Constrained Optimization of Fuel Efficiency for RCCI Engines ⁎

9th 9th IFAC IFAC International International Symposium Symposium on on Advances Advances in in Automotive Automotive 9th IFAC International Symposium on Advances in Automotive Control 9th IFAC International Symposium on Advances in Available online at www.sciencedirect.com Control 9th IFAC International Symposium on Advances in Automotive Automotive Control Orléans, June Symposium 23-27, 2019 2019 on Advances in Automotive Control 9th IFAC France, International Orléans, Control Orléans, France, France, June June 23-27, 23-27, 2019 Orléans, Control Orléans, France, France, June June 23-27, 23-27, 2019 2019 Orléans, France, June 23-27, 2019

ScienceDirect

IFAC PapersOnLine 52-5 (2019) 648–653

Constrained Optimization of Fuel Efficiency Constrained Optimization of Fuel Efficiency  Constrained Optimization of Fuel RCCI Engines  Efficiency Constrainedfor Optimization of Fuel Efficiency for RCCI Engines for RCCI Engines  for RCCI Engines ∗ ∗ ∗ Lu Bram Lu Xia Xia ∗∗ Robbert Robbert Willems Willems ∗∗ Bram de de Jager Jager ∗∗

Lu Xia ∗∗ Robbert Willems Bram de Jager ∗ ∗,∗∗ ∗ ∗,∗∗ ∗ Frank Willems Lu Willems Bram ∗,∗∗ Frank Willems Lu Xia Xia ∗ Robbert Robbert Willems Bram de de Jager Jager ∗ Frank Willems ∗,∗∗ ∗ Frank Willems ∗,∗∗ Lu Xia Robbert Willems Bram de Jager ∗ Frank Willems ∗,∗∗ ∗ Willems ∗ Dept. Mechanical Eng., Frank Eindhoven University of Technology (TU/e), Netherlands ∗ Dept. Mechanical Eng., Eindhoven University of Technology (TU/e), Netherlands Dept. Mechanical Eng., Eindhoven University of Technology (TU/e), Netherlands ∗ ∗ Dept. Mechanical Eng., Eindhoven University of Technology (TU/e), Netherlands (e-mail: {l.xia1, r.c.willems, a.g.de.jager, f.p.t.willems}@tue.nl). Dept. Mechanical Eng., Eindhoven University of Technology (TU/e), Netherlands (e-mail: {l.xia1, r.c.willems, a.g.de.jager, f.p.t.willems}@tue.nl). ∗ (e-mail: {l.xia1, r.c.willems, a.g.de.jager, f.p.t.willems}@tue.nl). ∗∗ Dept. Mechanical Eng., Eindhoven University of Technology (TU/e), Netherlands ∗∗ TNO (e-mail: {l.xia1, r.c.willems, a.g.de.jager, f.p.t.willems}@tue.nl). Automotive, Helmond, Netherlands. ∗∗ (e-mail: {l.xia1, r.c.willems, a.g.de.jager, f.p.t.willems}@tue.nl). TNO Automotive, Automotive, Helmond, Helmond, Netherlands. Netherlands. TNO ∗∗ ∗∗ TNO (e-mail: {l.xia1, r.c.willems, a.g.de.jager, f.p.t.willems}@tue.nl). Automotive, Helmond, Netherlands. TNO Automotive, Helmond, Netherlands. ∗∗ TNO Automotive, Helmond, Netherlands. Abstract: Fuel efficiency optimization Abstract: Fuel efficiency optimization and and emission emission reduction reduction have have become become essential essential parts parts of of Abstract: Fuel efficiency optimization and emission reduction have become essential parts of engine due growing for protection. In Abstract: Fuel optimization and reduction become parts engine research, research, due to to the the growing demand demand for environmental environmental protection. In this this paper, paper, Abstract: Fuel efficiency efficiency optimization and emission emission reduction have have become essential essential parts of ofaaa engine research, due to the growing demand for environmental protection. In this paper, computationally efficient optimization method has been applied to maximize the fuel efficiency engine research, due to the growing demand for environmental protection. In this paper, Abstract: Fuel efficiency optimization and emission reduction have become essential parts ofaa computationally efficient optimization method has been applied to maximize the fuel efficiency engine research, due to the growing demand for environmental protection. In this paper, computationally efficient optimization method has been applied to maximize the fuel efficiency under constraints of maximum pressure rise rate and various pollutant emissions using the computationally efficient optimization method has been applied to maximize the fuel efficiency engine research, due to the growing demand for environmental protection. In this paper, a under constraints of maximum pressure rise rate and various pollutant emissions using the computationally efficient optimization method has been applied to maximize the fuel efficiency under constraints of maximum pressure rise rate and various pollutant emissions using the combination of regression analysis and particle This optimization under constraints of pressure rise and various pollutant emissions using the computationally efficient optimization method has been applied to maximize the fuel efficiency combination of multiple multiple regression analysis andrate particle swarm optimization. This optimization under constraints of maximum maximum pressure rise rate and swarm variousoptimization. pollutant emissions using the combination of multiple regression analysis and particle swarm optimization. This optimization combination of regression analysis and particle swarm This optimization method has applied to Reactivity Controlled Compression Ignition First, under constraints of maximum pressure rise and variousoptimization. pollutant emissions using the combination of multiple multiple regression analysis andrate particle swarm optimization. This engine. optimization method has been been applied to a Reactivity Controlled Compression Ignition (RCCI) (RCCI) engine. First, method has been applied to aa Reactivity Controlled Compression Ignition (RCCI) engine. First, of multiple regression analysis and particle swarm optimization. This optimization method has been applied to a Reactivity Controlled Compression Ignition (RCCI) engine. acombination data-driven model has been identified, which shows good agreement with experimental data method has been applied to a Reactivity Compression Ignition (RCCI) engine. First, First, a data-driven data-driven model has been been identified,Controlled which shows shows good agreement agreement with experimental data a model has identified, which good with experimental data for gIMEP well as emissions. Using RCCI model in proposed optimization method, method hasas been to a Reactivity Controlled Compression Ignition (RCCI) engine. First, a data-driven model has been identified, which shows good agreement with experimental data fordata-driven gIMEP as wellapplied as has emissions. Using this this RCCI model in the the proposed optimization method, a model been identified, which shows good agreement with experimental data for gIMEP as well as emissions. Using this RCCI model in the proposed optimization method, the optimal operating conditions for highest gross indicated thermal efficiency are determined for gIMEP as well as emissions. Using this RCCI model in the proposed optimization method, a data-driven model has been identified, which shows good agreement with experimental data the optimal operating conditions for highest gross indicated thermal efficiency are determined for gIMEP asoperating well as emissions. Using this RCCI model in the proposed optimization method, the optimal conditions for highest gross indicated thermal efficiency are determined under various conflicting emission and safety constraints. the optimal conditions for gross indicated thermal efficiency are for gIMEP asoperating well as emissions. Using this RCCI model in the proposed optimization method, under various conflicting emission andhighest safety constraints. the optimal operating conditions for highest gross indicated thermal efficiency are determined determined under various conflicting emission and safety constraints. under various conflicting emission and safety constraints. the optimal conditions indicated thermal efficiency are determined under variousoperating conflicting emissionfor andhighest safety gross constraints. © 2019,various IFAC (International Federationand of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. under conflicting emission safety constraints. Keywords: engine efficiency optimization, particle swarm Keywords: engine engine efficiency efficiency optimization, optimization, particle particle swarm swarm optimization, optimization, multiple multiple regression, regression, Keywords: optimization, multiple regression, reactivity controlled compression ignition. Keywords: engine efficiency optimization, particle swarm optimization, multiple reactivity controlled compression ignition. Keywords: engine efficiency optimization, particle swarm optimization, multiple regression, regression, reactivity controlled compression ignition. reactivity compression ignition. Keywords: engine efficiency optimization, reactivity controlled controlled compression ignition.particle swarm optimization, multiple regression, reactivity controlled compression ignition. 1. INTRODUCTION INTRODUCTION imization scenario with MPRR and MP limitation. The 1. imization scenario with MPRR MP limitation. The 1. INTRODUCTION INTRODUCTION imization scenario with MPRRareand and MP limitation. The aforementioned optimizations generally implemented 1. imization scenario with MP The aforementioned optimizations areand generally implemented 1. INTRODUCTION imization scenario with MPRR MPRRare and MP limitation. limitation. The aforementioned optimizations generally implemented on physics-based models with indirect or direct correlation aforementioned optimizations are generally implemented Reactivity Controlled Compression Ignition (RCCI) is a 1. INTRODUCTION imization scenario with MPRR and MP limitation. The on physics-based models with indirect or direct correlation aforementioned optimizations are generally implemented Reactivity Controlled Compression Ignition (RCCI) is a on physics-based models with indirect or direct correlation Reactivity Controlled Compression Ignition (RCCI) is a to aphysics-based single operating operating input. on physics-based models with indirect indirect or direct direct correlation optimizations are generally implemented Reactivity Controlled Compression Ignition (RCCI) is aa aforementioned premixed, dual-fuel combustion concept, which has shown shown to a single input. on models with or correlation Reactivity Controlled Compression Ignition (RCCI) is premixed, dual-fuel combustion concept, which has to a single operating input. premixed, dual-fuel combustion concept, which has shown to aaphysics-based single input. models with indirect or direct correlation to provide dual-fuel very highcombustion thermal efficiency and low NOx and Reactivity Controlled Compression Ignition (RCCI) is a on premixed, concept, which shown single operating operating input. to provide very high thermal and low NOx and premixed, dual-fuel concept, which has shown In Dempsey and Reitz (2011), aa computational optimizato provide very simultaneously, highcombustion thermal efficiency efficiency and lowhas NOx and to In Dempsey and Reitz (2011), computational optimizato a single operating input. soot emissions see, e.g., Reitz and DuIn Dempsey and Reitz (2011), a