Simulation-Based Engine Calibration: Tools, Techniques, and

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future engines will feature new technology, such as variable valve actuation, that ... valve timings may require 14,400 points to be analyzed. ... Several methods were used to accelerate the simulation ..... flame speed during simulation convergence and stop the simulation ..... Calibration of Variable Valve Trains,” SAE Paper.
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2004-01-1264

Simulation-Based Engine Calibration: Tools, Techniques, and Applications Eric Rask and Mark Sellnau Delphi Research Labs

Reprinted From: Variable Valve Actuation 2004 (SP-1829)

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2004-01-1264

Simulation-Based Engine Calibration: Tools, Techniques, and Applications Eric Rask and Mark Sellnau Delphi Research Labs

Copyright © 2004 SAE International

ABSTRACT

INTRODUCTION

Calibration of engine management systems requires considerable engineering resources during the development of modern engines. Traditional calibration methods use a combination of engine dynamometer and vehicle testing, but pressure to reduce powertrain development cost and time is driving development of more advanced calibration techniques. In addition, future engines will feature new technology, such as variable valve actuation, that is necessary to improve fuel economy, performance, and emissions. This introduces a greater level of system complexity and greatly increases test requirements to achieve successful calibrations.

A variety of variable valve actuation (VVA) systems are emerging in the marketplace for spark-ignited engines. These systems may be as simple as variable valve timing control (VVT) for the intake valves, or may be as complex as fully flexible valve lift and timing control for both intake and exhaust. Because of the additional degrees of freedom (DOF) that these systems present, calibration complexity of these systems is greatly increased. For instance, an engine map comprised of 100 operating points with 12-intake valve timing possibilities may require 1200 points to analyzed. Whereas the same map with 12 intake and 12 exhaust valve timings may require 14,400 points to be analyzed. Further complexity is introduced to the system if variable valve lift (VVL), variable intake manifold (VIM), port throttling (PDA), exhaust gas recirculation (EGR), variable nozzle turbochargers (VNT), or combinations of these, are employed.

To address these problems, new simulation tools and procedures have been developed within Delphi to rapidly generate optimized calibration maps. The objective of the work is to reduce calibration effort while fully realizing the potential benefit from advanced engine technology. The procedure utilizes GT Power engine simulation software and engine models validated through limited dynamometer testing.

Conventional calibration methods rely on dynamometer mapping and transient vehicle testing to arrive at a powertrain calibration in a manner that is generally considered somewhat of an art. However, as powertrain complexity is increased, the calibration process, its duration, and its cost; grow exponentially with the number of DOF. Even for relatively simple systems, achievement of optimized calibrations may become impractical to accomplish.

A front end to GT Power was written to automatically call GT Power executables and produce the calibration dataset. Several methods were used to accelerate the simulation process. Calibrations are optimized using an additional software tool that includes a weightedoptimization scheme. User-defined constraints may be applied during optimization for cam phaser position, combustion dilute limits, exhaust temperature or any other variable defined in the engine model. The overall procedure includes vehicle simulation using ADVISOR to estimate fuel economy and emissions for the drive cycle.

There are several ways that powertrain calibration and optimization problems have been approached in recent years. Many of these techniques deal with statistical methods such as Design of Experiments (DOE)[1-8] and Response Surface Modeling (RSM)[9], or use of artificial neural networks (ANN)[10,11,12]. The goal of these techniques is to significantly decrease dynamometer test requirements by generating mathematical models of the engine outputs using a smaller subset of dynamometer tests. Once these mathematical models have been determined, the calibration maps can be optimized using

This paper describes the simulation tools and procedures, and presents calibration results for a modern V6 engine equipped with two-step VVA and intake cam phasing. Preferred two-step switching schedules and cam phaser position maps are presented. 1

techniques such as “simulated annealing” [13] or other “gradient procedures” [4,9,11].

software tool, and applied to calibration of a modern V6 engine equipped with two-step valve lift control and intake cam phasing.

