The Rapid Development ofDiesel Engines Using an
Optimization of the Fuel
Injection Control
KOJI SATAKE*1

TOSHIAKI MONAKA*2

SATOSHI YAMADA*3

HIROYUKI ENDO*4

MITSUHIKO YANAGISAWA*5

TAKAHARU ABE*5

With concerns over preventing global warming, the usage of diesel engines, which have excellent thermal efﬁciency properties andare expected to reduce CO2 emissions is attracting people’s attention. Furthermore, nitrogen oxide and particulate matter emissions
have been greatly reduced due to the development of emission reduction and combustion control technologies in recent years. To
apply the latest combustion control technologies, optimization of the control parameters is required to achieve both exhaust gas
suppression and heat efﬁciency improvement under various operation conditions. In this paper, we describe a method that optimizes
the control parameters in actual engines such that they can operate at high efﬁciency and accuracy.

1. Introduction
Recently, the role of carbon dioxide (CO 2 ) in global
warming has become an issue. To reduce CO 2 emissions,diesel engines have been re - evaluated for automobile
applications, and various manufacturers have focused theiref forts on the research and development of automobile
diesel engines. Controlling exhaust gas has been greatly
strengthened. On the other hand, exhaust gas regulations
have been greatly strengthened in Japan, the United States,
and Europe. In Europe, where diesel cars are more popular,
the implementation of Euro 6 is scheduled to take effect in2014, as shown in Fig. 1. Equivalent regulations are to be
implemented in Japan and the United States. Therefore,
a further reduction in exhaust gases, especially nitrogen

Exhaust gas regulation in Europe

PM ( /km)

2. Hybrid optimization using an RSM

Euro3 (’00)

0.05
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0.01
0

Euro4 (’05)
Euro6 (’14)
Euro5 (’09)
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NOx ( /km)

oxide (NOx) and particulate matter (PM), will be required.
For this reason, the technological development of a newgeneration of environmentally friendly diesel engines has
been promoted.
Several major technologies suppor t the latest clean
diesel engine, such as exhaust gas recirculation (EGR),
common-rail fuel injection systems, and variable geometry
turbochargers. To improve the engine performance andreduce the amount of exhaust gas, these control devices
must function properly and the control parameters must
be efficiently optimized. The conventional trial-and-error
method of engine testing has already been thoroughly
examined.
In this work, we investigated an optimization methodthat enables quick calibration of the control parameters andaccurate setting of the optimal values by combining engine
testing and a response surface model ( RSM)1 with the
optimization method.

0.5

0.6

Fig. 1 Exhaust gas control in Europe
Implementation of Euro 6 is scheduled for 2014. Similar regulations
are to be implemented in Japan and the United States.
*1 Takasago Research & Development Center, Technical Headquarters*2 Advanced Technology Research Center, Technical Headquarters*3 Nagasaki Research & Development Center, Technical Headquarters6 6*4 Yokohama Research & Development Center, Technical Headquarters*5 Mitsubishi Motors Corporation

An RSM describes the input/output relationship of thesystem in terms of how the output data are related to the
input data. An RSM can make use of polynomial and neuralnetworks. If a high-accuracy model can be established,predictions and optimizations can be performed efficiently.
The basic procedure for the hybrid optimization of an engine
experiment and the subsequent analysis by an RSM is asfollows.
(1) S et t he ra nges a nd levels of t he eng i ne operat ing
conditions and control parameters, and determine thetest combinations (create an orthogonal array, apply thedesign of experiments methodology).
Mitsubishi Heavy Industries, Ltd.
Technical Review Vol. 45 No. 3 (Sep. 2008)