computational optimizato provide very high thermal efficiency and low NOx and premixed, dual-fuel combustion concept, which has shown soot emissions simultaneously, see, e.g., Reitz and Duto provide very simultaneously, high thermal efficiency andReitz low NOx and tion In Dempsey and Reitz (2011), a computational optimizahas been applied to the gasoline-diesel RCCI engine soot emissions see, e.g., and DuIn Dempsey and Reitz to (2011), a computational optimization has been applied to the gasoline-diesel RCCI engine soot emissions simultaneously, see, e.g., Reitz and Duraisamy (2015). The most common characteristic for RCCI to provide very high thermal efficiency and low NOx and tion has been applied the gasoline-diesel RCCI engine soot emissions simultaneously, see, e.g., Reitz and Duraisamy (2015). The most common characteristic for RCCI with a low compression ratio using a multi-dimensional In Dempsey and Reitz (2011), a computational optimization has been applied to the gasoline-diesel RCCI engine raisamy (2015). The most common characteristic for RCCI with a low compression ratio using a multi-dimensional tion has been applied to the gasoline-diesel RCCI engine soot emissions simultaneously, see, e.g., Reitz and Duwith a low compression ratio using a multi-dimensional raisamy (2015). The most common characteristic for RCCI is to use a low-reactivity fuel, like gasoline, as pre-mixed raisamy (2015). The most common characteristic for RCCI is to aa low-reactivity fuel, like gasoline, as pre-mixed CFD model and nondominated sorting genetic algorithm with aamodel low compression using aa multi-dimensional tion has been applied to ratio the gasoline-diesel RCCI engine is to use use low-reactivity fuel, like gasoline, asdirect pre-mixed CFD and nondominated sorting genetic algorithm with low compression ratio using multi-dimensional CFD model and nondominated sorting genetic algorithm charge and a high-reactivity fuel, like diesel, as injecraisamy (2015). The most common characteristic for RCCI is to use a low-reactivity fuel, like gasoline, as pre-mixed charge and high-reactivity fuel, like diesel, as injecis to use a aalow-reactivity fuel, like gasoline, asdirect pre-mixed CFD and nondominated sorting genetic algorithm (NSGA II). Six objectives, including PM, CO, unwith amodel low compression ratio using aNOx, multi-dimensional charge and high-reactivity fuel, like diesel, as direct injecCFD model and nondominated sorting genetic algorithm (NSGA II). Six objectives, including NOx, PM, CO, untion to promote auto-ignition. The utilization of two fuels (NSGA II). Six objectives, including NOx, PM, CO, uncharge and high-reactivity fuel, like diesel, injecis to to use a aalow-reactivity fuel, like pre-mixed tion promote auto-ignition. The utilization of two fuels charge and high-reactivity fuel, likegasoline, diesel, as asasdirect direct injecCFD model and nondominated sorting genetic algorithm (NSGA II). Six objectives, including NOx, PM, CO, untion to promote auto-ignition. The utilization of two fuels burned hydrocarbons (HC), indicated specific fuel con(NSGA II). Six objectives, including NOx, PM, CO, unburned hydrocarbons (HC), indicated specific fuel conwith different reactivities provides engines larger control tion to promote auto-ignition. The utilization of two fuels charge and a high-reactivity fuel, like diesel, as direct injecburned hydrocarbons (HC), indicated specific fuel conwith different reactivities provides engines larger control tion to promotereactivities auto-ignition. The utilization of two fuels (NSGA II). Six objectives, including NOx, PM, CO, unwith different provides engines larger control burned hydrocarbons (HC), indicated specific fuel consumption (ISFC), and MPRR, have been minimized siflexibility compared to mono fuel combustion strategies burned hydrocarbons (HC), indicated specific fuel conwith different reactivities provides engines larger control sumption (ISFC), and MPRR, have been minimized sition to promote auto-ignition. The utilization of two fuels flexibility compared to mono fuel combustion strategies with different reactivities provides engines larger control sumption (ISFC), and MPRR, have been minimized siflexibility compared to mono fuel combustion strategies burned hydrocarbons (HC), indicated specific fuel consumption (ISFC), and MPRR, have been minimized simultaneously by varying six engine design parameters. A flexibility compared to mono fuel combustion strategies like Homogeneous Charge Compression Ignition (HCCI) with different reactivities provides engines larger control sumption (ISFC), and MPRR, have been minimized simultaneously by varying six engine design parameters. A flexibility compared to mono fuel combustion strategies like Homogeneous Charge Compression Ignition (HCCI) multaneously by varying six engine design parameters. A like Homogeneous Charge Compression Ignition (HCCI) similar optimization approach has also been applied sito sumption (ISFC), and MPRR, have been minimized multaneously by varying six engine design parameters. A flexibility compared to mono fuel combustion strategies like Homogeneous Charge Compression Ignition (HCCI) similar optimization approach has also been applied to and Partially Premixed Combustion (PPC). The RCCI multaneously by varying six engine design parameters. A like Homogeneous Charge Compression Ignition (HCCI) similar optimization approach has also been applied to and Partially Premixed Combustion (PPC). The RCCI and Partially Premixed Combustion (PPC). The RCCI similar optimization approach has also been applied to natural gas (NG)-diesel RCCI in Nieman et al. (2012) and multaneously by varying six engine design parameters. A like Homogeneous Charge Compression Ignition (HCCI) similar optimization approach has also been applied to and Partially Premixed Combustion (PPC). The RCCI natural gas (NG)-diesel RCCI in Nieman et al. (2012) and combustion process can be controlled by changing relative and Partially Premixed Combustion (PPC). Therelative RCCI similar natural gas (NG)-diesel RCCI in Nieman et al. (2012) and combustion process can be controlled by changing combustion process can be controlled by changing relative optimization approach has also been applied to natural gas (NG)-diesel RCCI in Nieman et al. (2012) and methanol-diesel RCCI in Li et al. (2014) using the same and Partially Premixed Combustion (PPC). The RCCI natural gas (NG)-diesel RCCI in Nieman et al. (2012) and combustion process can be controlled by changing relative amounts of port port fuelcan injection (low-reactivity fuel) relative and didi- methanol-diesel methanol-diesel RCCI RCCI in in Li Li et et al. al. (2014) (2014) using using the the same same combustion process be controlled by changing amounts of fuel injection (low-reactivity fuel) and amounts of port port fuelcan injection (low-reactivity fuel) relative and didi- natural gas (NG)-diesel inal. Nieman etusing al. (2012) and methanol-diesel RCCI in Li (2014) the same computational tools. et al. (2017) applied combustion process be controlled by changing amounts of fuel injection (low-reactivity fuel) and methanol-diesel RCCIBendu inRCCI Li et et al. (2014) using themultisame rect injection (high-reactivity fuel), implementing multiple computational tools. Bendu et al. (2017) applied multiamounts of port fuel injection (low-reactivity fuel) and direct injection (high-reactivity fuel), implementing multiple computational tools. Bendu et al. (2017) applied multirect injection (high-reactivity fuel), implementing multiple methanol-diesel RCCI in Li et al. (2014) using the same computational tools. Bendu et al. (2017) applied multiobjective optimization to an ethanol fuelled HCCI engine amounts of port fuel injection (low-reactivity fuel) and di- computational rect (high-reactivity fuel), implementing multiple tools. Bendu et al. (2017) applied multidirect injections or varying varying the direct injection timing. objective optimization to an ethanol fuelled HCCI engine rect injection injection (high-reactivity fuel), implementing multiple direct injections or the direct injection timing. objective optimization to an fuelled HCCI engine direct injections or varying the direct injection timing. by evaluating fitnessBendu function with(2017) different priority on computational et al. applied multiobjective optimization to an ethanol ethanol fuelled HCCI engine by evaluating aaatools. fitness function with different priority on rect injection (high-reactivity fuel), implementing multiple direct injections or varying the direct injection timing. objective optimization to an ethanol fuelled HCCI engine by evaluating fitness function with different priority on direct injections or varying the direct injection timing. With growing system complexity, engine control is no each objective hybrid regression neural by evaluating aausing fitness function with different priority on With growing system complexity, engine control is no objective optimization to an generalized ethanol fuelled HCCI engine each objective using hybrid generalized regression neural by evaluating fitness function with different priority on With growing system complexity, engine control is no direct injections or varying the direct injection timing. each objective using hybrid generalized regression neural longer straight forward. More precisely, due to the growth With growing system complexity, engine control is no network and particle swarm optimization. A similar multieach objective using hybrid generalized regression neural longer straight forward. More precisely, due to the growth evaluating a fitness function with different priority on With growing system complexity, engine control is no by network and particle swarm optimization. A similar multieach objective using hybrid generalized regression neural longer straight forward. More precisely, due to the growth network and particle swarm optimization. A similar multiof the applied air and fuel path actuators and increasingly longer straight forward. More precisely, due to the growth With growing system complexity, engine control is no objective optimization study is applied in Zhang et al. network and particle swarm optimization. A similar similar multiof the applied and fuel path actuators and objective using swarm hybrid generalized regression neural longer straightair forward. More precisely, due toincreasingly the growth each objective optimization study is applied in Zhang et al. network and particle optimization. A multiof the applied air and fuel path actuators and increasingly objective optimization study is applied in Zhang et al. strict requirements on robust real-world performance, enof applied and fuel path actuators and longer straightair forward. More precisely, the growth objective optimization study is in Zhang et al. (2017) experimentally optimize aa diesel engine using strict on robust performance, enparticle swarm optimization. A