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Diagnostic Method for 2-Stroke Cycle Diesel Engine 57
October 1999
Technical Papers
(3)
* Translated from Journal of MESJ Vol.33, No.10
(Manuscript received Dec. 15, 1997)
** Kobe University of Mercantile Marine (Kobe City)
*** Kobe Nippon Kisen Kaisha, Ltd. (Kobe City)**** Kawasaki Kisen Kaisha, Ltd. (Minato-ku Tokyo)
Diagnostic Method for 2-Stroke Cycle Diesel Engine*
by Measurement of Vibration on Cylinder-Jacket− Observation of Change in Normal Vibration Pattern− Ryuichi Kimura**, Wataru Terashima**, Noboru Nakai**,
Tetsuo Yamada***, Shou Takeda****
It is necessary to arrange the system to monitor the operational condition by various methods to achieve the safe
operation of the engine. Based on the idea that the information on the engine condition can be obtained from its
vibration signal, this paper carries out the experiment of the diesel engine of the actual ship. The vibration was
measured for a long time (7800 hours) by means of a vibration sensor on the cylinder jacket. The hand touch cannot recognize the time change of the vibration, but the three-dimensional expression of the vibration data through
the frequency analysis allows the good understanding of the change of the vibration. The vibration is always
changing if the vibration is observed on the long running hours of engine basis even in the stationary operation
(engine revolution: 103 rpm) of the diesel engine. We executed the statistical analysis as one method to estimate the
condition of engine by the information from the vibration.
All the data of vibration was recorded on a normal engine condition, as a result we could not examine on an
abnormal engine condition. Thus, the vibration data of low engine revolution (30 rpm) was used as the data of
abnormal condition in this analysis. As the result of the analysis, it is found that the abnormal can be recognized from
the above-mentioned engine condition. We succeeded to make the statistical model which can diagnose an engine
condition.
1. Introduction
The reliability of the main engine must be ex-
tremely high in order to ensure the safe navigation of
ships. It is thus necessary to locate the phenomena of
inconveniences and troubles even when they are small
and insignificant, and to pinpoint the causes and take
countermeasures therefor. We have known empirically
that the abnormal vibration and the abnormal sound
generated in a main engine are the symptom of possible
failures or accidents. It is understood from these fact-
findings that much information to indicate the state of
the engine is contained in the radiant noise and the
vibration of the engine. From such a viewpoint, the
paper has aimed at the construction1),2) of the monitor-
ing system capable of grasping the condition of the
engine by positively using these information.
In any equipment including marine diesel en-
gines, deterioration and abrasion are surely generated
in each part. The phenomena gradually increased in the
elapse of the running time, and eventually, leading tofailures or accidents. In order to prevent these failures
or accidents beforehand, it is necessary to grasp the
information related thereto from various angles.
In this experiment, the vibration of the side wall
part of the low-speed diesel engine was recorded for a
long time, and the condition that the vibration is changed
as the running time was examined. Firstly, the recorded
vibration was frequency-analyzed to store the data on
the vibration to construct the diagnosis system. The
analysis method of the running condition introduced
here includes the visual judgment, which grasps the
motion of the engine based on the information by
indicating the data of the radiant noise in a three-
dimensional manner. The statistical analysis is then
achieved in an objective manner based on the data
information, in addition to the visual judgment, the
results were evaluated and examined, and the diagnos-
tic system capable of coping with the phenomenon to be
changed with the time, was also considered.
2. Experiments
Two-stroke cycle diesel engine mounted on a carcarrier (19,000 dwt) was used as a test engine in this
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Bulletin of the M.E.S.J., Vol. 27, No.2
58 Diagnostic Method for 2-Stroke Cycle Diesel Engine
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study. The specification of this engine is 8-cylinder and
16,320 kW in output. The data collection was started
immediately after the manufacture of the engine, and
the data obtained in one and a half years after the ship
went into service (the running time of the engine : 7800
hours). Fig. 1 is a section of the engine, a vibration
sensor is mounted on the part indicated by an arrow in
the figure, and the radiant sound was recorded at the
position away from the vibration sensor mounting
position by 5 cm in the vertical direction. And, at the
same time, the synchronous pulse signal to measure thesynchronization of the data on the vibration and the
radiant sound with the rotation of the engine was also
taped. The above-mentioned sensor was mounted on
No. 1 cylinder, and the cylinder was subjected to the
examination. The collected data on the vibration and
radiant sound was frequency-analyzed by an FFT ana-
lyzer. More specifically, the time of one cycle was
divided into 120 sections, and frequency-analyzed in
the measurement range of 20 kHz.
