A correlation-based model order reduction algorithm is developed using support vector machine to model emission and break mean effective pressure of a medium-duty diesel engine. The support vector machine–based model order reduction algorithm is used to reduce the number of features of a 34-feature full-order model by evaluating the regression performance of the support vector machine–based model. Then, the support vector machine–based model order reduction algorithm is used to reduce the number of features of the full-order model. Two models for emission and break mean effective pressure are developed via model order reduction, one complex model with high accuracy, called high-order model, and the other with an acceptable accuracy and a simple structure, called low-order model. The high-order model has 29 features for and 20 features for break mean effective pressure, while the low-order model has nine features for and six features for break mean effective pressure. Then, the steady-state low-order model and high-order model are implemented in a nonlinear control-oriented model. To verify the accuracy of nonlinear control-oriented model, a fast response electrochemical sensor is used to experimentally study the engine transient emissions. The high-order model and low-order model support vector machine models of and break mean effective pressure are compared to a conventional artificial neural network with one hidden layer. The results illustrate that the developed support vector machine model has shorter training times (5–14 times faster) and higher accuracy especially for test data compared to the artificial neural network model. A control-oriented model is then developed to predict the dynamic behavior of the system. Finally, the performance of the low-order model and high-order model is evaluated for different rising and falling input transients at four different engine speeds. The transient test results validate the high accuracy of the high-order model and the acceptable accuracy of low-order model for both and break mean effective pressure. The high-order model is proposed as an accurate virtual plant while the low-order model is suitable for model-based controller design.
VuorinenA. Planning of optimal power systems. Vammala: Vammalan Kirjapaino Oy, 2009.
2.
TutakWJamrozikABereczky LukacsÁK. Effects of injection timing of diesel fuel on performance and emission of dual fuel diesel engine powered by diesel/E85 fuels. Transport2018; 33(3): 633–646.
3.
ChangYCLeeWJWuTSWuCYChenSJ. Use of water containing acetone–butanol–ethanol for NOx-PM (nitrogen oxide-particulate matter) trade-off in the diesel engine fueled with biodiesel. Energy2014; 64: 678–687.
4.
BohlTSmallboneATianGRoskillyAP. Particulate number and NOx trade-off comparisons between HVO and mineral diesel in HD applications. Fuel2018; 215: 90–101.
5.
JohnsonTV. Review of vehicular emissions trends. SAE Int J Engines2015; 8: 1152–1167.
6.
PraveenaVMartinMLJ. A review on various after treatment techniques to reduce NOx emissions in a CI engine. J Energy Inst2018; 91: 704–720.
7.
GengPTanQZhangCWeiLHeXCaoE, et al. Experimental investigation on NOx and green house gas emissions from a marine auxiliary diesel engine using ultralow sulfur light fuel. Sci Total Environ2016; 572(Suppl. C): 467–475.
8.
Blanco-RodriguezID. Modelling and observation of exhaust gas concentrations for diesel engine control. Cham: Springer, 2014.
9.
KoebelMElsenerMKleemannM. Urea-SCR: a promising technique to reduce NOx emissions from automotive Diesel engines. Catal Today2000; 59(34): 335–345.
10.
MaiboomATauziaXHétetJF. Experimental study of various effects of Exhaust Gas Recirculation (EGR) on combustion and emissions of an automotive direct injection Diesel engine. Energy2008; 33(1): 22–34.
11.
EbrahimiKAliramezaniMKochCR. An HCCI control oriented model that includes combustion efficiency. IFAC-PapersOnLine2016; 49(11): 327–332.
12.
GordonDWoutersCWickMLehrheuerBAndertJKochC, et al. Development and experimental validation of a field programmable gate array-based in-cycle direct water injection control strategy for homogeneous charge compression ignition combustion stability. Int J Engine Res2019; 20: 1101–1113.
13.
ChavannavarP. Development and implementation of a mapless, model based SCR control system. SAE Int J Engines2014; 7: 1113–1124.
14.
AliramezaniMKochCRHayesRE. Estimating tailpipe NOx concentration using a dynamic NOx/ammonia cross sensitivity model coupled to a three state control oriented SCR model. IFAC-PapersOnLine2016; 49(11): 8–13.
15.
