MODELLING OF THE CAR ENGINE CHARACTERISTICS USING
ARTIFICIAL NEURAL NETWORKS
Jarosław Mamala
1a, Szymon Kołodziej
1b, Krystian Hennek
1c1 Opole University of Technology, Faculty of Mechanical Engineering, Department of Vehicles
a j.mamala@po.opole.pl, b s.kolodziej@po.opole.pl, c k.hennek@po.opole.pl
Summary
The complexity of changes and processes occurring in a combustion engine leads to a situation when literature contains numerous mathematical models describing only selected aspects of the engine operation. Due to multidi- mensional and nonlinear types of the engine characteristics, as well as the degree of complexity and only partial depicting of particular interrelations, their usability is limited. Tests carried out by means of a digital simulation based on an analysis of static characteristics of the engine, are one of the methods used to solve that type of prob- lem in the early phase of a power transmission system designing. This method enables, among others, determina- tion of fuel consumption and engine torque depending on a selected operation point. Methods based on approxi- mation and adaptation properties of artificial neural networks are used in innovative solutions. Authors of this paper prove that it is possible to use artificial neural networks to predict the engine characteristics with the use of Matlab software.
Keywords: neural networks, combustion engine characteristics, fuel consumption, driving cycle
MODELOWANIE CHARAKTERYSTYK SILNIKA SAMOCHODU Z WYKORZYSTANIEM
SZTUCZNYCH SIECI NEURONOWYCH
Summary
Złożoność zmian i procesów zachodzących w silniku spalinowym prowadzi do sytuacji, w której literatura tere- nowa zawiera liczne modele matematyczne opisujące tylko wybrane aspekty pracy silnika. Ze względu na wielo- wymiarowość i nieliniowość charakterystyk silnika, a także stopień ich złożoności i jedynie częściowe obrazowanie poszczególnych zależności, użyteczność tych charakterystyk jest ograniczona. Testy przeprowadzone za pomocą cyfrowej symulacji opartej na analizie statycznej charakterystyk silnika są jedną z metod rozwiązywania tego typu problemów we wczesnej fazie projektowania układu napędowego. Metoda ta umożliwia między innymi określenie zużycia paliwa i wielkości momentu obrotowego silnika w zależności od wybranego punktu roboczego. Metody oparte na właściwościach przybliżających i adaptacyjnych sztucznych sieci neuronowych są stosowane w innowa- cyjnych rozwiązaniach. Autorzy niniejszej publikacji wykazują możliwość wykorzystania sztucznych sieci neuro- nowych do przewidywania charakterystyki silnika przy użyciu oprogramowania Matlab.
Słowa kluczowe: sieci neuronowe, charakterystyki silnika spalinowego, zużycie paliwa, cykle jezdne
1. INTRODUCTION
Correct preparation of engine characteristics considering its optimal efficiency, thus elementary fuel consumption and torque, requires carrying out relevant and time-
consuming stand tests. Great complexity of an engine, where many mechanical and thermodynamic phenomena take place, hinders simple determination of occurring
interrelations as the engine is in no way
object. Testing of car power transmission systems by means of digital simulation or synthesis of
algorithms requires a precise mathematical descrip the driving unit [4]. General engine characteristics, which are depicted with the use of a numerical matrix including points of an equable network covering the engine operation field, are used in simula
These are usually characteristics of torque and fuel consumption per time unit expressed as a function of crankshaft rotational speed and throttle
partial vacuum in the intake manifold.
od that uses artificial neural networks for depicting engine characteristics. The possibility of using artificial neural networks to predict selected operating
was examined in the study. Engine operating obtained with the use of artificial neural network compared to indicators acquired by means of interpol tion of traditional engine matrix characteristics, which uses “Lookup Table” matrix reading technique. Engine operating indicators obtained with the use of a digital simulation were compared to actual measuremen acquired during stand tests of a spark ign
2. GENERAL ENGINE CHARACTERISTICS
The problem brought up in the study was examined using the characteristics of a spark ignition (SI) engine.
Basic parameters of the tested engine were Table 1. Measurements were taken at a test by determining speed characteristics for 15 arbit assumed values of throttle inclination.
Table 1. Engine technical parameters Parameter
Cubic capacity (cm3) DIN maximum power (kW) Maximum power rotational speed (rotation/min)
DIN maximum torque (N·m) Maximum torque rotational speed (rotation/min)
Every partial speed characteristic consists of 11 points where the engine operating indicators were measured and recorded for 10 seconds after a 30 second stabiliz tion period. The engine speed characteristics were r corded every 500 RPM in the first stage. General cha acteristics, stored in a computer memory in the form of a matrix, were completed as a result of approximation of the engine speed characteristics, described in
the literature.
interrelations as the engine is in no way a stationary Testing of car power transmission systems by means of digital simulation or synthesis of its controlling a precise mathematical description of ]. General engine characteristics, with the use of a numerical matrix including points of an equable network covering the engine operation field, are used in simulation tests.
