An Improved Model-Based Methodology for Calibration of an Alternative Fueled Engine THESIS

Transcription

1 An Improved Model-Based Methodology for Calibration of an Alternative Fueled Engine THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Ryan Vincent Everett Graduate Program in Mechanical Engineering The Ohio State University 211 Thesis Committee: Dr. Giorgio Rizzoni, Advisor Dr. Shawn Midlam-Mohler, Advisor Dr. Yann Guezennec

2 Copyright by Ryan Vincent Everett 211 i

3 ABSTRACT The EcoCAR challenge is a three year competition with the goal of re-engineering a 29 General Motors crossover utility vehicle to improve vehicle emissions and fuel economy, while maintaining drivability and consumer acceptability. Ohio State s team has selected an extended range electric vehicle (EREV) architecture with a 1.8 L compressed natural gas (CNG) Honda engine as the auxiliary power unit. This engine was chosen because of its 12.5:1 compression ratio, which results in higher brake efficiencies than a traditional spark-ignition (SI) engine. The Honda engine is converted to run on E85 fuel, which requires the engine control software to be rewritten. The purpose of this project is to improve the engine control strategy to reduce tail-pipe emissions and increase fuel economy. This research investigates a model-based calibration methodology to develop accurate engine calibrations for several operating parameters. The methodology utilizes design of experiments (DoE) techniques for data collection and advanced data analysis tools in MATLAB to develop accurate and robust engine control calibrations. The control software developed by Ohio State to run the Honda engine on E85 fuel resulted in a peak engine brake efficiency of 41% and a vehicle that meets EPA Tier II Bin 3 emissions standards. ii

4 DEDICATION This thesis is dedicated to my parents, Dave and Patty, and my girlfriend Erica for all of their patience, love, and support. iii

5 ACKNOWLEDGMENTS I would especially like to thank Dr. Shawn Midlam-Mohler for his guidance during the project. His enthusiasm and dedication to teaching is unparalleled and inspiring. I would also like to thank Dr. Giorgio Rizzoni for his support of programs like EcoCAR that give engineering students the ability to gain real-world experience. Thanks to everyone at the OSU Center for Automotive Research for providing amazing support to students engaged in research and motorsports. I would also like to thank my teammates Eric Schacht, Beth Bezaire, Katherine Bovee, John Kruckenberg, and Brad Cooley for their help in many of the aspects of the research conducted in my thesis. iv

6 VITA February 1, Born Canfield, Ohio December, B.S. Mechanical Engineering, The Ohio State University January, 211 to Present...Graduate Research Associate, Department of Mechanical Engineering, The Ohio State University Fields of Study Major Field: Mechanical Engineering v

7 TABLE OF CONTENTS Page Abstract ii Dedication.....iii Acknowledgments...iv Vita.. v List of Tables...ix List of Figures xi Chapters: 1. Introduction Introduction Vehicle Architecture Engine Selection EcoCAR Vehicle Technical Specifications Thesis Overview Literature Review Model-Based Calibration Honda R18A3 Engine Volumetric Efficiency Tailpipe Emissions Experimental Setup and Numerical Tools vi

8 3.1 Engine Instrumentation Data Acquisition System and Software Numerical Tools Developing a Test Plan and Inputting Data Selecting and Building Models to Fit Response Surfaces Generating Calibrations Summary of Numerical Tools Introduction to Calibration Techinques Traditional Calibration Model-Based Calibration Design of Experiments Forming Response Surfaces and Model Validation Model-Based Calibration Summary A New Approach to Model-Based Calibration Design of Experiments with Test Minimization Procedure Validation of Response Surfaces with Application Input Summary of New Model-Based Calibration Methodology Summary of Calibration Techniques Model-Based Calibration for Engine Mapping Introduction Design of Experiments and Establishing Error Criteria for Engine Calibration Design of Experiments Establishing Error Criteria Defining the Performance Factor from Vehicle Data Fitting and Validating Response Surfaces for Engine Mapping Response Surface Development with Initial DoE Utilizing the Test Minimization Procedure Additional Design of Experiments Considerations for Improving Response Surface Quality Effect of Test Point Randomization on Response Surface Development Using Performance Factor Information to Account for Error Dense Regions Using Occurrence Weights to Improve Design of Experiments in Advance Additional Response Surfaces Developed Using Model-Based Calibration Summary Conclusions and future work Conclusions Future work vii

9 7. Bibliography Appendix A: List of Symbols and Abbreviations viii

10 LIST OF TABLES Table Page Table 1: OSU EcoCAR vehicle technical specifications... 8 Table 2: List of sensors used for this research project Table 3: Honda R18A3 engine specifications [3] Table 4: Types of Radial Basis Functions [8] Table 5: Summary statistics for model comparison in MBC Toolbox Table 6: Comparison of calibration methods Table 7: Parameters to be modeled with data from DoE... 8 Table 8: Error targets for VE response surface validation Table 9: Normalized weighting factor for each zone, F z... 9 Table 1: Model fit comparison for 25 test DoE... Table 11: Validation results for multiquadric RBF model ix

11 Table 12: Model fit results from test minimization procedure Table 13: Response surface fit results for test randomization analysis Table 14: Regions of operation boundaries and quantity of tests x

12 LIST OF FIGURES Figure Page Figure 1: Schematic of EREV architecture... 3 Figure 2: Diagram of twin-clutch transmission and front powertrain... 4 Figure 3: Engine exhaust system schematic... 5 Figure 4: 2.2L DOHC Engine with Dual-Independent Variable Cam Phasing, Continuously Variable Intake Valve Lift, and a Variable Geometry Turbocharger [2] Figure 5: Model configuration for 2.2 L engine[2] Figure 6: Model-Based Calibration Overview [2] Figure 7: 2 point space-filling DoE for 2.2 L engine [2] Figure 8: Final calibrations for 2.2 L engine [2] Figure 9: Variable length intake runner system [3] Figure 1: Lift profiles for high-output and delayed closure cam settings [3] xi

13 Figure 11: Factors that influence volumetric efficiency [5] Figure 12: Engine out emissions for a 2.4 L gasoline engine Figure 13: Catalyst conversion efficiency for NO (dashed line), CO (dot-dashed line), and HC (solid line) emissions for a three-way catalyst as a function of air/fuel ratio for gasoline [7] Figure 14: Location of crank encoder Figure 15: Location of MAP sensor, MAF sensor, IAT sensor, and TPS Figure 16: Location of Pre-CAT UEGO and ECT sensors Figure 17: Data acquisition system schematic for engine dynamometer testing Figure 18: Engine dynamometer cooling system schematic Figure 19: Process flow and tool list for generating calibrations Figure 2: Test plan developer in MBC Toolbox Figure 21: DoE editor in MBC Toolbox Figure 22: Data editor in MBC Toolbox Figure 23: RBF response surface example [8] Figure 24: Model setup browser in MBC Toolbox... 4 xii

14 Figure 25: Response model browser in MBC Toolbox Figure 26: Model prediction/observation plot and response surface Figure 27: Cross-section viewer of response surface in model selection tool Figure 28: Model selection interface in MBC Toolbox Figure 29: Main functions of CAGE Toolbox [2] Figure 3: GUI for optimization feature in CAGE Toolbox Figure 31: Optimized calibration in tradeoff feature of CAGE Toolbox Figure 32: V-model design process for control system development... 5 Figure 33: Process flow for traditional calibration Figure 34: Break points for calibration Figure 35: Model-based calibration process flow Figure 36: Examples of classical design of experiments techniques Figure 37: Examples of space-filling design of experiments techniques Figure 38: 5-center multiquadric RBF response surface for volumetric efficiency... 6 Figure 39: 11 th order polynomial response surface for volumetric efficiency... 6 Figure 4: Design space PEV xiii

15 Figure 41: Procedure for evaluating validation data Figure 42: Cross-section view of model output and validation data Figure 43: Process flow for new calibration technique Figure 44:Halton Sequence designs of 5,, 2, and 5 tests Figure 45: Example operating region bubble plot Figure 46: Zone weighting factor method Figure 47: Error sensitivity penalty function Figure 48: Result of iterative test minimization strategy Figure 49: Methodology for fitting models and validating response surfaces Figure 5: 3 test Halton Sequence DoE Figure 51: 25 test Halton Sequence validation DoE Figure 52: Down-sampled space-filling test plans Figure 53: Response surface validation procedure Figure 54: Operating zones for engine in OSU EREV Figure 55: Vehicle speed trace for UDDS, HWFET, and OSU HWY drive cycles xiv

16 Figure 56: Bubble chart of engine operating points for UDDS, HWFET, and OSU HWY drive cycles... 9 Figure 57: Fuel-Air EQR of engine for UDDS, HWFET, and OSU HWY drive cycles 92 Figure 58: VE error sensitivity function, ϕ(e) Figure 59: VE as a function of MAP and engine speed in data editor tool Figure 6: Linear models for VE response surface with 25 test DoE Figure 61: Radial basis models for VE response surface with 25 test DoE Figure 62: PEV for multiquadric RBF VE response surface Figure 63: VE response surfaces for 25, 5, 75,, 125, and 15 test plans Figure 64: Test number effect on response surface error criteria Figure 65: Effect of test number randomization on response surface error Figure 66: 9 different 5 point test plans for randomization analysis Figure 67: Test randomization effect on response surface error criteria Figure 68: Normalized weighted zone error surface for the 25 test DoE Figure 69: Improved 5 test DoE with test point bias in high error dense regions Figure 7: Normalized weighted zone error surface for the 5 test DoE xv

17 Figure 71: Improved 75 test DoE with test point bias in high error dense regions Figure 72: Performance factor results with test point bias in high error dense regions Figure 73: Normalized weighted zone error surface for the imprvoed 5 test DoE with bias in error dense regions Figure 74: Normalized weighted zone error surface for the imprvoed 75 test DoE with bias in error dense regions Figure 75: Modified calibration process flow with consideration for error dense regions Figure 76: Bubble chart of engine operating points for UDDS, HWFET, and OSU HWY Figure 77: 5 test DoE accounting for frequency of occurrence weights based engine operating points for UDDS, HWFET, and OSU HWY drive cycles Figure 78: Performance factor results with occurrence weight biased DoE Figure 79: Modified calibration process flow with consideration of occurrence weights in advance to bias initial design of experiments Figure 8: Spark timing response surface Figure 81: Engine brake torque map contour xvi

18 Figure 82: Engine torque manager Figure 83: Throttle position response surface for feed forward setpoint Figure 84: Air per cylinder map contour Figure 85: Fuel flow rate response surface Figure 86: ECMS control algorithm Figure 87: Engine brake efficiency map contour Figure 88: Engine operating points for HWFET drive cycles Figure 89: Final calibration process flow xvii

19 CHAPTER 1 1 INTRODUCTION 1.1 Introduction With the high cost of gasoline and talk of green technology in everyday conversation, it is no secret that modern automotive engineers are researching solutions to these problems. The transportation industry consumes about 1/3 of all energy produced, and ninety percent of the energy used in the transportation industry is tied to petroleum. Improving engine technology can help shift the transportation industry away from oil dependence. Hybrid electric vehicles (HEVs) were introduced to the global economy in the late 199s and use sophisticated technology to increase fuel economy and reduce emissions. HEVs incorporate multiple power sources in order to improve efficiency, performance, and emissions. This technology is currently being researched by all of the major car companies and most have HEVs in production. The Ohio State University (OSU) is one of sixteen North American universities participating in EcoCAR: The Next Challenge, a vehicle development competition headline-sponsored by the United States Department of Energy (DOE) and General Motors (GM). This three-year competition challenges student teams to re-engineer a GM crossover utility vehicle for increased fuel economy and decreased emissions while 1

20 maintaining the vehicle s original performance and consumer acceptability. Each team s task is to design, build, and optimize a new powertrain for their vehicle, resulting in a fully functioning, prototype vehicle The EcoCAR engineering team at Ohio State has selected an extended range electric vehicle, or E-REV, architecture for the competition. The E-REV powertrain has an electric drive train on board, which will allow the vehicle to travel 4 miles on a single charge. Li-Ion batteries will supply power to the electric drive train. If the driver must exceed the range of the battery pack, an auxiliary power unit (APU) is equipped. The APU selected is a compressed natural gas (CNG) engine that has been converted to run on E85 fuel, a mix of 85% ethanol and 15% gasoline. The EcoCAR team is going to take advantage of the natural gas engine s high compression ratio (12.5:1) to increase the engine efficiency. By using E85, the automobile will reduce the petroleum consumption by 85% and emissions when the APU is needed because of the use of renewable bioethanol. Through extensive testing, control design, and calibration, peak brake efficiencies of 41% were achieved on the converted E85 engine. In advanced automotive technology, modeling and simulation techniques must be applied to write control software of complex systems. In this case, the system is a 1.8 L Honda engine. The process of converting the 1.8 L CNG to run on E85 fuel requires some hardware modification, including fuel injectors, but the majority of the work was in rewriting control software for this engine. This project involved a substantial amount of modeling, control design, and calibration effort, which was conducted by several 2