(2) Following the orthogonal array, conduct the engine tests
and measure the response values, such as the exhaustgas emissions.
(3) Create a response surface model from the combinationsof test conditions and response values.
(4) Using the RSM, implement an optimization calculation todetermine the control parameters that yield the desired
exhaust gas characteristics.
(5) Perform a conﬁrmation test on an actual engine using the
optimal solution.
T he or t hogona l a r r ay is a met hod t hat prov ides ac ombi n a t ion of t e s t c ond it ions t h a t c a n t horou gh l yinvestigate the response characteristics of the parameter
space with the least number of tests. Because the engine
characteristics were non-linear, an orthogonal array of athree-level system, such as L18, L27, and L36 was basicallyused and an orthogonal array of a multi-level system of fourlevels or more was used in some cases.
The polynomial expression model was used as an RSM.
Figure 2 shows the method used to create the model.
Starting from the first-order polynomial, the accuracy ofthe model was improved by sequentially adding or deleting
second- or higher-order terms. To further improve the model
accuracy, the weight of each term on the model accuracy was
analyzed using the t-test. 2 The t-test is a statistical methodthat rejects a term when the standard error of the term
coefﬁcient is large and bears no signiﬁcance. Furthermore,
to address the model accuracy before and after adding ordeleting a term, the Akaike information criterion (AIC)2 was
calculated before and after the addition or deletion. If thevalue decreased after a term was added, the model accuracy
had improved and that term was chosen. The A IC is anindex that suppresses the excessive ﬁtting accuracy by using
multiple terms and is a standard that can be used to analyze
which model, out of multiple models, is the most robust andthe most accurate; the sum of the accuracy of the model andthe number of terms serve as an evaluation function. It is not
an absolute standard, but an index for determining relative
high or low numerical values. The process terminates when
the squared multiple correlation coefficient, adjusted for adegree of freedom that expresses how closely the model ﬁts
a given data point, meets or exceeds a given value. With
this method, an optimal polynomial expression model canbe obtained by automatically executing the calculation,by computer, based on the given data. For the case of acomplete polynomial that uses all of its terms, it is necessary
to conduct more tests tha n the number of the ter ms.
However, if the above method is used, an orthogonal arraycan be adopted with fewer tests; therefore, the efﬁciency of
the tests is greatly improved.

3. Adoption of the optimization method during a twostage injection
3.1 Veriﬁcation of the accuracy of the response
surface
To confirm the effectiveness of the method described in
Section 2, the method was adopted for a two-stage injection
consisting of a main injection plus a pre-injection. There
were ﬁve control variables: rail pressure (Pcr), pre-injection
quantity (PreQ), pre-injection period (Pre-interval), main
injection timing (MainIT), and EGR rate. Six responses were
measured: NOx, HC, CO, PM emissions, brake speciﬁc fuelconsumption (BSFC), and noise. The adopted test conditions
were (i) speed of rotation = 1,500 min -1 and cylinder internal

Create first order polynomial.
Add or delete one second- or higher-order term.
Check significance of all the terms(apply t-test).
Compare accuracies of polynomial expression models
before and after the addition/deletion of the term(apply Akaike information criterion).

Is correlation with given data point sufficient(apply the squared multiple correlation coefficient adjusted
for the degrees of freedom)?

High-accuracy polynomial expression modelFig. 2 Creation of an RSM
The terms of a polynomial expression model are chosen based on a statistical method to improvethe model accuracy.

Mitsubishi Heavy Industries, Ltd.
Technical Review Vol. 45 No. 3 (Sep. 2008)

7

NOx (Relative value)

and the RSM estimated value (%)

Error between the measured value

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: Measured value: Response surface predicted value

1.2

30

1.0
0.8
0.6
0.4
0.2
0.0
on
ec

s

Ba

Number of experimental conditions
Fig. 3 Conﬁrmation of the accuracy of the RSM
This ﬁgure shows the errors between the measured value and theRSM estimated value at the test conditions in the orthogonal array.
The prediction accuracy of the response surface is sufﬁcient.

era

Op

)

t (1

oin

p
tion

era

Op

)

t (2

oin

p
tion

t (3

oin

p
tion

)

era

Op

Fig. 5 Comparison between RSM predictions and measured
valuesThe prediction accuracy is excellent for all conditions. The
measured value is 1.0.

3.2 Application of the optimization method
Next, the optimization method was applied using thecreated response surface. The optimization was based on
the simulated annealing (SA) method. The SA method
deter mines the opt imal solut ion in a large domain by
avoiding a local solution when the existence of multiple
local opt imal solut ions is expected. To minimi ze theNOx emissions, the optimization was implemented under
the restrictions of setting upper limit values to the PM
and BSFC on the response surface created based on thedata from test condition (ii). As a result, we obtained acondition that reduced NOx emissions by 11% compared toconventional conditions. When we executed a conﬁrmation
test, we obtained approximately the expected result. The
optimization calculations on the response surface could
be p er for med qu ick ly be c ause t he opt i m i z at ion was
implemented using a given polynomial. Accordingly, efﬁcientengine control optimization could be achieved without
executing a trial-and-error test only if a response surface thatsatisﬁed the prediction accuracy could be created.

