Forecasting Piston Rod Seal Failure Based on Acoustic Emission Features in ARIMA Model

Abstract

Fluid leakage due to piston rod seal failure in hydraulic cylinders results in unscheduled maintenance, machine downtime and loss of productivity. Therefore, it is vital to understand the piston rod seal failure at initial stages. In literature, very few attempts have been made to implement forecasting techniques for piston rod seal failure in hydraulic cylinders using acoustic emission (AE) features. Therefore, in this study, we aim to forecast piston rod seal failure using AE features in the auto regressive integrated moving average (ARIMA) model. AE features like root mean square (RMS) and mean absolute percentage error (MAPE) were collected from run-to-failure (RTF) tests that were conducted on a hydraulic test rig. The hydraulic test rig replicates the piston rod movement and fluid leakage conditions similar to what is normally observed in hydraulic cylinders. To assess reliability of our study, two RTF tests were conducted at 15 mm/s and 25 mm/s rod speed each. The process of seal wear from unworn to worn state in the hydraulic test rig was accelerated by creating longitudinal scratches on the piston rod. An ARIMA model was developed based on the RMS features that were calculated from four RTF tests. The ARIMA model can forecast the RMS values ahead in time as long as the original series does not experience any large shifts in variance or deviates heavily from the normal increasing trend. The ARIMA model provided good accuracy in forecasting the seal failure in at least two of four RTF tests that were conducted. The ARIMA model that was fitted with 15 pre-samples was used to forecast 10 out of sequence samples, and it showed a maximum moving absolute percentage error (MAPE value) of 28.99 % and a minimum of 4.950 %. The forecasting technique based on ARIMA model and AE features proposed in this study lays a strong basis to be used in industries to schedule the seal change in hydraulic cylinders.

Full text

EUROPEAN CONFERENCE OF THE PROGNOSTICS AND HEALTH MANAGEMENT SOCIETY 2022
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Forecasting piston rod seal failure based on acoustic emission
features in ARIMA model
Jørgen. F. Pedersen1, Rune Schlanbusch2, Vignesh. V. Shanbhag3
1,2,3 Norwegian Research Centre, Energy & Technology Department, Jon Lilletuns Vei 9 H, 3. etg, 4879, Grimstad, Norway
jorgen.fone.pedersen@gmail.com
rusc@norceresearch.no
vigs@norceresearch.no
ABSTRACT
Fluid leakage due to piston rod seal failure in hydraulic
cylinders results in unscheduled maintenance, machine
downtime and loss of productivity. Therefore, it is vital to
understand the piston rod seal failure at initial stages. In
literature, very few attempts have been made to implement
forecasting techniques for piston rod seal failure in hydraulic
cylinders using acoustic emission (AE) features. Therefore,
in this study, we aim to forecast piston rod seal failure using
AE features in the auto regressive integrated moving average
(ARIMA) model. AE features like root mean square (RMS)
and mean absolute percentage error (MAPE) were collected
from run-to-failure (RTF) tests that were conducted on a
hydraulic test rig. The hydraulic test rig replicates the piston
rod movement and fluid leakage conditions similar to what is
normally observed in hydraulic cylinders. To assess
reliability of our study, two RTF tests were conducted at 15
mm/s and 25 mm/s rod speed each. The process of seal wear
from unworn to worn state in the hydraulic test rig was
accelerated by creating longitudinal scratches on the piston
rod. An ARIMA model was developed based on the RMS
features that were calculated from four RTF tests. The
ARIMA model can forecast the RMS values ahead in time as
long as the original series does not experience any large shifts
in variance or deviates heavily from the normal increasing
trend. The ARIMA model provided good accuracy in
forecasting the seal failure in at least two of four RTF tests
that were conducted. The ARIMA model that was fitted with
15 pre-samples was used to forecast 10 out of sequence
samples, and it showed a maximum moving absolute
percentage error (MAPE value) of 28.99 % and a minimum
of 4.950 %. The forecasting technique based on ARIMA
model and AE features proposed in this study lays a strong
basis to be used in industries to schedule the seal change in
hydraulic cylinders.