These are usually characteristics of torque and fuel expressed as a function of throttle inclination or manifold. There is a meth- cial neural networks for depicting the engine characteristics. The possibility of using artificial operating indicators operating indicators artificial neural networks were compared to indicators acquired by means of interpola- tion of traditional engine matrix characteristics, which uses “Lookup Table” matrix reading technique. Engine with the use of a digital simulation were compared to actual measurements of a spark ignition engine.
p in the study was examined characteristics of a spark ignition (SI) engine.
were included in urements were taken at a test stand [5, 6]
by determining speed characteristics for 15 arbitrarily
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consists of 11 points indicators were measured and recorded for 10 seconds after a 30 second stabiliza- tion period. The engine speed characteristics were re- in the first stage. General char- ory in the form of completed as a result of approximation of the engine speed characteristics, described in details in
a)
b)
Fig. 1. Characteristics of engine torque as a function of rotation speed and a throttle
as a numerical network of equidistant points covering the engine operation field, b) as a map
A result matrix of 101 × 101 elements dimensions, for rotation speed changes interval 1000 ÷
throttle inclination interval 0 ÷ 100 was assumed in the tested case. Appropriate determination of the precise claimed value of engine torque (
(Fig. 2) requires the use of numerical methods in order to interpolate values occurring among the matrix points.
Every matrix point contains values corresponding to coordinates of the engine operation point:
• crankshaft rotation speed [rotation/min],
• throttle inclination [%],
• torque [Nm] or fuel stream
1. Characteristics of engine torque as a function speed and a throttle inclination: a) presented as a numerical network of equidistant points covering the engine operation field, b) as a map
101 elements dimensions, for rotation speed changes interval 1000 ÷ 6000 and a 100 was assumed in the tested case. Appropriate determination of the precise claimed value of engine torque (Fig. 1) or fuel stream 2) requires the use of numerical methods in order to interpolate values occurring among the matrix points.
values corresponding to of the engine operation point:
speed [rotation/min],
orque [Nm] or fuel stream [g/s].
a)
b)
Fig. 2. Characteristics of fuel stream as a function of rotation speed and throttle inclination: a) presented as a numerical network of equidistant points covering the operation field, b) as a map
The “Lookup Table” reading technique used in the first stage of the readout
interpolation. The principle of this numerical operation is shown in figure 3. A network point is being dete mined for which the assumed value of
tion and crankshaft rotation speed are the closest to the value of the constant matrix network point, for which the claimed engine parameters, such as torque, fuel stream, etc. are read. After such a point has been found, its position is being set as an element of the network [i, j]. Simultaneously other elements of the network [i + 1, j], [i, j + 1] and [i + 1, j + 1] are being dete mined. Apart from a complicated and time
process of the characteristics preparation, such a way of recording of the engine characteristics
ally requires the use of “Lookup Table” technique for reading selected operating indicators out of this
However, preparing the engine characteristics
use of artificial neural networks is a new method used in simulation testing and consists in training artificial 2. Characteristics of fuel stream as a function of crankshaft
: a) presented as numerical network of equidistant points covering the engine
reading technique is commonly stage of the readout. It uses linear . The principle of this numerical operation A network point is being deter-
throttle inclina- the closest to the network point, for which , such as torque, fuel . After such a point has been found, its position is being set as an element of the network [i, j]. Simultaneously other elements of the network , [i, j + 1] and [i + 1, j + 1] are being deter- mined. Apart from a complicated and time-consuming process of the characteristics preparation, such a way of matrix addition- ally requires the use of “Lookup Table” technique for
tors out of this matrix.
engine characteristics with the use of artificial neural networks is a new method used in in training artificial
neural networks directly with measurements results.
This assumption follows from the characteristic prope ties of the neural network, especially from the ability of representing strongly nonlinear, multidimensional corr lations. Such complicated correlations occur in real driving conditions. By this means the ‘feed
propagation’ type of artificial neural networks out of the Matlab calculation programs library was chosen to be used in this research (Fig. 4).
Fig. 3. The principle of torque interpolation for any chosen crankshaft rotation speed and throttle inclination: the grey fields mark the knots of the mesh, the dotted and lined fields mark the results of interpolations and the
final result
Fig. 4. The structure of used feed-forward back propagation neural network with the dimensions of 2x9x1neurons The target network structure is shown in fig includes two inputs, one output and one hidden layer consisting 9 neurons. For neuron training, the Leve berg-Marquardt algorithm was used with
aim of training. In this way, the number of neurons was sought to reach the assumed aim
racy with the minimum number of neurons, whi
INPUT DATA
HIDDEN LAYER
Crankshaft rotation speed
Throttle inclination
3.ELEMENT (i, j + 1) ns(i, j+1)
θθθ θ(i, j+1) Mo (i, j+1)
1.ELEMENT (i, j) ns(i, j)
θθ θθ (i, j) Mo (i, j)
Mo x1234 Mo=(Mo 1234
+ Mo 1324)/2
Mo y1234
Crankshaft rotation
speed ns
Mo x12 Throttle
inclination
%
Mo y13
Crankshaft rotation
speed ns
Mo x34
neural networks directly with measurements results.
