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0.9920% and 7.2613%, respectively. Similarly, for the fuel consumption, RMSE, R2 and

MAPE were 0.2860%, 0.9299% and 7.5448%, respectively. With these results, we believe that

the ANN can be used for the prediction of engine performance as an appropriate method for

spark-ignition (SI) engines. 2004 Elsevier Ltd. All rights reserved.

Keywords: Artificial neural-network; Spark-ignition engine; Variable valve-timing; Engine performance

1. Introduction

Valve control is one of the most important parameters for optimizing efficiency

and emissions, permitting combustion engines to conform to future emission

targets and standards. Control of the intake valve provides optimal filling of the

cylinder at all engine speeds. This natural supercharging, and the improved en-

gine-torque and power that accompany it, makes it possible to downsize engine-

capacity and thus reduce fuel consumption at all operating conditions. For many

years, in order to increase the performance of internal-combustion engines, many

studies have been conducted. One of the most important of these studies is the

Nomenclature

ANN artificial neural-network

aBDC after bottom-dead-center

aOT after original-timing

aTDC after top-dead-center

bTDC before top-dead-center

bBDC before bottom-dead-center

bOT before original-timing

CA crankshaft angle ()

LM LevenbergMarquardtMAPE mean absolute percentage error

o output value

OT original timing

p pattern

R2 absolute fraction of variance

RMSE root-mean-squared error

SCG scaled conjugate gradient

SFC specific fuel-consumption (g/kWh)

SI spark-ignition

t target valueVVT variable valve-timing

188 M. Golcu et al. / Applied Energy 81 (2005) 187197

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one which tries to optimize the amount of timing and opening of the intake and

exhaust valves for all intervals of engine load and speed in SI engines [13].

Traditionally, valve timing has been designed to optimize the operation at high

engine-speeds and wide-open throttle conditions [2,4]. Variable valve-timing(VVT) relates to both the opening time and the duration of the valves open-interval.

Controlling valve-timing can improve the torque curve, the brake-power curve, or

the indicator-power curve of a given engine. Variable valve-timing can also be used

to reduce the fuel consumption and, to a small extent, the engine emissions [5]. This

is achieved by controlling the maximum temperature in the cylinder and the amount

of residuals remaining at the commencement of the compression stroke (i.e., exhaust-

gas recirculation control) [6]. Numerous VVT systems have been proposed and some

of these have been demonstrated in engines [713].

The ANN technique can be used as an alternative method in modeling highly-

complex and ill-defined problems, engineering analysis and prediction. ANNs donot require a precise formulation of the physical relationship of the concerned

problem. In other words, they only need solution examples concerning the prob-

lem. ANNs have been used for energy systems, such as internal-combustion en-

gine performance [14], thermodynamic analysis of an ejectorabsorption cycle

[15], mapping and estimation of solar potential in Turkey [16], prediction of ax-

ial-piston pump performance [17] and energy consumption prediction of passive-

solar buildings [18].

In this study, ANNs are used to determine the effects of intake valve-timing on

engine performance and fuel economy. Experimental studies were complete to obtain

training and test data. Intake valve-timing and engine speed have been used as the

input layer; engine torque and fuel consumption have been used as the output layer.

Pattern numbers (77) have been obtained from the experiments. Inputs for the net-

work were the intake valve-timing and engine speed, while the outputs were torque

and fuel consumption. The results of the system indicate a relatively good agreement

between the predicted values and the experimental ones. The experimental study to

determine power, torque and fuel consumption in a spark-ignition engine is complex,

time consuming and costly. It also requires specific tools. To overcome these difficul-

ties, an ANN can be used for the prediction of performance and fuel consumption in

a SI engine.

2. Artificial neural-networks

Artificial intelligence consists of two major branches, namely the study of ANNs

and expert systems. During the last ten years, there has been a substantial increase in

the interest in ANNs. A neuron is the fundamental processing element of a neural

network. An artificial neuron is a model, whose components have direct analogs

to components of an actual neuron. ANNs have been used successfully in solving

complex problems in various fields of engineering, economics, neurology, mathemat-ics, medicine, meteorology and many others. Some of the most important ones are

in pattern, sound and speech recognition, in the identification of explosives in

M. Golcu et al. / Applied Energy 81 (2005) 187197 189

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passenger suitcases and in the identification of military targets [1921]. A neural net-

work operates like a black box model and does not require detailed information

about the system. On the other hand, it learns the relationship between the input

parameters and the controlled and uncontrolled variables by studying previously re-corded data, in a similar way that a non-linear regression might behave. Another

advantage of using ANNs is their ability to handle large and complex systems with

many interrelated parameters. They simply ignore existing data that are of minimal

significance and concentrate instead on the more important inputs [22].

The output of a specific neuron is a function of the weighted input, the bias of

the neuron and the transfer function. Fig. 1 shows the basic artificial neuron of

the hidden layer. The input layer, some hidden layers and an output layer are

usually basic features of the network. In its simple form, each single neuron is

connected to other neurons of a previous layer through adaptable synaptic

weights. Knowledge is usually stored as a set of connection weights. The outputof any neuron is given by:

si Xnj1

xjwij bj; 1

where

yj fsi: 2

The transfer function f can be selected from a set of readily-available functions.