similar of the the requirements applied air and fuel pathreal-world actuatorsdue andtoincreasingly increasingly objective optimization study is applied applied in Zhang et al. (2017) to toand experimentally optimize diesel engine multiusing strict requirements onand robust real-world performance, en- network to experimentally optimize aa diesel engine using gine calibration time costsreal-world are foreseen foreseen toincreasingly show conconstrict requirements on robust performance, enof thecalibration applied airtime and fuel path actuators andto gine costs are show objective study is applied in Zhang al. (2017) to optimization experimentally optimize diesel engine et using strict requirements onand robust real-world performance, en- (2017) an improved artificial bee colony algorithm. gine calibration time and costs are foreseen to show con(2017) to experimentally optimize a diesel engine using an improved artificial bee colony algorithm. tinuous exponential growth; especially, when map-based an improved artificial bee colony algorithm. gine calibration time and costs are foreseen to show constrict requirements on robust real-world performance, entinuous exponential especially, when gine calibration timegrowth; and costs are foreseen to map-based show con- (2017) to experimentally optimize a diesel engine using an improved artificial bee colony algorithm. tinuous exponential growth; especially, when map-based improved artificial bee colony algorithm. In this paper, aa computationally efficient optimization control approaches are followed. As foreseen result, model-based tinuous exponential growth; especially, when map-based gine calibration time and costs are show con- an In this paper, computationally efficient optimization control approaches are followed. As aaa result, model-based tinuous exponential growth; especially, whento map-based In this paper, aa applied computationally efficient optimization an improved artificial bee colony algorithm. control approaches are followed. As result, model-based method has been to aa RCCI engine to maximize approaches are of of great great interest. However, amodel-based systematic, In this paper, computationally efficient optimization control approaches are followed. As a result, tinuous exponential growth; especially, when map-based method has been applied to RCCI engine to maximize approaches are interest. However, a systematic, In this paper, a computationally efficient optimization control approaches are followed. As a result, model-based method has been applied to a RCCI engine to maximize approaches are of great interest. However, a systematic, control-oriented optimization method regarding multiple method has been applied to a RCCI engine to approaches are of great interest. However, a systematic, the gross Indicated Mean Effective Pressure (gIMEP) with In this paper, a computationally efficient optimization control approaches are followed. As a result, model-based control-oriented optimization method regarding multiple method been applied to a RCCI engine(gIMEP) to maximize maximize approaches are of great interest. However, a systematic, the gross grosshas Indicated Mean Effective Effective Pressure (gIMEP) with control-oriented optimization method regarding multiple the Indicated Mean Pressure with parameters to obtain highest efficiency is still under recontrol-oriented optimization method regarding multiple method has been applied to a RCCI engine to maximize approaches are of great interest. However, a systematic, the gross Indicated Mean Effective Pressure (gIMEP) with respect to a fixed amount of total fuel energy, using mulparameters to obtain highest efficiency is still under recontrol-oriented optimization method regarding multiple the gross Indicated Mean Effective Pressure (gIMEP) with respect to a fixed amount of total fuel energy, using mulparameters to obtain highest efficiency is still under rerespect to a fixed amount of total fuel energy, using mulparameters to highest efficiency is research, as shown shown in, e.g., e.g., Willems (2018). control-oriented optimization method regarding multiple tiple linear analysis and particle swarm optiIndicated Mean Effective Pressure (gIMEP) with respect to aa regression fixed amount of total fuel energy, using mulparameters to obtain obtain highest efficiency is still still under under re- the search, as in, Willems (2018). tiplegross linear regression analysis and particle swarm optirespect to fixed amount of total fuel energy, using mulsearch, as shown in, e.g., Willems (2018). tiple linear regression analysis and particle swarm optiparameters to obtain highest efficiency is still under re- tiple search, as shown in, e.g., Willems (2018). mization. Compared to the aforementioned multi-objective linear regression analysis and particle swarm optirespect to a fixed amount of total fuel energy, using mulsearch, as shown in, e.g., Willems (2018). mization. Compared to the aforementioned multi-objective tiple linear regression analysis and particle swarm optiCompared to the aforementioned multi-objective Eriksson and Sivertsson (2016) minimized minimized the fuel fuel concon- mization. Eriksson Sivertsson (2016) optimization studies, deals a search, asand shown in, e.g., Willems (2018). the mization. Compared tothe theproposed aforementioned multi-objective linear regression analysis and method particle swarmwith optiEriksson and Sivertsson (2016) minimized thetrace fuel for con-a tiple optimization studies, the proposed method deals with a mization. Compared to the aforementioned multi-objective optimization studies, the proposed method deals with a Eriksson and Sivertsson minimized the fuel consumption by searching searching the(2016) optimal combustion large number of conflicting constraints by adding penalty Eriksson and Sivertsson (2016) minimized the fuel consumption by the optimal combustion trace for a optimization studies, the proposed method deals with a mization. Compared to the aforementioned multi-objective large number of conflicting constraints by adding penalty sumption by searching the optimal combustion trace for a optimization studies, the proposed method deals with a large number of conflicting constraints by adding penalty pseudo two-zone model,the with constraint of maximum maximum presEriksson and Sivertsson (2016) minimized thetrace fuel prescon-aa functions sumption by searching optimal combustion for to the cost function, where the highest gross inpseudo two-zone model, with constraint of large number of conflicting constraints by adding penalty sumption by searching the optimal combustion trace for optimization studies, the proposed method deals with a functions to the cost function, where the highest gross inpseudo two-zone model, with constraint of maximum preslarge number of conflicting constraints by adding penalty functions to the cost function, where the highest gross inpseudo two-zone model, with constraint of maximum pressure rise rate (MPRR), maximum pressure (MP), knock sumption by searching the optimal combustion trace for a dicated efficiency can be achieved under various conflicting functions to the the cost function, where the highest gross inpseudo two-zone model, with constraint of maximum pres- large number of cost conflicting constraints by adding penalty sure rise rate (MPRR), maximum pressure (MP), knock dicated efficiency can be achieved under various conflicting functions to function, where the highest gross insure rise rate (MPRR), maximum pressure (MP), knock dicated efficiency can be achieved under various conflicting pseudo model, with constraint of maximum pres- functions sure rise rate maximum pressure (MP), knock constrained conditions, such aswhere MPRR, maximum engineand NO, using numerical optimal control software CasADi. dicated can be achieved under conflicting to conditions, the cost thevarious highest gross insure risetwo-zone rate (MPRR), (MPRR), maximum pressure (MP), knock constrained as MPRR, maximum engineand NO, using numerical optimal control software CasADi. dicated efficiency efficiency can function, besuch achieved under various conflicting conditions, such as MPRR, maximum engineand NO, using numerical optimal control software CasADi. out PM, CO and emissions. Furthermore, the A similar heat (MPRR), release shaping shaping process is software applied for RCCI constrained sure rise using rate maximum pressure (MP), knock constrained conditions, such as maximum engineand NO, numerical optimal control CasADi. dicated efficiency achieved under various conflicting out NOx, NOx, PM, COcan andbeHC HC emissions. Furthermore, the ininA similar heat release process is applied for RCCI constrained conditions, such as MPRR, MPRR, maximum engineand NO, using numerical optimal control software CasADi. out NOx, PM, CO and HC emissions. Furthermore, the inA similar heat release shaping process is applied for RCCI of different constraints the engine performance out NOx, PM, CO HC emissions. Furthermore, the A heat release is applied RCCI constrained conditions, such as on MPRR, maximum enginecombustion in numerical Guardiola et al. al. process (2017), where thefor selection and NO, using optimal control software CasADi. fluence of different constraints on the engine performance out NOx, PM, CO and and HC emissions. Furthermore, the ininA similar similar heat release shaping shaping process is applied for RCCI fluence combustion in Guardiola et (2017), where the selection fluence of different constraints on the engine performance combustion in Guardiola et al. (2017), where the selection has also bePM, studied by tuning different weights of penalties. penalties. fluence of different constraints on the the Furthermore, engine performance performance NOx, CO and HC emissions. the inA similar release shaping process applied for RCCI combustion in Guardiola et al. (2017), where the selection of gasolineheat fraction is studied studied under fuelis consumption min- out has also be studied by tuning different weights of fluence of different constraints on engine combustion in Guardiola et al. (2017), where the selection of gasoline fraction is under fuel consumption minhas also be studied by tuning different weights of penalties. of gasoline fraction fraction is studied studied under fuelwhere consumption min- fluence has also be studied tuning of constraints on the weights engine performance combustion in Guardiola et al.under (2017), the selection of gasoline is fuel consumption minalsoof bedifferent studied by by tuning different different weights of penalties. penalties.  of gasoline fraction is studied under fuel consumption min-a has work is by research programme “Towards  has also be studied by tuning different weights of penalties. This work fraction is supported supported by the the under researchfuel programme “Towards a  This of gasoline is studied consumption minThis work is supported by the research programme “Towards a 

