paper No. 951367. Shilling, I. (2004) Analytical Investigation of Cam Strategies for 35 Millo, F., Ferraro, C.V. and Pilo, L. (2000) A Contribution to SI Engine Part-Load Operation. SAE Technical Paper No. 2004- Engine and Vehicle Performance Prediction. SAE Technical 01-0997. Paper No. 2000-01-1266. 17 Kramer, U. and Philips, P. (2002) Phasing Strategy for an 36 Filipi, Z., and Assanis, D.N. (1991) Quasi-dimensional computer Engine with Twin Variable Cam Timing. SAE Technical Paper simulation of the turbocharged spark-ignition engine and its use No. 2002-01-1101. for 2- and 4-valve engine matching studies. SAE Technical 18 Wu, B., Prucka, R.G., Filipi, Z.S., Kramer, D.M. and Ohl, G.L. Paper No. 910075. SAE Trans., 100, Sect. 3. (2005) Cam-Phasing Optimization Using Artificial Neural 37 Filipi, Z. (1994) Investigation of Variable Valve Area Strategies Networks as Surrogate Models – Maximizing Torque Output. for a Turbocharged SI-Engine. Proceedings of the IMechE 5th SAE Technical Paper No. 2005-01-3757. SAE Trans. – J. International Conference on Turbocharging and Turbochargers, Engines. London, pp. 93-102. 06108_O_Wu 13/11/07 15:10 Page 553

B Wu et al. / A Simulation-Based Approach for Developing Optimal Calibrations for Engines with Variable Valve Actuation 553

38 Filipi, Z.S. and Assanis, D.N. (2000) The Effect of Stroke-to- 43 McKay, M.D., Beckman, R.J. and Conover, W.J. (1979) A com- Bore Ratio on Combustion, Heat Transfer and Performance of a parison of three methods for selecting values of input variables Homogeneous-Charge Spark-Ignited Engine of Given in the analysis of output from a computer code. Technometrics, Displacement. Int. J. Engine Res., 1, 2, JER0500, London, 191- 208. 21, 2, 239-245. 39 Tabaczynski, R.J., Trinker, F.H. and Shannon, B.A. (1980) 44 Lunani, M., Sudjianto, A. and Johnson, P.L. (1995) Generating Further refinement and validation of a turbulent flame propaga- efficient training samples for neural networks using Latin tion model for spark-ignition engines. Combust. Flame, 39, 2, Hypercube sampling. Proceedings of the 1995 Artificial Neural 111-121. Networks in Engineering (ANNIE’95), St. Louis, MO, USA, 40 Poulos, S.G. and Heywood, J.B. (1983) The effect of chamber Nov. 12-15, pp. 209-214. geometry on spark-ignition engine combustion. SAE Technical Paper No. 830334. 45 Demuth, H. and Beale, M. (2002) Neural Network Toolbox 41 Ho, S.Y. and Kuo, T. (1997) A Hydrocarbon Autoignition User’s Guide (Version 4), Mathworks Inc. Model for Knocking Combustion in SI Engines. SAE Technical 46 Rublewski, M.J. and Heywood, J.B. (2001) Modeling No Paper No. 971672. Formation in Spark Ignition Engines With a Layered Adiabatic 42 Wu, B., Filipi, Z., Kramer, D.M., Ohl, G.L., Prucka, M.J. and Core and Combustion Inefficiency Routine. SAE Technical DiValentin, E. (2005) Using Neural Networks to Compensate paper No. 2001-01-1011. Altitude Effects on the Air Flow Rate in Variable Valve Timing Engines. SAE Technical Paper No. 2005-01-0066. SAE Trans. – J. Engines. Final manuscript received in October 2006

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