The time relationship between the synchronous
pulse signal generated for each cycle of the engine and
the opening/closing condition of each cylinder valve is
shown in the valve timing in Fig. 2. The figures at the
left end show the number of each cylinder, and the
completely black-covered parts E.V. on each line show
the opening condition of the exhaust valve. The ignition
order of the cylinders is 1-8-3-4-7-2-5-6.
3. Three-dimensional indication of soundlevel and vibration level
Figs. 3 to 6 show the spectrum of the radiant sound
and the vibration in the shop trial run of the engine in a
three-dimensional manner. Here, the spectrum imme-
diately after the manufacture of the engine is examined,and its temporal transition is also evaluated and exam-
ined. On the basis of the data of one cycle of the engine
(1 rotation of the crank shaft) obtained through the
frequency analysis, the three-dimensional figures of
the sound pressure level and the vibration level in the
light-and-shade pattern with the frequency (100-20
kHz) on the Y-axis and with the crank shaft angle (0-
360°) on the X-axis, the figure of the valve timing is
also indicated on the upper part of the three-dimen-
sional figure to explain both the behaviors of the piston
and the valve of each cylinder and the temporal change
in the three-dimensional figure. The scale of the soundpressure level or the vibration level is indicated in the
pattern below the three-dimensional figure.
The three-dimensional figures of the radiant sound
and the vibration in three hours after the shop trial run
was started, are shown in Fig. 3 and Fig. 4, respectively.
The result (Fig. 3) of the radiant sound shows thick lines
in the Y-axis direction in the ranges of A (0-40°), B (80-
120°), and C (210-250°). When reviewed together with
the figure of the valve timing above, it is proved that
these agree with that combustion in No. 1, No. 3 and
No. 2 cylinders. There fore, it is concluded that they are
attributable to the combustion. On the other hand, when
reviewed from the result (Fig. 4) of the vibration, a
Fig. 2 Valve timing
Fig. 1 Test engine
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Diagnostic Method for 2-Stroke Cycle Diesel Engine 59
October 1999 (5)
completely different pattern is shown from that in Fig.
3. It is characterized in that the distribution of high level
values is present at 2, 4, 6, 8, 10, 12 and 14 kHz around
Point a (70°), Point b (160°) and Point c (295°). The
level change is characteristic, showing the bow-shaped
pattern which is symmetrical in the right-to-left direc-
tion around three crank angles. The bow-shaped pattern
is considered to be generated by the sliding of the piston
moving vertically with the cylinder liner wall. That is,
because the source of generation of the vibration passes
in the vicinity of the installation place of the sensor, the
change in the vibration appears as the change in the
frequency between in the approaching time and after
the passing. From this finding, the position of threecrank angles at the center of the pattern show the timing
when the piston passes the measurement point, and
from the figure of the valve timing, three points (a, b,
and c) indicates the passing timing of the piston of No.
1 cylinder is moved from the top dead center to the
bottom dead center, the passing timing of the piston of
No. 2 cylinder is moved from B.D.C to T.D.C. and the
passing timing of the piston of No.1 cylinder is moved
from B.D.C. to T.D.C.. In the same figure, light and
shade lines indicating the high level similar to that in
Fig. 3 can be seen in the ranges of the crank angles A,
B and C. These lines can be concluded to be thevibration attributable to the combustion of No. 1, No. 3
Fig. 4 Three-dimensional figure of vibration
(3 hours)
Fig. 3 Three-dimensional figure of radiant sound
(3 hours)
and No. 2 cylinders. When Fig. 3 is again compared
with Fig. 4, the change in the frequency can also be seen
at Points a, b and c similar to Fig. 4. This change does
not show a bow-shaped pattern as clear as that in the
vibration (Fig. 4), but shows that the sound by the piston
slide is indicated in a bow-shaped pattern. Figs. 5 and
6 are the three-dimensional figures indicating the radi-
ant sound and the vibration in ten hours after the shop
trial run was started. In Fig. 5 of the radiant sound, the
sound in the combustion appears in the ranges of A, B,
and C similar to Figs. 3 and 4. However, any bow-
shaped pattern attributable to the piston slide con-
firmed in Fig. 3 can hardly be confirmed. On the other
hand, in Fig. 6 to indicate the vibration, the vibrationcaused by the combustion appears in the ranges of A, B
and C, and the characteristic bow-shaped pattern attrib-
utable to the piston motion can be confirmed at 3 points
of a, b and c. However, compared with Fig. 4, the
vibration level is dropped by about 10 dB.