HiEff engine” through the Netherlands Organisation for Scientific This work is supported the programme “Towards a  HiEff engine” through the by Netherlands Organisation for Scientific Thisengine” work isthrough supported by the research research programmefor “Towards a HiEff the Netherlands Organisation Scientific Research under STW project 14927.  HiEff engine” through the by Netherlands Organisation for Scientific Research under STW project 14927. This work is supported the research programme “Towards a HiEff engine” through the Netherlands Organisation for Scientific Research under STW project 14927. Research underthrough STW project project 14927. HiEff engine” the Netherlands Organisation for Scientific Research under STW 14927. 2405-8963under © 2019, IFAC (International Research STW project 14927. Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright 2019 IFAC 648 Copyright © 2019 648 Peer review© responsibility of International Federation of Automatic Copyright © under 2019 IFAC IFAC 648 Control. Copyright © 2019 IFAC 648 10.1016/j.ifacol.2019.09.103 Copyright © 2019 IFAC 648 Copyright © 2019 IFAC 648

2019 IFAC AAC Orléans, France, June 23-27, 2019

Lu Xia et al. / IFAC PapersOnLine 52-5 (2019) 648–653

CO2, THC, CO, O2, NOx

Exhaust surge tank

EGR cooler Diesel tank

Toil Mass flow fuel

Common rail Gasoline tank

Stack

Speed

Tcoolant

Pin

3. DATA-DRIVEN MODELING USING MULTIPLE LINEAR REGRESSION ANALYSIS

M

P-1

Pcyl

design of experiment (DoE) approach as in Willems et al. (2018). It should be noted that the EGR rate in Table 2 is based on volumetric values. Although a fixed amount of total fuel energy (QmTOTAL ) is targeted in this study, there still are some deviations due to oscillating injection pressure or measurement disturbances. Therefore, the QmTOTAL will be also considered in the modeling process.