KEYWORDS:
Hydraulic cylinder, Piston rod seal, Root mean square,
Variable speed condition, Auto-regressive integrated moving
average, Acoustic emission.
1. INTRODUCTION
A hydraulic cylinder is a linear actuator which is widely used
in material handling applications in oil and gas (O&G),
maritime, mining and construction industries. Based on the
material handling requirements: load handling and speed
condition of hydraulic cylinders frequently change. In most
applications, customized large hydraulic cylinders are used
by the industries where all the internal components are also
custom-made (See ref. (“Large Hydraulic Cylinder”)). Any
abrupt failure of a hydraulic cylinder component can cause
machine downtime, affect productivity, and increase
maintenance cost as most of the components in large
hydraulic cylinders are custom made and require several
weeks time of planning, manufacturing, and assembling the
part back into the hydraulic cylinder. Seal wear in hydraulic
cylinders can be because of particle contaminants present in
fluid or seal ageing and can cause instability during operation
(X. Zhao et al. 2015; Shanbhag et al. 2021b). Therefore, it is
important to continuously monitor and forecast the health of
crucial components such as the piston rod seals in the
hydraulic cylinders.
In recent years, acoustic emission sensors have been widely
used to monitor fluid leakage due to seal wear in hydraulic
cylinders. Acoustic emission (AE) sensors are preferred by
researchers because of their high frequency range (0.5-2.5
MHz) which make them suitable to use in noisy or harsh
environments, and they be used to simultaneously monitor
the health of multiple components in hydraulic cylinders. For
example, (Chen et al. 2007), monitored the health of seals in
water hydraulic cylinders using time domain (root mean
square (RMS) and count) and frequency domain (power
spectral density (PSD)) features. Fluid leakage (< 1.0 L/min)
due to seal wear could be monitored using energy-based
Jørgen. F. Pedersen et al. This is an open-access article distributed under
the terms of the Creative Commons Attribution 3.0 United States License,
which permits unrestricted use, distribution, and reproduction in any
medium, provided the original author and source are credited.
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features (e.g., RMS). A correlation could be observed
between fluid leakage rate and RMS. In the PSD plot, the
fluid leakage was dominant in the frequency range of 50-300
kHz with a peak at 120 kHz. In the other work of (Petersen et
al. 2005), monitored the health of the piston in a water
hydraulic system using AE and wavelet analysis. RMS, PSD,
and RMS of wavelet co-efficient were used to detect cracks
in the piston rod. Using time domain feature RMS, it was
possible to identify crack conditions in the piston rod.
Compared to PSD, RMS calculated from wavelet co-efficient
showed better separability between no-cracks and cracks in
the piston rod. (Shanbhag et al. 2020), monitored the health
of piston rod seals (unworn, semi-worn and worn conditions)
on a customized hydraulic test rig using AE time-domain and
frequency-domain features at different pressure conditions. It
was observed that, the mean-frequency feature showed a
good repeatability with sensitivity in identifying different
seal wear conditions in the hydraulic test rig. In another work,
(Shanbhag et al. 2021a) monitored the health of multiple
components (piston rod seals and bearing strips) in the
hydraulic test rig using AE time-domain and frequency-
domain features to the bandpass filtered AE signal. Here, the
unworn and worn bearing strips were monitored when
unworn, semi-worn and worn seals were used in the test rig.
The median-frequency features showed good repeatability in
identifying piston rod seal wear and bearing wear conditions
at different pressure and fluid leakage conditions. Also,
mean-frequency and median-frequency showed good
sensitivity in identifying fluid leakage due to piston rod seal
wear during RTF tests (17 hours). (Zhang et al. 2021)
monitored no leakage and different severities of fluid leakage
(small, medium, and severe) in a hydraulic cylinder using an
AE sensor. To classify the severity of fluid leakage, an
optimization deep belief network (DBN) combined with the
Complete Ensemble Empirical Model Decomposition with
Adaptive Noise (CEEMDAN) was used and classification
accuracy up to 93 % was achieved. (Pedersen et al. 2021),
performed run-to-failure tests at different pressure and speed
conditions on a hydraulic test rig to understand the AE
features that can be evaluated to determine fluid leakage
initiation. RMS features were proposed as potential condition
monitoring indicators to understand fluid leakage initiation.