Computer Aided Engineering (CAE) tools have recently been applied to simulate and optimize calibrations of advanced powertrains. Simulation-based calibration (SBC) has been enabled by improvements in simulation software as well as continuous advancements in computing technology, but complex interactions between the engine, engine control unit (ECU), and the vehicle make this a challenging modeling task. Burk, Jacquelin, and Wakeman [14,15,16] used 1-D cycle simulation (WAVE) [17] and i-Sight [13] to develop a calibration methodology for spark-ignited engines with cam phasers. Edwards et al. [18] used 1-D cycle simulation with DOE to study feasibility of a Miller Cycle on a heavy-duty turbo-charged truck engine. Osborne [19,20] applied 1-D cycle simulation in co-simulation with Matlab Simulink [21] to analytically calibrate a mediumduty, turbo-charged diesel engine.

METHODOLOGY The overall methodology for simulation-based calibration is shown in Figure 1. As a first step, engine dynamometer pretesting is necessary to develop and validate the engine model. Pretesting is a relatively limited exercise but is important to achieve a high fidelity engine model. The engine model is then processed using a front end to the 1-D cycle simulation, which is designed to rapidly and automatically produce the calibration dataset. GT Power software [22] was used exclusively in this work. Once the calibration dataset is generated, optimization is conducted in two steps. The phaser schedule optimizer (PSO) parses the calibration dataset for each cam profile per the specified optimization criteria. The cam schedule optimizer (CSO) then compares results for each cam profile. The result is optimized values of cam lift and timing over the operating map. The optimized calibration is then processed in ADVISOR [23] to estimate fuel economy and NOx emissions for the specified vehicle model and drive cycle.

The objective of the current work is to develop a methodology for simulation-based calibration in an automated software tool. Results from the work include 1) methods to significantly accelerate 1-D cycle simulation for rapid grid data collection, and 2) efficient optimization methods for large engine datasets. These methods were integrated into an efficient, user-friendly

Figure 1. Methodology for Simulation-Based Calibration (SBC) 2

Application of user-defined constraints in the optimization process is a vital utility of the tool. Application of constraints is needed to provide realistic limitations on engine components, such as cam phasers. Another important constraint for spark-ignited engines is combustion dilute limits. The front end employs a “flame speed correlation method” [24] to estimate combustion dilute limits.

ENGINE SIMULATION TOOLS Front End Description An important step in SBC is the generation of the calibration database (see Figure 1). This is a complex task due to the immense volume of data that must be simulated and recorded. As a means to improve the efficiency and accuracy of this process, a front end was developed to automate the simulation execution and data collection process. The front end was written using Microsoft Visual Basic for Applications [25] and linked to Microsoft Excel [26], Matlab, and GT Power to transition seamlessly from an input spreadsheet, that defines the operating grid, to formatted simulation output data. Automation of simulation execution also enables subsequent automation of the calibration optimization process. For background information about the front end, see reference [24].

The overall procedure can be used iteratively to study the impact of engine calibration on fuel economy and emissions before actual vehicle testing. For example, cam phaser default positions and authority are key component design parameters for many advanced engines. Yet, the impact of phaser default and authority on fuel economy, emissions, and performance is very difficult to determine experimentally. Using SBC, a range of optimization constraints for cam phasers (for example) may be specified during calibration optimization. In this way, the functional relationship between phaser design specifications and vehicle fuel economy and emissions can be predicted. Similar relationships between phaser design and vehicle performance may also be determined.

The general flow of the SBC approach used in this work is to complete an intake valve opening timing (IVO) sweep for a given intake cam profile, exhaust cam profile, exhaust valve opening timing (EVO), and desired set of engine speed-load points. This “single profileEVO” at a time procedure allows some optimization to be completed while other profiles-EVOs are being simulated. With this approach in mind, the input spreadsheet was split into three sections: Engine Setup, IVO Array, and Speed-Load Array. An example spreadsheet can be seen below in Figure 2. In the Engine Setup section, the user inputs the engine and friction files, cam profiles, EVOs, spark retard, valvetrain follower types, and output filename. The IVO Array contains the range of IVO values to be simulated. Similarly, the Speed/Load Array consists of the desired brake mean effective pressure (BMEP) values for each desired engine speed.