Back pressure valve

Pexh Texh

Pfuel

Smoke

Tin

CO2 Mass flow fuel

Intake surge tank

Electrical heater

Pin

EGR valve

8 bar air (dry) Mass flow air

Fig. 1. Schematic of engine test setup based on Willems et al. (2018) 2. EXPERIMENT SETUP All the datasets employed in this paper are generated on a DAF XEC engine in the TU/e engine lab. A schematic is shown in Fig. 1, where a 2.1 liter single cylinder is isolated as the test cylinder and cylinder 4-6 are operated by stock DAF engine control unit to control crankshaft speed in cylinder 1. The in-cylinder pressure is measured by an AVL GU21C uncooled transducer and a Heidenhain ROD 420 3600 rotary encoder is employed to collect the crank angle information. In addition, gaseous emissions are measured using a Horiba analyser, whereas PM is detemined based on the correlation with Filter Smoke Number (FSN), which is obtained from an AVL 415S smoke meter. A detailed description of the test setup can be found in Willems et al. (2018). The engine specifications and operating conditions are given in Table 1. To demonstrate the potential of the proposed method, an arbitrary mid-load point with gIMEP at 800 [kPa], has been investigated at a constant engine speed for varying start of actuation for direct injection (SOADI ), exhaust gas recirculation (EGR) rate and ratio of injected port fuel energy to direct injection, namely blend ratio (BR). According to the definition of RCCI from Reitz and Duraisamy (2015), a well-mixed charge of gasoline, air and recirculated gas will be introduced to the combustion chamber at the intake valve opening and a single injection of diesel fuel will be subsequently employed to control the combustion phasing, where diesel fuel is used as the direct injection and gasoline as the port injection. The operating ranges of the input parameters are shown in Table 2 and the experiments are implemented according to the same Table 1. Specifications of the engine setup and its nominal operating conditions PFI fuel DI fuel Compression ratio DI rail pressure Intake pressure Intake temperature gIMEP Engine speed

Gasoline (EN228) Diesel (EN590) 15.8 [-] 52000 [kPa] 168 [kPa ] 35 [◦ C] 800 [kPa] 125.6 [rad/s]

Table 2. Input sweep range Input SOADI EGR rate BR QmTOTAL

Range -83 to -66 31 to 48 2.6 to 8.3 39

649

Unit [◦ CA ATDC] [%] [-] [kJ/s]

649

In this section, the optimization models are presented. The models are generated using multiple linear regression analysis with interactions, providing accurate descriptions of relationship between input variables, ui,t ∈ {SOADI , EGR, BR, QmTOTAL }, and outputs yt , such as gIMEP, MPRR and engine out emissions like gross indicated specific NOx (gISNOx), gISPM, etc., for sample t ∈ 1, . . . , n, over n experimental observations. The gross indicated emission gISem is calculated by m ˙ em gISem = , (1) gPower where gPower is the gross indicated power and m ˙ em is the mass flow of em, for em ∈ {NOx, PM, CO, HC}.

Multiple linear regression analysis is a powerful approach to model the relationship between a scalar dependent variable and multiple explanatory variables (Jobson, 1991). It is widely applied in practical applications, due to its linearin-parameter property, where the system performance can be estimated using the linear combinations of various basis functions. The regression basis function for our model is defined as p−1 p p−1    F(Ut )1k+1×1 = 1 + ui,t + ui,t uj,t , (2) i=1

i=1 j=i

2

where Ut = [u1,t , u2,t , . . . , up,t ] and k = p 2+p , with p explanatory variables, for sample t ∈ 1, . . . , n. This basis function describes not only the linear and quadratic relation between input variables and output variable, but also the cross-relation between each inputs. Here, the total energy QmTOTAL , represented by up,t , will not be involved in the cross-terms, since the deviations are very small which can make the model very sensitive to disturbances. Using least square estimation, the related outputs yt , such as gIMEP, MPRR, gISNOx and gISPM, at samples t, can be estimated as b, (3) yˆt = F(Ut )ˆ where ˆ b indicates the regression parameters to be estimated. The accuracy of the regression model is normally evaluated by the coefficient of determination R2 . Generally, a larger R2 indicates higher accuracy, but absolute errors will be also considered in our paper.

Considering the structure of (2), the basis functions might be highly correlated to each other, which might cause multicollinearity in the regression analysis (Allen, 1997), consequently an ill-conditioned problem. This can be addressed by standardizing the regression coefficients. The standardized coefficients can be obtained by applying regression analysis on the unit normal scaled predictors and response, given by ¯i yˆt − y¯ ui,t − u u∗i,t = and yt∗ = , (4a) si sy where u ¯i and y¯ are mean values of the predictor i and the response; si and sy are standard deviations of the predictor i and the response, with i ∈ 1, . . . , p. Then, the regression model after standardization can be presented as γ, (4b) yˆt∗ = F(Ut∗ )ˆ

2019 IFAC AAC 650 Orléans, France, June 23-27, 2019

Lu Xia et al. / IFAC PapersOnLine 52-5 (2019) 648–653

with Ut∗ = [u∗1,t , u∗2,t , . . . , u∗p,t ]. The simulation results and validation of the model will be discussed in detail later. 4. OPTIMIZATION ALGORITHM

4.2 Particle Swarm Optimization

In this section, the aforementioned data-driven models are further employed to formulate the optimization problems, leading to a quadratically constrained quadratic program. 4.1 Problem Formulation Besides the fuel economy, factors like operational safety, emissions, and noise level are also very crucial for engines. The limit on the MP will avoid mechanical stress limit. MPRR, calculated by the first derivative of the cylinder pressure, is a favorite indication to the level of vibrations during the combustion process in compression ignition engines. Since the experiments are implemented at midload operating condition, the MP will not exceed its limit. Considering the constraints on emissions, CO2 will be generally reduced with the increase of efficiency. NOx can be normally reduced by the lean NOx trap and selective catalytic reduction technology. Due to the low combustion temperature in RCCI, CO and unburned HC emissions will increase, so diesel oxidation catalytic converters are required. However, these after-treatment systems will cause extra costs. So our optimization problem will be constructed by adding the constraints to MPRR, gISNOx, gISPM, gISCO, and gISHC. The indicated efficiency ηf,i is a very important parameter that can indicate the efficiency of an engine in converting fuel energy to work during each cycle (Eriksson and Nielsen, 2014). For a dual fuel engine, ηf,i is specified by Wi , (5) ηf,i = QmTOTAL with QmTOTAL = mPFI qLHVpfi + mDI qLHVdi , where mPFI and mDI are the mass of gasoline and diesel fuel injected to the engine for each cycle, qLHVpfi = 44 [kJ/g] and qLHVdi = 43 [kJ/g] are the approximated specific heating values and Wi is the indicated work generated by the engine. Another essential parameter is the IMEP, which is proportional to Wi in each cycle, given by Wi IMEP = . (6) Vd where Vd is the displaced volume. Based on the definition above, the highest indicated efficiency can be achieved by maximizing the IMEP with respect to the total energy converted from the fixed amount of fuel injected (QmTOTAL ), realizing an energy-based optimization problem. Due to the fixed valve events and displacement volume in our test setup, our optimization objective will be focused on gross IMEP (gIMEP), given by maxp gIMEP(Ut ) (7a) Ut ∈R

