Abstract

Modern internal combustion (IC) engines have complex configurations with many parameters to be tuned, and this system complication usually leads to a large amount of engine calibration experiments. In this study, the active subspace method was used to build predictive models for the gas exchange-related parameters, including volumetric efficiency, intake mass flow and pumping loss, and the power-related parameters, including engine torque and engine power. The results show that the predicted outputs fit well with the experimental data, with satisfactory coefficients of determination and average absolute errors (AAE). Further, the contributions and influence directions of the input parameters to the outputs were provided based on a sensitivity analysis, which is consistent with the existing knowledge, and therefore, verifies the reliability of the predictive model built based on the active subspace method. Finally, the relation between the training group size and the prediction performance was explored. It is shown that a reduction, up to 66%, in the training group size is still able to maintain good predictive performances of the models, indicating the substantial capability of the active subspace method to reduce the experimental efforts.

References

1.
Xu
,
G. F.
,
Jia
,
M.
,
Li
,
Y. P.
,
Chang
,
Y. C.
,
Liu
,
H.
, and
Wang
,
T. Y.
,
2019
, “
Evaluation of Variable Compression Ratio (VCR) and Variable Valve Timing (VVT) Strategies in a Heavy-Duty Diesel Engine With Reactivity Controlled Compression Ignition (RCCI) Combustion Under a Wide Load Range
,”
Fuel
,
253
, pp.
114
128
.10.1016/j.fuel.2019.05.020
2.
Olesky
,
L. M.
,
Vavra
,
J.
,
Assanis
,
D. N.
, and
Babajimopoulos
,
A.
,
2012
, “
Effects of Charge Preheating Methods on the Combustion Phasing Limitations of an HCCI Engine With Negative Valve Overlap
,”
ASME J. Eng. Gas Turbines Power
,
134
(
11
), p.
112801
.10.1115/1.4007319
3.
Genzale
,
C. L.
,
Kong
,
S. C.
, and
Reitz
,
R. D.
,
2008
, “
Modeling the Effects of Variable Intake Valve Timing on Diesel HCCI Combustion at Varying Load, Speed, and Boost Pressures
,”
ASME J. Eng. Gas Turbines Power
,
130
(
5
), p.
052806
.10.1115/1.2938270
4.
Li
,
B. W.
,
Liu
,
H. Y.
,
Yu
,
L. J.
,
Wang
,
Z.
, and
Wang
,
J. X.
,
2019
, “
Optimization of Piston Bowl and Valve System in Compression Ignition Engine Fueled With Gasoline/Diesel/Polyoxymethylene Dimethyl Ethers for High Efficiency
,”
Int. J. Engine Res.
,
141
.10.1177/1468087419865384
5.
Vos
,
K. R.
,
Shaver
,
G. M.
,
Lu
,
X. T.
,
Allen
,
C. M.
,
McCarthy
,
J.
, and
Farrell
,
L.
,
2019
, “
Improving Diesel Engine Efficiency at High Speeds and Loads Through Improved Breathing Via Delayed Intake Valve Closure Timing
,”
Int. J. Engine Res.
,
20
(
2
), pp.
194
202
.10.1177/1468087417743157
6.
Modiyani
,
R.
,
Kocher
,
L.
,
Van Alstine
,
D. G.
,
Koeberlein
,
E.
,
Stricker
,
K.
,
Meckl
,
P.
, and
Shaver
,
G.
,
2011
, “
Effect of Intake Valve Closure Modulation on Effective Compression Ratio and Gas Exchange in Turbocharged Multi-Cylinder Engines Utilizing EGR
,”
Int. J. Engine Res.
,
12
(
6
), pp.
617
631
.10.1177/1468087411415180
7.
Corti
,
E.
,
Forte
,
C.
,
Mancini
,
G.
, and
Moro
,
D.
,
2014
, “
Automatic Combustion Phase Calibration With Extremum Seeking Approach
,”
ASME J. Eng. Gas Turbines Power
,
136
(
9
), p.
091402
.10.1115/1.4027188
8.
Bozza
,
F.
,
De Bellis
,
V.
, and
Teodosio
,
L.
,
2017
, “
A Numerical Procedure for the Calibration of a Turbocharged Spark-Ignition Variable Valve Actuation Engine at Part Load
,”
Int. J. Engine Res.
,
18
(
8
), pp.
810
823
.10.1177/1468087416674653
9.
Maniatis
,
P.
,
Wagner
,
U.
, and
Koch
,
T.
,
2019
, “
A Model-Based and Experimental Approach for the Determination of Suitable Variable Valve Timings for Cold Start in Partial Load Operation of a Passenger Car Single-Cylinder Diesel Engine
,”