Another use of SBC is for optimization of the calibration map for sometimes conflicting optimization objectives. This necessitates simultaneous optimization for two or more optimization criteria or parameters. For example, a 60 percent weighting factor could be specified to maximize fuel economy, while a 40 percent weighting factor could be specified to minimize NOx emissions. Used iteratively in a parameter study, the loss function between fuel economy and NOx, for instance, can be determined. Many interesting scenario studies can be easily performed using one calibration dataset. A more detailed description of simulation-based calibration tools and procedures may be found in the following paragraphs. Interpolator Setup File Engine File Int 1 Profile Int 2 Profile Ext 1 Profile Ext 2 Profile Friction File Exh 1 Opening Exh 2 Opening Save File As

C:\VVA_EMR\Engines\3.5L V6 DICP Model(24Feb3).dat C:\VVA_EMR\cams\TK6Nv1_7.0.prn C:\VVA_EMR\cams\TK6Nv1_7.0.prn C:\VVA_EMR\cams\Line6Pexh_9.51.prn C:\VVA_EMR\cams\Line6Pexh_9.51.prn C:\VVA_EMR\Friction\V6 Friction Finder(5Aug02).xls 125 125 V6 7PCM

IVO (CAD)(L=0) 280 285 290 295 300 305 310 315 320 325 330 335 340 345 350 355 360

Engine Speed (RPM) Load Range (kPa) (BMEP or NMEP)

IVO Array

Spark Retard Int Follower Exh Follower Save GPX (y/n)

0 r r n

Speed/Load Array

Engine Setup 800 100 200 300 400 500 600 700 800 900 1000 1200

Figure 2. Input Spreadsheet for the Front End. 3

1000 100 200 300 400 500 600 700 800 900 1000 1200

1200 100 200 300 400 500 600 700 800 900 1000 1200

1400 100 200 300 400 500 600 700 800 900 1000 1200

1600 100 200 300 400 500 600 700 800 900 1000 1200

2000 100 200 300 400 500 600 700 800 900 1000 1200

Single IVO and RPM

Input Spreadsheet

Throttle Hook

All IVO/RPM Simulated (Y)

Final Interpolate/ Output

All Profiles/EVO Simulated (N) Calibration Database (Y)

(N)

Figure 3. Calculation Process Used in Front End. The simulation is started by specifying the input worksheet (file) and executing the macros. The data is processed in two steps: the Throttle Sweep phase and the Final Interpolate/Output phase. The general flow of the process is shown in Figure 3.

Throttle and Output Interpolation Throttle hooks are performed for the entire range of desired loads for each IVO and RPM combination. This processing order allows the use of interpolation to speed up the throttle iteration process. In conventional simulation, the throttle is iterated at each point to converge on the desired load. This technique has fairly high overhead since all iterations are forgotten once the desired value has been reached. By applying the Matlab PCHIP (piece-wise cubic hermite interpolating polynomial) to the throttle sweep as it collects data, the throttle response curve for a given IVO/RPM combination can be reasonably estimated. With this estimated response curve, the proper throttle values can be estimated much more quickly. Experience has shown that the number of simulation calls may be reduced about 2.8 times relative to conventional methods for a throttle sweep with eight desired loads. A typical throttle response curve is shown in Figure 4.

At each speed and IVO combination a throttle sweep is run to generate the simulation output over the range of desired loads. Once the throttle sweep phase has been completed for every speed and IVO combination, the Final Interpolate/Output phase accesses this raw data and processes it to be used in the calibration database. The whole process is then repeated for different profiles and EVO values using a different input spreadsheet. Within this process there are a few noteworthy features, which significantly accelerate generation of the calibration database. These features are discussed in the following sections.

1000

BMEP (kPa)

800 600 400 200 0 0

20

40

60

Throttle Diameter (mm) Figure 4. Example of Throttle Response Curve Generated with the Front End. 4

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Interpolation has also been employed to calculate the output values from the raw throttle sweep data. Within the throttle sweep, a +/- 5-kPa tolerance is used. It has been found that engine output data within these ranges can be acceptably interpolated (less than 1% error) using the PCHIP function. This relatively loose tolerance allows the desired throttle responses to be determined quickly. Both of these interpolation techniques significantly reduce the simulation time of a calibration database while insignificantly reducing accuracy.