21 graduate and undergraduate students. Model-based control design was used to reduce the calibration effort and make the engine control more robust. This thesis outlines the refinement of engine control software to maximize brake efficiency, minimize tail pipe emissions, and integrate an advanced alternative fueled engine into a hybrid powertrain Vehicle Architecture The vehicle architecture developed by the Ohio State University EcoCAR team is shown in Figure 1. The design features a 1.8-L high compression ratio E85 internal combustion engine (ICE) coupled to an 82-kW front electric machine (FEM) via a unique twin-clutch transmission designed to enable greater operating efficiency through limited parallel operation. The twin-clutch arrangement permits coupling the engine and/or the FEM to the front axle, which is shown in Figure 2. This transmission design allows the vehicle to operate in series or parallel hybrid mode and allows front axle regenerative braking. Figure 1: Schematic of EREV architecture 3

22 Figure 2: Diagram of twin-clutch transmission and front powertrain To meet emission targets, the exhaust after-treatment system features a close-coupled three-way catalyst (TWC) with an integrated electrically-heated catalyst (EHC) and secondary air injection (SAIR) upstream of the EHC, which heats the catalyst to light-off before the engine starts, essentially eliminating cold start emissions. A schematic of the exhaust system is shown in Figure 3. 4

23 Figure 3: Engine exhaust system schematic A 22-kWh lithium ion battery pack is used for the onboard energy storage packaged as a split pack with two modules in the front console area and three modules in the rear of the vehicle. A 13-kW rear electric motor (REM) provides pure electric vehicle capability and allows rear axle regenerative braking. The battery pack with the front and rear electric machines gives the vehicle an all electric range of 4 miles. In addition, the vehicle has an onboard DC-DC converter for converting between the 12-V and high voltage and an AC-DC charger allowing the vehicle to charge through a 28-V or 11-V outlet Engine Selection Once the electric range is depleted, an E85 internal combustion engine is engaged for range extension of 3 miles. The engine was selected based on a desire for a high 5

24 compression ratio in order to benefit from the high octane rating of E85. A balance of the diminishing returns of increased compression ratio on efficiency lead the team to search for an engine with a nominal compression ratio around 13:1. This target was derived from predictive combustion simulations using GT-Power. After a search of production engines and high compression engine components, the team decided on a factory-built Honda engine that has a compression ratio of 12.5:1 that was originally designed to be fueled by compressed natural gas. By maintaining the factory specification of 12.5:1, the engine mechanical design was robust enough to tolerate the high in-cylinder pressures associated with high compression ratios. This selection required a complete re-design of the engine fuel system, exhaust after-treatment system, and engine control unit for the E85 hardware and software. This thesis will outline some of the control algorithms developed using traditional and model-based calibration techniques in order to achieve a robust control strategy for the converted engine EcoCAR Vehicle Technical Specifications The OSU EcoCAR vehicle technical specifications (VTS) goals were developed considering various factors. First, the EcoCAR vehicle was expected to exceed the original vehicle fuel economy without reducing performance. This goal set the OSU team s minimum allowable acceleration, towing, and braking performance. A second factor was the availability of significant R&D support for plug-in vehicles at the OSU Center for Automotive Research (CAR), where the vehicle would be designed and built. The OSU SMART@CAR program s current research projects and industry partnerships 6

25 are well aligned with the goal of developing a plug-in vehicle that would have a significant all-electric range and could be recharged from a plug-in connection. A third consideration was the desire to drastically lower petroleum consumption. The fourth and last factor considered in setting the VTS goals was that the EcoCAR project be sufficiently ambitious to educate students on current and future technology. The factors and goals outlined in this brief introduction helped to mold the architecture and design, which were then used in simulation to set the VTS goals that would be achieved by the final vehicle designed and built by the team. Overall, the OSU EREV design was able to meet or exceed each of the competition goals and the donated vehicle platform. Table 1 shows the final vehicle results compared to the competition targets and donated vehicle platform. The results were validated at several industry standard locations, including Transportation Research Center (East Liberty, Ohio), GM Desert Proving Grounds (Yuma, AZ), EPA National Vehicle Fuel and Emissions Laboratory (Ann Arbor, Michigan), GM Milford Proving Grounds, and OSU CAR. In relation to the engine work done, the vehicle was able to reduce substantially emissions, petroleum usage, and well-to-wheel greenhouse gas emissions. The fuel economy was also increased from 28.3 mpgge (miles per gallon gasoline equivalent) to 74 mpgge. This was all completed without sacrificing performance and with little reduction in cargo capacity. 7

26 Table 1: OSU EcoCAR vehicle technical specifications Specification EcoCAR Competition Goals Donated Platform OSU EREV ECOCAR COMPETITION REQUIREMENTS Acceleration -6 (s) 14 s 1.6 s 1 s Acceleration 5-7 (s) 1 s 7.2 s 5.8 s Towing Capacity (kg, (lb)) %, 2 72 kph (45 mph) 68 kg (1,5 lb) %, 2 72 kph (45 mph)* Cargo Capacity (mm, (in)) Height: 457 mm (18 ) Depth: 686 mm (27 ) Width: 762 mm (3 ).83 m 3 Height: 73 mm (28.7 ) Depth: 8 mm (31.5 ) Width: 9 mm (35.4 ) Passenger Capacity Braking 6- (m, (ft)) < 51.8 m (17 ft) 38-43m ( ft) 37 m (121.5 ft) Mass (kg, (lb)) 2,268 kg (5, lb) 1,758 kg (3,875 lb) 2,2 kg (485 lb) Starting Time (s) 15 s 2 s 4 s Ground Clearance (mm, (in)) 178 mm (7 in) 198 mm (7.8 in) 165 mm (6.5 in) Range (km, (mi)) 32 km (2 mi) > 58 m (36 mi) 399 km (248 mi) ECOCAR COMPETITION TARGETS Fuel Consumption, CAFÉ Unadjusted, Combined, Team: UF Weighted (l/km) 7.4 l/km (32 mpgge) 8.3 l/km (28.3 mpgge) 3.2 l/km (74 mpgge) Charge Depleting Fuel Consumption (l/km) Charge Sustaining Fuel Consumption (l/km) Charge Depleting Range (km, (mi)) Petroleum Usage (kwh/km) N/A N/A l/km (ge) N/A N/A 8.5 l/km (ge) N/A N/A 64 km (4 mi).77 kwh/km.85 kwh/km.8 kwh/km Exhaust Emissions Tier II Bin 5 Tier II Bin 5 Tier II Bin 3 WTW GHG Emissions (g/km) 224 g/km 25 g/km 19 g/km 8

27 1.2 Thesis Overview This project will help the overall performance of the 1.8 L E85 engine in the EcoCAR vehicle by refining the control software. The work includes more accurate and robust calibrations on common engine maps including spark timing and volumetric efficiency. Model-based calibration techniques were used to fit models to data collected using a design of experiments (DoE) for more accurate coverage of the design space. Modeling techniques were used to develop efficiency and torque maps of the engine to be used on the vehicle supervisory control, which allows for real-time optimization of the torque and power split between the engine and 2 electric machines in the hybrid powertrain. Development of model-based control algorithms and calibrations were used extensively in the conversion of the Honda 1.8 L CNG engine to run on E85 fuel. This has allowed for the successful integration of a clean and efficient engine into the OSU EcoCAR hybrid powertrain, and thus the team was able to deliver a vehicle with decreased tailpipe emissions and increased fuel economy. The organization of the thesis is as follows: Chapter 2 Literature Review Chapter 3 Experimental Setup and Numerical Tools o Chapter 3 discusses the engine instrumentation and the data acquisition system used for testing. It also describes some of the advanced numerical tools used for data analysis. 9

28 Chapter 4 Introduction Calibration Methods o Chapter 4 discusses the advantages and disadvantages to different calibration methodologies and details a new approach to minimizing the number of tests needed for developing an accurate calibration. Chapter 5 Model-Based Calibration for Engine Mapping o Chapter 5 explains how model-based calibration and the optimal testing procedure were used to develop lookup tables for engine calibration. Chapter 6 Conclusions and Future Work o Chapter 6 summarizes the work completed and future work to be done. 1

29 CHAPTER 2 2 LITERATURE REVIEW 2.1 Model-Based Calibration Increased complexity in engine technology has driven the need for optimized calibration techniques. The architectures involve more control variables and degrees of freedom than ever, which makes studying interactions of physical processes more difficult. This has lead to the rise of statistical modeling and design of experiments techniques that allow for visual realization of parameter interactions, which aids in calibration generation [1]. Consider the 2.2L DOHC engine with dual-independent variable cam phasing, continuously variable intake valve lift, and a variable geometry turbocharger shown in Figure 4, and a calibrator is challenged to develop models for all of the interactions of the control variables and physical parameters subject to several system constraints. For each speed and load condition, optimal cam phasing, spark timing, and AFR must be determined in order to achieve maximum brake torque, subject to exhaust temperature and turbocharger speed limitations [2]. Figure 5 shows the model configuration that must be developed in order to develop calibrations for the engine. This requires a more advanced approach to calibration. 11

30 Figure 4: 2.2L DOHC Engine with Dual-Independent Variable Cam Phasing, Continuously Variable Intake Valve Lift, and a Variable Geometry Turbocharger [2] Figure 5: Model configuration for 2.2 L engine[2] Figure 6 shows a systematic model-based approach to developing robust calibrations. It involves using design of experiments, statistical modeling, and calibration generation in order to implement tables or models on an embedded controller. For most modern engine 12

31 controllers, calibrations are limited to lookup tables typically because of computation limitations, but as hardware improves, models could potentially be implemented on the controller directly. Figure 6: Model-Based Calibration Overview [2] Design of experiments (DoE) for an advanced engine is a non-trivial task due all of the complex interactions and constraints [1]. Figure 7 shows a 2 point space-filling DoE for the 2.2L engine. By using a Sobol sequence space-filling randomization algorithm, 2 points are able to capture the entire operating space of the engine. This shows how powerful design of experiments can be. By intelligently choosing tests, rather than using ad hoc methods, fewer tests can be performed to produce more robust calibrations. This results in reduced costs in testing for companies and better engine performance. 13

32 Figure 7: 2 point space-filling DoE for 2.2 L engine [2] Figure 8 shows the final calibrations that were developed from the 2 point space-filling DoE. These calibrations were developed using statistical modeling tools in the MBC Toolbox in MATLAB. Discussion on how to construct models for response surface development is in section 3.3. By using the model-based calibration technique, robust optimal calibrations were achieved in a multi-degree of freedom engine with 2 experiments. Brake torque was maximized over the entire engine operating range, while still adhering to exhaust temperature and turbine speed constraints. By using design of experiments, testing was kept to a minimum and complex interactions were visually realized in order to better understand the system. 14

33 a. Intake Cam Advance b. Intake Valve Lift c. Air/Fuel Ratio d. Exhaust Cam Retard e. VGT Vane Open Fraction f. Spark Advance Figure 8: Final calibrations for 2.2 L engine [2] 15

34 2.2 Honda R18A3 Engine The Honda R18A3 engine was used for the research conducted in this project. This engine has several unique features and the settings for those features should be noted. There is an intake tuning valve that allows air to flow along a long or short intake runner length [3]. The runner length is adjusted by opening or closing a tuning valve. Optimum induction can be achieved by closing the bypass valve for low engine speeds and opening the bypass valve at high engine speeds [3]. Figure 9 shows the motion of the bypass valves. Shortened runner lengths are advantageous at higher engine speeds than are going to be used by the vehicle in which this engine will be implemented and was not studied. Figure 9: Variable length intake runner system [3] 16

35 A second feature this engine has is cam phasing. The intake cams can be set to a high output setting or a delayed closure setting. Figure 1 shows the lift profiles of the two cam settings. The high output cam functions synchronously with engine events, which opens at the start of intake stroke and closes at the start of the compression stroke[3]. The delayed closure setting keeps the intake cams open for a period of time during the compression stroke allowing more air to enter the cylinder by taking advantage of the inertia of the incoming air[3]. In previous research on this engine, it was found that the most efficient combination of settings was using the long runner length and high output cam setting [4]. This is because the engine will primarily be used at high MAP, which reduces the need for delayed intake cam timing, and at engine speeds less than 42 rpm, which eliminates the need for the short intake runner length setting of the bypass valve. Figure 1: Lift profiles for high-output and delayed closure cam settings [3] 17

36 2.3 Volumetric Efficiency Volumetric efficiency can be defined as the volume flow rate of air in the intake manifold divided by the rate at which volume is displaced by the piston [5]. Referring to equation (1), the speed density equation, volumetric efficiency is the ratio of air entering the intake manifold to air exiting the intake and be used in combustion. The 2 indicates that there are two revolutions per combustion events, is the mass flow rate of air into the intake system, is the density of air entering the engine, V d is the displacement volume of the engine, and N is the engine speed. (1) Either manifold pressure or ambient pressure can be used to calculate the density of the intake air. If manifold pressure is used, then volumetric efficiency defines the effectiveness of the induction system downstream of the throttle plate. This includes valves, ports, runners, and the plenum. If ambient pressure is used, then volumetric efficiency represents the effectiveness of the entire induction system, including air box and pipes leading up to the throttle. For this project, volumetric efficiency will be calculated using manifold pressure. Volumetric efficiency is influenced by many factors that interact in complex ways, increasing and decreasing the efficiency of induction. Factors such as charge heating, backflow, and flow friction decrease volumetric efficiency. Intake tuning and the ram effect can increase volumetric efficiency by taking advantage of dynamic wave 18