The scaling factors based on sensor location and speed were
applied to the sampled RMS features to estimate the fluid
leakage threshold. From the literature, in the work performed
using AE to monitor seal wear, most of the work is focused
on condition monitoring (diagnostics) and very limited
attempts in forecasting the deterioration and seal failure
(prognostics).
The auto-regressive integrated moving average (ARIMA)
model is a time series forecasting technique that is widely
used in different applications such as disaster management,
business forecasting, and machine prognostics. The ARIMA
model can be used to understand the change in signal features
with spatial heterogeneity over time (Li et al. 2021). In
literature, the ARIMA technique has been applied using AE
features to predict a) energy change in gas-liquid two-phase
flow (N. Zhao et al. 2021), b) coal and gas outburst (Li et al.
2021). As the ARIMA technique has successfully been used
with the AE features for forecasting the process change or
failure of components, the ARIMA technique in this research
is used with AE features for forecasting the seal degradation.
In this paper, the AE data from our previous experimental
study conducted by (Pedersen et al. 2021) is used for
forecasting analysis.
2. METHODOLOGY
2.1. Hydraulic test rig and process parameters
In this study, experiments were conducted on a test rig
installed in an upright position (Figure 1) and was designed
to replicate the fluid leakage conditions of a hydraulic
cylinder. The test rig consists of three major items: a) test
arrangement (electromechanical cylinder with pressure
chamber), b) hydraulic system providing hydraulic power, c)
control box which controls and monitors the test rig. The
control box is connected to a laptop using an Ethernet cable
and the test rig is controlled using the Bosch Rexroth
software “IndraworksDs- 14.24.6”. A hydraulic power unit
(HPU) supplies pressure to the pressure chamber in the test
rig, which can be controlled using a pressure valve. The
pressure chamber is connected to an electromechanical
cylinder. The electromechanical cylinder consists of
servomotor, spindle, and piston rod. The electromechanical
cylinder uses a spindle and nut to convert rotational motion
to translational motion. The servomotor drives the spindle,
and the driven nut is connected to the piston rod. The piston
rod in the test rig reciprocates through the pressure chamber
that is made pressure tight using a typical rod-sealing
concept. During the experiments, the chamber is pressurized
while circulating medium (fluid) through the chamber to
absorb heat and any debris caused by the seal wear.
In the test rig, five types of seals were used: a) wiper seal, b)
excluder seal, c) secondary rod seal, d) primary rod low
friction seal, and e) rod bearing ring. In this study, only the
secondary rod seal and primary rod low friction seal were
replaced with new seals during every test as the wear of these
seals results in fluid leakage. Replacement took place during
every test as the wear of these seals used to results in fluid
leakage. Seal failure was defined when fluid leakage was
observed from the leakage port in test rig. Typically, the seal
life used in hydraulic cylinders in industry is for several
years. However, in this study, the seal wear was accelerated
by inducing scratches on the piston rod using a hard metal tip
scribing tool. The process parameters used for the
experiments are listed in Table 1.
Fluid in test rig
Water glycol
Rod material
Chromium-molybdenum steel
(+QT) with 20µm HCr coating
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Primary and secondary
seal material
Polytetrafluoroethylene
(PTFE)
Pressure
15 bar
Piston rod speed
15 mm/s (Test 2 & 3) and 25
mm/s (Test 1 & 4)
Number of tests
4
Test run time
Until fluid leakage observed
Stroke length
75 mm (Test 1 & 4); 150 mm
(Test 2 & 3)
Table 1. Experimental details.
Figure 1. Schematic view of test rig.