TriantafyllopoulosGKatsaounisDKaramitrosDNtziachristosLSamarasZ. Experimental assessment of the potential to decrease diesel NOx emissions beyond minimum requirements for Euro 6 Real Drive Emissions (RDE) compliance. Sci Total Environ2018; 618: 1400–1407.
16.
SendaTHarumiK. Prospects and challenges for the future of marine power systems. Mar Eng2018; 53(3): 279–284.
17.
TangWSianiAChenFChenB. On developing advanced catalysts systems to meet china new regulations. SAE technical paper 2019-01-0978, 2019.
18.
WongPKWongHCVongCM. Online time-sequence incremental and decremental least squares support vector machines for engine air-ratio prediction. Int J Engine Res2012; 13(1): 28–40.
19.
AliramezaniMKochCRPatrickR. Phenomenological model of a solid electrolyte NOx and O2 sensor using temperature perturbation for on-board diagnostics. Solid State Ionics2018; 321: 62–68.
20.
AnsariEMenucciTShahbakhtiMNaberJ. Experimental investigation into effects of high reactive fuel on combustion and emission characteristics of the Diesel-Natural gas Reactivity Controlled Compression Ignition engine. Appl Energy2019; 239: 948–956.
21.
PotenzaRDunneJVulliSRichardsonDKingP. Multicylinder engine pressure reconstruction using NARX neural networks and crank kinematics. Int J Engine Res2007; 8(6): 499–518.
22.
HeYRutlandC. Application of artificial neural networks in engine modelling. Int J Engine Res2004; 5(4): 281–296.
23.
RezaeiJShahbakhtiMBahriBAzizAA. Performance prediction of HCCI engines with oxygenated fuels using artificial neural networks. Appl Energy2015; 138: 460–473.
24.
MoizAAPalPProbstDPeiYZhangYSomS, et al. A machine learning-genetic algorithm (ML-GA) approach for rapid optimization using high-performance computing. SAE Int J Commer Veh2018; 11(5): 291–306.
25.
BadraJKhaledFTangMPeiYKodavasalJPalP, et al. Engine combustion system optimization using CFD and machine learning: a methodological approach. In: Internal combustion engine division fall technical conference, Chicago, IL, 20–23 October 2019, vol. 59346, p.V001T06A007. New York: American Society of Mechanical Engineers.
26.
OwoyeleOPalP. A novel active optimization approach for rapid and efficient design space exploration using ensemble machine learning. In: ASME 2019 internal combustion engine division fall technical conference, Chicago, IL, 20–23 October 2019. New York: American Society of Mechanical Engineers.
27.
XuYGuoRWangL. A twin multi-class classification support vector machine. Cogn Comp2013; 5(4): 580–588.
28.
TanveerM. Robust and sparse linear programming twin support vector machines. Cogn Comp2015; 7(1): 137–149.
29.
BertramAMKongSC. Computational optimization of a diesel engine calibration using a novel SVM-PSO method. SAE technical paper 2019-01-0542, 2019.
30.
HanuschkinASchoberSBodeJSchorrJBöhmBKrügerC, et al. Machine learning–based analysis of in-cylinder flow fields to predict combustion engine performance. Int J Engine Res. Epub ahead of print 14 March 2019. DOI: 10.1177/1468087419833269.
31.
YusriIMMajeedAPPAMamatRGhazaliMFAwadOIAzmiWH. A review on the application of response surface method and artificial neural network in engine performance and exhaust emissions characteristics in alternative fuel. Renew Sustain Energ Rev2018; 90: 665–686.
32.
SilitongaASMasjukiHHOngHCSebayangAHDharmaSKusumoF, et al. Evaluation of the engine performance and exhaust emissions of biodiesel-bioethanol-diesel blends using kernel-based extreme learning machine. Energy2018; 159: 1075–1087.
33.
WongPKGaoXHWongKIVongCM. Online extreme learning machine based modeling and optimization for point-by-point engine calibration. Neurocomputing2018; 277: 187–197.
34.
AliramezaniMNorouziAKochCR. Support vector machine for a diesel engine performance and NOx emission control-oriented model. In: 21st IFAC World Congress, IFACPapersOnLine, Berlin, Germany, 11–17 July, 2020.
35.