37 propagation in the intake system. Figure 11 shows graphically how volumetric efficiency is affected by different engine parameters. At low engine speeds, charge heating and back flow can significantly reduce volumetric efficiency. At high engine speeds, factors like flow friction and flow choking can drastically decrease the effectiveness of the induction process. At the same time, wave dynamics can be used to increase volumetric efficiency at high engine speeds. For the engine being studied in this project, wave dynamics will not be significant because the engine speed range is limited between - 42 rev/min. Figure 11: Factors that influence volumetric efficiency [5] Volumetric efficiency can be found by testing the engine at steady state. From test data, a map can be calibrated and implemented on the ECU. The volumetric efficiency map is used as a table lookup to calculate the mass air flow entering the cylinders with equation 19

38 (1). The table is stored as a function of MAP and engine speed, which are both measured quantities. Volumetric efficiency is critical for controlling transient emissions. It helps provide a more accurate estimate of the air mass entering the cylinder compared to the measured air flow from the MAF sensor during transients. Precise air-fuel ratio control is necessary to maximize three-way catalyst efficiency in order to meet emissions standards [6]. Precise air-fuel ratio begins with an accurate feed forward estimate of air mass entering the cylinders. This requires the development of an accurate volumetric efficiency map. 2.4 Tailpipe Emissions Tailpipe emissions have become a growing concern over the last three decades. Since the change to port-fuel injection, automotive engineers have investigated ways of reducing harmful exhaust gas emissions, including carbon monoxide (CO), unburned hydrocarbons (HC), and nitrogen oxides (NOx). Three-way catalysts have become the standard for converting harmful emissions into inert exhaust gases through oxidation and reduction reactions in the exhaust pipe[5]. Figure 12 shows the engine out, pre-cat, emissions of a 2.4 L gasoline, spark-ignited engine. Data was taken by varying the closed-loop, post-cat oxygen sensor enabled, fuel/air equivalence ratio and time averaging steady state data for 3 second increments. The emissions characteristics were measured with a Horiba exhaust gas analyzer. NOx emissions increase as the equivalence ratio decreases. On the other hand, HC and CO emissions increase as the equivalence ratio is increased; thus, the best balance of engine 2

39 THC Emissions (PPM) NOx Emissions (PPM) CO Emissions (PPM) out emissions is achieved if the air/fuel ratio (AFR) stays at stoichiometry, or an equivalence ratio of 1. Similar results are expected for E85 as a fuel source, rather than gasoline x NOx CO THC EQR chem Figure 12: Engine out emissions for a 2.4 L gasoline engine Figure 13 shows the catalyst conversion efficiency of NOx, HC, and CO emissions. This plot is specifically for gasoline as a fuel source, but similar principles apply for E85. The stoichiometric AFR for E85 is Three-way catalysts are more than 98% efficient at converting harmful exhaust emissions if a tight AFR tolerance about stoichiometry is achieved [7]. If AFR deviates too much from the stoichiometric relationship, catalyst conversion efficiency drops significantly, which results in poor tail-pipe emissions. 21

40 Figure 13: Catalyst conversion efficiency for NO (dashed line), CO (dot-dashed line), and HC (solid line) emissions for a three-way catalyst as a function of air/fuel ratio for gasoline [7] 22

41 CHAPTER 3 3 EXPERIMENTAL SETUP AND NUMERICAL TOOLS The Center for Automotive Research at The Ohio State University provided the facilities used for the research conducted in this project. The research was conducted in an engine dynamometer test cell. The dynamometer used was a 2 hp, four-quadrant DC motor. The dynamometer was used for speed control of the engine and would absorb the load from the engine to maintain constant engine speed. For engine control, a rapid prototyping, 128-pin Woodward engine control unit (ECU) was used. The rapid prototyping capability allowed engine control software to be modified with MATLAB/Simulink programming software. Motohawk Control Solutions provided a software package to be used in Simulink to communicate with the Woodward hardware. The engine used was a 1.8 L compressed natural gas (CNG) spark-ignition engine with a compression ratio of 12.5:1. The engine was converted to run on E85 ethanol, requiring a new control system. The testing facility was also equipped with a Horiba exhaust gas analyzer that can to measure CO, NOx, O 2, HC, and CO 2 emissions. Since the engine will be implemented in the OSU EREV architecture, it will only operate over a limited engine speed range of -42 rev/min in order to maximize efficiency. 23

42 The engine must work in tandem with a Remy HVH25 permanent magnet electric machine. The Remy motor has significantly decreased efficiency at higher speeds. This makes it advantageous to limit the range of both the engine and electric motor to operate at high combined efficiency points. 3.1 Engine Instrumentation The Honda engine is equipped with a wide range of sensors, some for fault detection, while others are for engine control. Table 2 shows the relevant sensors used for the purpose of this research project. Table 3 shows the specifications for the Honda R18A3 engine used in this project. Figure 14, Figure 15, and Figure 16 show the location of some of the relevant sensors used for this project. The number associated with the arrow in each figure correlates to the sensor information shown in Table 2. Table 2: List of sensors used for this research project ECU Sensors 1 Crank Shaft Position Sensor 2 Manifold Air Pressure (MAP) Sensor 3 Mass Air Flow (MAF) Sensor 4 Intake Air Temperature (IAT) Sensor 5 Throttle Position Sensor (TPS) 6 Engine Coolant Temperature (ECT) Sensor 7 Pre-CAT UEGO Sensor 24

43 Table 3: Honda R18A3 engine specifications [3] Cylinder Configuration In-line 4-cylinder Bore x Stroke (mm) 81 x 87.3 Displacement (cm 3 ) 1799 Compression Ratio 12.5 Valve Train SOHC Variable valve timing inlet delayed close Number of valves 16 Intake Manifold Variable intake system 1 Figure 14: Location of crank encoder 25

44 3 & Figure 15: Location of MAP sensor, MAF sensor, IAT sensor, and TPS 7 6 Figure 16: Location of Pre-CAT UEGO and ECT sensors 26

45 3.2 Data Acquisition System and Software Several types of software and hardware were used to complete this project. The software reads data from the engine with multiple types of data acquisition equipment. ETAS modules, ES41, ES411, and ES42 were used to monitor data from sensors. The ES41 module is an 8 channel analog unit. The ES411 is an 8 channel analog unit with sensor supply voltage. The ES42 module is an 8 channel unit for thermocouples. The ETAS modules are connected together and the final signal bus is sent to the control laptop with an ETAS custom Ethernet cable. Control software for the Woodward rapid prototyping ECU was written in MATLAB/Simulink using a Motohawk Control Solutions block set. Simulink uses a block diagram approach to write software. The Motohawk block set allows tunable variables to be implemented in the control software and be updated during engine calibration in Mototune or INCA. Mototune was used to create distinct engine controller calibrations and flash the control software onto the Woodward ECU. This program populates the engine control software written in Simulink with tunable calibration parameters. Inca, produced by ETAS, is used to record live engine test data and monitor relevant engine parameters while the engine is running. The operator laptop is equipped with a PCMCIA card that allows for communication with the Woodward ECU. Communication is conducted via the CAN Calibration Protocol (CCP) network. This allows the engine operator to adjust parameters such as, throttle position and fuel injection timing. It also 27

46 allows the engine operator to monitor parameters like exhaust gas temperature and oil pressure for fault detection and safe engine operation regulation. Because INCA is produced by ETAS, communication with the previously mentioned data acquisition modules is convenient and effective. INCA provides an interface for users to develop plots to study trends over time or monitor live data. Figure 17: Data acquisition system schematic for engine dynamometer testing The complete data acquisition system schematic is shown in Figure 17. Communication with the engine electronics occur over several different lines. The operator can adjust calibrations and acquire engine sensor data in INCA via a CCP connection with the PCM-CIA card or with the USB-Smartcraft Motonet Interface hardware and Mototune software. Each of these connections then is routed through a Smartcraft junction box to communicate with the ECU via a Smartcraft cable. Additional engine instrumentation 28

47 can be read in the laptop with an custom ETAS ethernet cable and ETAS modules. The modules have BNC and thermocouple connectivity. Testing in the engine dynamometer was all conducted at steady state. This consists of making sure pre-catalyst exhaust and engine coolant temperature stabilize between each test. Engine coolant was kept at approximately 8 o C for each test by adjusting coolant flow rate with the centrifugal pump and adjustable thermostat. The cooling system also has the ability to chill engine coolant with a radiator and ice bath connected in series with a cooling tower. This is used for cold-start tuning. The engine dynamometer cooling system schematic is shown in Figure 18. Figure 18: Engine dynamometer cooling system schematic 29

48 3.3 Numerical Tools Once the DAQ system was in place, numerical tools were needed to analyze the data collected in the experiments. The research conducted in this projects makes use of MATLAB extensively, including several of the more advanced features. The Model- Based Calibration Toolbox (MBC) was used to generate the design of experiments and develop mathematical models to fit to the data. The model accuracy was then analyzed using validation data collected. If the calibration model met all error criteria, it was then implemented into the Calibration Generation Toolbox (CAGE). The CAGE Toolbox is used to produce optimal fits of calibration data. The MBC graphical user interface (GUI) in MATLAB provides an organized approach to collecting and analyzing data to develop optimal calibrations for complex systems. The MBC Toolbox was used extensively in this project to define a test plan, fit statistical models, and generate calibrations. The calibrations were used for feed-forward lookup tables in the engine control strategy. 3

49 Develop Test Plan Tools: MBC Toolbox - Test Plan Editor Tasks: Establish Inputs/outputs, define number of stages in test plan Design of Experiments Tools: MBC Toolbox DoE Browser Tasks: Choose number of tests and test arrangement type Data Collection Tools: Experimental setup, DAQ, and MBC Toolbox Data Editor Tasks: Run experiments, import data, initial data check Model Setup Tools: MBC Toolbox Model Setup Tasks: Define model class, initialize model parameters Fit Response Surfaces Tools: MBC Toolbox Response Model Browser Tasks: Fit models, check model quality Generate Calibration Tools: CAGE Toolbox Tasks: Optimize calibrations, apply output boundary conditions, export lookup tables for control system Figure 19: Process flow and tool list for generating calibrations 31

50 3.3.1 Developing a Test Plan and Inputting Data To begin the MBC process, a test plan must be developed. Figure 2 shows the layout for the test plan. The organization flows from left to right, beginning with the test inputs, followed by the type of model for the calibration, and lastly the response surface. The inputs for this test plan are engine speed and manifold air pressure. Engine speed ranges from -42 rev/min and manifold pressure ranges from 1-11 kpa. The type of test plan used for this project is a One-Stage Global test plan. This means that there is only a single dependency between the inputs and responses. Alternatively, a Two-Stage test plan is offered, which would be developing a system with multiple dependencies. An example of this is in the case where the desired response is brake torque, which can be modeled as function of manifold pressure and engine speed, but the maximum brake torque (MBT) spark timing has not been determined for the engine. In this case, the peak brake torque is locally dependent on spark timing and is globally dependent on manifold pressure and engine speed. For this engine, the MBT spark timing was determined using the DoE, but not with the Two-Stage test plan. This was done because MBT timing was knock limited at certain points due to the high compression ratio of the engine. This did not allow for a local quadratic maximum to be used for the spark advance at each test case. 32

51 Figure 2: Test plan developer in MBC Toolbox Once the inputs are established, the design of experiments must be set up. The MBC Toolbox has a design tool to aid in setting up the DoE. The DoE browser allows the user to interactively change the design type, number of points, input ranges, and several other options. The design browser also graphically allows the user to display the tests points. Figure 21 displays interface with setting up a DoE. 33

52 DoE Design Type Options: Input Variable Ranges Visually Preview DoE Figure 21: DoE editor in MBC Toolbox 34

53 After the DoE is set up and the data is collected and sorted, the data can be imported to the MBC Toolbox via the data editor. The data can be imported in several formats, including.mat,.xls, and.csv formats. It is important to include variable names and units in the file to be imported because the MBC Toolbox will keep track of this information for later data analysis. Figure 22 shows the Data Editor tool. The data editor displays test data in table and graphical format to easily check the validity of test results. The display variables can be changed quickly, which reduces the amount of time spent writing intermediate plotting scripts. Figure 22: Data editor in MBC Toolbox 35

54 3.3.2 Selecting and Building Models to Fit Response Surfaces Once the data is imported and checked, response surfaces can be fit for calibration for calibration development. Models are used for calibration, rather than the direct data, because it is important to understand the system in between data points. This helps avoid excess interpolation that can potentially be error prone. To begin this process, the type of model must be selected for the response surface fitting. The types of models offered by the MBC Toolbox are the following: Linear Models Multi-Linear Models Radial Basis Function (RBF) Neural Network Hybrid RBF Transient Interpolating RBF The MBC Toolbox aids in fitting models to the data set. By offering built-in models, the calibrator does not need to write extensive script files for data processing. This helps save time and allows one to study many different models quicker. Linear models are limited to polynomials and hybrid splines. Polynomial models are of the form The hybrid spline models combine linear polynomial models with piecewise polynomial functions in order to fit data smoothly together [8]. Linear polynomial models are typically used for smooth systems, whereas, hybrid splines would be used when a system is linear with respect to most variables, but is non-linear in others. The linear parts can 36

55 be modeled as such and the non-linear components are modeled as piecewise polynomials. Radial basis functions are radially symmetric functions that can be used to model complex surfaces with limited data [8]. These functions can be networked together into a series of peaks and valleys minimizing the distance between the function center and the data provided. This makes modeling complex surfaces relatively simple where otherwise fitting linear models would be difficult. Radial basis functions are of the form where x is a vector of length n of input values, μ is vector of length n of radial basis function centers, and denotes the Euclidian distance between x and center μ [8]. The profile function f can be of many different forms. Some examples of profile functions and RBFs offered by the MBC Toolbox are shown in Table 4. 37