These four three-dimensional figures show that
the data on the radiant sound and the vibration in 3
hours and in 10 hours after the shop trial run was started,
is respectively changed. In particular, in the three-
dimensional figure of the radiant sound, the bow-
shaped pattern is almost in-recognizable in only 10
hours after the engine was started. It can be concludedto be difficult from the above-mentioned the radiant
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Bulletin of the M.E.S.J., Vol. 27, No.2
60 Diagnostic Method for 2-Stroke Cycle Diesel Engine
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Fig. 5 Three-dimensional figure of radiant sound
(10 hours)
Fig. 6 Three-dimensional figure of vibration
(10 hours)
sound results to detect the information by the slide. On
the other hand, regarding the vibration, the pattern to
indicate the slide of the piston is clearly shown, and it
may be said that the vibration is the source of informa-
tion suitable for understanding the slide condition of
the piston ring, etc. Accordingly, it is decided to exam-
ine the information on the vibration among the two
shown above in this study.
The change in the spectrum of the radiant sound
and the vibration in a short time was shown above, and
it was examined how the spectrum term changes if the
running time is further increased. The below-men-
tioned results are those obtained during the service after
the engine was mounted on the test ship. The dataimmediately after the engine was mounted to the data
in approximately one year and 6 months layer, were
used for the analysis. Here, the result after 190 hours,
2300 hours, and 6000 hours are shown in Figs. 7, 8 and
9. As mentioned above, these are the three-dimensional
figures of the vibration. In the result of Fig. 7, the
vibration by the slide is observed at Points a, b, and c
similar to the results of Figs. 4 and 6. However, the
condition was slightly changed in Figs. 8 and 9. For
example, a high level pattern generated in the range of
70-160° and 250-290° in crank angle of in Fig. 7, (a
band-like pattern of not less than 90dB generated overthe whole frequency band) is not present as the band-
like pattern in Fig. 8 where 2300 hours are elapsed.
Besides, the level is not more than 60 dB in the higher
frequency band (over 15 kHz), which is not indicated
by the pattern of the figure. This trend is intensified
with the time, and in Fig. 9 where 6000 hours are
elapsed, the pattern of not more than 60 dB (a white
pattern) is spread close to 10 kHz in a part of crank
angles in Fig. 9. The bow-shaped pattern by the slide
shows the trend that the level is dropped as the time is
elapsed through it is slight. For example, in Fig. 7, the
bow-shaped patterns distributed over higher frequency
bands (of not less than 15 kHz) are continuous at the
level of approximately 100 dB or over. However, in
Fig. 9, the bow-shaped pattern is reduced in size, andonly a part thereof is shown as dots.
As mentioned above, it is observed that the vibra-
tion level is changed by and by as the time is elapsed.
However, the data is for the normal running condition
of the engine, and does not indicate that the engine is in
the abnormal condition. In other words, even in the
normal running condition, the secular change always
works on the engine, and the degree of indication of the
secular change is shown in Figs. 7 to 9. Though the
factor is natural, the running time of the engine surely
affects each member of the engine, and the effect of the
abrasion, etc., is indicated more clearly. For the studyaiming at the construction of the abnormality monitor-
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Diagnostic Method for 2-Stroke Cycle Diesel Engine 61
October 1999 (7)
ing system using the vibration, it is one of the important
objects to elucidate the regularity of the vibration
which is changed with the running time of the engine.
If the regularity can be understood, generation of an
abnormality in the changing normal pattern can be
understood. From the above-mentioned viewpoint, in
the following chapter, the event is examined by apply-
ing the statistical analysis.