GordonDWoutersCWickMXiaFLehrheuerBAndertJ, et al. Development and experimental validation of a real-time capable field programmable gate array–based gas exchange model for negative valve overlap. Int J Engine Res2020; 21(3): 421–436.
36.
DuanHHuangYMehraRKSongPMaF. Study on influencing factors of prediction accuracy of support vector machine (SVM) model for NOx emission of a hydrogen enriched compressed natural gas engine. Fuel2018; 234: 954–964.
37.
LiuBHuJYanFTurksonRFLinF. A novel optimal support vector machine ensemble model for NOx emissions prediction of a diesel engine. Measurement2016; 92: 183–192.
38.
NiuXYangCWangHWangY. Investigation of ANN and SVM based on limited samples for performance and emissions prediction of a CRDI-assisted marine diesel engine. Appl Therm Eng2017; 111: 1353–1364.
39.
ZuoQZhuXLiuZZhangJWuGLiY. Prediction of the performance and emissions of a spark ignition engine fueled with butanol-gasoline blends based on support vector regression. Environ Prog Sustain Energy2019; 38(3): e13042.
40.
AzzamMAwadMZeaiterJ. Application of evolutionary neural networks and support vector machines to model NOx emissions from gas turbines. J Environ Chem Eng2018; 6(1): 1044–1052.
41.
ZhouHZhaoJPZhengLGWangCLCenKF. Modeling NOx emissions from coal-fired utility boilers using support vector regression with ant colony optimization. Eng Appl Artif Intel2012; 25(1): 147–158.
42.
LvYLiuJYangTZengD. A novel least squares support vector machine ensemble model for NOx emission prediction of a coal-fired boiler. Energy2013; 55: 319–329.
43.
LvYYangTLiuJ. An adaptive least squares support vector machine model with a novel update for NOx emission prediction. Chemometr Intell Lab Syst2015; 145: 103–113.
44.
WongKIWongPKCheungCSVongCM. Modeling and optimization of biodiesel engine performance using advanced machine learning methods. Energy2013; 55: 519–528.
DietterichT. Overfitting and undercomputing in machine learning. ACM Comp Surv1995; 27(3): 326–327.
47.
BrownGPocockAZhaoMJLujánM. Conditional likelihood maximisation: a unifying framework for information theoretic feature selection. J Mach Learn Res2012; 13: 27–66.
48.
PengHLongFDingC. Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy. IEEE Trans Patt Anal Mach Intel2005(8): 1226–1238.
49.
NguyenXVChanJRomanoSBaileyJ. Effective global approaches for mutual information based feature selection. In: Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, 24–27 August 2014, pp.512–521. New York: ACM, https://dl.acm.org/doi/pdf/10.1145/2623330.2623611
HallMA. Correlation-based feature selection for machine learning. PhD Thesis, The University of Waikato, Hamilton, New Zealand, 1999.
52.
HeWWangZJiangH. Model optimizing and feature selecting for support vector regression in time series forecasting. Neurocomputing2008; 72(1–3): 600–611.
53.
TaoXRenmuHPengWDongjieX. Input dimension reduction for load forecasting based on support vector machines. In: 2004 IEEE international conference on electric utility deregulation, restructuring and power technologies, Hong Kong, China, 5–8 April 2004. pp.510–514, vol. 2. New York: IEEE.
54.
HiraZMGilliesDF. A review of feature selection and feature extraction methods applied on microarray data. Adv Bioinformatics2015; 2015: 198363.
55.
SchölkopfBSmolaAMüllerKR. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation1998; 10(5): 1299–1319.
56.
Salah MohamedK. Machine learning for model order reduction. Cham: Springer, 2018.
57.
WangJMChuCCYuQKuhES. On projection-based algorithms for model-order reduction of interconnects. IEEE Trans. Circuit Syst I2002; 49(11): 1563–1585.
58.
AlamMNieuwoudtAMassoudY. Wavelet-based passivity preserving model order reduction for wideband interconnect characterization. In: 8th international symposium on quality electronic design (ISQED’07), San Jose, CA, 26–28 March 2007, pp.432–437. New York: IEEE.
59.
BarrassoDTamrakarARamachandranR. A reduced order PBM–ANN model of a multi-scale PBM–ANN description of a wet granulation process. Chem Eng Sci2014; 119: 319–329.
60.