This assumption follows from the characteristic proper- ties of the neural network, especially from the ability of representing strongly nonlinear, multidimensional corre-
h complicated correlations occur in real driving conditions. By this means the ‘feed-forward back propagation’ type of artificial neural networks out of the Matlab calculation programs library was chosen to be
The principle of torque interpolation for any chosen crankshaft rotation speed and throttle inclination: the grey fields mark the knots of the mesh, the dotted and lined fields mark the results of interpolations and the white field marks the
forward back propagation neural network with the dimensions of 2x9x1neurons
is shown in fig. 4. It one output and one hidden layer 9 neurons. For neuron training, the Leven- Marquardt algorithm was used with a considered
ing. In this way, the number of neurons was aim of the training accu- with the minimum number of neurons, which was
OUTPUT DATA OUTPUT LAYER
Torque 4.ELEMENT (i + 1, j + 1) ns(i+1, j+1)
θθ θθ(i+1, j+1)
Mo (i+1, j+1)
2.ELEMENT (i + 1, j) ns(i+1, j)
θθ θθ (i+1, j)
Mo (i+1, j) 1234
)/2
Crankshaft
Throttle inclination
%
Mo y24 Crankshaft
finally set to 9. Further increasing of the ber did not improve the accuracy of the network engine characteristics were shown in fig.
the points obtained directly from the measurements and the corresponding characteristics made using artificial neural networks are shown. For such a mapped chara teristic, a relative error was calculated usin
The crankshaft rotation speed and the
tion were chosen for the neural network input data in the real system these are the main parameters d scribing the engines working conditions.
a)
b)
Fig. 5. Matrix characteristics of an engine generated with the use of artificial neural networks of: a) engine
stream
The designed neural networks were trained on the basis of measurement data gathered during measuring of speed characteristics. Qualitative comparison of selected engine operating indicators during the work of an iter tion program and of the artificial neural
presented in fig. 6.
Measurement points were marked with triangles in 6. Both the iteration process and the neural model operation take place near the measurement points. The quality of depicting the engine characteristics with the use of artificial neural networks is highly dependent on parameters used in the process of the network training.
Networks containing a large number of neurons in the hidden layer and of low spread value, are characterized the neurons num- the accuracy of the network and the
. 5. In this figure points obtained directly from the measurements and cteristics made using artificial . For such a mapped charac-
using formula (1).
he crankshaft rotation speed and the throttle inclina- for the neural network input data;
system these are the main parameters de- scribing the engines working conditions.
. Matrix characteristics of an engine generated with the torque, b) fuel
esigned neural networks were trained on the basis of measurement data gathered during measuring of speed characteristics. Qualitative comparison of selected work of an itera- f the artificial neural network was
ere marked with triangles in fig.
. Both the iteration process and the neural model urement points. The the engine characteristics with the artificial neural networks is highly dependent on parameters used in the process of the network training.
Networks containing a large number of neurons in the hidden layer and of low spread value, are characterized
by fidelity of showing the measurement da
such networks easily oscillate during work of a neural engine model, whereas there is a need for reading of the engine operating indicators for non
throttle inclination or the crankshaft a)
b)
Fig. 6. Partial characteristics of the torque, b) fuel stream
The relative error was calculated
∆x
∑∑where:
xp – result of the road test power measurement, xs – result of the simulation.
The calculated volume of the relative
the neural simulation of the engine torque and fuel steam was both lower than 1%. This can be the confi mation for the neural network usage in virtual engine characteristic preparing process.
a)
b)
the measurement data. However, such networks easily oscillate during work of a neural engine model, whereas there is a need for reading of the icators for non-total values of
crankshaft rotation speed.
. Partial characteristics of the SI engine for: a) engine
The relative error was calculated using formula (1):
(1),
result of the road test power measurement,
The calculated volume of the relative error according to of the engine torque and fuel . This can be the confir- mation for the neural network usage in virtual engine
Fig. 8. Matrix characteristics of the SI engine generated with the use of artificial neural networks of: a)
(lambda), b) NOx emissions
The artificial neural networks can also be used to pr pare other engine characteristics, for instance
air-ratio or the toxic exhaust substances emissions.
Examples of such characteristics obtained with a neu method are shown in fig. 8. In this case it is important for the graphs to match each other in some characteri tic points or zones. According to the a) part of the fig at crankshaft rotation speeds between about 3500 RPM
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3. CONCLUSION
Presented diagrams and the error calculation results prove that it is a possible to use artificial neural ne works to predict the engine operating
a digital simulation. Moreover, they can also be used to depict the engine characteristics.
with this method have been rema
the data derived from the measurements
networks are an effective tool for such types of tasks and they successfully replace the “Lookup Table” technique of reading data out of the matrix.
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