4. Data analysis
In order to grasp a normal condition and an abnor-
mal condition of an engine from the pattern of the
vibration data to be changed with the service time of theengine, the relationship between the running time of the
engine and the vibration must be examined. Thus, the
possibility of explaining the relationship using the
multiple regression analysis was considered. The mul-
tiple regression analysis is a technique to explain the
dependent variables by explanatory variables of
multivariates, and in this study, the multiple regression
equation was obtained with the value of the vibration
data obtained through the frequency analysis as the
explanatory variable, and with the running time of the
engine as the dependent variable. In preparing the
above-mentioned three-dimensional figures, the re-quired number of the variables is 24000 in total, be-
Fig. 7 Three-dimensional figure of vibration
(190 hours)
Fig. 8 Three-dimensional figure of vibration(2300 hours)
Fig. 9 Three-dimensional figure of vibration
(6000 hours)
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Bulletin of the M.E.S.J., Vol. 27, No.2
62 Diagnostic Method for 2-Stroke Cycle Diesel Engine
cause one cycle is composed of 120 sections and one
section is composed of 200 variables. The multivariate
analysis with using all variables is doubtful from both
the calculation time and the expected effect, and in this
study, it is decided to extract the data on the crank angle
capable of sufficiently explaining the above-mentionedrelationship from one cycle of the engine. As described
before, the bow-shaped vibration pattern is character-
istic and clearly changed with the running time of the
engine, the data in the vicinity of the crank angle is
examined. More specifically, the bow-shaped pattern
(the slide vibration of No. 1 cylinder) is generated
twice, i.e., when the piston is lowered and when the
piston is elevated, and the data at the bow-shaped top
point when the piston is lowered at the crank angle of
72° was adopted. At this angle, when 200 variables
obtained in one frequency analysis are referred to as the
data of one case, one case is constituted by allotting thespectrum values at 100 Hz, 200 Hz, ...., 20 kHz to the
explanatory variables of x1, x2, ..., x200. 85 cases of the
data under the same condition were prepared in the
analysis, and 22 groups data were prepared for each
different running time of the engine. When the ob-
served value is explained using a plurality of variables
x1, x2, ..., xp, the expected value of y is expressed by p
variables as follows.
E [y] = β0+β1 x1+β2 x2+………+β p x p (1)
The probability fluctuation part ε is added thereto,
and the observed value leads to as follows.
y = β0+β1 x1+β2 x2+………+β p x p+ε (2)
The equation (2) is the multiple regression equa-
tion of y to x1, x2, ..., xp, and the data is expressed as
indicated in Table 1.
The dependent variable of y is the running time
(runh) of the engine , and ε is the remainder of the
estimated value subtracted from the observed value. Inthis case, the multiple regression model and the re-
mainder are expressed by (3) and (4), respectively.
runh j = β0+β1 x1, j+β2 x2, j+……+βp xp, j+ε j (3)
where, (j= 1, 2,...., N), N: total case number
ε j = runh j- (β0+β1 x1, j+β2 x2, j+……+βp xp, j) (4)
The multiple regress analysis is the analytical
technique to obtain the estimated values b0, b1, b2, ....,
bp of β1, β2, ..., βp so that the sum of squares of theremainder is minimum, and the multiple regression
equation can be obtained as (5) below.
runh j = b0+b1 x1, j+b2 x2, j+……+bp xp, j (5)
The multiple correlation coefficient of the mul-
tiple regression equation obtained above is R =0.935,
and the decision coefficient R2 =0.873. It is indicated
that the multiple regression equation obtained from this
result applies well. The multiple correlation coefficient
is the result using 200 variables, but it can not be always
concluded that the analysis is achieved with only the
variables affecting the dependent variables among 200
explanatory variables. Thus, to select the variables to
be used for the analysis, the stepwise method is used.
The analysis is achieved with the input probability of
0.05 and the removal probability of 0.1 as for the
significant probability of the F-value in inputting or
removing the explanatory variables in/from the mul-
tiple regression equation, and 60 variables are finally
obtained. As a result of the analysis using the variables,
the multiple correlation coefficient R=0.928, and the
coefficient of decision R2=0.861. The rest of 140 vari-
ables except the selected 60 variables less affect the
dependent variables, and it can be concluded that 140
variable may be excepted.The average processing of the cases is taken in
order to decrease the noise component contained in the
data when the dependent variables are calculated using
the obtained multiple regression equation. Fig. 10 is the
figure to indicate the relationship between the average
number and the error. As shown in the figure, there is
not linear relationship between the average number and
the error, and the error time is rapidly reduced in the
range between 1 and 20, and then, gradually decreased.
As shown in the result, the error is 330 at the average
number of 100, and further reduction of the error can
not be expected. In this study, it is desired to reduce theerror as much as possible in obtaining the estimated
Table 1 Data constitution
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Diagnostic Method for 2-Stroke Cycle Diesel Engine 63
October 1999 (9)
value from the regression equation, but it is also neces-
sary to select an appropriate average number when
taking into consideration the calculation time. The
average number where the error is approximately 400
hours was adopted here.