56 Table 4: Types of Radial Basis Functions [8] Type Profile Function/ Kernal Radial Basis Function Gaussian Multiquadric Reciprocal Multiquadric Linear Cubic Logistic Thin Plate Spline - σ is standard deviation of profile function These radial basis functions can then be linked to together in networks built upon the number of center points. In other words, each center point has a radial basis function associated with it, and the entire system is modeled as a linear combination of n radial basis functions with n centers. The RBF network is given by where β is a weighting factor for j th radial basis function centered at μ j and is the output, which approximates the target set of values y [8]. 38

57 Figure 23 shows an example of an RBF model. It is important to keep in mind the relative ease of over-fitting since an RBF network can model complexities with high precision. Choosing the number of centers is a critical component to developing RBF models because one can essentially fit a model to the data that is statistically equal, but the response surface does not make any physical sense. It is typical practice to use a 1:4 ratio of number of centers to number of data points [2]. For this project, the only models considered were linear and RBF models. This is because accurate fitting was achieved using only linear polynomial models or hybrid radial basis functions. The model setup browser is used for selecting the model class, which includes the previously mentioned types of models, and also selecting the fitting parameters. Figure 24 shows the GUI for the model setup browser. Figure 23: RBF response surface example [8] 39

58 Figure 24: Model setup browser in MBC Toolbox For linear models, the order of the polynomial needs to be selected, the interaction order of the cross-terms, and which variable is to have hybrid splines or not. For RBF models, the type of profile function or kernel must be chosen along with the initial width and lambda. The width refers to size of the peak or valley and the lambda term is used for smoothing between RBF centers [8]. Each of these parameters must be initialized before running through an optimization routine used to fit the model to the data set. Once the model type and parameters are set, the response surface can then be fit by building models. The MBC Toolbox makes it easy to fit many models, which is useful when limited information about the surface is known, and select the one that fits best to develop the calibration. 4

59 The Response model browser is next used to assess the quality of the model developed. It displays the model fit statistics numerically and graphically, as well as, the response surface describing the data. Figure 25 shows the interface for analyzing response models. The model tree is outlined in blue. Several different models can be built for each response surface, which makes the model tree useful for organizing multiple models. The graphical display is outlined in red. The graphical display can plot the model residuals, the response surface or contour, show data outliers, and the values a model predicts compared to the measured data. This is a useful feature because it bypasses the stage where one would normally need to write intermediate script files to develop plots and calculate the model error. Figure 26 shows an example prediction/observation plot and response surface plot, which can easily be developed in the graphical display tool. The statistical analysis tool is outlined in green. This displays the fit statistics of the response surface to the data provided. It organizes them into a summary table and ANOVA table. Overall, the response model viewer provides an effective tool for organizing, building, and analyzing response surfaces. 41

60 Predicted VE [mult.] Model Tree Graphical Display Statistical Analysis Figure 25: Response model browser in MBC Toolbox RBF center Predicted = Observed Data Outliers Predicted/Observed VE [mult.] Figure 26: Model prediction/observation plot and response surface Once multiple models are built, the Model Selection tool can be used to pick the most accurate model. This tool has all of the same features as the response model browser, but also takes the analysis one step further. The model selection tool shows the predictive nature of the model. This displays the values of the model in-between data points and the statistical confidence intervals. An example of the showing the predictive nature of the 42

61 model is displayed in Figure 27. The contour in the cross-section viewer can be adjusted, so the entire range of the model can be checked. This process should be done for each model, and the best fit should be selected. If none of the models meet the necessary error criteria, then more models should be investigated. Figure 28 shows the model selection tool interface. The model selection tool has a feature in which the response surface model can be exported. The model can be exported as a.mat file or to the workspace. The refinement of the model can be adjusted directly in the tool. This data can then be used directly to make a lookup table for calibration parameters. Eng. Spd. constant: 15 rpm MAP constant: 9kPa Figure 27: Cross-section viewer of response surface in model selection tool 43

62 Figure 28: Model selection interface in MBC Toolbox Generating Calibrations Using the MBC Toolbox, a response surface was fit to characterize the input-output relationship, but that model still can be improved further without taking additional data. The CAGE Toolbox is used specifically for generating lookup table calibrations. CAGE provides a user-friendly way of implementing table bounds, tradeoffs, and optimizing calibrations for embedded control design. Figure 29 shows the main features of CAGE Toolbox. The GUI makes it easy to organize different models, tables, optimization routines, and tradeoffs, which can become quite useful when working with multiple models and calibrations. 44

63 Figure 29: Main functions of CAGE Toolbox [2] The first step to using CAGE is by importing a model developed in the MBC Toolbox. The model developed in the MBC Toolbox can be transferred directly into CAGE. Then variable definitions should be setup in the variable dictionary feature. From the variable list and model, lookup tables can begin to be made in the tables feature. This helps to develop raw breakpoint and table data from the response surface fit in the MBC Toolbox. This is denoted as raw data because it has not been optimized or had bounds applied to it. In the table feature, the refinement of the lookup tables must be selected. The lookup tables can then be improved in the optimization feature. The optimization functionality is most useful in multiple degree of freedom systems, where relationships are not easily understood. Suppose an engine has variable valve 45

64 timing, exhaust gas recirculation, and a variable geometry turbocharger, it is not at all obvious when the spark timing is to achieve maximum brake torque for every possible combination. This feature will look at the model developed for each component and help put together an optimized spark map considering all degrees of freedom. The optimization feature requires a fair amount of initialization, which includes setting parameters like type of solver, number of iterations, boundary constraints, and exit criteria or tolerances. These often must be determined by trial and error and are unique to the application. Figure 3 shows some of the interface for setting up the optimization routine. It displays the parameters that must be initialized and the constraint editor. For the application shown, minimum and maximum bounds were put on one of the input parameters. The optimization routine can also be processed in parallel. This is useful to reduce the time processing data if the computer being used is a multi-core CPU system. The CAGE Toolbox works seamlessly with the Parallel Processing Toolbox to distribute runs over multiple cores and requires no additional setup beyond enabling the function for the optimization routine. The engine studied in this project does not have enough degrees of freedom to truly take advantage of the features offered by the optimization tool, but it was still investigated for the purpose of improving the models developed in the MBC Toolbox. Further research should be conducted to investigate the full benefits of the optimization feature. 46

65 Figure 3: GUI for optimization feature in CAGE Toolbox Once the optimization routine is complete, the optimized table is able to be reviewed in the tradeoff feature. The interface is shown in Figure 31. This feature displays the calibration sensitivity and shows the adjusted values from the optimization routine in yellow. The improved lookup table with optimum calibration can then be exported and checked with additional validation data. This will help benchmark the calibration with data that was not used to calibrate the model. 47

66 Figure 31: Optimized calibration in tradeoff feature of CAGE Toolbox Summary of Numerical Tools The MBC Toolbox and CAGE Toolbox were used extensively in the feed-forward control design for the engine control strategy. The tools help develop a test plan and conduct a design of experiments, fit complex models to form response surfaces, study input-output relationships in multiple degree of freedom systems, and generate optimal calibrations for control design. The following chapters will describe in more depth how these tools were used develop engine control calibrations and how to assess the quality of the models. 48

67 CHAPTER 4 4 INTRODUCTION TO CALIBRATION TECHINQUES Modern engine technology is becoming increasingly complex. This leads to more controllable parameters and thus increases the control algorithm development time. The traditional approach to engine calibration is becoming too time consuming and ultimately expensive. The rise of model-based calibration techniques has occurred to shorten the calibration timeline of engines and improve the quality of control systems. Since the OSU EcoCAR team is taking on the challenge of writing their own engine control strategy, engine testing and calibration must completed quickly and effectively. Figure 32 shows the V-model design process that the OSU EcoCAR team uses for control system development. The V-model provides a methodical approach to design, test, calibrate, and validate control algorithms. It also outlines that a test plan should be developed when the algorithms are designed, and validation results should be checked with the initial system requirements through the horizontal connections between processes. The OSU team also use software-in-the-loop (SIL) and hardware-in-the-loop (HIL) simulation before implementing control algorithms into the vehicle. HIL and SIL are used to make sure the control system is robust, but the algorithms still must be 49

68 calibrated on actual hardware to prove reliable operation and optimize performance. The time spent testing and calibrating to develop engine control systems is quite substantial, and this chapter will describes the differences between calibration techniques and explains a new approach improve calibration quality and minimize experimental efforts. Figure 32: V-model design process for control system development 4.1 Traditional Calibration In most applications, calibration and algorithm development are completely independent and by different people. For most applications, the algorithm must be determined before the physical system has been built, which leaves less flexibility to the calibrator in 5

69 developing robust calibrations. This is primarily because OEMs use standardized control algorithms for multiple platforms. Standardization prevents the possibility of software glitches causing product faults or failures. Figure 33 shows the process flow for traditional calibration methods. The calibrator often receives a lookup table structure. The structure dictates the input-output relationship to be calibrated and the total number of data points allowed in the table. It is usually up to the calibrator to choose the break points in the table structure. Figure 34 shows the concept of how break points are used in calibration. The calibrator will choose which points to collect data in order to capture the input-output relationship. Ideally, more refinement is chosen in complex regions and less in linear regions. Choosing break points is typically completed by experience. He or she should have a basic understanding of the system to be calibrated and would choose to increase refinement in certain regions and less in others, or the calibrator could choose to even space the test points into a grid. In either case, the approach lacks scientific support that performing a DoE would have and requires the calibrator to have knowledge of the system response. Once the data is acquired, a lookup table is calibrated. If the system operates in points between the break points interpolation is performed. At this point, the table can be implemented on the embedded controller or an optional validation is performed. 51

70 Figure 33: Process flow for traditional calibration Figure 34: Break points for calibration Validation of the calibration is often optional in traditional calibration methods, but is critical in analyzing how the calibration will perform in regions where data was not 52

71 taken. This helps determine the predictive nature of the table lookup. The issue with validation in traditional calibration methods is that there is not a clear procedure to do if the fit does not meet expectations. If the fit meets expectations, then it is simply implemented on the embedded controller. If not, a few of the options are to start over, pass the calibration on without improving, or adjust the break points and perform an ad hoc refinement. These are just some of the options the calibrator has. The common feature between them is that the options lack systematic approach to improving the quality of the calibration. Traditional calibration techniques are performed widely across industry. This calibration methodology can be completed quickly and does not require the calibrator to have skill in numerical modeling and statistics. Although traditional calibration is typically effective, the end product is not as robust as it could be if a more organized approach were used. A better defined experimental design and validation procedure would assist in developing more accurate calibrations. 4.2 Model-Based Calibration A statistical model-based approach to developing calibrations reduces the amount of experiments needed to accurately describe the design space. This methodology is designed to help choose the experimental data points intelligently and help develop more accurate, robust calibrations. Model-based design improves on traditional calibration because it uses fitting techniques to view the system response where data was not acquired. Figure 35 shows an overview of the methodology from the design of 53

72 experiments (DoE) to the implementation in real-time control. The model-based approach begins with a design of experiments and then is followed collecting data. Advanced statistical modeling is used to fit response surfaces to the data set to form a calibration model. The engineer will iteratively fit new response surfaces to the data set until fit is considered successful. The calibration model formed into a lookup table and implemented on to an engine control unit (ECU). Figure 35: Model-based calibration process flow The model-based calibration approach addresses some of the shortcomings of traditional calibration by using design of experiments and data fitting to study the entire system response. However, it still does not provide a procedure on how to obtain a robust calibration with the fewest tests possible, and it does not outline exactly how to choose the best model. The validation procedure still requires the calibrator to make subjective decisions in whether the model fit is good enough. 54

73 4.2.1 Design of Experiments The first step to the calibration development process is the design of experiments. Design of experiments are used to eliminate the trial-and-error approach to conducting tests. It is a systematic technique that considers all variables simultaneously. There are two important questions to answer when conducting a design of experiments. The first is, how many data points or tests are needed to cover the entire design space? The second is, what data points or tests should one select to capture the entire design space? Both of which are difficult questions to answer and depend on the complexity of the system or plant on which the tests are conducted. To address the question of which tests to choose, there are two types of design of experiments organization schemes. This is referring to the arrangement of the test structure. The first type is under the category of classical design. This involves an organized arrangement or evenly-spaced set of experiments. The MBC Toolbox offers several different types of classical designs. Figure 36 shows two of the types of classical designs. The designs are based on fictitious input variables, X 1, X 2, and X 3, which each range between and. The central composite design offers a circular pattern with a center point for a 2 degrees of freedom (DOF) case and a spherical pattern with a center point in 3-DOF. The full factorial design offers a grid pattern in both 2 DOF and 3 DOF cases. These examples are not limited to 3 DOF and can be extended to n-dimensional space, but cannot be visualized easily. 55

74 X3 X3 X2 X2 Central Compostie Design: 3D Full Factorial Design: 3D X1 5 X2 5 X1 5 X2 Figure 36: Examples of classical design of experiments techniques Classical design methods offer evenly spaced points, which makes post-processing of the data and developing lookup tables relatively simple. The full-factorial design covers the entire design space, but contains regions in between the grid pattern that are not captured in the data set. This problem can be addressed by conducting more experiments and reducing the space between points, but this increases the time spent testing and collecting data. The central composite design is lacking because it does not fully capture the boundaries of the design space, which is necessary when developing control calibrations. Alternatively, the design of experiments can be arranged into a space-filling design. These types of designs offer a pseudo-random approach to selecting experiments. They are not completely random due to the fact that an algorithm is used to sort the points, but are more chaotic than the classical approaches. Each of the examples shown in Figure 37 display a DoE of 5 experiments and offer a different approach to space-filling the 3 variable design space. 56

