Article citation information:
Czech, P. Diagnosing
faults in the timing system of a passenger car spark ignition engine using the
Bayes classifier and entropy of vibration signals. Scientific Journal of Silesian University of Technology. Series
Transport. 2022, 116, 83-98.
ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2022.116.5.
DIAGNOSING FAULTS IN THE TIMING SYSTEM OF A PASSENGER CAR SPARK IGNITION
ENGINE USING THE BAYES CLASSIFIER AND ENTROPY OF VIBRATION SIGNALS
1. INTRODUCTION
Very
dynamic development of automotive technology has been observed over the last
years. Currently produced vehicles are characterized by high power and speeds
as car manufacturers aim to optimize the mass and weight of vehicles [7, 18, 20,
23, 28]. These two factors may cause a rise in the
level of vibrations and noise generated by vehicles, which is caused by the
fact that part of the energy processed by the vehicle is always emitted to the
environment in the form of vibroacoustic phenomena. Presently, used design
methods do not give a full guarantee of the construction of a structure with
predetermined vibroactivity [7, 18, 20, 23, 28].
Among
the methods of solving vibroacoustic problems, the following stages can be
distinguished:
·
experimental identification of vibroacoustic
phenomena of working machines,
·
development of models of vibroacoustic phenomena,
·
development of theoretical and experimental
methods of studying models,
·
development of methods for calculating
vibroacoustic states,
·
setting the design principles for low-emission
machines,
·
experimental verification of experiments results
on prototypes and in production,
·
development of
standards determining acceptable vibroacoustic conditions of machines.
Vibrations
may cause disturbances in the correct operation of the machine and other
devices and reduce their durability and reliability. In addition,
it should be mentioned that mechanical vibrations are often a working
factor deliberately introduced by machine builders as an indispensable element
for the implementation of technological processes. They are also
a valuable source of information, as, through them, one can assess the
technical condition of the machine and its build quality [1, 9-11, 27, 32-34].
In
recent years, methods of non-invasive diagnostics of technical conditions in
which vibrational and acoustic signals emitted during work are used have been
developed around the world [1, 9-11, 27, 32-34].
The
diagnostic process, aimed at identifying the technical condition of the object,
is carried out usually during the normal operation of the object, and it can be
done at any stage of its life. Occurrence of damage to the machines or
deterioration of their operational status is recognized based on the symptoms,
which are represented by the features of diagnostic signals [17, 21, 29, 31, 38,
39, 40, 42-44, 45].
It
should be considered that the vibrations produced in one of the elements can be
transmitted and cause vibrations in a completely different, remote element. For
example, vibrations generated by the crankshaft system of a car engine can be
transferred by attaching the engine to the chassis members, then the bodywork,
and by fixing the hinges to the boot lid, causing it to resonate. In this case,
despite the source of vibration being at the front of the vehicle, vibrations
with the highest intensity – in the form of vibrations or noise –
will reach the vehicle user from a completely different angle.
Research
is being carried out to find the appropriate tools to support the process of
vibroacoustic diagnostics of objects' conditions through experiments related to
the application of new algorithms of registration, ordering and processing of
data according to specific rules, enabling the classification of states. The
different characteristics and determinants of such tasks to a specific object
mean that despite the existence of many proven methods, there is still a need
for further research in this area.
2. RESEARCH PROBLEM
According to the trade literature for car service plants
[6, 13, 15, 25, 36], the repair of the timing gear is an expensive and
time-consuming operation. For example, some of the valve failures that occur
lead to serious failures of the entire engine, and the repair itself may be
unjustified for economic reasons.
The combustion engine timing system is responsible for
controlling the start and end of the filling process with fresh load and
exhaust gas outlet. This must be in full synchronization with the movement of
the piston, which depends on the position of the crankshaft. The movement of
the intake and exhaust valves, on the other hand, is caused by the rotation of
the camshaft, which is driven by the engine's crankshaft.
The timing system must also provide a refrigerant flow
field to maintain proper flow rates. The flow field depends on the dimensions
of the valve seat, valve plug and valve stem and changes its value with the
valve lift. The lift and diameter of the intake valves are increased to improve
cylinder filling. It should be noted, however, that valves with a smaller
diameter deform less and remain tight for longer [6, 13, 15, 25, 36].
Exhaust valves are particularly exposed to harsh working
conditions, as they have to operate at temperatures of up to 700oC.