QmTOTAL = constant Umin ≤ Ut ≤ Umax G(Ut ) ≤ C   MPRRmax gISNOxmax   C=  gISPMmax  , gISCOmax gISHCmax

s.t.

with

objective function and constraints, it turns out that (7) is a non-convex optimization problem, indicating the existence of local optima.

(7b) (7c) (7d)

(7e)

and G(Ut ) is a vector function, indicating different constraints, where Umin and Umax are the boundaries of the input variables, guaranteeing the feasibility of the datadriven models. By checking the Hessian matrix of the 650

Particle swarm optimization (PSO) is a very popular method for solving unconstrained global optimization problems (Marini and Walczak, 2015). It is inspired by the artificial life like bird flocking and is widely applied in many applications, owing to its large flexibility in dealing with optimization problems with nonlinearities. The optimal solution is found by searching the best position among a group (swarm) of candidate (particle) solutions by comparing particle’s own best performance to their neighbors’ best performance. In the PSO algorithm, a group of N particles in pdimensional space is defined as: U = {U1 , U2 , . . . , UN }, (8a) where Ur = [u1,r , u2,r , . . . , up,r ] (8b) is the r-th individual particle comprised of p parameters, for r ∈ 1, 2, . . . , N . By evaluating the cost functions (3) for different particles, the best personal and global positions, represented as Pr and Gp respectively, can be searched based on the following iteration process (9a) Ur (δ + 1) = Ur (δ) + vr (δ + 1), and the “velocity” of the r-th particle is defined as vr (δ + 1) = (9b) c0 vr (δ) + c1 (Pr − Ur (δ))d1,r + c2 (Gp − Ur (δ))d2,r , where δ ∈ N is the iteration step and c0 is the inertia weight; c1 and c2 are the positive acceleration constants; d1,r and d2,r are random numbers uniformly distributed in [0, 1]. The selections of these parameters will influence the convergence of PSO and detailed discussion can be found in Marini and Walczak (2015). By applying PSO, the maximum gIMEP can be found by searching the optimal combinations of the input variables SOADI , EGR and BR for a specific amount of fuel energy. Further, the constraints can be evaluated by adding a penalty function to the cost function (Smith and Coit, 1997), given by maxp

Ur ∈R

s.t.

with

gIMEP(Ur ) −

I 

φi (ki , gi )

QmTOTAL = constant Umin ≤ Ur ≤ Umax g(Ur ) = G(Ur ) − C

φi (ki , gi ) =



(10a)

i

0 for gi ≤ 0, ki gim for gi > 0,

(10b) (10c) (10d) (10e)

where g(Ur ) = [g1 (Ur ), . . . , gi (Ur ), . . . , gI (Ur )]T is a vector function, indicating the distance between constraint functions and their upper bounds, and I is the total number of constraints. Considering different units in the objective function and constraints, feature scaling is further applied to normalize the objective function and constraints from 0 to 1, given by  r ) = gIMEP(Ur ) − gIMEPmin gIMEP(U gIMEPmax − gIMEPmin and gi − gi,min ˜i = g ; gi,max − gi,min

2019 IFAC AAC Orléans, France, June 23-27, 2019

Lu Xia et al. / IFAC PapersOnLine 52-5 (2019) 648–653

gIMEPmax and gi,max indicate the maximum optimal results within the feasible range, and minimum results for gIMEPmin and gi,min ; ki and m are constants, indicating the different penalty on the i-th boundary. Here, we choose m = 2 to achieve a strictly increasing continuous function (Smith and Coit, 1997) and ki will be chosen accordingly based on the importance of each constraint, to deal with multiple conflicting constraints, which will be further discussed in Section 5.2. To guarantee the global convergence of PSO, the iteration has been repeated Q times, where the global optima can be obtained by comparison of Q optimal results. The iteration process of the aforementioned optimization problem is generally presented in Algorithm 1, the unconstrained PSO iteration process can be found in Marini and Walczak (2015). 5. SIMULATION STUDY In this section, first, the accuracy of the proposed datadriven models will be studied and validated experimentally. The optimization results will be presented under various constrained and unconstrained conditions. It should be noted that all simulation results presented in the following are specific for the engine cell and operating conditions described in Section 2. The optimization approach and the analysis techniques are general and can be repeated for different engine setups with different operating conditions.

8 7

BR [-]

MPRR [kPa/CAD]

gIMEP [kPa]

2600 2400

800

2000

1

2

3

6

3 2 30 50

-85

-80

-75

-70

2

3

4

2

3

0

4

3

4

1

2

3

4

gISHC [g/kwh]

gISCO [g/kwh] 1

# experimental data

2

3

2

2

1

-3

1

# experimental data

4

3

10 -2

0

5

4

1 1

2

3

4

0

# experimental data

# experimental data

Fig. 3. Validation of predicated outputs. 5.1 Data-driven modeling The accuracy of the data-driven models are evaluated based on R2 over 37 sets of experimental data and maximum absolute errors |e|max between experimental data with gIMEP larger than 820 [kPa] and their fitted responses, since global optima are achieved by maximization of gIMEP, those data with low gIMEP are not valuable for evaluation. A detailed description of accuracy for each response is given in Table 3. To validate the aforementioned data-driven models, 4 operating points have been implemented on the engine setup with random combination of SOADI , EGR and BR within the input ranges, shown in Fig. 2. A comparison of the outputs, gIMEP, MPRR, gISNOx, gISPM, gISCO and gISHC, between predicted results and experimental results are given in Fig. 3, where the root-mean-square errors are 7.450 [kPa], 83.090 [kPa/CAD], 0.140 [g/kWh], 0.003 [g/kWh], 0.211 [g/kWh] and 0.231 [g/kWh], respectively, showing accurate predictions of the regression models. These regression models will be employed to formulate the optimization problem and the results will be discussed in the next subsection. 5.2 Optimization results

gIMEP MPRR gISNOx gISPM gISCO gISHC

4

40

1

# experimental data

-1

5

EGR [%]

1600

4

# experimental data

1

0.5

1800

700

2

1.5

2200

750

10

2.5

gISNOx [g/kwh]

850

10

Experimental data

3 Predicted data

2800

Due to the data generating method of DoE, the feasible range of the regression models are in a diamond shape. To guarantee the feasibility of the optimization problem, the input constraints in (10) are set as in Table 4, to strictly fit in the model domain. Table 3. Accuracy of model fit