OPTIMIZATION TOOLS Phasing Schedule Optimizer Once the data creation process has been completed, the next task is to find the optimal phasing schedule for each point on the operating map. This task involves optimization of one or more quantities subject to design and operating constraints. The design constraints used are the intake and exhaust phaser authority, the intake and exhaust phaser default positions, and the minimum RPM for intake and exhaust phaser operation. The operating constraints are selectable from all simulation output parameters.

Simulation Restrictions (Real Time) The inclusion of real-time simulation restrictions during simulation also enables significant timesavings. These restrictions observe the current dilution and laminar flame speed during simulation convergence and stop the simulation and throttle sweep if these quantities are exceed acceptable ranges. This allows a significant amount of unnecessary simulations to be skipped. For example, at low engine speeds, many very advanced IVO values have very low laminar flame speeds and high dilution values. The real-time restrictions would skip these unrealistic points, which are also very computationally intensive.

The Phasing Schedule Optimizer (PSO), shown below in Figure 5, is used to optimize the phasing schedule for each intake cam profile in an efficient manner. For each operating point on the engine map, the PSO parses the calibration dataset and determines the optimal phasing per the specified optimization criteria. The following sections discuss the important features of the PSO in greater depth.

Phaser Restrictions (A):

To use these constraints in the throttle sweep format, a subtle processing order rule was implemented. The throttle sweep must start with the highest load values and go to the lower load values. This is done since the dilution will increase and laminar flame speed will decrease with any further throttle reduction. Using this approach, a large number of unnecessary simulations may be skipped without skipping the useful operating points. These restrictions are an efficient way to ensure the majority of the simulation time is spent on creating realistic calibration data.

An optimal VVA strategy will often require a large range of phasing values over the engine map. This may not be feasible or may require a more expensive phaser. To address these issues in the phasing schedule optimization, the Phaser Restrictions section of the PSO (see section labeled with an “A”) allows the user to input the possible phasing ranges for both the intake and exhaust valves. For example, in the PSO example shown in Figure 5, the intake and exhaust phasers are limited to the ranges of 300 to 350 and 105 to 155 crank degrees, respectively.

Limitations of Methodology

Phaser Defaults (B):

Given proper simulation procedures and model validation, these techniques provide an efficient and cost effective supplement to traditional calibration techniques. However, the methodology does have some limitations. The current work uses steady state simulation to address steady state calibration issues and does not treat transient, cold start, or engine warm-up phenomenon. The method could be extended to address transient effects by use of co-simulation.

In addition to the general range of the phasers, there is often a minimum speed required to generate enough oil pressure to actuate the phasers. The Phaser Defaults section allows the user to input the minimum engine RPM to enable control for each phaser. At engine speeds less than the minimum, the default phasing is used. At speeds greater than the minimum speed, the optimal phasing is used.

Related Quantity Restrictions (C):

The quality of the analysis is limited by the fidelity and accuracy of the engine model and simulation tool. For example, current modeling techniques are lacking in terms of hydrocarbon emissions (HC) predictive capability. Also, the engine model has to contain enough physical representation to be sensitive to engine control and actuator changes, and also quantitatively predict sensor signals as inputs to the controller. Therefore, it is crucial to have a high fidelity validated engine model as well as an engine pretest that spans a meaningful range of operating conditions.