The valve plug is the most heat-loaded. Cyclically, heat is removed therefrom
through the valve face to the seat and head when the valve is closed and
continuously through the valve stem and guide. The intake valves operate under
much milder conditions.
During
the long-term use of an engine, one of the basic operating factors negatively
affecting its operation by changing the conditions of heat exchange in the
elements surrounding the combustion chamber is carbon deposit (Figure 1).
The process of carbon deposit formation is influenced by many factors, which
include, among others [6, 13, 15, 25, 36]:
·
incomplete combustion of too heavy fuel,
·
presence of asphalt and resin substances in the
fuel,
·
presence of unsaturated hydrocarbons and sulfur
compounds,
·
the content of mineral impurities that create
ash during the combustion process,
·
combustion of
engine oil due to leakage in the cylinder space.
Fig. 1. Examples of valve damage
resulting from carbon deposits [14]
Exemplary results of numerical calculations of
temperature distributions, temperature gradients and stresses in the exhaust
valve of the internal combustion engine can be found in [14, 16, 19].
The valves must be characterized by [6, 13, 15, 25, 36]:
·
good heat conductivity,
·
resistance to work in impact conditions,
·
corrosion resistance,
·
abrasion
resistance.
The automotive industry literature [6, 13, 15, 25, 36] provides the following as causes of valve failures:
·
thermal or mechanical overloads,
o
plastic deformation of the valve head,
o
changes in the material structure of valves,
o
thermal corrosion of the hollow valves,
o
corrosion pitting on valve faces,
o
surface cracks,
o
break off of the valve stem,
o
burnout of
the hollow valves.
·
disruptions in the operation of the valve drive
system,
o
failure of the camshaft drive,
o
defective valve stem mounting,
o
eccentric thrust of the rocker arm,
o
too tight valve guide,
o
valve guide too loose,
o
no rotation of the valve during operation,
o
too
intense valve rotation.
·
errors in closing the valves,
o
too large valve clearance,
o
too small valve clearance,
o
deformation of
the valve seat.
·
incorrect
selection of valve material.
·
faulty assembly of valves,
o
misalignment of seat and valve guide,
o
wrong valve clearance,
o
valve
marking.
·
construction defects,
o
defective shape of the valve disc,
o
defective
shape of the valve stem foot.
·
defects in workmanship,
o
overheating during forging,
o
the disadvantages of stelliting,
o
the disadvantages of heat treatment,
o
the disadvantages of chrome plating,
o
the defects of hardening the valve's foot,
o
faulty
fiber path.
·
material defects,
o
inclusions and contamination of the material,
o
surface defects,
o
defects in
the structure of the material.
The most common cause of valve failure is [6, 13, 15, 25, 36]:
·
heat or mechanical overload: 38%,
·
workmanship defects: 22%,
·
timing system failures: 10%,
·
material defects: 9%,
·
defective assembly and operation: 8%,
·
structural defects: 7%,
·
other:
6%.
To prevent valve damage, the instructions for auto
mechanics give the following guidelines [6, 13, 15, 25, 36]:
·
valve clearance must be precisely set,
·
control times must be precisely set,
·
after replacing the toothed belt or the chain,
the tensioner should also be replaced,
·
after machining the cylinder head, check the
return position of the valves,
·
the valve spring must be properly seated during
installation,
·
new washers for valve seats should be used,
·
new locks of the valve spring should be used,
·
the valve guide and the valve face must be
parallel,
·
only parts specified by the manufacturer should
be used,
·
when
installing the engine, all foreign bodies must be removed from the combustion
chamber and the fuel supply system.
3. BASICS OF BAYESIAN
CLASSIFIER OPERATION
In
technical diagnostics systems, statistical methods are included in the group of
possible to use pattern classification methods [8, 21, 26, 37, 41]. In this research, the possibility of using one of such
methods – the Bayes classifier, was checked. The operation of the Bayes
classifier is based on the Bayes theorem [2-4, 12, 30, 35].
According
to the theory of probability:
where:
Transforming
(1) and (2), we get:
Hence:
Formula
(5) is called the Bayes rule.
At
the same time, the total probability is:
Assuming
that Y represents a given class, and X is a set of data attributes defining
the selected class, depending on the number of classes and attributes, the
Bayesian rule can be written in the form:
·
for one class and one attribute:
·
where:
·
for N
classes and one attribute, the probability of the K class:
·
for N
classes and M attributes, the
probability of K class:
If
the independence of the attributes is assumed, formula (9) can be written as:
The
highest value of the probability of a specific class occurrence means that the
belonging of the input data described by the accepted X attributes belongs to that class.