75 The space-filling designs provide a more randomized approach to capturing the design space; however, certain designs do a better job of capturing the entire design space than others. The Halton and Sobol sequence designs provide uneven spacing and contain no obvious pattern to the test point selection. There are small gaps where data would be lacking, but there is no repetition to the location of the gaps. This would provide a more complete coverage of the design space. The Lattice design has good coverage in two of the input variable interactions, but lacks completely in the third with the straight line of data points. The Stratified Latin Hypercube contains regions in which there is a grid pattern and thus will contain gaps in data coverage. For the type of testing conducted in this project, the Halton and Sobol sequence designs provide the best randomization strategies. The second question of how many tests are needed to develop an accurate and robust calibration cannot be answered with this methodology. The number of tests must be chosen up front and is typically decided by experience. This poses a problem when the calibrator has limited experience or when a new complex system is being studied, and an accurate, robust calibration is needed for the application. To select the number of experiments, the calibrator must then just choose what he or she believes is enough tests and hope that when moving on to the data analysis stage there are not any gaps or areas of limited data. 57

76 X3 X3 X2 X2 X3 X3 X2 X2 Halton Sequence Design: 3D Sobol Sequence Design: 3D X1 5 X2 5 X1 5 X2 Lattice Design: 3D Stratified Latin Hypercube Design: 3D X1 5 X2 5 X1 5 X2 Figure 37: Examples of space-filling design of experiments techniques Forming Response Surfaces and Model Validation Data acquired in the DoE then must be fit with response surfaces to characterize the system behavior over the entire design space. In order to fit response surfaces to the data, some preliminary inspection of the data must be performed. This is to develop an initial idea of how complex the surface will be. In simple systems, it would be desirable to fit linear models to the data set, whereas, in complex systems non-linear models must be used. Section 3.3.2, discusses the types of models studied for this project. Linear models were limited to polynomials and hybrid splines, and non-linear models were limited to 58

77 radial basis functions. The preliminary data check will provide insight on whether linear models or RBF models should be used. Data investigation and model fitting can be completed in the MBC Toolbox. This section will outline a procedure for building, comparing, and improving models with data from the space-filling DoE. Model building in the MBC Toolbox is simple in that one just needs to select the model type and configure the initialization parameters in the GUI. This makes it convenient to construct several response surfaces and compare the quality of fit. The response surfaces should be compared in a few different capacities. The first being to visually inspect the surface and look for anomalies in the fit. Figure 38 is an RBF fit for the volumetric efficiency of an engine. This surface has a couple of features that should be evident to the calibrator that the fit is poor. The first is the curling effect happening in the region of manifold pressure below 2 kpa. The second is the bulging effect in the low speed-low map region. Bulging occurs when using radial basis functions and there is limited data in a given region. Figure 39 shows an 11 th order polynomial fit for the volumetric efficiency response surface. This surface has some undulations or waviness that occurs at high engine speeds. This is characteristic of higher order polynomials used for fitting and is caused by over-fitting the data. These are just a few examples of common issues that arise when trying to fit response surfaces to complex systems and can be seen by visually inspecting the response surface. 59

78 VE VE Bulging Engine Speed [rev/min] 15 Curling Manifold Pressure [kpa] Figure 38: 5-center multiquadric RBF response surface for volumetric efficiency 1 Undulation Engine Speed [rev/min] Manifold Pressure [kpa] Figure 39: 11 th order polynomial response surface for volumetric efficiency 6

79 The next step to checking the fit quality is to study the model fit statistics. This includes looking at the residuals or root mean square error (RMSE), maximum error, and predicted error sum of squares (PRESS) root mean square error. Each of these factors gives a slightly different insight into how well the model fit is. RMSE measures the magnitude of the error between the actual value and predicted value [9]. PRESS RMSE is a metric that is used to judge the predictive nature of the model. It removes each run individually and uses the data from that run as validation against the model prediction[1]. Table 5 shows the summary statistics that the MBC Toolbox displays for model comparison. It is then up to the model developer to interpret the results and decide if the model is good enough or not. The error metrics are purely statistical terms and do not take into account knowledge of the application of the model. Table 5: Summary statistics for model comparison in MBC Toolbox The prediction error variance (PEV) is an additional metric that is used to assess the quality of the DoE conducted and the predictive nature of the model. PEV acts as a multiplier on the error in table data. Regions in which the PEV < 1 reduces error by using the model fitting process and PEV >1 magnifies error in the data 61

80 measurements[1]. This means that it is desirable for a response surface to have a PEV tending towards zero. A PEV plot is shown in Figure 4. Notice that the contours in the center and top have PEV of.1, which would indicate the response surface has high predictive capability in between data points taken in this region. The regions with MAP < 15 kpa and regions of high engine speed have PEV > 1, which would indicate that the model has poor predictive capability. Predictive capability of the surface can be improved by taking more data these regions. Figure 4: Design space PEV After a response surface is selected, it should also be checked for accuracy with the validation data acquired. This will help assess the predictive nature of the model because this data was not used to calibrate the response surface. The validation involves a statistical analysis of the validation data with the model prediction. Similar to model development, the RMSE, PRESS, and maximum error are studied. Based on experience 62

81 of the calibrator, a tolerance for each of these metrics must be established. Using the MBC Toolbox, validation data can be imported and compared with the response surface directly. Figure 41 shows the procedure for selecting the validation data for evaluation. This is done by choosing evaluate other data under the model menu, and then by selecting the test validation data. The model validation browser will then open and the data can be viewed. In this browser, the residuals can be viewed, the data can be plotted on a crosssection view of the model, and the fit statistics are displayed. Figure 41: Procedure for evaluating validation data Figure 42 shows the cross-section view of the validation results. It displays the contour predicted by the model along with the confidence intervals, then plots the points acquired in the validation data. This allows for visual inspection of the results. The fit statistics are also given at the bottom of the browser. 63

82 Figure 42: Cross-section view of model output and validation data The validation procedure does not contain a clear point at which the calibrator can determine if the response surface is good enough. From experience, he or she will determine if the response surface meets the needs of the calibration. If it does not, new response surface models should be developed to try to improve the calibration until the error requirements are met. If requirements cannot be met, then there is not a clear process to follow to improve the quality of the model. An additional test plan must be considered for improvement. This usually involves ad hoc test refinement in regions in which model accuracy is low Model-Based Calibration Summary The model-based calibration methodology is a systematic approach to developing response surface calibrations. It aids in design of experiments and advanced statistical modeling for development of robust calibrations. Using the MBC Toolbox enhances and 64

83 accelerates the data analysis process by fitting a wide array of models easily, summarizing model statistics, and displaying graphically response surfaces. This makes viewing complex input-output relationships simpler than with traditional data processing techniques, but fails to outline a procedure for assessing model accuracy and test number minimization. 4.3 A New Approach to Model-Based Calibration Model-based techniques offer advantages of fitting response surfaces, statistical comparison of models, and graphically viewing input-output relationships, but leave the issue of accuracy and minimization of experimental effort unaddressed or to the subjectivity of the calibrator. There is no procedure of how to reduce the number of tests needed for accurate calibration development. The method only relies on pure statistics to choose the best model. It also does not take into account the application input space or sensitivity to error. This section will discuss an alternative to the model-based calibration technique previously explained that addresses some of the short-comings. Similar to the model-based calibration method, the new approach begins with a design of experiments; however, this procedure outlines how to select the quantity of tests. After the data is acquired, response surfaces must be fit to build calibration models. The quality of the model is then to be checked with validation data. This process also develops a new performance metric to check the quality of the model, which takes into account error sensitivity and location of error based on frequency of operation in that zone in the application. If the model does not meet requirements, the DoE is then 65

84 extended to more tests. Adding more tests is intended to improve response surface quality. This is then repeated until model quality is acceptable and calibration can be implemented on the ECU. Figure 43 shows an overview for the proposed calibration procedure. Notice that there are several more decisions to make in the process flow than the model-based calibration technique. The calibrator can assess if adding tests is improving the model accuracy or if the final test number is reached. The intent of this process is to reduce the total amount of tests conducted for developing a calibration. The process also requires the calibrator to set validation targets, error sensitivity, and the operating space of the application. It is important to know the quality requirements of the calibration before undergoing testing. The sensitivity and operating space parameters will be used in developing a performance factor, which will give some insight in to the model quality in the specific application rather than just relying on statistics. 66

85 Figure 43: Process flow for new calibration technique Design of Experiments with Test Minimization Procedure To begin the design of experiments, a test arrangement must be chosen. This process can be found in section The method of choosing test arrangement has not been changed for the new calibration technique. Once the type of test is chosen, the quantity of tests must also be selected. Reducing the number of tests to a minimum is important because of accelerated development time lines and high costs of running experiments. For those reasons, it is desirable to have a methodical approach to minimizing the number of tests conducted while still obtaining enough data to accurately describe the system being tested. The designs proposed in this section are based on fictitious input variables, X 1, X 2, and X 3, which each range between and. 67

86 The first step is to generate a large DoE, which has an excess number of tests to accurately quantify the system, and a DoE of validation tests. The tests in the large DoE will be used for calibration development and the validation DoE will be used to benchmark the calibration model. The next step is to select a smaller space-filling subset of the large DoE. To select a smaller subset, there are several pseudo random techniques in MATLAB that can be implemented. The first is by using the haltonset( ) command, which is a space-filling randomization algorithm. A second approach is to use the rand( ) command in a loop and seed it with the CPU clock. There are certainly other randomization algorithms, but were not investigated for this project. Chapter 5 will address the effect of different randomization techniques on calibration quality. Figure 44 shows the initial 5 test DoE and smaller 2,, and 5 experiment subsets of the original design, using haltonset(.). In the 5 test design, there is limited space between each test point and likely would more than enough test points to develop a response surface for the input-output relationships. However, in the 5 test design, there is a lot of space between points and noticeable gaps where additional data would likely need to be taken. 68

87 X3 X3 X2 X2 X3 X3 X2 X2 5 Test Halton Sequence Design 2 Test Halton Sequence Design X1 5 X2 5 X1 5 X2 Test Halton Sequence Design 5 Test Halton Sequence Design X1 5 X2 5 X1 5 X2 Figure 44:Halton Sequence designs of 5,, 2, and 5 tests The calibrator is to take data from the smallest DoE, and then fit a response surface to that data set. The response surface fitting is completed by using the procedure in section using visual inspection and an initial statistical analysis. This new approach to model-based calibration will change the response surface validation procedure Validation of Response Surfaces with Application Input Validation of response surfaces should include all of the statistical metrics and visual inspection described in the model-based calibration technique, but it should also include 69

88 application input. For most applications, there is data available of where the system to be calibrated will operate. In this project, an engine is to be calibrated, so data from the vehicle or vehicle simulator should be considered when developing response surface calibrations. This data can be used to study common operating points, which will help dictate where models should be the most refined. Figure 45 shows an example bubble plot for engine torque and speed operating points over a city and highway drive cycle for the OSU EcoCAR. A large bubble corresponds to a frequent operating point for the engine, and a small bubble corresponds to a less frequent operating point. Circled in green is the region in which engine operation is most frequent, and thus the model developed should most accurate there. The plot shows the entire operating range for the engine. Notice there are regions in which the engine did not operate at all. This does not mean calibration should be skipped in those areas; it just does not need to be quite as refined as common operating points. This section will discuss a new performance metric that validation should take into account. The performance metric is a zone weighted parameter that accounts for fit accuracy, frequency of occurrence, and sensitivity to better assess model quality from the perspective of some regions require higher accuracy, while others do not. 7

89 Engine Brake Torque [Nm] Region of Most Frequent Operation Engine Speed [rev/min] Figure 45: Example operating region bubble plot In order to develop the performance metric, the operating region must be divided into different zones. The generic example used in this section has 2 input variables, X 1 and X 2. The operating region for each input variable should be divided into separate bins. A zone is comprised of the region of overlapping bins. Figure 46 shows one way of sorting data into zones. The method shown would establish break points in X 1 and X 2. Column break points are given by n and row break points are given by m. The data can then be placed into the corresponding zone, Z, based on which break points it fits under. 71

90 Figure 46: Zone weighting factor method Once the data is sorted into zones, the number of occurrences per zone, f z, can be counted. The normalized weighting factor for each zone, F z, is then given by equation (2). (2) where. The fit accuracy compares the measured or actual value with the value predicted by the model and is given by equation (3). (3) 72

91 where e is error, y actual is the measured value, and y predict is the response surface prediction. The weighted zone error is found by sorting the error results, averaging the error, and applying the weighting factor. This is given by equation (4). (4) where e z, is the error for each data point in a given zone and N is the total number of data points in a given zone. The error sensitivity, K e, is defined by the application and is given generically by equation (5). (5) where ϕ is a penalty function that is governed by the error, e. The error sensitivity is essentially multiplier that penalizes large error and rewards small error. Figure 47 shows an example of a error sensitivity penalty function. The example shows a quadratic function, which grows larger as error increases and is a minimum value of 1 when error is zero. The function ϕ should be determined by the application. The final performance factor, P, is the average weighted zone error and is given by equation (6). (6) 73

