Abrupt changes refers to the mean changes in term of nature behavior that occur
very fast with respect to the sampling period of the measurements, if not instantaneously.
The detection of abrupt changes on the other hand, refers to tools that help
in decide whether such a change occurred in the characteristics of the considered
subject. The change detection tools were used in problems that exist in signal
processing, time series analysis, automatic control and industrial control (Basseville
and Nikirov, 1993). The generic problem of detecting abrupt changes in process
parameters has been widely studied. These changes may be due to shifts that
exist in the mean value (i.e., edge detection) or a variation in signal dynamics
(Nopiah et al., 2008b).
This study is on the development of abrupt changes detection technique that
exists in mechanical fatigue signal data. Since, there a large part of the information
contained in the measurement lies in their nonstationarities and because of
most adaptive estimation algorithms basically can follow only slow changes,
a new method are needed to be developed in detecting the abrupt changes that
exist in the fatigue data (Basseville and Nikirov, 1993).
In solving this problem, a new technique called Running Damage Extraction (RDE) method was proposed. This method was developed by combining the overlapping window concept and fatigue damage calculation. The objective of this study was to investigate whether, this method can be used accurately to segment the typical fatigue histories by isolating the low and high amplitude event into different segmentation.
A signal is a series of number that come from a measurement, typically obtained
using some recording method as a function of time (Nopiah
et al., 2008a). In real applications, signals can be classified into
two types which are stationary and non-stationary behavior. A signal representing
a random phenomenon can be characterised as either stationary or nonstationary
behavior. The stationary signals exhibit the statistical properties remain unchanged
with the changes in time. On the other hand, statistics of non-stationary signal
is dependent on the time of measurement. In the case of fatigue research, the
signal consists of a measurement of cyclic loads, i.e. force, strain and stress
against time. The observations of a variable were taken at equally spaced intervals
of time (Abdullah et al., 2008).
All the data measured from this experiment are recorded as strain time histories. Thus, it is also important to have a better understanding about the behavior of this data before applying the detection of abrupt changes algorithm. The identification of fatigue data behavior is based on the existence of time series component which involves with the identification of trend, cyclical, seasonal and irregular component in time period t.
The method used in the identification of this component is called classical
decomposition of time series. This process is used to segregate and to analyse
the existence components in a systematic manner. The trend component represents
the long-run growth or decline over time. On the other hand, the cyclical component
refers to the rises and falls of the series over unspecified period of time.
The seasonal component also known as seasonal variation, refers to the characterization
of regular fluctuations occurring within a specific period of time. Although,
this component is individually identified, they are related to each other in
a certain mathematical functional form. The type of relationship that these
components have is divided into two; which are multiplicative effect and additive
effect. Multiplicative effect refers to the components interaction such, the
increase in sizes of the seasonal variation within the level of data. On the
other part, additive effect assumed the components of the series are interacted
in additive manner (Lazim, 2007).
In normal practice, the global signal statistical values are frequently used
to classify random signals. In this study, mean, root mean square (r.m.s.) and
kurtosis were used (Nopiah et al., 2008a). For
a signal with n data points, the mean value of
is given by:
On the other hand, root mean square (rms) value, which is the 2nd statistical moment, is used to quantify the overall energy content of the signal and is defined by the following equation:
where, xj is the jth data and n is the number of data in the signal.
The kurtosis, which is the signal 4th statistical moment, is a global signal
statistic which is highly sensitive to the spikeness of the data. It is defined
by the following equation:
where, rms is the root mean square as calculated in Eq. 4
is the mean value of the signal data. Kurtosis is used in engineering for detection
of fault symptoms because of its sensitivity to high amplitude events (Qu
and He, 1986).
It is common that the service loadings caused by machines and vehicles is evaluated
using a strain-life fatigue damage approach (Abdullah et
al., 2005). The strain-life approach considers the plastic deformation
that occurs in the localised region where fatigue cracks begin under the influence
of a mean stress.
The total strain amplitude, εa is produced by the combination of elastic and plastic amplitudes:
where, εea is the elastic strain amplitude and εpa is the plastic strain amplitude. The elastic strain amplitude is defined by:
while the plastic strain amplitude is given as:
where, σa is the stress amplitude, Nf is the number of cycles to failure, b is the fatigue strength coefficient, b is the fatigue strength exponent, ε'f is the fatigue ductility coefficient, c is the fatigue ductility component and E is the modulus of elasticity.