The selected ANN structure of a multi-layer is shown in Fig. 2. It consists of twoinput layers, one hidden layer, and two output layers. The output of the output layer

is a result of the combined effect of all the neurons in the network. Each input is mul-

tiplied by a connection weight. In the simplest case, the products and biases are sim-

ply summed, then transformed through a transfer function to generate a result, and

finally an output obtained. Networks with biases can represent relationships between

inputs and outputs more easily than networks without biases.

Fig. 1. Presentation of a basic artificial neuron.


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Back-propagation algorithms and their variants are the most popular learning

algorithms. The back-propagation algorithm in an ANN is one of the most effective

learning algorithms. The training of all patterns of a training data group is named an

epoch [22,23].Gradient descent and gradient descent with momentum are generally slower for

practical problems because of their requiring small learning rates for stable learning

than the other algorithms. Moreover, success in the algorithms depends on the user-

dependent parameters learning-rate and the momentum constant. Algorithms such

as conjugate gradient (SCG), BFGS quasi-Newton and LevenbergMarquardt

(LM) are faster algorithms than the other algorithms and use standard numerical

optimization-techniques. An ANN with a back propagation algorithm learns by

changing the weights, and these changes are stored as perception information, or

knowledge.

The error is described by the root-mean-squared error (RMSE) and defined as

follows:

RMSE 1=p Xj

tj oj 2 !1=2 3

In addition, the absolute fraction of variance (R2) and mean absolute percentage

error (MAPE) are defined, respectively, as follows:

R

2

1 Pj tj oj

2

Pj oj

2 !

4

and

Fig. 2. ANN architecture used for 15 neurons in a single hidden-layer.


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3600 rpm at 200 rpm intervals, after the engine reached the working temperature of

80 C. During the experiments, the average ambient temperature and atmospheric

pressure were 22 C and 752 mm-Hg, respectively.

4. Application of the artificial neural-network

ANNs have been used in a broad range of applications, including pattern classi-

fication, identification, prediction, optimization and control procesess. ANNs learn

by using some examples, namely patterns. In other word, to train and test a neural

network, input data and corresponding target values are necessary. The examples in

this study are numerical values performed by using the experimental results and 77

patterns were obtained from the experiments. Here, ANNs were used for the mod-

eling of fuel consumption and torque in a spark-ignition engine. Inputs for the net-work are engine speed and intake valve timing; the outputs are torque and fuel

consumption.

The experimental results were used to train and test: 62 experimental results, from

the total of 77, were employed as data sets to train the network, while 15 results were

used as test data. The architecture of the ANN becomes 2-15-2, 2 corresponding to

the input values, 15 for the number of hidden layer neurons and 2 for the outputs.

The back-propagation learning algorithm has been used in a feed-forward, single

hidden layer. Variants of the algorithm used in the study are the LM and scaled con-

jugate gradient (SCG). The selected neural-network architecture consists of one hid-

den layer of log-sigmoid neurons followed by an output layer of one linear neuron.

Linear neurons are those which have a linear transfer-function. The transfer function

is purelin. Back propagation networks use the log-sigmoid (logsis), or the tan-sig-

moid (tansig) transfer-function. A logistic sigmoid (logsis) transfer-function has been

used i.e.,

Table 2

Samples for input and output

Engine speed (rpm) Intake-valve timing (CA) Torque (Nm) Fuel consumption (kg/h)

1600 30 bOT 10.07 0.6456

2200 30 bOT 11.05 0.9562

2600 20 bOT 10.13 1.0432

3000 20 bOT 9.22 1.1165

1800 10 bOT 10.15 0.7353

2400 10 bOT 11.2 1.050

2600 0 OT 11.25 1.123

3600 0 OT 9.43 1.4667

1600 10 aOT 9.53 0.661

2800 10 aOT 10.97 1.195

1800 20 aOT 9.43 0.7582

2600 20 aOT 10.5 1.10962200 30 aOT 9.22 0.9370

3400 30 aOT 10.13 1.3971


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fx 1

1 ex6

where x is the weighted sum of the input.

A computer program has been performed under MATLAB 6.3. In the training, an

increased number of neurons (from 15 to 19) is used in a single hidden-layer. When

the network training was successfully finished, the network was tested with test data.

Some statistical methods, R2, RMSE and MAPE values, have been used for compar-

ison. Selected sample data sets used for training and testing the network are shown in

Table 2.

5. Results and discussion

Numerical results obtained from experimental and the related parameters have

been used to train the network. The intake valve timing, engine speed, fuel consump-

tion and torque for a single-cylinder four-stroke spark-ignition engine have been

used to train the network. Initially, fifteen hidden neurons in a single hidden-layer

have been used for all the algorithms. Then, the number of neurons has been in-

creased. The results revealed that the optimum number of hidden neurons is different

for different algorithms. Of all the variants that we studied, the fastest learning is ob-

tained with the LM algorithm. SCG is also fast, but it produces slightly more errors

compared with errors with the LM.