In addition to the phaser constraints, the PSO allows the user to specify constraints on any other output parameter from the simulation. These are termed quantity restrictions. To enable a quantity restriction, the user selects the quantity, constraint value and the type of constraint. For example, in Figure 5, the user has selected to only use phasing possibilities that have Laminar Flame Speeds greater than 0.45 m/s. Other examples of quantity restrictions include total charge dilution, EGR level, and exhaust temperature. 5

A

C B D

Figure 5. Input Template for Phaser Schedule Optimizer (PSO)

A B

Figure 6. Input Template for Cam Schedule Optimizer (CSO) Tool

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Weighted Sorting (D):

Parameter Low Lift Cam Profiles High Lift Cam Profile IVO Range Min. RPM for Phaser Min. Flame Speed Optimization Criteria

As mentioned previously, the main task of the PSO is to find the optimal phasing schedule for a given set of optimization criteria. The Weighted Sorting section of the PSO is where the quantities to be optimized are specified. Optimization may be performed using any parameter from the simulation output as well as any combination of parameters. For example, one might optimize brake efficiency and NOx emissions with the relative weights of 0.6 and 0.4, respectively. By including multiple parameters in the optimization, the optimization will typically yield a more realistic optimal phasing that does not greatly sacrifice one quantity for the sake of slightly improving another.

Values 4, 5, 6, 7 10.95 280 to 350 800 0.45 Max. Brk Th. Eff.

Units mm mm CAD atdcf rev/min m/s %

Table 1. Parameters Specified for Calibration Optimization of Two-Step VVA System. represents the ideal boundary between operation on the LLC and operation on the HLC. For discussion purposes, only the results for a LLC of 4mm and the HLC of 10.95mm are presented. While results are exemplary for LLC of 4mm, improved results for other LLC may be achieved [24].

Cam Schedule Optimizer Once the optimal phasing schedules for each cam profile have been determined, the next step to optimize calibration of a VVA system is to find the optimal cam profile at each point on the engine map. Using the output from the PSO, the Cam Schedule Optimizer (CSO) determines the best overall cam settings from a given set of optimal phasing maps.

As shown in Figure 7 for IVO, the procedure determined that the LLC (4mm profile) would generally be used only for loads less than 500 to 600 kPa NMEP. The data in Figure 7 shows that the intake phaser is mildly advanced for operation on the LLC, but may be advanced to as much as 280 to 290 CAD for operation on the HLC. The close spacing of contour lines around the switch line indicates that the cam phaser must move quickly during transitions from the LLC (4mm) to the HLC. This highlights possible transient issues in the calibration during switch transitions.

The CSO, shown in Figure 6, only has two inputs for optimization: Steps Used in Switch Sort, and Switching Criteria. The Steps Used (section A in Figure 6) allows the user to specify which cam profiles will be included in the optimization process. This enables calibration for 2Step lift systems or more complicated fully flexible VVA. The Switching Criteria section is similar to the Weighted Sorting section of the PSO, and enables optimization to be carried out using a variety of simulation parameters.

MAP for the operating map is shown in Figure 9. The data shows a large operating region below the switch line for which MAP is greater than 90 kPa. This indicates significant unthrottling of the engine occurs during operation on the LLC.

CASE STUDY FOR 2-STEP VVA SYSTEM The techniques developed in this work were applied to optimize the calibration of a naturally aspirated, sparkignited V6 engine that was equipped with two-step VVA and intake cam phasing. A description of this engine may be found in reference [24]. The purpose of this optimization exercise was to determine which lift profiles and phaser schedules produce the highest brake thermal efficiency for the operating map. It was also necessary to determine where, on the operating map, to switch between the low-lift cam (LLC) and the high-lift cam (HLC).

Figure 13 shows the reduction of pumping mean effective pressure (PMEP) for the engine with two-step valve lift control compared to the baseline engine with conventional fixed cams. For a large portion of the region below the switch line, PMEP is reduced up to 80 or 90 percent, indicating that two-step lift control can be effective in reducing gas exchange losses. The impact of this PMEP reduction on brake thermal efficiency (BTE) is shown in Figure 14. As expected, the largest BTE improvement occurs at the lowest loads. At 200kPa load, between 1000 and 2000 rpm, the data shows that BTE was improved over 16 percent relative to the conventional fixed-cam baseline.

The optimization was performed for engine speeds from 800 to 7000 rpm, and loads from 100 to 900 kPa net mean effective pressure (NMEP). Table 1 summarizes the valve lift profiles used, the optimization criteria, and the constraints applied during the optimization process.