92 where M is the total number of zones. This final performance factor will be an additional validation metric that takes into account the error sensitivity and a weighted error based on frequency of operation. 12 (e) Error Sensitivity, K e Unweighted Error, e Figure 47: Error sensitivity penalty function For the application, error and performance factor criteria should be established before taking data. Once the data is collected and response surfaces are developed, the performance factor, P, along with the statistical, PEV, and visual analysis should then be used in to benchmark the model. If the response surface validation does not meet the error and performance criteria, then the test minimization procedure should be conducted. 74

93 Additional tests are performed by extending the space-filling DoE. This data is then used to develop a more accurate response surface. The iterative testing and modeling process is continued until the model error and performance criteria are within the allowable tolerance, or until procedure yields diminishing returns and accuracy is not within the specification. The result of this process is to develop a more accurate response surface calibration with fewer tests. The response surface will be more accurate because of the new performance metric established that takes into account the application input space and sensitivity. There will be fewer tests because of the test minimization strategy outlined. Error Allowable error Improving calibration Error criteria met # of Data Points Figure 48: Result of iterative test minimization strategy Summary of New Model-Based Calibration Methodology The new model-based calibration technique addresses some of the disadvantages of the original model-based approach. It utilizes the advantages offered by DoE and statistical response surface fitting, but also outlines a procedure on how to minimize the quantity of tests need to produce a robust calibration. The validation also provides insight into the 75

94 quality of the response surface by accounting for application specific data with the performance factor. 4.4 Summary of Calibration Techniques Each of the calibration techniques studied has advantages and disadvantages. Traditional calibration requires minimal training, but has unclear validation plans, which yields nonideal calibrations. The model-based approach addresses some of the short-comings of the traditional method by using DoE for data collection and statistical fitting for response surface development. The improved new model-based approach utilizes all of the advantages offered by the model-based method and adds in a test number minimization strategy along with a performance factor for model validation. The performance factor takes into account error sensitivity and the input space of the application. Table 6 provides a comparison of each of the calibration techniques. 76

95 Table 6: Comparison of calibration methods Methodology Advantages Disadvantages Traditional Low overhead for training and process development Subjectivity in data point selection, usually experience based Unclear validation procedure Model-Based Improved Model- Based Uses DoE for selecting data points Statistical fitting of response surfaces Robust calibrations Uses DoE for selecting data points and iterative test minimization strategy Statistical fitting of response surfaces with performance factor validation Potentially faster than model-based More robust calibrations Requires more calibrator training Does not provide a test minimization strategy Does not take into account application input for validation Requires more calibrator training Requires initial application data 77

96 CHAPTER 5 5 MODEL-BASED CALIBRATION FOR ENGINE MAPPING 5.1 Introduction The constant push for reduced tail-pipe emissions and increased fuel economy in engine development requires optimized calibrations of engine control software. The OSU EcoCAR team has used the model-based calibration techniques along with the new approach to minimizing time spent testing to ensure robust calibrations were implemented on the ECU. The accelerated development timeline associated with the 3 year competition makes it critical to reduce the amount of time spent calibrating. The procedure for the iterative test minimization strategy used is shown in Figure 43. The overall process of fitting and validating models is shown in Figure 49. The process flow shows that multiple models should be investigated from a single data set. This includes checking linear and radial basis function models. If, after exploring all of the different models, none meet the error criteria, then one should move on to the iterative test minimization strategy. This chapter will describe in detail the development of a volumetric efficiency map for the feed-forward fueling algorithm using the new calibration technique. 78

97 Figure 49: Methodology for fitting models and validating response surfaces 79

98 5.2 Design of Experiments and Establishing Error Criteria for Engine Calibration For this project, engine calibration maps intended for feed-forward control design were to be developed. The maps to be developed include the parameters listed in Table 7. Each parameter is needed for the development of the OSU EcoCAR engine and vehicle supervisory control strategies. The parameters are to be determined as a function of manifold absolute pressure (MAP) and engine speed. This effectively structures the data into a 2-DOF system with respect to engine speed and manifold pressure. For this project, the engine speed is limited from - 42 rev/min and MAP ranges from 1-11 (atmospheric) kpa. Table 7: Parameters to be modeled with data from DoE Variable Definition Use in Control System η v volumetric efficiency Engine fueling algorithm m apc air mass per cylinder Engine torque algorithm θ thr throttle position Engine torque algorithm θ spark spark advance Spark timing algorithm T brake brake torque Supervisory torque split fuel flow rate Supervisory torque split η f brake efficiency Supervisory torque split 8

99 5.2.1 Design of Experiments For the engine maps to be developed, it is important to capture the interactions between input variables most completely with as few tests as possible. This makes the Halton and Sobol sequence design techniques the best options for the DoE. For this project, the Halton sequence was selected to choose which data points will be tested in the DoE. The quantity of tests needed to accurately capture the system will be determined using the iterative testing procedure outline in section 4.3. The first step to the iterative process is to set a large DoE with more than enough points to fully describe the system. This going to have to be done by experience. The number of points selected here are not intended to be all be tested, so having an excess is not a concern. Not having enough would be detrimental to the iterative test minimization strategy. Figure 5 shows a 3 test Halton Sequence DoE. 3 tests would certainly be an excessive number of tests to be able develop an accurate calibration for the engine maps needed. The arrangement also provides a randomized test plan capturing the entire design space including the boundaries. The 3 test plan is then down-sampled to smaller test plans in order to follow the iterative test minimization procedure. Figure 51 shows the 25 test Halton Sequence validation DoE. This will be used for assessing the response surface quality and not used for developing models. 81

100 MAP [kpa] MAP [kpa] 3 Tests Engine Speed [rev/min] Figure 5: 3 test Halton Sequence DoE 25 Tests Engine Speed [rev/min] Figure 51: 25 test Halton Sequence validation DoE 82

101 MAP [kpa] MAP [kpa] MAP [kpa] MAP [kpa] MAP [kpa] MAP [kpa] 25 Tests 5 Tests Engine Speed [rev/min] Engine Speed [rev/min] 75 Tests Tests Engine Speed [rev/min] Engine Speed [rev/min] 125 Tests 15 Tests Engine Speed [rev/min] Engine Speed [rev/min] Figure 52: Down-sampled space-filling test plans 83

102 Figure 52 shows the down-sampled test plan for 25, 5, 75,, 125, and 15 tests. The down-sampling algorithm used was haltonset( ). A study of different randomization routines was also conducted and will be discussed in a later section. The test plan can be extended to more tests if the ability to develop accurate calibrations and all error criteria are not met after 15 tests. Data collection should begin with the fewest number of tests, which for this case is 25. Using that data, a calibration model is to be developed using the procedure described in the upcoming sections. To check the quality of the model, error criteria must be established for validation Establishing Error Criteria Before beginning the design of experiments, it is important to establish error targets. For this study, maximum error, RMSE, PRESS RMSE, and performance factor, P, were considered for error targets against validation data along with visual inspection of the model for anomalies. Table 8 shows the error targets for VE response surface validation. Each of these factors gives a slightly different insight into how good the model fit is. These targets were established based on the characteristics of a known effective volumetric efficiency calibration. The calibration was implemented on a vehicle that met EPA emissions standards and achieved these error targets. Section provides a detailed discussion on these parameters. Fit and validation are used to distinguish between modeling and validation data, respectively. There is a tighter tolerance on the fit data because it was used to develop the response surface, whereas, validation data was not. The visual inspection is to make 84

103 sure the model makes physical sense and does not experience qualities such as undulation due to over-fitting, curling, or bulging. The performance factor for this analysis will be discussed in detail in section Once the error criteria is established, the calibrator can begin acquiring data and modeling. Table 8: Error targets for VE response surface validation Maximum validation error, e max, val +/- 7 % Fit RMSE, e rmse, fit +/-.75 % Validation RMSE, e rmse, val +/- 1 % Fit PRESS RMSE, e press, fit +/- 1% Validation Performance factor, P val.14 * Discussion provided in section on establishing this metric The validation of a model will occur in three steps. The first step is to compare several response surfaces developed from a single data set by visual inspection. The second is checking Fit RMSE and Fit PRESS RMSE. To aid in choosing the best model, a simple cost function is used for comparison. The cost function weights RMSE and PRESS RMSE evenly at 5% each. Each of these parameters are equally important. RMSE gives great insight into how good the model fits the data, and PRESS RMSE tells the predictive nature of the model and will indicate if over fitting has occurred. The cost function, C(e), is shown in (11). This only analyzes the quality of the response surface with respect to the fit data, but it is not worth pursuing a model if it cannot be validated against the data that was used to develop it. Once the best model is determined from the fit data, it can 85

104 then be analyzed with the validation data. The validation includes checking the validation RMSE, performance factor, and maximum error. The validation procedure process flow is shown in Figure 53. (7) Figure 53: Response surface validation procedure The test plan also needs to be repeatable. To accomplish this, all of the tests were conducted at steady state under the following conditions: Each test was recorded for 3 seconds Coolant temperature held constant at 8 o C Before recording, pre-catalyst exhaust temperature had to stabilize Engine speed was held constant by dynamometer control (+/- 2 rev/min) MAP was held constant by throttle control (+/- 3 kpa) 86

105 5.2.3 Defining the Performance Factor from Vehicle Data To define the response surface performance factor, P val, application data must be acquired. For this project, vehicle data is used to find the frequent operating points of the engine and subsequently develop a weighting factor for each zone of operation. The engine maps to be developed will be determined as function of the calibration index variables, in this case MAP and engine speed; thus, these parameters will be used to sort the engine operating points into bins. The bins have the following refinement: MAP (kpa) 1, 25, 4 11 (atmospheric) Engine Speed (rev/min) -, 12, This equates to 6 regions in MAP and 16 regions in engine speed, which gives a total of 96 zones. These 96 zones cover the entire operating space of the engine used in the OSU extended range electric vehicle. The zones are shown visually in Figure 54. Section derives equations (2) - (11) used for determining the performance factor. 87

106 Figure 54: Operating zones for engine in OSU EREV The data used for this analysis is from the Environmental Protection Agency (EPA) and OSU developed drive cycles. The drive cycles include 2 EPA Urban Dynamometer Drive Schedule (UDDS), 1 Highway Fuel Economy Driving Schedule (HWFET), and 1 OSU highway cycle (OSU HWY). The UDDS cycles give a good insight into where the engine would typically operate during city driving. The HWFET captures a moderate highway drive cycle, and the OSU HWY captures a more aggressive highway cycle. The UDDS and HWFET cycles were driving by professional drivers at the EPA National Vehicle Fuel and Emissions Laboratory, and the OSU HWY cycle was driven by one of the EcoCAR team members, who had driven this course many times and provides repeatable results. These 4 cycles provide a nearly even split between city and highway driving and capture a broad sample of expected vehicle operating points. Even though 88

107 Vehicle Speed [mph] actual drive cycle data was used for this project, a model or data from a previous application could be used to predict operating points. 8 OSU HWY 7 6 UDDS HWFET UDDS Time [s] Figure 55: Vehicle speed trace for UDDS, HWFET, and OSU HWY drive cycles Figure 56 shows the regions in which the engine operates during the 4 drive cycles. The size of the bubble corresponds to the frequency of occurrence, f z. Thus, a large bubble indicates the engine operates in that region quite frequently, whereas, a small bubble indicates a region where the engine rarely operates. Table 9 shows the normalized weighting factor for each zone. The values were normalized to the zone with the maximum number of occurrences, which can be found in equation (2). A minimum value of.1 was applied to make every zone have a weight associated with it, even if it is not a common operating region. This was done to ensure that every zone has some influence. 89

108 Engine Speed [rev/min] Figure 56: Bubble chart of engine operating points for UDDS, HWFET, and OSU HWY drive cycles Table 9: Normalized weighting factor for each zone, F z MAP [kpa] Zones with zero operating points were given a minimum value of.1 9

109 The weighting factor is then applied to the calculated error between the response surface prediction and the measured value in the validation data. The error is multiplied by the sensitivity for the application. Control system and application requirements must be taken into account to develop a proper error sensitivity function. A good sensitivity function will penalize calibrations that cause operation outside of allowable tolerances, and reward ones that maintain operation within desired limits. It is experience based on a previous successful application, rather than theoretically, because it embodies many aspects of the control system. To determine the sensitivity for the application of volumetric efficiency, it is appropriate to study how frequently and the magnitude by which the air-fuel ratio of an engine deviates from stoichiometry. A histogram for the fuel-air equivalence ratio over the 4 cycles is shown in Figure 57. The fuel-air equivalence ratio (EQR) of the engine is in a narrow band of operation. Because of the narrow band of operation, it is desirable for the error sensitivity to provide a large penalty for volumetric efficiency values subject to high error. Alternatively, the error sensitivity should have little impact if the volumetric efficiency response surface has low error. A quadratic function has both of these characteristics and was chosen for the validation of the volumetric efficiency response surface. Equation (8) shows the error sensitivity function used for this project. The error sensitivity, K(e), is equal to 1. if the predicted VE is within +/- 2% of the actual VE; otherwise, K(e) is the output of the quadratic portion of the piecewise equation. This function is shown in Figure