Statistical values such as RMSE, R2

and MAPE of the torque and fuel consump-tion are given in Tables 3 and 4 for different training algorithms and hidden number

of neurons respectively. Comparisons of some experimental and ANN-predicted

data are also given in Table 3 for the torque. The LM algorithm, with 15 neurons,

has produced the best results. It shows that R2 is 0.9920%, MAPE is 7.2613% and

the RMSE value is 0.9017% in the test. As for the training, R2 is 0.9935% and MAPE

is 6.6644%, while the RMSE value is 0.8071%. For fuel consumption, it shows that

R2 is 0.9299%, MAPE is 7.5448% and the RMSE value is 0.2860% in the test. As for

Table 3Error values of the ANN approach for torque used in training and testing

Algorithm Hidden

number

RMSE-test R2-test MAPE-test RMSE-training R2-training MAPE-

training

LM 15 0.9017 0.9920 7.2613 0.8071 0.9935 6.6644

LM 16 1.0771 0.9884 9.3971 1.0730 0.9885 9.2242

LM 17 0.9242 0.9916 8.0124 0.8769 0.9923 7.2603

LM 18 0.9776 0.9906 8.3436 0.8804 0.9922 7.1448

LM 19 2.0223 0.9634 11.7415 0.7821 0.9939 5.8978

SCG 15 0.8932 0.9888 8.8819 0.7288 0.9910 7.8691

SCG 16 1.1255 0.9815 11.1495 1.0770 0.9799 11.7259

SCG 17 1.1282 0.9815 10.2462 0.9954 0.9828 10.7015SCG 18 1.2834 0.9761 14.1361 1.2530 0.9729 14.3240

SCG 19 0.9214 0.9884 9.1869 0.9302 0.9859 10.4135


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the training, R2 is 0.9988% and MAPE is 2.9744%, while the RMSE value is

0.0372%.

Fig. 4 compares the calculated experimental and predicted engine performance

values for the test data. As shown in the figure, the values predicted by the ANN

approximately match the experimental values. Fig. 5 shows the effect of the number

Table 4

Error values of the ANN approach for fuel consumption used in training and testing

Algorithm Hidden

number

RMSE-test R2-test MAPE-test RMSE-training R2-training MAPE-

trainingLM 15 0.2860 0.9299 7.5448 0.0372 0.9988 2.9749

LM 16 0.3109 0.9166 7.8440 0.0273 0.9994 2.1699

LM 17 0.3022 0.9228 7.1863 0.0247 0.9995 1.8757

LM 18 0.3040 0.9195 7.5993 0.0355 0.9989 2.7299

LM 19 0.3321 0.9024 11.7153 0.0232 0.9995 1.7823

SCG 15 0.2535 0.9225 8.1570 0.0388 0.9978 3.4550

SCG 16 0.2668 0.9121 9.5868 0.0372 0.9980 3.1932

SCG 17 0.2868 0.8901 15.7186 0.1051 0.9825 9.5916

SCG 18 0.2623 0.9152 10.6323 0.0514 0.9961 4.5956

SCG 19 0.2617 0.9126 9.8629 0.0499 0.9962 3.9420

300

350

400

450

500

550

0 4 8 12 1

Test pattern

SFC(g/kWh)

6

exper imental predicted

0

0,4

0,8

1,2

1,6

2

0 4 8 12 1

Test pattern

Fuelconsumption(kg/h)

6

experimental predicted

6

8

10

12

14

0 4 8 12Test pattern

Enginetorque(Nm)

16

exper imental predicted

1

2

3

4

5

0 4 8 12

Test pattern

Power(kW)

16

experimental predicted

Fig. 4. Experimental and ANN-predicted results for engine performance.


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of neurons in the hidden layer on the root mean square errors for torque and fuel

consumption. The training epoch for each neural network is 30,000. It is shown that

the training error is minimized when 15 neurons are used for both the LM and SCG

algorithms for torque and fuel consumption. Thus, these ANN models, with mini-

mum errors, are adopted for further studies.

6. Conclusion

The aim of this paper was to use neural networks for the estimation of a the per-formance and fuel consumption of a spark-ignition engine using different initial

valve timings and engine speeds. The overall results show that the networks can

be used as an alternative way for predicting the performances of these systems.

This paper introduced the ANN technique for modeling the variable-intake valve-

timing in a spark-ignition engine. It used 62 results as data sets to train the network,

while 15 results were used as test data from the total of 77 experimental results. LM

and SCG algorithms have been studied and the best results were obtained from the

LM algorithm with 15 neurons and the mean absolute percentage error was limited

to 7.28.8% for both the LM and SCG algorithm. So, these ANN predicted results

can be considered to be within acceptable limits. It is observed that the predicted re-sults for the torque are better than those for the fuel consumption. The results show

good agreement between the predicted and experimental values.

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