4. DESCRIPTION OF THE RESEARCH EXPERIMENT
The
test object was a passenger car spark ignition internal combustion engine with
a capacity of 1,6 dm3.
This
research aims to develop a method for diagnosing damage to the exhaust valve of
an internal combustion engine based on vibration signals generated by the
engine.
In
this study, registered signals for accelerators of the engine head close to:
·
the intake valve of the first cylinder,
·
the outlet valve of the first cylinder,
·
the outlet valve of the fourth cylinder,
·
the
gearbox.
The
measurements were made on a car dynamometer at various driving speeds.
Vibration signals were recorded for:
·
third gear,
·
fourth gear,
·
fifth gear,
at
engine rotational speeds of:
·
2000 rpm,
·
3000 rpm,
·
4000 rpm.
In
the experiments for registration of vibration signals, a multi-channel National
Instruments registration equipment was used. The recorder allowed for
synchronous sampling at a frequency of 50 kHz. PCB Piezotronics Accelerating
Transducers were used in the measurements. An application developed in the
LabView environment was used to control the data acquisition system.
During
the conducted tests, the vibration signals of the efficient internal combustion
engine and engine with a damaged outlet valve were recorded. Damage to the
outlet valve was made up by performing the incision of its valve climb (Figure
2).
Fig.
2. Modeled damage to the spark ignition engine exhaust valve
Examples
of recorded vibration signals of an efficient and damaged internal combustion
engine of a passenger car are shown in Figure 3.
The
recorded vibration signal was processed with the use of a discrete wavelet
transform (DWT) [21, 24]. Signal
analysis selected for these experiments can be defined as:
where:
The
result of the analysis is to obtain a multi-level signal decomposition x(t) for high-frequency dj(t) and low-frequency
components aj(t):
Fig. 3.
Vibration signal of the engine without damage (left)
and with a damaged exhaust valve of the combustion engine (right)
The
occurring changes in the vibration waveforms in the decomposed approximation
and detail signals were described by the entropy of the signal:
For
the construction of the patterns, the number of decomposition levels and the
type of the base wavelet also had to be assumed. The usefulness of 52 base
wavelets and 10 levels of decomposition were checked in this research. Wavelets
from the following family were used:
·
haar,
·
daubechies,
·
biorthogonal,
·
coiflets,
·
symlets,
·
reverse biorthogonal,
·
discrete
Meyer.
Depending
on the assumed number of decomposition levels, the size of the pattern was from
two for 1 decomposition level to eleven for 10 decomposition levels. The
experiments were checked for the impact that the correctness of the diagnostic
classification has on the size of the pattern used.
The
diagnostic classification consisted in determining whether the vibration signal
was registered for the internal combustion engine in good technical condition
and the internal combustion engine with damage in the timing system.
The
Bayes classifiers were constructed with the use of patterns created for 10
variants of the pattern size, and each variant was checked for 52 base
wavelets.
According
to the assumptions made during this research, in equation (10), the number of
attributes is from 2 to 11 (X1,X2
or X1,X2,X3
or ... or X1,X2,X3,…,X11),
while the number of classes is 2 (Y1
or Y2).
In
conducting this research, 400 different sets of teaching and testing patterns
were used. Two hundred examples were used to learn the diagnostic models. The examples
included 100 patterns for each of the recognized classes. The same number of
patterns was used in the process of testing the diagnostic models.
An
example of the distribution of data used in the process of learning and testing
the diagnostic models is shown in Figure 4.
Fig. 4.
Sample distribution of data used in the learning process (left)
and testing (right)
In
the conducted tests, the correctness of the operation of the diagnostic models
using vibration signals registered in various measurement locations and for
various operating conditions, as well as patterns obtained with different
base wavelets at a different number of decomposition levels of vibration
signals, were checked.
5. RESULTS OF RESEARCH
EXPERIMENT
During
the experiment, the operation of classifiers using patterns derived from
vibration signals recorded in a specific place (4 measuring points: 1st
cylinder exhaust valve, 1st cylinder inlet valve, 4th
cylinder outlet valve, gearbox) was checked for an engine operating at a
specific gear (3 gears), and at a fixed speed (3 speeds).
The
influence of the selection of the wavelet on the correctness of the pattern
classification in the testing process, depending on the place of vibration
signal registration, is shown in Figures
5 and 6.