110 Number of Occurences (8) F/A Equivalence Ratio Figure 57: Fuel-Air EQR of engine for UDDS, HWFET, and OSU HWY drive cycles 12 (e) 12 (e) 1 VE Error Sensitivity, K e VE Error Sensitivity, K e Percent Error [%] Percent Error [%] Figure 58: VE error sensitivity function, ϕ(e) 92

111 The final performance factor is given by equation (9). The performance factor takes into account the frequency of operation with zone weighting and the error sensitivity. This metric will provide some insight into how well the volumetric efficiency response surface will perform in a normal operating situation. (9) where, e i is the error of data point i, see equation (3) K(e) is the sensitivity, see equation (8) N is total number of data points in a given zone F z is the normalized weighting factor per zone, see equation (2) M is the total number of zones Z is the zone number Since the performance factor is being derived in this project, the target value is not yet known. To find an acceptable value, the iterative test minimization strategy will be carried out until diminishing returns in error and performance factor are obtained with improved modeling capability governed by more available data. This will help establish the performance metric to be used in future applications. 93

112 5.3 Fitting and Validating Response Surfaces for Engine Mapping A volumetric efficiency response surface can be developed and assessed for the use in calibration with the data collected in the smallest DoE. If the fewest number of tests, cannot accurately develop a response surface, then the test plan should be extended to a larger set of space-filling experiments. This procedure is outlined in section Response Surface Development with Initial DoE Experimental data is first time averaged over the 3 second cycle. This provides a large sample size of data for a more accurate estimate of the volumetric efficiency at each state. Once the data is processed into single state values, it should then be imported into the MBC Toolbox with the data editor browser. This tool aids in the initial inspection of the data set to make sure there are no outliers or points that should be re-taken. Shown in Figure 59 is the raw data for relationship of volumetric efficiency as a function of MAP and engine speed for the 25 test DoE. The plot shows that volumetric efficiency increases with manifold pressure and that it has a dependence with engine speed. This is what is expected for a volumetric efficiency surface, and there does not appear to be any obvious outliers in the data set. The data meets expectations and is ready for model fitting. 94

113 Figure 59: VE as a function of MAP and engine speed in data editor tool Data was acquired from the 25 test DoE and was used to develop volumetric efficiency response surfaces. Using the MBC Toolbox, a number of models were used to quantify the input-output relationship of MAP and engine speed to volumetric efficiency over the entire engine s operating range. The models include linear polynomials, cubic spline, and hybrid radial basis functions. For more information on how to choose, setup, and build models, see section For the purpose of this research, models are being used as tools and are not part of the core process. The MBC Toolbox builds the models selected with its own algorithms and offers different settings to fine tune the algorithm. Many different models were explored for the response surfaces developed in this project. With radial basis functions, several profile functions and minimization algorithms were considered. 95

114 Figure 6 shows graphically the linear models. Overall, the linear models, with the exception of cubic spline, did not successfully fit a reasonable response surface for volumetric efficiency. The 2 nd order model shows a peak in volumetric efficiency at a manifold pressure less that atmospheric, which does not physically make sense. The 5 th order model has an unusually large spike in volumetric efficiency greater than 1. at high MAP and high engine speed, which is uncharacteristic of a VE response surface. The 4 th order has a decrease in VE at high MAP and engine speed that does not typically occur in a VE surface. The cubic spline and 3 rd order fits appear to have a reasonable VE response with some slight divergence at high MAP and engine speed. After visual inspection, only the cubic spline and 3 rd order models should be considered for the volumetric efficiency calibration with the 25 test DoE. 96

115 Volumetric Efficiency Volumetric Efficiency Volumetric Efficiency Volumetric Efficiency Volumetric Efficiency Volumetric Efficiency 1 st order 2 nd order Manifold Air Pressure [kpa] Engine Speed [rpm] Manifold Air Pressure [kpa] Engine Speed [rpm] 3 rd Order 4 th Order Manifold Air Pressure [kpa] Engine Speed [rpm] Manifold Air Pressure [kpa] Engine Speed [rpm] 5 th Order Cubic Spline Manifold Air Pressure [kpa] Engine Speed [rpm] 8 6 Manifold Air Pressure [kpa] Engine Speed [rpm] Figure 6: Linear models for VE response surface with 25 test DoE 97

116 Figure 61 shows the radial basis function models for the VE response surface development. Each of the models was built using a radial basis network of 6 centers. 6 centers were chosen for the network because 6 is approximately 25% of 25, which is accepted practice when fitting radial basis functions. The Gaussian, logistic, and reciprocal multiquadric profile functions do not provide a reasonable fit because of curling at low manifold pressure across all engine speeds and some bulging at high engine speed and moderate MAP. The linear, cubic, and multiquadric kernals are able to better capture a smooth VE response surface. Each of them does have some slight divergence at high engine speed and high MAP, but overall the results make physical sense and should be further considered for statistical comparison. The divergence is likely due minimal data in that region. The MBC Toolbox offers many models to choose from and each of which has different setting to fine tune. This makes determining when to stop fitting models and collect more data to characterize the response surface difficult. The best approach to address this problem is to look at the general trends of the models. It may become evident that there are regions that could use more data, and no matter what model is fit there, will be error regions of high error. One must consider the additional time it will take to conduct more tests. In this case, there are regions at high MAP and high speed, as well as, low MAP and low speed, where model divergence is evident. Extending the test plan from 25 tests to 5 tests is less than a day of testing, so it is likely time better spent to collect more data than making small adjustments with models. For that reason, the analysis was limited to 12 models for further validation. 98

117 Volumentric Efficiency Volumetric Efficiency Volumetric Efficiency Volumetric Efficiency Volumetric Efficiency Volumetric Efficiency Gaussian RBF Linear RBF Manifold Air Pressure [kpa] Engine Speed [rpm] 8 6 Manifold Air Pressure [kpa] Engine Speed [rpm] Cubic RBF Logistic RBF Manifold Air Pressure [kpa] Engine Speed [rpm] Manifold Air Pressure [kpa] Engine Speed [rpm] Multiquadric RBF Reciprocal Multiquadric RBF Manifold Air Pressure [kpa] Engine Speed [RPM] Manifold Air Pressure [kpa] Engine Speed [rpm] Figure 61: Radial basis models for VE response surface with 25 test DoE 99

118 Table 1 shows the model fit statistics for each of the response surfaces in the 25 test DoE. The 5 th order polynomial statistically provides the best fit, but since it does not pass the visual inspection, it was not considered the best model. Of the models that passed visual inspection, the multiquadric RBF was best with a RMSE of 2.8%, PRESS RMSE of 2.46%, and a resulting cost function value of 2.27% for the model fit data. Figure 62 shows the prediction error variance of the multiquadric RBF model. It shows that the model has high predictive capability for the most part, with the exception at high MAP and high engine speed where PEV > 1. Overall, this model provides a good estimate of the VE response surface for the engine and can be further analyzed with validation data. Table 1: Model fit comparison for 25 test DoE Models Profile Function # of Centers Fit RMSE Fit PRESS RMSE Cost Function Visual Inspection Linear n/a n/a 6.79% 7.59% 7.19% n Quadratic n/a n/a 4.57% 6.2% 5.3% n Cubic n/a n/a 3.19% 5.73% 4.46% y Poly 4 n/a n/a 1.7% 5.1% 3.36% n Poly 5 n/a n/a 1.16% 1.38% 1.27% n Cubic Spline n/a n/a 2.1% 5.88% 3.99% y Hybrid RBF Gaussian 6 1.8% 4.55% 2.82% n Hybrid RBF linear % 3.4% 3.3% y Hybrid RBF cubic % 3.1% 2.84% y Hybrid RBF logistic 6 2.6% 3.74% 2.9% n Hybrid RBF multiquadric 6 2.8% 2.46% 2.27% y Hybrid RBF reciprocal multiquadric 6 1.8% 4.55% 2.82% n

119 Poor predictive capability Figure 62: PEV for multiquadric RBF VE response surface Using the validation data, the multiquadric RBF model can be assessed with data that was not used to build the model. This will determine the true predictive nature of the VE response surface. The validation data should be imported to the MBC Toolbox and checked in similar manner as the model fit data. The model developed can then be evaluated against the validation data using the procedure outline in section The results from the validation analysis are shown in Table 11. The response surface is not able to meet any of the error criteria established. Since the validation results do not meet all error criteria, the test plan should be extended to a larger space-filling DoE. The next step is the 5 test DoE, which adds 25 tests to the original plan of 25 tests. 11

120 Table 11: Validation results for multiquadric RBF model Max Validation # of Validation Fit PRESS Validation Performance Fit RMSE Tests RMSE RMSE Error Factor Target - 1% 7%.14.75% 1% Multiquadric RBF % 12% % 2.46% Utilizing the Test Minimization Procedure Since a valid response surface could not be fit using 25 test DoE, the test plan was extended to a larger space-filling DoE. The same procedure of first building models, visually inspecting, and initial statistical analysis was conducted. This is then followed by evaluation of the best response surface against the validation data. For this project, the test minimization procedure was carried out for 5, 75,, 125, and 15 tests. At each of these test points, linear polynomial, cubic splines, and radial basis function models were considered. More models can be considered as more data points are available. These include higher order polynomials and different size radial basis function networks. This section will show only the best model chosen for test quantity. For all of the test plans, the radial basis function models provided the best response surface. There was not a consistency in which profile function provided the best RBF model. As more tests were added, the model statistics and performance factor improved, which confirms that a more robust calibration can be developed with more data; however, the amount by which the model improved decreased as more tests were added. Figure 63 shows the volumetric efficiency response surfaces using the different size test plans. Each of the surfaces has a similar shape, but as more tests were added, the model captures 12

121 Volumentric Efficiency [%] Volumentric Efficiency [%] Volumentric Efficiency [%] Volumentric Efficiency [%] Volumentric Efficiency [%] Volumentric Efficiency [%] more detail in the system response. This detail is reflected in the improvement in model fit and validation statistics, which is shown in Table Tests 5 Tests MAP [kpa] Engine Speed [RPM] 8 6 MAP [kpa] Engine Speed [RPM] 75 Tests Tests MAP [kpa] Engine Speed [RPM] 8 6 MAP [kpa] Engine Speed [RPM] 125 Tests 15 Tests MAP [kpa] Engine Speed [RPM] 8 6 MAP [kpa] Engine Speed [RPM] Figure 63: VE response surfaces for 25, 5, 75,, 125, and 15 test plans 13

122 Table 12: Model fit results from test minimization procedure # of Tests # of Centers Validation RMSE Max Validation Error Validation Performance Factor Fit RMSE Fit PRESS RMSE Target - - 1% 7%.14.75% 1% Multiquadric RBF % 11.1% % 2.46% Cubic RBF % 9.86% % 1.48% Logistic RBF % 8.52% % 1.7% Gaussian RBF 25.81% 6.24%.139.6%.88% Multiquadric RBF % 5.41% %.65% Cubic RBF % 3.59%.11.48%.55% Figure 64 shows the influence of test number on the model fit results. Each of the statistical parameter targets was achieved by the test case. From this study, the target performance factor can be chosen as the value from the test case of.14. This can be the target because beyond this point there is very little improvement in the performance factor. There was a large improvement between 25 and test, which would indicate the magnitude of the error decreased significantly in the regions of frequent operation. With this analysis complete, the response surface from any of the DoE greater than or equal to tests can be confidently implemented as a volumetric efficiency calibration on the ECU. Each meets all error criteria and has good predictive capability in regions of common operation. 14

123 Performance Factor Validation RMSE [%] Validation Peak Error [%] Fit RMSE [%] Fit PRESS RMSE [%] % Target 1 1% Target 5 15 Number of Tests 5 15 Number of Tests % Target 1 1% Target Number of Tests 5 15 Number of Tests Target # of Tests Figure 64: Test number effect on response surface error criteria 15

124 5.4 Additional Design of Experiments Considerations for Improving Response Surface Quality Sections 5.2 and 5.3 showed the effect of test quantity on response surface quality. In each test plan the same randomization routine was used to develop the space-filling design. The test plans also did not account for regions of high error or common operation when choosing the test points. Model quality is influenced by which test points are selected and this section will investigate some potential outcomes and try to improve the overall calibration process Effect of Test Point Randomization on Response Surface Development The previous study showed that by increasing the number of test points, a more accurate response surface can developed. This is because the larger DoE always included the points from the previous DoE, as well as, the additional number of points. It would be naïve to think that any set of randomized space-filling points of a given quantity would potentially output a response surface of equivalent accuracy At a certain number of points with different randomization algorithms, there would be a spread in the quality of the response surface developed, some being more accurate than others. This presents an interesting problem because there are several outcomes that could occur as the number of tests increases with different space-filling randomization algorithms. Figure 65 shows conceptually the effect of using different space-filling test plans in response surface development. It shows in green, the expected outcome that the response 16

125 surface error would decrease as more tests are added. It is also conceivable that the error could increase as the number of tests is increased, if the perfect test locations were chosen in smaller test plan and a poor test selection occurred in the larger test plan. This outcome is shown in red. Another possibility is that model error remains nearly constant as more tests are added, which is shown in blue. The error deviation should theoretically decrease as the number of tests is increased because the maximum distance between test points decreases as the number of points increases. To gain some understanding of how selecting different tests affects the response surface quality, a case study of 9 different 5 test randomization strategies was conducted. Figure 65: Effect of test number randomization on response surface error 17