Combining Eq. 8 and 9 gives the Coffin-Manson
relationship, which is mathematically defined as:
which is essentially Eq. 7 above and is the foundation of the strain-life approach. Some realistic service loads involve nonzero mean stresses.
Fatigue damage is derived from the number of cycles to failure where the relationship is:
and therefore fatigue damage values have the range [0, 1] where, zero denotes no damage (extremely high or infinite number of cycles to failure) and 1 means total failure (one cycle to failure).
The RDE plot in this study has many non-parallel lines that contain a significant
number of local optima, which can be classified as either peaks or valleys.
A peak is defined to be associated with change in the slope from positive to
negative, while a valley is associated with a change in the slope from negative
to positive (Xiong and Shenoi, 2008). Peaks in a RDE
are essentially the local maxima and valleys are the local minima. Depending
on the resulting RDE, some points can be classified as neither peaks nor valleys.
Peak-Valley (PV) identification can be used to segment signals so that each
segment may contain certain numbers of peaks and/or valleys, according to the
needs of the study. This is particularly useful for fatigue time series data,
since peaks and valleys feature predominantly in rainflow counting algorithms
for fatigue damage calculations (Bigerelle et al.,
2008). PV-based techniques are also used in mechanical modeling (Kuroda
and Marrow, 2008), quantifying roughness of materials (Kuroda
and Marrow, 2008; Hiziroglu et al., 2008;
Anderberg et al., 2008) and image segmentation
(Zhang et al., 2007).
In signal processing, a segmentation algorithm were used to splits the signal
into homogenous segments, the lengths of which are adapted to the local characteristics
of the analyzed signal. The homogeneity of a segment can be in terms of the
mean level or in terms of the spectral characteristics (Basseville
and Nikirov, 1993). This type of application is applied in fatigue life
assessment study in which the fatigue signal extraction is described as a method
to summarise a fatigue signal.
The first step of summarizing the fatigue signal is to isolate the low and high amplitude events in different segmentation. All the extracted segments (the complete section between the start and the end of the segments) are selected based on peak and valley time location of the running damage values.
MATERIALS AND METHODS
The data that was used in this study is variable fatigue strain loading data. It was collected from an automobile component during vehicle road testing. It was obtained from a fatigue data acquisition experiment using strain gauges and data logging instrumentation. The experiment was conducted in the year 2008 by covering certain road areas in Malaysia.
The collected fatigue data were measured on the cars front lower arm
suspension as, it was subjected to the road load service.
factor for fatigue data road condition
All the data that were measured from this experiment are recorded as strain
The strain value from this test was measured using a strain gauge that was connected to a device, a data logger for data acquisition. Experimental parameters that need to be controlled in this test such as sampling frequency and type of output data being measured were specified in data acquisition software.
In order to collect a variety of data, the car was driven on three different road surfaces which are explained in Fig. 1. All data were taken from different road conditions: pave route, highway and campus.
Experimentally, the data was collected for 60 sec at a sampling rate of 500 Hz, which gave 30,000 discrete data points. This frequency was selected for the road test because this value does not cause the essential components of the signal to be lost during measurement. The road load conditions were from a stretch of highway road to represent mostly consistent load features, a stretch of brick-paved road to represent noisy but mostly consistent load features and an in-campus road to represent load features that might include turning and braking, rough road surfaces and speed bumps.
As to fulfill the main purpose of this study, the RDE algorithm is used to identify and extract the abrupt changes for fatigue damaging events. This technique is based on the running concept which the original data are separated by using overlapping window. For a signal with n data points, the numbers of overlapping window is given by xiεX where, X is the signal data, h is the size of overlap and m is the size of the window:
i = 1, 2, 3, .....
J = 1,1+h,1+2h, ....
K = m,m+h,m+2h, .....
A flowchart describing the RDE algorithm is presented in Fig.
2 and it involves with several stages: the input signal and global statistics
parameter; classical decomposition analysis for fatigue time series data; calculation
of running damage based on the overlapping window; identification of optimized
running damage; the identification and extraction of abrupt changes for fatigue
damaging events; and decision making process.
flowchart of the RDE algorithm technique
The first stage of RDE algorithm is to display the three different types of
fatigue data in times series plot and global statistic parameter. In normal
practice, the global signal statistical values are frequently used to classify
random signals. In this study, mean, root mean square (rms) and kurtosis were
used (Nopiah et al., 2008a).