NOx ( /h)
EGR ratio
(%)

on

diti

2 4 6 8 10 12 14 16 18 20 22 24 26 28 3032 34 36

MainlT(de ATDC)

Fig. 4 One example of a response surface
The figure provides a visual under standing of theengine characteristics. MainIT and EGR rate are control
parameters and NOx is the response characteristic.

pressure Pme = 0.4 MPa, and (ii) speed of rotation = 2,000
min -1 and cylinder internal pressure Pme = 0.7 MPa. For theengine test to yield the response surface, we used an L36
orthogonal array of three levels with ﬁve control variables.
First, we discuss the prediction accuracy of the response
surface for test condition (i). The accuracy of the fit of
the created response surface to the sampling point can beassessed with the squared multiple correlation coefficientadjusted for the degrees of freedom; its value is R 2 = 0.95
for any response value. For example, NOx has a modelwith excellent accuracy for the respective test conditions,as shown in Fig. 3. Figure 4 shows the response surface
for NOx when the MainIT and the EGR rate were taken as
control variables. Visualizing the response surface aidsin understanding the parameter space for engine control.
Furthermore, in Fig. 5 the results are compared withthe measured values, along with four control variables
whose response values are different, in order to verify theprediction accuracy of the response surface. For any of
the responses, excellent prediction accuracy was obtained
quantitatively.

4. Adoption of the optimization method during multistage injection
4.1 Accuracy degradation of a response surface
subjected to multiple variables
Although we showed that an excellent optimal condition
can be predicted if an appropriate response surface canbe created, there are some cases where the appropriate
response sur face ca nnot be created i f t he number of
injections is increased. Following are two cases where theappropriate response surface cannot be created.
(1) T here is a la rge discrepa nc y bet ween t he opt imal
condition predicted from the initial response surface
that was created from the orthogonal array and the
conﬁrmation test results.
(2) T he c a lc u l at e d v a lues of c er t a i n res p ons es havenegative values (values that cannot exist from a physical
Mitsubishi Heavy Industries, Ltd.
Technical Review Vol. 45 No. 3 (Sep. 2008)8

viewpoint) based on the initial response surface createdfrom the orthogonal array.
Insufﬁcient accuracy of the response surface is the cause
for both cases. T he net mesh becomes rougher as thenumber of variables increase when we use the same size oforthogonal array. When the interaction between variables
or non-linear parameters increases and the number of data
points is not sufﬁcient, either degradation of the prediction
accuracy or a negative value occurs. Although the best
response surface can be created for the given data withthe method described in Section 2, there are some cases
where degradation of the accuracy cannot be avoided where
sampling data is not sufﬁcient. In this work, the successive
updating method described below was adopted to improve
the prediction accuracy of the response surface.

of NOx emissions was selected as the optimization parameter
under the following constraints: set the upper limit values ofCO, PM, fuel consumption, and noise. No negative values
were identified after creating a response surface from an
L 36 orthogonal array; therefore, the optimal condition
was determined using SA optimization. The engine test
was performed by adding five conditions together with the
L 4 orthogonal array conditions, using the rail pressure,main injection timing, and EGR rate as variables, whose
sensitivities to NOx were high around the optimal condition
that varied at two levels. By incorporating these results,t he response sur face was recreated, a nd t he opt ima lcondition was determined using SA optimization. When the
conﬁrmation test was performed after this ﬁrst updating, theprediction accuracy was improved, as shown in Fig. 6, and ahighly accurate optimal condition was obtained.

4.2 Improvement of the response surface by
successive updating

NOx relative error (%)

After creating the response surface described in Section
2, we checked to determine whether there was a negative
response value. This checking was performed in a roundrobin manner for all combinations of the respective threelevel control variables. If negative values appeared, themaximum negative value was extracted for each response.
Using this response surface, the optimal condition wasdetermined using SA optimization. The engine test was
performed using the condition of the extracted maximum
negative value and the optimal condition. By adding the
newly obtained test data to the initial orthogonal array test
data, the response surface was recreated. When there wereno negative values, the three control variables that werehighly sensitive to the response value around the optimal
condition were selected in addition to the optimal condition,
and an L4 orthogonal array was created. The engine test was
conducted with five additional test conditions, besides the
optimal condition, and the response surface was recreatedby adding these data. The L4 orthogonal array is an arrayof two levels of respective variables and was utilized for two
purposes: ﬁrst, to determine how close we were to the true
optimal condition by investigating the response sensitivity
around the optimal condition selected by the SA method; andsecond, to improve the prediction accuracy by increasing
the number of data points around the optimal condition.
If the expected optimal condition and the results of the
conﬁrmation test nearly agreed, the process was terminated,
and the solution was deemed converged close to the optimal
condition.
W ith this successive updat ing method, the opt imal
condition can be reached more quickly with fewer tests
compared to the use of a large-scale orthogonal array.