Fitted inputs Validated inputs

9

3000

900

gISPM [g/kwh]

Algorithm 1: Constrained PSO algorithm 1: for N particles and run=1: Q, r ∈ 1 : N 2: Initialization • Position: Ur (0) ∈ [Umin , Umax ] • Speed: vr (0) = 0.01Ur (0) • Personal best position: pr (0) = Ur (0) • Global best position: [Gv(0), Gp(0)] = max(F(U(0))ˆ b) 3: while Gv(δ + 1) − Gv(δ) > tol 4: Update particle speed according to (9b) 5: Update particle position according to (9a) 6: Evaluate constraints according to (10d) 7: Evaluate fitness function according to (10a)  I  I  8: if gIMEP- i φi (Ur (δ + 1)) > gIMEP− i φi (pr ) 9: update personal best position: pr = Ur (δ + 1) 10: end if 11: if maximum value fmax of (10a) over N particles > Gv(δ) 12: update global best position: [Gv(δ + 1), Gp(δ + 1)] = [fmax , arg max(10a)] 13: end if 14: end while 15: G(run)=Gp(δ + 1) 16: end for 17: Find maximum value of G

651

-65

R2 0.93 0.94 0.95 0.93 0.94 0.92

|e|max 16.52 [kPa] 95.27 [kPa/CAD] 0.17 [g/kWh] 0.01 [g/kWh] 0.34 [g/kWh] 0.13 [g/kWh]

Table 4. Input constraints

SOADI [ o CA ATDC]

Fig. 2. Randomly distributed input variables for datadriven models validation

651

Input SOADI EGR BR

Range -80 to -70 35 to 47 3 to 7.6

Unit [◦ CA ATDC] [%] [-]

2019 IFAC AAC 652 Orléans, France, June 23-27, 2019

1800

39

39.5

1600 38

640

gISCO2 [g/kWh]

620

2 f,i [%]

600 580

38.5

39

Qm TOTAL [kJ/s]

48

5

46

4

44

38.5

39

Qm TOTAL [kJ/s]

39.5

40 38

38.5

39

QmTOTAL [kJ/s]

39.5

38.5

39

Qm TOTAL [kJ/s]

39.5

Fig. 4. Comparison of optimal gIMEP, MPRR, gISCO2 and gross indicated efficiency ηf,i between various constrained and unconstrained conditions, with respect to different amount of fuel energy. Based on the EURO VI emissions constraints, the constraints of gISNOx, gISPM, gISCO and gISHC are set at 0.40 [g/kWh], 0.01 [g/kWh], 1.50 [g/kWh] and 0.13 [g/kWh], respectively, while the constraint of MPRR is arbitrarily set at 1800 [kPa/CAD]. Considering the uncertainties of the regression models in Section 5.1, the model of gISHC is not accurate enough to fit the constraint, but is still required to be minimized. To achieve a robust optimal result, the constraints of gISNOx, gISPM, gISCO and MPRR are deducted by the model uncertainties, set at 0.260 [g/kWh], 0.007 [g/kWh], 1.289 [g/kWh] and 1717 [kPa/CAD], respectively. To study the influence of different constraints on the engine performance, the following conditions will be compared and discussed in this section: • Case A: unconstrained condition; • Case B: constrained MPRR; • Case C: constrained NOx, PM, CO and HC; • Case D: constrained MPRR, NOx, PM, CO and HC

Considering the aforementioned cases, the penalty in (10e) can be chosen as ki =0 or ki = K, depending on the availability of each constraint, where K is a constant. For Case A, ki is chosen to be 0, for i ∈ {1, . . . , 5}, to deactivate the constraints. The minimal values of MPRR, gISNOx, gISPM, gISCO and gISHC, that can be achieved within the feasible range, are 1675 [kPa/CAD], 0.124 [g/kWh], 0.004 [g/kWh], 1.827 [g/kWh] and 1.632 [g/kWh]. Specifically, the gISCO and gISHC will never fit the constraints. Therefore, soft constraints are required to strike a balance among those conflicting constraints, and any penalty can be chosen as long as it is large enough to lead the PSO to choose the largest cost function (10a). Here, we choose k = [100, 0, 0, 0, 0] for Case B. Considering Case C, soft constraints have been applied to emissions, with equal importance, specifically k = [0, 100, 100, 100, 100]. Similarly, k = [100, 100, 100, 100, 100] for Case D.

Figure 4 shows the comparison of the optimal gIMEP, MPRR, gISCO2 and ηf,i between unconstrained and constrained conditions with respect to slightly different amounts of energy consumption, where the black dash-line indicates the level of constraint and the experimental data are indicated by blue circles, showing the corresponding outputs regarding to different input sweeps. Fig. 5 illustrates the comparison of corresponding emissions, such as gISNOx, gISPM, gISCO and gISHC. Comparing these 652

38.5

39

39.5

38.5

39

39.5

QmTOTAL [kJ/s]

5 4 3 2

2 1 38

38

6

3

42

560

10 -2

10 -1 38

39.5

Experimental data Optimal results for Case A Optimal results for Case B Optimal results for Case C Optimal results for Case D

gISHC [g/kWh]

38.5

Qm TOTAL [kJ/s]

10 0

gISPM [g/kWh]

2000

800

540 38

gISNOx [g/kWh]

2400 2200

850

750 38

10 -1

2600

gISCO [g/kWh]

gIMEP [kPa]

900

Experimental data Optimal results for Case A Optimal results for Case B Optimal results for Case C Optimal results for Case D

MPRR [kPa/CAD]

950

Lu Xia et al. / IFAC PapersOnLine 52-5 (2019) 648–653

1

38.5

39

QmTOTAL [kJ/s]

39.5

0 38

QmTOTAL [kJ/s]

Fig. 5. Comparison of gISNOx, gISPM, gISCO and gISHC between various constrained and unconstrained conditions, with respect to different amount of fuel energy. two figures, it can be seen that the maximum gIMEP for the unconstrained optimization (Case A), indicated by red stars, is achieved with lowest gISCO simultaneously, but the corresponding gISCO2 does not necessarily reach the lowest level. The highest ηf,i is 47.8[%] for the unconstrained condition. For the optimization results with constrained MPRR (Case B), given in yellow diamonds, the gISPM, the gISCO and the gISHC will increase notably, while the gISCO2 will slightly decrease. By limiting the MPRR to 1717 [kPa/CAD], the gIMEP is largely reduced and the highest ηf,i is 45.8 [%]. It should be noted that the MPRR does not always satisfy the constraint, indicating a MPRR limitation in this operating range. Further, if we only add constraints to emissions (Case C), such as PM, NOx, CO and HC, indicated by black squares in Fig. 5, the gISPM, the gISCO and the gISHC will reach the lowest levels in this operating range and the gISNOx will be round 0.5 [g/kWh]. However, the gISCO2 and MPRR will increase notably. In this condition, the highest ηf,i will decrease from 47.8 [%] to 46.9 [%] compared to the unconstrained condition. By adding constraints to MPRR, NOx, PM, CO and HC simultaneously (Case D), given in purple triangles in Figs. 4 and 5, the gISCO2 will reach the lowest level among these four different conditions. Both gISNOx and gISPM will partially satisfy their constraints, but the gISCO and gISHC will increase as the decrease of MPRR, indicating conflicting constraints of these parameters. The maximal achievable ηf,i will fall from 47.8[%] to 47.7 [%] compared to the unconstrained condition and the highest value of MPRR will decrease from 2060 [kPa] to 1951 [kPa], at sacrifice of gISCO and gISHC. A summary of the optimal outputs, such as highest ηf,i , MPRR, gISNOx, gISPM, gISCO, gISHC and gISCO2, for the aforementioned conditions can be found in Table 5. It can be seen that the lowest CO2 does not necessarily indicate the highest efficiency, but can be accompanied by high CO and HC emissions. The corresponding optimal inputs for the aforementioned conditions are illustrated in Fig. 6. It can be seen that late SOADI and high EGR are both required to achieve the highest efficiency for unconstrained and constrained condition, while the EGR will be slightly adjusted according to BR when high proportion of gasoline is employed. The utilization of high proportion of gasoline will reduce PM, CO and HC emissions simultaneously, and will raise MPRR and gIMEP. It is not surprising to see