Overall, use of simulation-based calibration has been shown to be an effective tool to generate base calibrations for modern engines equipped with VVA systems.

Results of the simulation and optimization process are shown in Figures 7 through 14. Each figure includes a dashed line superimposed on the operating map that indicates the cam profile switch line. The switch line 7

Intake Valve Opening (CAD atdcf)

Switch Line

Figure 7. Intake Valve Opening Timing for the Operating Map

Spark Timing (CAD atdcf)

Figure 8. Spark Timing for the Operating Map

MAP (kPa)

Figure 9. Manifold Absolute Pressure for the Operating Map 8

Total Dilution (%)

Figure 10. Total Charge Dilution for the Operating Map

Net Thermal Efficiency (%)

Figure 11. Net Thermal Efficiency for the Operating Map

BSNOx (g/kW-Hr)

Figure 12. Brake Specific Oxides of Nitrogen for the Operating Map 9

Pumping Work Reduction (%)

S witch Line

Figure 13. Pumping Work Reduction Relative to the Fixed-Cam Engine for the Operating Map

BTE Improvement (%)

Figure 14. Improvement of Brake Thermal Efficiency for the Operating Map

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2. Raynaud, Y., et al., “Application of Adaptive Online DOE Techniques for Engine ECU Calibration,” 2002 IMECHE Conference on Statistics and Analytical Methods in Automotive Engineering. 3. Stuhler, H., et al., “Automated Model-Based GDI Engine Calibration Adaptive Online DOE Approach,” SAE Paper 2002-01-0708, 2002. 4. Roepke, K., and Fischer, M., “Efficient Layout and Calibration of Variable Valve Trains,” SAE Paper 2001-0668, 2001. 5. Ward, M.C., et al., “Bayesian Statistics in Engine Mapping,” Paper No. C606/020/2002, IMECH E, 2002. 6. Accelerated Powertrain Calibration with DOE, AVL FOCUS Magazine, 1/03, pg 30,31, May 2003. 7. Butler, K., “Virtual Partner; Automotive Powertrain Calibration Finally Becomes a Virtual Reality”, Engine Technology International, Issue 2/03, 2003. 8. Haines, S. N. M., et al., “The Application of an Automatic Calibration Optimization Tool to DirectInjection Diesels”, Statistics for Engine Optimization, Professional Engineering Publishing Ltd, London, 2000. 9. Stinstra, E., et al., “Design Optimization: Some Pitfalls and Their Remedies,” Centre for Quantitative Methods, Eindhoven, Netherlands. 10. Lowe, D., et al., “Validation of Neural Networks in Automotive Engine Calibration,” Artificial Neural Networks, 7-9July, 1997. Conference Publication No. 440, IEE, 1997. 11. Mitterer, A., and Zuber-Goos, F., “Model-Based Optimisation – a New Approach Towards Increasing Efficiency in Control-Unit Calibration,” ATZ 102, (2000) 3. 12. Meyer, S., and Greff, A., “New Calibration Methods and Control Systems with Artificial Neural Networks,” SAE Paper 2002-01-1147, 2002. 13. i-SIGHT Version 6, Engenious Software Manual, 2001. 14. Burk, R., Jacquelin, F., and Wakeman, R., “Using Co-Simulation Methods to Establish Variable Valve Actuation Hardware Specifications and Control Strategies,” Paper No. 2001-ICE-427, ICE-Vol. 37-3, 2001, American Society of Mechanical Engineers, 2001. 15. Jacquelin, F., Burk, R., and Wakeman, R., “Cam Phaser Actuation Rate Performance Impact on Fuel Consumption and NOx Emissions Over the FTP-75 Drive Cycle,” SAE Paper 2003-01-0023, 2003. 16. Burk, R., et al., “A Contribution to Predictive Engine Calibration based on Vehicle Drive Cycle Performance,” SAE Paper 2003-01-0225. 17. WAVE Users Manual, Ricardo Consulting Engineers, 2002. 18. Edwards, S.P., et al., “The Role of Statistics in the Engine Development Process,” Statistics for Engine Optimization, Professional Engineering Publications, Ltd, London, 2000. 19. Osborne, R., “Concurrent WAVE/Matlab Simulink Simulation Applied to HSDI Diesel ECU Calibration,”