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0

InitialFirst updating

Fig. 6 Improvement of RSM prediction accuracy during
the addition of an after injection
By updating the RSM once, the prediction accuracy of NOx
improved. The relative error is shown using the measured value as
the standard.

4.4 Three-stage injection—the addition of pilot
injection
Next, we describe the results obtained after adding a pilot
injection instead of an after injection. When the existenceof a negative value was investigated for the response surface
created f rom the L 36 or thogonal array, the prediction
accuracy of PM was low, and many negative values wereidentified. Then, two additional tests were conducted by
combining the condition of the maximum negative value
and the optimal condition for the minimum NOx on this
response surface, and the response surface was recreated.
Since a negative PM value occurred even on the recreatedresponse surface, additional tests were conducted using two
conditions of the maximum negative values and the optimal
condition, and the response surface was recreated again.
At this point, the negative PM value disappeared. An L4
orthogonal array was created with the optimal condition,
determined by the optimization calculation, using the railpressure, main injection timing, and EGR rate as variables,
whose sensitivities were high around the optimal condition.
Five additional test conditions were determined. With a
total of three successive updates for the response surface,

4.3 Three-stage injection—the addition of after
injection
We describe here the results from applying seven control
variables, where two control variables, the quantity of theafter injection and the injection timing, were added to thetwo-stage injection described in Section 3. The minimization

Mitsubishi Heavy Industries, Ltd.
Technical Review Vol. 45 No. 3 (Sep. 2008)

9

NOx relative error (%)
PM relative error (%)

has demonstrated that the accuracy improvement fromsuccessive updating of the response surface is effective when
predicting the optimal condition during multi-stage injection
by adding the minimum number of additional tests to theinitial orthogonal array.

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5

5. Conclusion0

We demonstrated that the hybrid optimization method,which combines orthogonal array testing, an RSM, andoptimization, is ef fective when optimizing the control
parameters of the latest diesel engine, which has many
control variables. Compared to conventional engine testing,approximately 54% of man-hour testing can be avoided byusing the hybrid optimization method, as shown by theexample of three-stage injection with the addition of a pilot
injection. We plan to upgrade combustion control technology
and the optimization method described in this paper toreduce engine exhaust gas emissions, measures for exhaustgas regulations during the transient period and maintain ourcustomers’ trust by developing an environmentally friendly
engine.

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ial

Init

F

ing

dat

up
irst

g
atin

con
Se

pd
du

g

atin

pd
du

r
Thi

Fig. 7 Improvement of RSM prediction accuracy during
the addition of a pilot injection
The prediction accuracy of NOx and PM was improved by updating
the RSM three times. The relative error is shown using themeasured value as the standard.

References

a converged value approximating the optimal condition was
obtained.
Figure 7 shows the transition of the predicted andexperimental NOx and PM values for the optimal condition.
D u r i ng t he fou r t h con f i r mat ion t est , t he pred ic t ion
accuracy of NOx and PM improved, and results below theconstraint conditions could be obtained for the PM, CO,fuel consumption, and noise. There were seven control
variables because of the addition of an after injection or apilot injection. The reason for the larger degradation of
the prediction accuracy and the need for three iterations
for the pilot injection case is that the addition of the pilot
injection affected the pre-injection and main injection due
to the change of injection condition. The resulting strong
interaction or non-linear actions significantly degraded
the prediction accuracy. Since an after injection occurs
subsequent to the pre-injection and main injection, it does
not have a large effect on the engine combustion. This study

1. R . H . M ye r s a n d D. C . Mo nt g o m e r y, R e s p o n s e S u r f a c e
Methodology, John Wiley & Sons, Inc,(2001)
2. Sadao Ishimura, Multivariate A nalysis: The Easy Way, Tokyo
Tosho (2000) pp.2–57

Koji Satake

Toshiaki Monaka

Satoshi Yamada

Hiroyuki Endo

Mitsuhiko Yanagisawa

Takaharu Abe

Mitsubishi Heavy Industries, Ltd.
Technical Review Vol. 45 No. 3 (Sep. 2008)10