2.2. Acoustic emission and signal processing
The AE sensor was mounted at two locations on the test rig:
a) directly on the piston rod and, b) on the section of the
cylinder below the seal head (see red squares indicating the
positions in Figure 1). These two locations were selected as
the measured AE signal energy was higher compared to other
locations on the test rig. A mid-frequency range AE sensor
with a frequency operating range of 50-400 kHz and resonant
frequency of 150 kHz was used in the study. The AE sensor
was securely clamped on the test rig using an adhesive bond
together with adhesive tape. The AE sensor was connected to
a pre-amplifier and the pre-amplifier was further connected
to an AE data acquisition system. The data acquisition system
was connected to a laptop through a USB port. The AE data
acquisition was performed using the Vallen AE suite
software.
For all the experiments, the AE data acquisition was
performed in continuous mode at a sampling rate of 1 MS/s
and pre-amplifier gain of 40 dB. Due to the high sampling
rate and the large size of the AE files, the AE data acquisition
was limited to 90 seconds (five piston rod strokes) and data
acquisition was performed at 15 minutes interval until the
fluid leakage was observed. The AE signal was further
analyzed using the MATLAB software. The AE signal of the
extension and retraction strokes was observed to be similar
(Figure 2). Therefore, only the AE signal from the extension
stroke was used for forecasting analysis.
Figure 2. Raw AE signal recorded from test rig (Pedersen et
al. 2021)
For every RTF test, a new piston rod seal was used in the seal
head. Therefore, every test required the removal of the AE
sensor from the test rig. To ensure, that the AE sensor
clamping is consistent for every test, the Hsu-Nielsen pencil
lead break test (See ref (“Acoustic Emission (AE): Hsu-
Nielsen Source”)) was performed before the start of each test.
The pencil lead break test was performed by breaking a 0.5
mm diameter pencil lead on the test rig surface near the
mounted sensor. The amplitude of the AE burst response and
magnitude of AE frequency response was calculated and
compared during every test to ensure consistency of the AE
sensor clamping on the test rig.
2.3. Auto-regressive moving average model
The ARIMA model is used in prediction of different types of
time series data, e.g. financial or disaster prediction, as it can
make the difference calculation in non-stationary time series
data to form a stable series (Li et al. 2021). The ARIMA
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model: a) auto-regressive (AR), b) integrated part (I), c)
moving average part (MA). The ARIMA model is
represented as ARIMA (p, d, q). Where, p is the order of the
regressive model, d is the degree of difference, and q is the
order of moving average model. The p, d, and q are used to
make the model data as fit as possible. As per (Lee et al.
2011), the ARIMA model can be represented as a
combination of past observations and past errors. The auto-
regressive (AR) model uses past values in the time series to
predict the future values in a time series. The AR model of
order p, can be represented as:
      (1)
where in Eq. (1),
 is the stationary time series,  is
Gaussian white noise series, and , ,…,  are the AR
constants determined by an optimisation algorithm such as
ordinary least squares (Shumway et al. 2017).
The moving average (MA) model uses its previous errors to
make a prediction of future values. Here, the errors are the
difference between the predicted value and the observed
value. The MA model of order q, can be represented as:
     (2)
where in Eq. (2),  is white noise, and , ,…,  are
parameters (Shumway et al. 2017).
The integrated part (I) in the ARIMA model, means that the
original timeseries are transformed from  to  via Eq. (3),
  (3)
to make it stationary. The order of the integration parameter
d is the order of difference performed on the time series.
2.3.1. Modelling of the condition monitoring data
In this study, the RTF test data was fitted using the ARIMA
model. The Box-Jenkins model was used to select ARIMA
(p, d, q) parameters and to validate the model fit. Each data
set from the RTF test was used to fit in the ARIMA model to
the most suitable condition monitoring data. To replicate a
real-life condition, where the future data is unknown, only a
portion of the initial samples were applied to fit the ARIMA
model. The initial samples are labelled as pre-sample data.
For creating the ARIMA model, fifteen samples from each
RTF test were used as the pre-sample data. To test the
accuracy of the developed ARIMA model, the next ten
samples were used to forecast and to calculate the residual
error. Based on the residual error, the root mean square error
(RMSE) and the mean absolute percentage error (MAPE)
was calculated as shown in Eq. (4). and Eq. (5).