Int. J. Engine Res.
,
20
(
1
), pp.
141
154
.10.1177/1468087418817119
10.
Rask
,
E.
, and
Sellnau
,
M.
,
2004
, “
Simulation-Based Engine Calibration: Tools, Techniques, and Applications
,”
SAE
Paper No. 2004-01-1264. 10.4271/2004-01-1264
11.
Duan, H., Huang, Y., Mehra, R. K., Song, P. P., and Ma, F. H.,
2018
, “
Study on Influencing Factors of Prediction Accuracy of Support Vector Machine (SVM) Model for NOx Emission of a Hydrogen Enriched Compressed Natural Gas Engine
,”
Fuel
,
234
, pp.
954
964
.10.1016/j.fuel.2018.07.009
12.
Huang
,
H. Z.
, and
Su
,
W. H.
,
2008
, “
Application of Micro-Genetic Algorithm for Calibration of Kinetic Parameters in HCCI Engine Combustion Model
,”
Front. Energy Power Eng. China
,
2
(
1
), pp.
86
92
.10.1007/s11708-008-0003-8
13.
Nola
,
F. D.
,
Giardiello
,
G.
,
Gimelli
,
A.
,
Molteni
,
A.
,
Muccillo
,
M.
,
Picariello
,
R.
, and
Tornese
,
D.
,
2018
, “
Reduction of the Experimental Effort in Engine Calibration by Using Neural Networks and 1D Engine Simulation
,”
Energy Procedia
,
148
, pp.
344
351
.10.1016/j.egypro.2018.08.087
14.
Turin
,
R. C.
,
Zhang
,
R.
, and
Chang
,
M. F.
,
2008
, “
Volumetric Efficiency Model for Variable Cam-Phasing and Variable Valve Lift Applications
,”
SAE
Paper No. 2008-01-0995. 10.4271/2008-01-0995
15.
Gölcü
,
M.
,
Sekmen
,
Y.
,
Erduranlı
,
P.
, and
Sahir Salman
,
M.
,
2005
, “
Artificial Neural-Network Based Modeling of Variable Valve-Timing in a Spark-Ignition Engine
,”
Appl. Energy
,
81
(
2
), pp.
187
197
.10.1016/j.apenergy.2004.07.008
16.
Atashkari
,
K.
,
Nariman-Zadeh
,
N.
,
Gölcü
,
M.
,
Khalkhali
,
A.
, and
Jamali
,
A.
,
2007
, “
Modelling and Multi-Objective Optimization of a Variable Valve-Timing Spark-Ignition Engine Using Polynomial Neural Networks and Evolutionary Algorithms
,”
Energy Convers. Manage.
,
48
(
3
), pp.
1029
1041
.10.1016/j.enconman.2006.07.007
17.
Francesco
,
D.
,
Giovanni
,
G.
, and
Alfredo
,
G.
,
2019
, “
Volumetric Efficiency Estimation Based on Neural Networks to Reduce the Experimental Effort in Engine Base Calibration
,”
Fuel
,
244
, pp.
31
39
.10.1016/j.fuel.2019.01.182
18.
Constantine
,
P. G.
,
2015
,
Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies
,
Siam
,
Philadelphia.
19.
Ji
,
W. Q.
,
Wang
,
J. X.
,
Zahm
,
O.
,
Marzouk
,
Y. M.
,
Yang
,
B.
,
Ren
,
Z. Y.
, and
Law
,
C. K.
,
2018
, “
Shared Low-Dimensional Subspaces for Propagating Kinetic Uncertainty to Multiple Outputs
,”
Combust. Flame
,
190
, pp.
146
157
.10.1016/j.combustflame.2017.11.021
20.
Ji
,
W. Q.
,
Ren
,
Z. Y.
,
Marzouk
,
Y.
, and
Law
,
C. K.
,
2019
, “
Quantifying Kinetic Uncertainty in Turbulent Combustion Simulations Using Active Subspaces
,”
Proc. Combust. Inst.
,
37
(
2
), pp.
2175
2182
.10.1016/j.proci.2018.06.206
21.
Guan
,
C.
,
Zhai
,
J. Q.
, and
Han
,
D.
,
2019
, “
Cetane Number Prediction for Hydrocarbons From Molecular Structural Descriptors Based on Active Subspace Methodology
,”
Fuel
,
249
, pp.
1
7
.10.1016/j.fuel.2019.03.092
22.
Guan
,
C.
,
Lu
,
M. R.
,
Zeng
,
W.
,
Yang
,
D. J.
, and
Han
,
D.
,
2020
, “
Prediction of Standard Enthalpies of Formation Based on Hydrocarbon Molecular Descriptors and Active Subspace Methodology
,”
Ind. Eng. Chem. Res.
,
59
(
10
), pp.
4785
4791
.10.1021/acs.iecr.9b06319
23.
Constantine
,
P. G.
,
Dow
,
E.
, and
Wang
,
Q. Q.
,
2014
, “
Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces
,”
SIAM J. Sci. Comput.
,
36
(
4
), pp.
A1500
A1524
.10.1137/130916138
24.
Constantine
,
P. G.
,
Emory
,
M.
,
Larsson
,
J.
, and
Iaccarino
,
G.
,
2015
, “
Exploiting Active Subspaces to Quantify Uncertainty in the Numerical Simulation of the HyShot II Scramjet
,”
J. Comput. Phys.
,
302
, pp.
1
20
.10.1016/j.jcp.2015.09.001
25.
Johnson
,
R. W.
,
2001
, “
An Introduction to the Bootstrap
,”
Teaching Stat.
,
23
(
2
), pp.
49
54
.10.1111/1467-9639.00050
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