The
figures show the distribution of the number of cases for which the classifiers
were characterized by the minimum testing error value using a given base
wavelet (regardless of the selected gear – 3 gears, engine
rotational speed – 3 speeds, pattern size – 10 variants of
decomposition level). The best base wavelet would have several cases equal to 90. However, such a situation did
not occur in the experiment.
When
analyzing the presented results, it can be noticed that regardless of the
selected place of vibration signal registration, the best wavelet used in the
pattern building process is
the discrete Meyer wavelet.
Furthermore, the presented
figures also show that the best measurement place among the tested during the experiment was the area of the
exhaust valve of the 1st cylinder. This may be because the measurement, in this case, was carried out closest to the
place where the simulated failure occurred.
Fig.
5. Influence of the selection of the wavelet on the correctness of the
classification for the patterns obtained from the signals recorded in the
vicinity of the outlet valve of the 1st cylinder (left) and the 4th
cylinder (right)
Fig.
6. Influence of the selection of the wavelet on the correctness of the
classification for the patterns obtained from the signals recorded in the
vicinity of the inlet valve of the 1st cylinder (left) and gearbox
(right)
Interestingly,
similar results were obtained during the research on the detection of damage to
the gasket under the head of a spark ignition internal combustion engine, as presented in [5].
Figure
7 shows the influence of the selection of the wavelet on the correct
classification of the pattern in the testing process, regardless of the place
of vibration signal registration.
The
best base wavelet would have several
cases equal to 360. Such a situation did not occur in the experiment. Consequently, the best
wavelet was the discrete Meyer wavelet.
Figures
8 and 9 show an exemplary influence of the pattern size, that is, the selected number of
decomposition levels, on the correctness of the classification result.
In
the case of the Bayes classifier models, which were characterized by a greater
error, it was possible to notice a tendency of the test error to decrease
with the increase of the pattern size, that is, the selected number of decomposition levels. For
variants of models with low values of test errors, it is not possible to
unequivocally determine the influence of the pattern size on the obtained
result. A summary of the best results obtained is shown in Table 1.
Fig.
7. Influence of the selection of the wavelet on the correctness of the
classification, regardless of the place where the vibration signal is measured
Fig.
8. An example of the impact of the selection of the number of decomposition
levels on the classification result for the patterns obtained from the signals
recorded in the vicinity of the exhaust valve of the 1st cylinder
(left) and 4th cylinder (right)
Fig.
9. An example of the impact of the selection of the number of decomposition
levels on the classification result for the patterns obtained from the signals
recorded around the inlet valve of the 1st cylinder (left) and the
gearbox (right)
Also,
in this case, the obtained results are consistent with those presented in [5]
and concerning the diagnosis of the occurrence of damage to the gasket under
the head of a spark ignition car internal combustion engine.
Tab.
1.
Summary
of the best obtained results
|
No. |
Measurement location |
Gear no. [-] |
Engine rotational speed
[rpm] |
Test error [%] |
|
1 |
Intake valve of the 1st cylinder |
3 |
2000 |
0,5 |
|
2 |
Intake valve of the 1st cylinder |
3 |
3000 |
0 |
|
3 |
Intake valve of the 1st cylinder |
3 |
4000 |
6 |
|
4 |
Intake valve of the 1st cylinder |
4 |
2000 |
3 |
|
5 |
Intake valve of the 1st cylinder |
4 |
3000 |
4 |
|
6 |
Intake valve of the 1st cylinder |
4 |
4000 |
1,5 |
|
7 |
Intake valve of the 1st cylinder |
5 |
2000 |
8,5 |
|
8 |
Intake valve of the 1st cylinder |
5 |
3000 |
0 |
|
9 |
Intake valve of the 1st cylinder |
5 |
4000 |
0 |
|
|
Outlet valve of the 1st cylinder |
3 |
2000 |
0,5 |
|
|
Outlet valve of the 1st cylinder |
3 |
3000 |
0 |
|
|
Outlet valve of the 1st cylinder |
3 |
4000 |
1 |
|
|
Outlet valve of the 1st cylinder |
4 |
2000 |
0 |
|
|
Outlet valve of the 1st cylinder |
4 |
3000 |
1 |
|
|
Outlet valve of the 1st cylinder |
4 |
4000 |
0 |
|
|
Outlet valve of the 1st cylinder |
5 |
2000 |
0 |
|
|
Outlet valve of the 1st cylinder |
5 |
3000 |
0,5 |
|
|
Outlet valve of the 1st cylinder |
5 |
4000 |
0 |
|
|
Outlet valve of the 4th cylinder |
3 |
2000 |
0 |