  
󰇻

󰇻

  (4)
  󰇛
󰇜

  (5)
where,  is the true value,  is the forecasted value, and n is
the number of forecasted samples.
The auto-correlation function (ACF) and partial auto-
correlation function (PACF) were used to graphically
represent the relationship of a data point in a timeseries to
data points from previous timesteps. These previous
timesteps are called lags. Thus, a lag of one represents one
timestep prior to the current timestep. Autocorrelation is then
the calculated correlation between the current value and the
values at the lags in a timeseries (Salvi 2019). Table 2 was
used as a reference to determine preliminary values of the p
and q parameters. The MATLAB in-built function was used
to estimate the ARIMA (p, d, q) model from the pre-sample
data. After estimating the model fitting parameters, the
goodness of fit was validated by inferring the residuals from
the fitted model. The selected ARIMA (p, d, q) model was
then used to forecast the datapoints of the holdout data. The
residuals were calculated from the known values of the
holdout data and subtracting it from the forecasted values,
and then the MAPE and RMSE were calculated. To compare
the error values, the pre-sample data and holdout data were
standardized by normalizing the values in the range of zero
to one. To increase accuracy of the forecasted timeseries, a
Monte Carlo simulation was applied to the forecasting
timeseries. The Monte Carlo simulation used one thousand
forecasting iterations with the pre-sample data as the input
data. The mean of the forecasted predictor values was then
used as the forecasted values.
AR(p)
MA(q)
ARMA(p,q)
ACF
Tails off
Cuts off
after lag q
Tails off
PACF
Cuts off after lag p
Tails off
Tails off
Table 2. Behavior of ACF and PACF for ARMA models
(Shumway et al. 2017).
3. RESULTS AND DISCUSSION
3.1. Pencil lead break test
Figure 3 a)-b) represent the AE time domain signal of the
background noise and from the pencil lead break test
respectively. The AE signal of background noise was
recorded while the HPU was circulating hydraulic fluid in the
pressure chamber. By comparing Figure 3 a)-b), the
maximum amplitude of the AE signal from the pencil lead
break test is at least hundred times higher compared to the
HPU background noise. Figure 3 c)-d), represent the AE
frequency response calculated using Welch’s method. The
frequency responses show that, the AE frequency peaks are
dominant in the frequency range of 65-190 kHz. The
maximum magnitude of the frequency response of the
background noise is about one thousand times smaller than
for the pencil break test. As the effect of ground noise on the
AE signal is minimal, bandpass filtering techniques were not
applied for the AE signal recorded during the RTF tests.
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Figure 3. AE signal from a) Background noise, b) Pencil lead break test; Frequency response calculated from AE signal c)
Background noise, d) Pencil lead break test.
3.2. ARIMA model using the RMS feature
From the RTF tests conducted a comparison of the time and
frequency domain features were conducted, and it was
observed that the RMS feature was the most suited for use as
condition monitoring indicators to identify wear of piston rod
seals (Pedersen et al. 2021). Therefore, in this study, the RMS
feature was used to develop the ARIMA model. Figure 4-a)
shows a plot of the RMS response for all four RTF tests. The
signal was subtracted by the first sample to remove the bias
and for easier comparison of the results. The increase in trend
is similar for RTF tests 2 and 3 (tests conducted at 15 mm/s
speed). For RTF 1 and 4, the trend shows a large difference
(tests conducted at 25 mm/s speed). The drop in RMS feature
in RTF 4, is mainly because the test was stopped at evening
and restarted next day (in most industries hydraulic cylinders
are used intermittently, not continuously). This has been done
to observe the changes in signal response when the test rig
was stopped. Tests 1 and 2 were run continuously, tests 3 and
4 were stopped in the night. In test 3, the next day system was
switched on and kept running to allow system to be stabilized.