SUMMARY AND CONCLUSIONS Simulation tools have been developed to rapidly generate and optimize calibration maps for complex powertrain systems. The work essentially creates a “virtual dynamometer”, and can be used to supplement other automated online calibration techniques. The focus of this work was to accelerate generation of the calibration dataset. Due to the highly nonlinear behavior of engine operating characteristics, it is believed that large databases may be necessary to achieve accurate calibration maps. It is hypothesized that future advances in computer technology will enable this “virtual dyno” technique to produce a large grid of accurate data without a large time issue. Additionally, many computers can be run in parallel to also enhance the speed of simulation. Although the current work focuses on generation of large calibration databases, it may also be combined with DOE techniques for further efficiency improvements to the overall process. These simulation and optimization tools have been applied to generate an optimized base calibration for a naturally aspirated, spark-ignited, V6 engine equipped with a two-step VVA system and intake cam phasing. The methodology can be used to investigate a wide variety of engine operating strategies in a comprehensive manner.

ACKNOWLEDGEMENTS The authors would like to thank Mr. Jim Niemeier of the Delphi Valvetrain Product Team, Mr. Gary Abusamra of the Delphi Forward EMS Team, and Dr. Mark Krage of Delphi Research Labs for their support and guidance over the course of this work.

CONTACT For additional information, Mark Sellnau [email protected] Delphi Research Labs 51786 Shelby Parkway Shelby Twp., MI 48315 Eric Rask [email protected] College of Engineering University of Michigan Ann Arbor, MI 48104

REFERENCES 1. Seabrook, J., et al., “Applications of Advanced Modeling Methods in Engine Development,” Paper No. C606/028/2002 IMECHE 2002. 11

20.

21. 22. 23. 24. 25. 26.

Proceedings of the Fourth Ricardo Software International User Conference, Detroit, March 1999. Osborne, R.P., “Total Vehicle System CAE Modeling Applied to Electronically Controlled Diesel Engine ECU Calibration,” Paper C587/004/2000, IMechE, 2000. MATLAB Version 6 Users Manual, The Math Works, Inc., 2001. GT Power Software, Version 5.2, Gamma Technologies, Inc, Westmont, Illinois, June 2002. ADVISOR 3.2, National Renewable Energy Laboratory, Advanced Vehicle Simulator Program, 2002. Sellnau, M., and Rask, E., “Two-Step Variable Valve Actuation for Fuel Economy, Performance and Emissions,” SAE Paper 2003-01-0029, 2003. Microsoft Visual Basic for Windows 2000, Microsoft Corporation, 2002. Microsoft Excel for Windows 2000, Microsoft Corporation, 2002.

NOMENCLATURE ANN ATDCf BMEP CAD CAE CSO DOE DOF ECP ECU EGR EVO GA HC HLC ICP IVO LLC NMEP NOx RPM PCHIP Polynomial PDA PMEP PSO RPM RSM SBC VIM VNT VVL VVT VVA

Artificial Neural Networks After Top Dead Center Firing Brake Mean Effective Pressure Crank Angle Degrees Computer Aided Engineering Cam Schedule Optimizer Design of Experiments Degrees of Freedom Exhaust Cam Phaser Engine Control Unit Exhaust Gas Recirculation Exhaust Valve Opening Genetic Algorithms Hydrocarbon Emissions High-Lift Cam Profile Intake Cam Phaser Intake Valve Opening Low-Lift Cam Profile Net Mean Effective Pressure Oxides of Nitrogen Emissions Revolutions per Minute Piece-wise Cubic Hermite Interpolation Port Deactivation Pumping Mean Effective Pressure Phaser Schedule Optimizer Revolutions per Minute Response Surface Modeling Simulation-Based Optimization Variable Intake Manifold Variable Nozzle Turbocharger Variable Valve Lift Variable Valve Timing Variable Valve Actuation

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