ParmarGMukherjeeSRasadR. Reduced order modelling of linear MIMO systems using genetic algorithm. Int J Simulat Model2007; 6(3): 173–184.
61.
SmolaAJSchölkopfB. A tutorial on support vector regression. Statis Comp2004; 14(3): 199–222.
62.
KihasDPachnerDBaramovLUchanskiMNaikPKhaledN. Concept analysis and initial results of engine-out NOx estimator suitable for on ECM implementation. SAE technical paper 2016-01-0611, 2016.
63.
QuérelCGrondinOLetellierC. Semi-physical mean-value NOx model for diesel engine control. Cont Eng Prac2015; 40: 27–44.
64.
GuardiolaCMartínJPlaBBaresP. Cycle by cycle NOx model for diesel engine control. Appl Ther Eng2017; 110: 1011–1020.
65.
RezaeiRHaydukCAlkanEKemskiTDelebinskiTBertramC. Hybrid phenomenological and mathematical-based modeling approach for diesel emission prediction. SAE technical paper 2020-01-0660, 2020.
66.
IrdmousaBKRizviSZVeiniJMNabertJShahbakhtiM. Data-driven modeling and predictive control of combustion phasing for RCCI engines. In: 2019 American control conference (ACC), Philadelphia, PA, 10–12 July 2019, pp.1617–1622. New York: IEEE.
67.
OğuzHSarıtasIBaydanHE. Prediction of diesel engine performance using biofuels with artificial neural network. Expert Syst Appl2010; 37(9): 6579–6586.
68.
TschanzFAmstutzAOnderCHGuzzellaL. Feedback control of particulate matter and nitrogen oxide emissions in diesel engines. Cont Eng Prac2013; 21(12): 1809–1820.
69.
AliramezaniMNorouziAKochCRHayesRE. A control oriented diesel engine NOx emission model for on board diagnostics and engine control with sensor feedback. In: Proceedings of combustion institute-Canadian section (CICS), Kelowna, BC, Canada, 13–16 May 2019, pp.1–6, https://www.researchgate.net/publication/333223847
70.
VapnikVLernerA. Generalized portrait method for pattern recognition. Automat Rem Contr1963; 24(6): 774–780.
71.
VapnikVChervonenkisA. A note on class of perceptron. Automat Rem Cont1964; 25: 103–109.
VapnikV. The nature of statistical learning theory. Berlin: Springer Science & Business Media, 2013.
75.
BellmanR. The theory of dynamic programming. B Am Math Soc1954; 60(6): 503–515.
76.
KarushW. Minima of functions of several variables with inequalities as side constraints. MSc Dissertation, Department of Mathematics, University of Chicago, Chicago, IL, 1939.
77.
KuhnHWTuckerAW. Nonlinear programming. In: NeymanJ (ed.) Proceedings of the second Berkeley symposium on mathematical statistics and probability. Berkeley, CA: University of California Press, 1951, pp.481–492.
IoffeSSzegedyC. Batch normalization: accelerating deep network training by reducing internal covariate shift. arXiv preprint arXiv:1502031672015, https://arxiv.org/abs/1502.03167
80.
JuszczakPTaxDDuinRP.Feature scaling in support vector data description. In: Proceedings of the 8th Annual Conference of the Advanced School for Computing and Imaging (ASCI), Delft, The Netherlands, June 2002, pp.170–177.
81.
NorouziAAliramezaniMKochCR. Diesel engine NOx reduction using a PD-type fuzzy iterative learning control with a fast response NOx sensor. In: Proceedings of combustion institute-Canadian section (CICS), Kelowna, BC, Canada, 13–16 May 2019, pp.7–12, https://www.researchgate.net/publication/333224129
82.
RenJ.ANNvs. SVM: which one performs better in classification of MCCs in mammogram imaging. Knowl Based Syst2012; 26: 144–153.
83.
Shalev-ShwartzSSrebroN. SVM optimization: inverse dependence on training set size. In: Proceedings of the 25th international conference on machine learning, 2008, pp.928–935. New York: ACM, http://icml2008.cs.helsinki.fi/papers/266.pdf
84.
NorouziAEbrahimiKKochCR. Integral discrete-time sliding mode control of Homogeneous Charge Compression Ignition (HCCI) engine load and combustion timing. IFACPapersOnLine2019; 52(5): 153–158.