126 MAP [kpa] MAP [kpa] MAP [kpa] Figure 66 shows the 9 different test randomization strategies for a 5 point DoE. Each one utilizes a different randomization algorithm. From each test plan, a unique response surface was developed and analyzed in a similar manner, which is outlined in section 5.3. For each case, the radial basis function models provided the best fit, and in each case, an RBF network of 12 centers was used. The profile function did vary from case to case. The model fit results are shown for all 9 cases in Table Engine Speed [rev/min] Engine Speed [rev/min] Engine Speed [rev/min] Figure 66: 9 different 5 point test plans for randomization analysis 18

127 Figure 67 shows the effect of test randomization on response surface error criteria. For each of the error metrics, the worst case was still better than that of the test plan of fewer tests, and the best case was still worse than the test plan of more test points. This confirms the idea that adding more tests improves the ability to produce a more accurate calibration. However, if this study were continued for each quantity of tests, there would likely be some overlap in the error deviation. This makes it possible that adding tests could result in more error or no improvement, if the wrong test points are selected. To avoid these issues, the larger test plan should always be built off of the previous smaller test plan. This would ensure that the modeling ability improves as tests are adding to the DoE. Table 13: Response surface fit results for test randomization analysis # of Tests Validation RMSE Max Validation Error Validation Performance Factor Fit RMSE Fit PRESS RMSE Target - 1% 7%.14.75% 1% Thinplate RBF % 9.86% % 1.48% Thinplate RBF % 11.68% % 1.29% Gaussian RBF 5 1.4% 9.19% % 1.25% Multiquadric RBF 5 1.6% 8.59% % 1.63% Cubic RBF % 8.7% % 1.33% Multiquadric RBF % 7.5%.47.89% 1.33% Thinplate RBF % 7.33% % 1.58% Cubic RBF % 1.43% % 1.85% Multiquadric RBF 5 1.8% 9.75%.39.84% 1.26% Average 1.63% 9.22%.43.96% 1.44% Maximum 1.84% 11.68% % 1.85% Minimum 1.4% 7.33%.39.84% 1.25% Standard Deviation.15% 1.39%.24.11%.21% - All RBF networks have 12 centers 19

128 Performance Factor Validation RMSE [%] Validation Peak Error [%] Fit RMSE [%] Fit PRESS RMSE [%] Number of Tests 5 15 Number of Tests Number of Tests 5 15 Number of Tests Number of Tests Figure 67: Test randomization effect on response surface error criteria 11

129 5.4.2 Using Performance Factor Information to Account for Error Dense Regions Up to this point, each of the studies conducted explore the effect of adding a fixed number of tests randomly over the entire design space. With information from the performance factor, it is possible to bias the additional tests into regions of the highest error density. This would improve the response surfaces in regions that are lacking fidelity and most sensitive to error. To demonstrate this notion, the volumetric efficiency response surface from the 25 and 5 test design of experiments were studied further to see if adding tests in strategic locations could produce a more robust calibration than by using a randomization algorithm. The normalized weighted zone error,, is given by equation (1). (1) where e i is the error given by equation (3), K e is the error sensitivity given by equation (8), F z is the normalized zone weighting factor given by equation (2), N is the total number of data points per zone, and M is the total number of zones. Figure 68 shows the normalized weighted zone error surface for the 25 test DoE. There is large amount of error between engine speeds of rpm and MAP of 8- kpa, as well as, between engine speeds of -15 rpm and MAP of 4-8 kpa. When extending the test plan from 25 to 5 tests, these regions should receive a larger portion of the additional tests than regions of less error. 111

130 Normalized Weighted Zone Error Engine Speed [rev/min] MAP [kpa] Figure 68: Normalized weighted zone error surface for the 25 test DoE Figure 69 shows the 5 test plan with test point biases in the regions of larger error. The regions with test point biases are circled in red. Each region contains 7 of the 25 additional tests, which corresponds to 28% of the additional tests. The rest of the test points were chosen using the halton randomization algorithm. This process was then repeated for the 5 test plan. Figure 7 shows the normalized weighted zone error surface for the 5 test DoE. The magnitude of the error was less in the 5 test case, but there were regions of high error that need refinement. Similarly, test points were added in regions of high error. The 75 test plan with error biasing is shown in Figure % of the points were added in the region between engine speeds of rpm and MAP of 8- kpa. 2% of the points were added in each of the other 2 regions. 112

131 Normalized Weighted Zone Error MAP [kpa] Regions with test point bias Initial 25 Additional Engine Speed [rev/min] Figure 69: Improved 5 test DoE with test point bias in high error dense regions Engine Speed [rev/min] MAP [kpa] Figure 7: Normalized weighted zone error surface for the 5 test DoE 113

132 MAP [kpa] Regions with test point bias Initial 5 Additional Engine Speed [rev/min] Figure 71: Improved 75 test DoE with test point bias in high error dense regions The data from the each of the test plans was used to develop a volumetric efficiency response surface. A multiquadric RBF model with 12 centers and 18 centers for the 5 and 75 test cases, respectively, provided the best fits. Figure 72 shows the performance factor results with the biased test plans compared to those with space-filling randomized test plans. By putting additional points in regions of high error, the performance factor was decreased significantly for both the 5 and 75 test cases compared to the original test cases. Figure 73 and Figure 74 shows the normalized weighted zone error surfaces of the improved 5 and 75 test plans. There is a significant reduction in the error in the zones with the test point bias. The volumetric efficiency response surfaces developed using the 114

133 Performance Factor test biasing are more effective calibrations because they have better performance in the regions of most frequent operation. The dashed line in red shows what the effect of biasing the test plan is projected to do. The improvement in performance factor will diminish as the number of tests is increased. This will result in a convergence between the randomized DoE performance factor and error biased DoE performance factor. The convergence will occur because there is diminishing returns on model improvement as the number of tests is increased..8.7 Error Biased DoE Projected Error Biased DoE Halton DoE # of Tests Figure 72: Performance factor results with test point bias in high error dense regions 115

134 Normalized Weighted Zone Error Normalized Weighted Zone Error Engine Speed [rev/min] MAP [kpa] Figure 73: Normalized weighted zone error surface for the imprvoed 5 test DoE with bias in error dense regions Engine Speed [rev/min] MAP [kpa] Figure 74: Normalized weighted zone error surface for the imprvoed 75 test DoE with bias in error dense regions 116

135 With additional information from the performance factor, the ability to construct more robust calibrations with less test points was achieved. This was done by biasing the additional test points into regions with higher error accounting for sensitivity and frequency of occurrence. The modified process flow is shown in Figure 75. The intention of the additional consideration is to suppress the error in regions with distinct peaks in the error distribution first. Once that is complete, add the rest of the points to the operating space with a space-filling algorithm. The motivation is to be more efficient with test point selection, focusing on high error regions first. This could result in meeting error targets with fewer tests. Figure 75: Modified calibration process flow with consideration for error dense regions 117

136 5.4.3 Using Occurrence Weights to Improve Design of Experiments in Advance In section 5.2.3, the operating points of the engine over 2 UDDS, 1 HWFET, and 1 OSU HWY drive cycles were determined. Figure 76 shows a bubble plot for the operating points. This information can be used to construct a DoE that biases test points in regions of frequent operation, while limits the number of points in infrequent regions of operation. With the same number of data points, a response surface can be developed with potentially higher accuracy in the most important operating regions. This section will investigate the benefit of using occurrence weights in the design of experiments process. Figure 76: Bubble chart of engine operating points for UDDS, HWFET, and OSU HWY 118

137 MAP [kpa] To begin using the occurrence weights for the design of experiemnts, the operating space of the engine was divided into 3 total regions based on the probability that the engine operates in that area. A 5 test plan was construced with 5% of the operating points in region of high probability, 3% in the region of moderate probability, and 2% in the region of low probability. The boundaries of the regions are shown in Table 14. Figure 77 shows the test points selected for the DoE. Table 14: Regions of operation boundaries and quantity of tests Operating Region Probability # of Tests Engine Speed Range [rpm] MAP Range [kpa] High 25 (5%) Moderate 15 (3%) -27 & Low 1 (2%) -42 & % of Tests 3% of Tests 2% of Tests Engine Speed [rev/min] Figure 77: 5 test DoE accounting for frequency of occurrence weights based engine operating points for UDDS, HWFET, and OSU HWY drive cycles 119

138 Performance Factor The data from the test plan was used to develop a volumetric efficiency response surface. A multiquadric RBF model with 12 centers provided the best fit. Figure 78 shows the performance factor result for the occurrence weight biased DoE compared to the original space-filling test plans. The 5 test DoE with occurrence weight biasing was able to achieve a lower performance factor than the original 5 test Halton randomization DoE. It is also able to provide a better fit than the 75 test DoE. The volumetric efficiency response surface with the improved test plan would be a more effective calibration the previous 5 test response surface develop using a space-filling algorithm..8.7 Occurence Weight Biased DoE Halton DoE # of Tests Figure 78: Performance factor results with occurrence weight biased DoE 12

139 By utilizing engine operating data, a more effective test plan was able to be developed. The test plan resulted in an improved volumetric efficiency response surface calibration. To improve the new model-based calibration process, the data regarding frequency of operation should be utilized when constructing the initial calibration and validation test plans. The modified process flow that incorporates the operating space in advance is shown in Figure 79: Modified calibration process flow with consideration of occurrence weights in advance to bias initial design of experiments 5.5 Additional Response Surfaces Developed Using Model-Based Calibration In addition to the volumetric efficiency engine map, several other response surfaces were developed using the model-based calibration technique described in this chapter. The 121

140 Spark Advance [deg btdc] response surfaces are used in different parts of the engine and supervisory control strategies. Each of these response surfaces was developed using the same rigorous fitting and validation procedure as the volumetric efficiency map. This section will just present the different models and discuss their use in the engine control algorithm. Figure 8 shows the spark timing response surface for the engine. The results of the spark map are expected. As engine speed increases, spark advance for maximum brake torque (MBT) also increased. Spark timing was retarded as MAP increased. Knock was a limiting factor at lower engine speeds. At speeds greater than 35 rpm and MAP less than 2 kpa, a spark advance of 4 deg btdc was necessary to produce any torque Manifold Pressure [kpa] Engine Speed [rpm] 1 Figure 8: Spark timing response surface 122

141 Intake Manifold Pressure [kpa] Figure 81 shows the engine brake torque, T brake, contour that resulted from the MBT spark timing. An engine torque map is important for the vehicle supervisory control. The supervisor controller decides the torque split between each of the electric motors and the engine. In order to achieve the requested torque from the supervisory control, the engine controller must have an estimate of the engine torque output. The prediction is based on the measured values of engine speed and manifold air pressure Brake Torque [Nm] Engine Speed [RPM] -2 Figure 81: Engine brake torque map contour Figure 82 shows the engine torque control algorithm. The ECU receives a torque request from the vehicle supervisory controller. From that torque request and the measured engine speed, a feed forward throttle position setpoint is commanded. The feed forward 123

142 throttle position response surface is shown in Figure 83. A feedback controller is also used to adjust the throttle position setpoint to ensure the requested torque is achieved. This controller utilizes an APC response surface, which is shown in Figure 84, and equation (11) to provide a MAF request estimate. The MAF estimate is compared to measured MAF, and the error is used as an input to a proportional-integral (PI) controller. The output of the feedback PI controller is then used to make small adjustments to the throttle position in order to meet the torque request from the supervisory controller. (11) where, MAF is mass air flow into the engine in g/s, m apc is the air mass entering each cylinder in grams, and N is the measured engine speed in rev/min. Figure 82: Engine torque manager 124

143 Brake Torque [Nm] Throttle Position [%] Brake Torque[Nm] Engine Speed [rev/min] Figure 83: Throttle position response surface for feed forward setpoint Air Per Cylinder [mg] Engine Speed [RPM] Figure 84: Air per cylinder map contour 125

144 Fuel Flow [g/s] Figure 85 shows the response surface of the fuel flow rate as a function of brake torque and engine speed. This map is used in the vehicle supervisory energy optimization control algorithm called ECMS, or equivalent consumption minimization strategy. The structure of the ECMS algorithm is shown in Figure 86. The algorithm utilizes torque and energy consumption maps for each power device in the vehicle and conducts a realtime optimization routine to minimize fuel and electrical energy needed to meet a torque request. From the result of the optimization routine, a torque request is sent to the engine and electric machines Engine Speed [RPM] 15 5 Brake Torque [Nm] Figure 85: Fuel flow rate response surface 126

145 m eqv m f m ress m f P s Q ress lhv Figure 86: ECMS control algorithm Figure 87 shows the engine brake efficiency contour. The engine operates at a peak efficiency of 41%, which is significantly high for a spark ignition engine. Since the engine is used in the OSU EcoCAR EREV powertrain, it is able to operate at high efficiency points quite often. Figure 88 shows the engine operating points for a HWFET drive cycle. The histograms show the operating points of the engine in both series and parallel modes. The engine is able to operate between 35-4% for the majority of the time, which is unlike an engine in a conventional vehicle. It also has a very limited number of operating points in regions of efficiency less than 3%. 127

146 Brake Torque [Nm] 4 Brake Efficiency [%] Engine Speed [rev/min] Figure 87: Engine brake efficiency map contour 128

147 Instances [%] 4 Instances [%] Brake Torque [Nm] Brake Efficiency [%] Engine Speed [rev/min] Series Mode 25 Parallel Mode Brake Efficiency [%] Brake Efficiency [%] Figure 88: Engine operating points for HWFET drive cycles 129