2019 IFAC AAC Orléans, France, June 23-27, 2019

Experimental data Optimal results 39.3 for Case A Optimal results for Case B Optimal results for Case C Optimal results 39.2 for Case D

39.3 39.2

39.2 39.1

39

39

39

38.9 38.8 38.7

QmTOTAL [kJ/s]

39.1

38.9 38.8 38.7

38.9

38.7

38.6

38.6

38.5

38.5

38.5

38.4

38.4

38.4

38.3

-80 -75 -70 o

SOA DI [ CA ATDC]

38.3 30

40

EGR [%]

50

6. CONCLUSION

38.8

38.6

38.3

4

6

8

BR [-]

Fig. 6. Comparison of corresponding optimal inputs between various constrained and unconstrained conditions, with respect to different amount of fuel energy. 4

Experimental data Pareto front

3.5

2.5

gISNOx [g/kWh]

In this paper, a computationally efficient optimization method has been applied to maximize gIMEP for a fixed amount of total energy supply. With the proposed optimization method, the optimal operating points are successfully obtained under various, conflicting constrained conditions like MPRR and emissions, such as NOx, PM, CO and HC. In the simulation study, the accuracy of the proposed data-driven models is validated experimentally, showing accurate predictions of the corresponding outputs, where the largest relative error of gIMEP between predicted results and experimental data is 1.5 [%]. For the studied operating conditions, the engine-out gISCO and gISHC will not satisfy the EURO VI emission limits, so after treatment systems are required. Within the EURO VI constraints for engine-out gISNOx and gISPM, the highest indicated efficiency that can be achieved is 47.7 [%]. As offline optimization is limited to the range of DoE, further work will be focused on combining PSO with DoE for different sweeps of QmTOTAL , in order to iteratively search for the global optima online. REFERENCES

3

2

1.5 1 0.5 0

653

the experimental data and Pareto front is given in black stars. The infeasible range is obtained by minimizing gISNOx and gISPM within the input constraints, given in red shadow. The green area indicates operating conditions satisfying the constraints of gISNOx and gISPM. It can be observed that, with the proposed optimization method, the optimal results are always on the Pareto front. A trade off between each constraint can be obtained by setting different values of penalties on each constraint.

39.3

39.1

QmTOTAL [kJ/s]

QmTOTAL [kJ/s]

Lu Xia et al. / IFAC PapersOnLine 52-5 (2019) 648–653

0

0.01

0.02

0.03

gISPM [g/kWh]

0.04

0.05

0.06

Fig. 7. Pareto front of gISNOx and gISPM for QmTOTAL = 38.32 [kJ/s] that gISNOx is hardly affected by BR, since SOADI is relatively early, where local air-fuel ratios are still lean enough for BR not to make a significant difference in NOx formation. As such, the optimal operating points can be different regarding to different constraints. The highest ηf,i in this operating range is achieved at SOADI = −70 [◦ CA ATDC], EGR=47.5 [%] and BR=7.6 [-]. Using the proposed method, the optimal solution can be obtained efficiently under various constrained conditions. Figure 7 shows the Pareto front of gISNOx and gISPM for QmTOTAL = 38.32 [kJ/s], where the blue circles indicate Table 5. Summary of optimal outputs for the unconstrained and constrained conditions Case maximal ηf,i [%] MPRR [kPa/CAD] gISPM [g/kWh] gISNOx [g/kWh] gISCO [g/kWh] gISHC [g/kWh] gISCO2 [g/kWh]

A 47.8 1925 0.008 0.2 2.1 2.8 565

B 45.8 1721 0.011 0.2 2.7 3.8 560

C 46.9 2092 0.009 0.4 1.8 2.3 580

D 47.7 1895 0.007 0.2 2.1 2.9 561

653

Allen, M.P. (1997). The problem of multicollinearity, 176–180. Springer US, Boston, MA. Bendu, H., Deepak, B., and Murugan, S. (2017). Multi-objective optimization of ethanol fuelled HCCI engine performance using hybrid GRNN–PSO. Applied Energy, 187, 601–611. Dempsey, A.B. and Reitz, R.D. (2011). Computational optimization of reactivity controlled compression ignition in a heavy-duty engine with ultra low compression ratio. SAE Int. J. Engines, 4(2), 2222–2239. Eriksson, L. and Nielsen, L. (2014). Modeling and Control of Engines and Drivelines. John Wiley & Sons. Eriksson, L. and Sivertsson, M. (2016). Calculation of optimal heat release rates under constrained conditions. SAE Int. J. Engines, 9(2), 1143–1162. Guardiola, C., Pla, B., Garcia, A., and Boronat, V. (2017). Optimal heat release shaping in a reactivity controlled compression ignition (RCCI) engine. Control Theory Technology, 15, 117–128. Jobson, J. (1991). Applied Multivariate Data Analysis Volume I: Regression and Experimental Design. Springer-Verlag New York. Li, Y., Jia, M., Chang, Y., Liu, Y., Xie, M., Wang, T., and Zhou, L. (2014). Parametric study and optimization of a RCCI (reactivity controlled compression ignition) engine fueled with methanol and diesel. Energy, 65, 319–332. Marini, F. and Walczak, B. (2015). Particle swarm optimization (PSO). A tutorial. Chemometrics and Intelligent Laboratory Systems, 149, 153–165. Nieman, D.E., Dempsey, A.B., and Reitz, R.D. (2012). Heavy-duty RCCI operation using natural gas and diesel. SAE Int. J. Engines, 5(2), 270–285. Reitz, R.D. and Duraisamy, G. (2015). Review of high efficiency and clean reactivity controlled compression ignition (RCCI) combustion in internal combustion engines. Progress in Energy and Combustion Science, 46, 12–71. Smith, A.E. and Coit, D.W. (1997). Penalty functions. Handbook of evolutionary computation, 97(1), C5.2. Willems, F. (2018). Is cylinder pressure-based control required to meet future HD legislation? IFAC-PapersOnLine, 51(31), 111– 118. Willems, R., Bakker, P., Dreezen, R., and Somers, B. (2018). The impact of operating conditions on post-injection efficacy; a study using Design-of-Experiments (no. 2018-01-0229). In WCX World Congress Experience. SAE International. Zhang, Q., Ogren, R.M., and Kong, S.C. (2017). Application of improved artificial bee colony algorithm to the parameter optimization of a diesel engine with pilot fuel injections. Journal of Engineering for Gas Turbines and Power, 139(11), 112801.