In the stage of classical decomposition for time series, a few methods has been selected in identify for the whole time series component. The method in detecting the existence of trend, cyclical, seasonal and irregular are by using linear trend line, the residual method, method of seasonal differencing and then also by using linear trend line, respectively. Purpose of using classical decomposition method as a tool in analyzing the fatigue time series data are to identify the variation and to have a better understanding in about the behavior of the data.
The next stage is the most crucial part in the development of RDE algorithm. At first, the data was divided in different window by using the overlapping algorithm. In each window, there are 500 data points. The data points in each window that consist of original data were then overlapped between each other from 10 to 90%. Then, the data that was produced in each window was transferred into Glyphwork software for calculating the value of fatigue damage. The purposed of overlapping in this study was based on the assumption to reduce the possibility of damaged calculation for each window that crosses over the peak values in the original signal and to mitigate the loss at the edges of the window.
The next stage in RDE algorithm is to identify the optimised running damage. Each overlapping window for running damage was plot over time. Then, a trend analysis is used to analyse the variation component in the running damage data. The trend values for the running damage were then compared to the trend values of original signal. In this study, it is proposed that the optimum value for overlapping running damage be based on the minimum values of trend analysis as it represents the removal of the trend component from the actual data.
In the third stages of RDE, abrupt changes which represent the fatigue damaging events or bumps are identified based on wave bump extraction method. In this stage, the RDE was combined with peak and valley calculation so that the decision function for the time series segmentation can be performed.
After the RDE data points were simplified by using peak and valley algorithm,
the decision function for the extraction is based on energy enveloping in the
original signal, the time points that correspond to valley data points are then
identified. Reference about this method of searching can be referred from this
article (Abdullah et al., 2005).
The last stage involve with the identification on whether, the RDE algorithm can detect transient events in fatigue data. It is assumed that the RDE algorithm can be used in predicting the abrupt changes that exist in fatigue data.
RESULTS AND DISCUSSION
Referring to Table 1, the pave gives the highest value of
mean which are 68.08. On the other hand, campus route shows the highest value
of RMS which is 88.22. Kurtosis results showed that all of the data are non-Gaussian
distribution since all the kurtosis value exceeds 3. From the findings, the
higher kurtosis values also indicate the presence of more extreme values than
should be found in a Gaussian distribution (Qu and He, 1986).
Table 2 shows all behavior of the components that exist in
the fatigue data except for seasonal component. In this analysis, seasonality
component was not considered as important such as the event that occurs in the
fatigue data is not the regular fluctuations occurring within a specific period
of time. The existence of regular fluctuations which involve with high amplitude
events in fatigue data are independent each other. These high amplitude events
are recognized as the fatigue damaging events. From the analysis of classical
decomposition method, it was found that all the data have positive trend, cyclical
and random effect.
||Fatigue time series component table
From this study, 80% overlapping window for original data has been chosen as
the optimal condition for RDE method. This is because the decision function
for data segmentation in change detection produced better results for the whole
case study data rather than using different value of overlapping. It also was
found that different value of overlapping will produce a different numbers of
Using overlapping algorithm and running damage calculation, it was found that
the RDE plot shows significant findings in detecting the high amplitude event
that exist in the all selected data. Figure 3-5
show the comparison between original RDE plot, RDE plot with peak and valley
and time series plot.
between RDE and time series plot for pavé route data
between RDE and time series plot for highway data
between RDE and time series plot for UKM Data
The RDE plot in Fig. 3 shows that each jump, which was related
to fatigue damage event was successfully detected. The line in time series plot
are drawn as to separate the high amplitude and low amplitude events that exist
in the strain data.
In the highway data (Fig. 4), the RDE algorithm shows significant result in detecting the abrupt changes that exist in the data. Each high amplitude event that exists in the highway data was also detected by using the RDE algorithm (by referring to the circled areas). Each existence of abrupt changes in the data was segmented based on the valley value of damage.
Finally, Fig. 5 shows the detection of abrupt changes by using RDE method plot also tends to be very high. Referring Fig. 5, it shows that all the high amplitude data which is related to fatigue damaging events are segmented (by referring to the circled area).
The study has demonstrated the use of Running Damage Extraction (RDE) method in the segmentation of time series data for fatigue analysis and classical decomposition method as a tool in analyzing the time series variation for fatigue data. The study showed that the proposed method can solve the problem very well in detecting and isolating the abrupt changes that exist in the fatigue time series.
The authors would like to express their gratitude to Universiti Kebangsaan
Malaysia through the fund of UKM-GUP-BTT-07-25-152, for supporting these research