|
|
Outlet valve of the 4th cylinder |
3 |
3000 |
0 |
|
|
Outlet valve of the 4th cylinder |
3 |
4000 |
2 |
|
|
Outlet valve of the 4th cylinder |
4 |
2000 |
16 |
|
|
Outlet valve of the 4th cylinder |
4 |
3000 |
6 |
|
|
Outlet valve of the 4th cylinder |
4 |
4000 |
7 |
|
|
Outlet valve of the 4th cylinder |
5 |
2000 |
6 |
|
|
Outlet valve of the 4th cylinder |
5 |
3000 |
3 |
|
|
Outlet valve of the 4th cylinder |
5 |
4000 |
4,5 |
|
|
Gearbox |
3 |
2000 |
0,5 |
|
|
Gearbox |
3 |
3000 |
0 |
|
|
Gearbox |
3 |
4000 |
2 |
|
|
Gearbox |
4 |
2000 |
5 |
|
|
Gearbox |
4 |
3000 |
9,5 |
|
|
Gearbox |
4 |
4000 |
6,5 |
|
|
Gearbox |
5 |
2000 |
14 |
|
|
Gearbox |
5 |
3000 |
7 |
|
|
Gearbox |
5 |
4000 |
1 |
The
conducted experiments allowed to confirm the usefulness of Bayes classifiers in
the diagnostic process of the technical condition of the spark ignition
engine timing system. Following
the conducted experiments, faultless or almost flawlessly operating Bayes
classifiers were built.
6.
CONCLUSIONS
During their operation,
all technical objects are a source of vibrations and noise. One should be aware
that the generation of the vibroacoustic phenomena by operating technical objects is
not synonymous with their poor technical condition. A certain level will always
be present and must be considered as the nominal one. Only the difference
between the model of a machine that is working properly or in good technical
condition, and the actual case that occurs, will indicate possible damage to
the elements.
Difficulties in using
vibroacoustic signals for diagnostic purposes, among other things, are the
result that they are generated simultaneously in various parts of a working machine. There
are many different generation sources of vibroacoustic processes in internal
combustion engines. The consequence of this is the high complexity of the
resultant signal used for diagnostic purposes.
To use vibroacoustic signals
to diagnose the state of a technical object, they must be appropriately
processed in advance in the domain of time, frequency or both time and
frequency. The purpose of signal processing is to obtain estimates that are
highly correlated with the monitored phenomenon.
One of the methods used to
pre-process vibroacoustic signals is the wavelet analysis. Wavelet analysis is
one of the methods usually used in vibroacoustic diagnostics
today. It enables
the linear decomposition of the examined vibroacoustic signal using any basis
function with a finite and short range, in which it takes values other
than zero. A properly selected wavelet allows isolating the proper signal from
random disturbances. Such disturbances after transformation are represented by
coefficients with small values. Such coefficients are removed from the
distribution by a threshold function. A properly selected wavelet is understood
as a wavelet that is consistent with the character of the tested signal.
The greatest advantage of
wavelet analysis is the ability to freely define the parameters of the analysis. This is
accomplished by selecting the base wavelet and the scale range.
In the conducted
experiments, the discrete wavelet transform (DWT) was used as a method of
pre-processing the recorded vibroacoustic signals. The character of changes in
the vibroacoustic
signals was described using the entropy of approximation and the
details of
the vibration signal. Patterns developed in this way were used to build a
technical condition classifier of a spark ignition engine timing system.
The possibility of using Bayesian classifiers to diagnose the occurrence of
damage was tested. The exhaust valve crack was modeled in the tests as
an undesirable condition. During the tests, the influence of the selection
of the place of vibration measurement, the operating conditions of the working
internal combustion engine, and the type of base wavelet used in the pattern
construction process were checked.
The results obtained in this research confirm the
possibility of using Bayes classifiers to diagnose the technical condition
of the spark ignition engine timing system used in
passenger cars. Finally, based on this research, it was possible
to obtain flawlessly working Bayes classifiers.
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Received 09.02.2022; accepted in
revised form 11.04.2022
Scientific Journal of Silesian University of Technology. Series
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[1] Faculty of Transport and Aviation Engineering, The Silesian University of Technology, Krasinskiego 8 Street, 40-019 Katowice, Poland. Email: piotr.czech@polsl.pl. ORCID: https://orcid.org/0000-0002-0884-8765