Whereas in test 4 the next day, the system was switched on
and data was recorded immediately to see the difference in
behaviour of AE features with that of AE features from test
3. Furthermore, the transient response for the first three hours
in RTF test 1 does not conform well to forecasting by the
ARIMA model due to its initial decreasing trend. This is
mainly because test rig pressure, and temperature require
some time to stabilize. Therefore, for remaining tests, test rig
was started only when test rig pressure and temperature were
stabilized. To be able to do a better prediction on the RTF test
1 dataset, the transient response was removed. Figure 4-b)
shows the responses for all RTF tests with the transient
decreasing trend of RTF test 1 removed. As seen from Figure
4, the RMS feature trend is not stationary due to the
increasing trend. To meet the stationary criteria of the
ARIMA model, the RMS feature was differentiated. For RTF
tests 1 and 3, a first order differentiation was applied, and for
RTFs test 2 and 4, a second order differentiation was applied.
Therefore, the differencing term ‘d’ in the ARIMA (p, d, q)
was thus set as one for RTF tests 1 and 3, and two for RTF
tests 2 and 4.
To identify the preliminary values of the AR (p) order, p, and
MA (q) order, q, the ACF and PACF were plotted using the
RMS features that were differentiated. Figure 5 shows the
ACF and PACF plots for all differentiated data of the RTF
tests. To find the initial parameters of the p, d, and q
parameters for the ARIMA model, the guide in Table 2 was
used to interpret the ACF and PACF plots. In Table 2, by
“tailing off” it indicates the gradually decreasing correlation
values, while the “cutting off” indicates the sudden large drop
in correlation value. It can be seen in the PACF plot for RTF
test 1 in Figure 5-e) that the PACF cuts off after the second
lag. The ACF plot in Figure 5-a) does not show any lag above
the threshold line, but it can be said to cut off after the first
lag, even though the first lag is not very significant. An
ARIMA (2,1,1) was thus suggested for the RMS signal from
RTF test 1. For RTF test 2, both the ACF and the PACF plots
in Figure 5-b) and Figure 5-f) show only one significant lag.
However, the ACF plot can be seen to tail off while the PACF
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plot cuts off at lag one. An ARIMA (1,2,0) model was thus
suggested for the RMS signal from RTF test 2. The ACF plot
for RTF test 3, in Figure 5, show very low correlation
throughout the series, and only the second lag appears to
show any correlation before it cuts off. The same can be seen
for the PACF plot in Figure 5-g). Thus, to best model the
RMS series for RTF test 3, an ARIMA (2,1,2) was suggested.
Finally, for RTF test 4, the ACF plot in Figure 5-d) shows
that it cuts off at the first lag. Similarly, the PACF plot in
Figure 5-h) shows the same, but here the second lag can be
seen to be more significant. Even though the second lag does
not reach above the threshold line, it should still be utilized
in the model. An ARIMA (2,2,1) was thus suggested for the
RMS series for RTF test 4.
The quantile-quantile (QQ) plots for the residuals of the fitted
model on the pre-sample data is shown in Figure 6. It can be
seen that all fitted models are reasonably normally
distributed, except for the possible outliers as seen for the last
quantile of RTF tests 1 and 4 in Figure 6-a) and Figure 6-d).
The ACF and PACF plots of the residuals of the fitted models
are represented in Figure 7. The models fitted to the RMS
series for all RTF tests show a low correlation of the residuals
both for the ACF and PACF. This indicates that the selected
p, d, and q parameters provide good model fits to the data.
Figure 4. a) With transient from RTF test 1, b) Transient removed from RTF test 1.
Figure 5. ACF and PACF for the differentiated RMS series of all RTF datasets, showing first 10 lags. a)-d) ACF, RMS
signals from RTF 1-4, e)-f) PACF, RMS signals from RTF 1-4.
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Figure 6. QQ plots for fitted ARIMA models to the RMS series of RTF tests 1 to 4: a) for ARIMA (2, 1, 1) model on RTF
test 1, b) for ARIMA (1, 2, 0) model on RTF test 2, c) for ARIMA (2, 1, 2) model on RTF test 3, d) ARIMA (2, 2, 1) model
on RTF test 4.