Fig. 11 is a scatter diagram between the observed
value and the estimated value using the data of 30
addition-averages. The estimated value at each time of
observation is plotted with the mark with the esti-
mated value on the Y-axis (the estimated running time)
and the observed value (the observed running time) on
the X-axis. In the figure, the linear relationship between
the observed value and the estimated value is strong,and the accuracy of estimation is excellent, and it is
found that the obtained multiple regression equation
agrees well. The previously obtained multiple correla-
tion coefficient R of the model is 0.928, also indicating
the strong correlation from the numerical viewpoint. In
reality, the estimated value is distributed around the
regression line with the mean error of approximately
400 hours at any time of observation. Taking the above-
mentioned points into consideration, the multiple re-
gression model obtained in this chapter estimates the
running time of the engine in a transition mode under a
normal running condition from the vibration data of the
engine. That means, the multiple regression modelexplains the regularity of the vibration data to be
changed together with the running time of the engine
under the normal condition of the engine, and the
running time corresponding to the inputted vibration
data can be estimated thereby. However, if the engine
is not in a normal condition, an appropriate running
time can not be estimated. Because the normal model in
a transition mode is prepared, it can be understood
whether or not the running condition is normal when
the vibration data obtained at the engine side is ob-
tained.
As the test ship is engaged in an actual service, no
abnormality can be artificially generated. In this ex-
periment, no abnormalities were generated in the
engine, and no extraction of abnormalities of the engine
could be detected. Thus, in this experiment, an exami-
nation was made what result is obtained in the esti-
mated value in a different running condition from the
normal one by inputting the vibration data of the engine
at the engine speed of 30 rpm which is different from
the normal engine speed of 103 rpm. The vibration data
at different engine speed is the one where the running
condition of the engine is changed, and the engine is notin any abnormal condition, but from the viewpoint that
the vibration data is different from the normal one, it
was regarded as the abnormal condition. Fig. 12 is a
scatter diagram between the observed value and the
estimated value where the estimated value of the above-
mentioned data (hereinafter, referred to as abnormal
data) is plotted with (one sample at the lower left in
the figure), and the estimated value of the normal data
used in Fig. 11 are plotted with marks. As clearly
shown in the figure, the estimated value of the abnor-
mal data is estimated at the different position from that
of the group of the estimated value of the normal data.The estimated value of the running time of the engine
of the abnormal data was 1085 hours, and the error hour
from the observed value was 1831 hours. Based on the
negative estimated value, and the large error time, it can
be diagnosed that the abnormal data shows the running
condition different from the normal running condition.
Based on the fact that even a slightest change in the
running condition can be detected by the above-men-
tioned method, it is thus considered that a serious
abnormality can be sufficiently detected by the present
diagnostic method when it is generated in an actual
engine. This point will further be clarified through theanalysis of the changing data as the proceeds.
Fig. 11 Scatter diagram of observed value andestimated value
Fig. 10 Average Processing
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Bulletin of the M.E.S.J., Vol. 27, No.2
64 Diagnostic Method for 2-Stroke Cycle Diesel Engine
Conclusion
Much information is included in the vibration
generated in one cycle of the engine, the vibration of the
side wall of the 2-cycle diesel engine for marine use was
obtained for a long time, and its characteristic was
examined, and also, it was examined how it was changed.
The radiant sound and the vibration in one cycle were
frequency-analyzed, and the sound and the vibration
attributable to the combustion and the slide of the
engine were clearly confirmed in a characteristic pat-
tern from the three-dimensional figure. In reviewing
the slide of the piston of the engine, it was judged from
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Fig. 12 Scatter diagram of observed value and
estimated value (normal and abnormal)
the pattern in the three-dimensional figure that the
information from the vibration directly propagated
from the engine body is more than that obtained from
the radiant sound. In this experiment, the information
from the vibration was used from the above-mentioned
reason, but it does not necessarily lead to that thediagnosis by the radiant sound is inferior. For example,
in a case of the extensive monitoring, the radiant sound
is more advantageous in the viewpoint of the simulta-
neous monitoring, and this point will also be examined.
The multivariate analysis was tried to examine the
relationship between the running time of the engine and
the change in the vibration. As a result, the normal
model for each engine running time could be prepared
by achieving the multiple regression analysis of the
vibration in a transition mode under the normal running
condition of the engine. In the example, the vibration
pattern under the normal condition is modeled, and thevibration pattern of the engine can be confirmed for the
running time, and it is possible to examine whether the
engine is in a normal running condition if the method is
advanced.
References
1) Kimura, Nakai & Kishimoto : Abnormal Sound
Detection by Neural Network in the Diesel En-
gine. Bulletin of the M.E.S.J.,Vol.26, No.1 (1998)
2) Kimura, Nakai & Mizutani : Diagnosis System of
Diesel Engine by Statistical Vibration Analysis.
Bulletin of the M.E.S.J., Vol.24, No.1 (1996)
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