Figure 7. ACF and PACF for the residuals of the fitted ARIMA models on the pre-sample data. ACF for residuals of a)
ARIMA (2, 1, 1) model on RTF test 1, b) ARIMA (1, 2, 0) model on RTF test 2, c) ARIMA (2, 1, 2) model on RTF test 3, d)
ARIMA (2, 2, 1) model on RTF test 4. PACF for residuals of e) ARIMA (2, 1, 1) model on RTF test 1, f) ARIMA (1, 2, 0)
model on RTF test 2, g) ARIMA (2, 1, 2) model on RTF test 3, h) ARIMA (2, 2, 1) model on RTF test 4.
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3.3. Forecasting using the ARIMA model
Table 3 represents the best fitted ARIMA model parameters
with the RMSE and MAPE values for the ten samples out of
sequence forecasts. Figure 8 represents the forecasting of the
RTF test data using the ARIMA model with the 95th
percentile of the forecasts from the Monte-Carlo simulation.
For all RTF tests, the forecasting plot can be seen to follow
the increasing trend of the true data. Comparing the
forecasting trend among the data from the RTF tests 1-4, for
the RTF tests 1 and 2, see Figure 8 a)-b), the accuracy is less
compared to RTF tests 3 and 4. The low accuracy of the
forecast trend in RTF test 1 is mainly due to the large variance
shift in the original dataset seen at around 4 hours, see Figure
4-a)). For the RTF test 2, the low accuracy for the ARIMA
model is attributed to the low correlation of sequence that was
seen in the related ACF and PACF. For RTF tests 3 and 4,
the ARIMA models displays good accuracy for the forecasted
values, see Figure 8 c)-d) despite the low correlation of
sequence also for these timeseries. The better accuracy of the
model for RTF 3 and 4, can also be attributed to a favorable
time of forecasting in the series.
RTF
AR (p)
I(d)
MA(q)
RMSE
(mV)
MAPE
(%)
1
2
1
1
0.187
20.26
2
1
2
0
0.326
28.99
3
2
1
2
0.053
4.95
4
2
2
1
0.104
8.88
Table 3. ARIMA (p, d, q) model parameters with the
respective RMSE and MAPE error.
Figure 8. Forecasted data on 10 sample forecasts for RMS series of all RTF tests. a) For ARIMA (2,1,1) model on RTF test
1, b) For ARIMA (1,2,0) model on RTF test 2, c) For ARIMA (2,1,2) model on RTF test 3, d) For ARIMA (2,2,1) model on
RTF test 4.
4. SUMMARY
In this study, the AE-RMS feature from four RTF tests was
used to forecast the seal degradation process in a hydraulic
test rig using an ARIMA model. The ARIMA model was able
to forecast the RMS values ahead in time as long as the
original RMS trend did not experience any large shifts in
variance or deviates from the normal increasing trend, as is
expected from this method. The ARIMA model showed that
it can perform with good accuracy for forecasting in at least
two of four RTF tests that were conducted. The ARIMA
model that was fitted with fifteen pre-samples, was used to
forecast ten out of sequence samples, and it showed a
maximum moving absolute percentage error (MAPE) a
maximum of 28.99 % and a minimum of 4.950 %.
Based on the work conducted in this study, the authors
conclude that further work is required with other modelling
approaches like different variants of neural network for
forecasting the seal failure, to improve the prediction when
there are large shifts in variance that was seen in the RMS
trend. Also, additional RTF tests need to be conducted with
similar conditions to assess the repeatability of the
forecasting technique.
Proceedings of the 7th European Conference of the Prognostics and Health Management Society 2022 - ISBN – 978-1-936263-36-3
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EUROPEAN CONFERENCE OF THE PROGNOSTICS AND HEALTH MANAGEMENT SOCIETY 2022
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Acknowledgement
The research presented in this paper has received funding
from the Norwegian Research Council, SFI Offshore
Mechatronics, project number 2378.
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