where E is the material modulus of elasticity, ε_{a} is a true strain amplitude, 2N_{f} is the number of reversals to failure, σ’_{f} is a fatigue strength coefficient, b is a fatigue strength exponent, ε’_{f} is a fatigue ductility coefficient and c is a fatigue ductility exponent. In order to estimate a fatigue damage event where mean stress/strain is involved, functional solutions, in addition to the normal fatigue stress/strain life curves, are introduced to predict mean stress and mean strain effects. Experimental results show that mean strain gives a secondorder effect if no severe work hardening has taken place^{[13]}. Consequently, the damage parameters are usually developed to consider mean stress effects on fatigue behaviour. Different mean stress effects have been documented for a variety of materials and testing techniques, with the result that various mean stress theories for strainlife relationship have emerged and no consensus exists that any one of them is superior to the others^{[13]}. For examples, the Morrow^{[14]} approach seems to work reasonably well for steels while the SmithWatsonTopper (SWT)^{[15]} appears to give good results for a wide range of materials and is a good choice for general use^{[13]}. The Morrow’s strainlife model is mathematically defined as the following expression: and the SWT strainlife model is defined according to this formulation:
where σ_{m} is the mean stress and σ_{max} is the
maximum stress, applicable for both Eq. 2 and 3.
From the strainlife model approach, the number of reversals or 2N_{f}, were determined in order to find cumulative fatigue damage. The values of σ’_{f}, E, ε’_{f}, b and c were the material properties of the particular material, while the value of ε’_{a} can be obtained from the rain flow cycle counting method. The cumulative fatigue damage was then determined using the PalmgrenMiner (PM) linear damage rule.
Fourier analysis is a one of the method to analyse random data based on the
frequency domain analysis. The frequency analysis data is typically presented
in graphical form as Power Spectral Density (PSD). Essentially a PSD display
the amplitude of each sinusoidal wave of a particular frequency. Frequency is
given on the xaxis. The mean squared amplitude of a sinusoidal wave at any
frequency can be determined by finding the area under the PSD over that frequency
range. Unfortunately, Fourier transform analysis has a drawback as it does not
provide the time localization information. Therefore timefrequency domain analysis
was applied to solve that problem. Many timefrequency analyses are based on
windowed or shorttime Fourier transforms^{[16]}. Sliding data windows
were used to obtain timelocalised spectra which together put up the timefrequency
representation of the data.
The STFT is performed by dividing the signal into small sequential or overlapping data frames, for which the Fast Fourier Transform (FFT) was applied to each data frame^{[17]}. The output of successive STFT can provide a timefrequency representation of the signal. In order to accomplish this, the signal is truncated into short data frames by multiplying it by a window so that the modified signal is zero outside the data frame. In order to analyse the whole signal, the window is then translated into a time and reapplied to the signal. The STFT is composed by the local spectra of segments of the primary function, as viewed through a translating window of fixed shape. The local spectra at all points on the primary time axis constitute the STFT^{[18]}. The STFT is generally expressed as the following: where h is the primary function, τ is the time and f is the frequency. The position of the translating window w is determined by t, which has the same units as τ. If w is replaced with the value of 1 in Eq. 2, the STFT reduces to H, i.e., the Fourier transform of h. The modulus of the STFT is also known as the spectrogram. In the related study^{[19]}, the STFT spectrogram has been applied in fatigue analysis for detection and monitoring of hidden fatigue crack growth. The STFT method was also widely used in locating the structure defect especially for gear and cutting tool using vibration data due to its capability to detect highly vibration event^{[20,21]}. In this study, the STFT method was used to transform the fatigue signal into timefrequency representation in order to detect the damaging event contained in the signal. STFT measures the energy in a timefrequency neighbourhood, specified by a resolution box. The damaging event will be determined basedon level of energy. RESULTS
The validation process STFTbased fatigue data editing was presented as a flowchart
in Fig. 1. In order to achieve this purpose, the strain time
histories named as SAESUS (this data was obtain from the database of Society
of Automotive Engineers or SAE) was used for evaluating the newly developed
fatigue data editing technique associated with the STFT.
 Fig. 1: 
Simplified flowchart for the validation of STFT effectiveness 
 Fig. 2: 
Time history plot of the SAESUS fatigue signal 
The data was collected on a suspension component of a car and it was assumed
to be sampled at 204.8 Hz for 25,000 data points. It gave the total record length
of the signal of 122 sec, as illustrated in Fig. 2. The signal
was chosen due to the prior success with it by another researcher^{[22]}
in the fatigue history editing using wavelet approach.
The time domain fatigue signal was then edited for shortening the signal length with the removal of low amplitude cycles. These cycles were removed based on time domain analysis. The module for fatigue damage editing in the GlyphWorks^{®} software package was applied to perform the time signal shortening. The editing process was retained at 100% damage level of the original signal. In this process all the strain range less than the gate value were removed, for which the gate value was calculated based on CoffinManson strainlife relationship. The selected material for the simulation purpose was the SAE1045 steel and this type of material was commonly used in the automotive industry^{[23]} for fabricating a lower suspension arm. The material properties and their definitions are given in Table 1. For the SAE 1045 steel material, the gate value is the strain range that gave the fatigue life value of 2×10^{8} reversals. The removed low strain range cycle from the original signal was shortening the length of the signal. The 100% retained damage strain range edited was successful removed approximately 50% low amplitude cycles with 57 seconds time reduced, as illustrated in Fig. 3. For this case, the removed data was assumed as nondamage segments because the departures of those segments did not change the value of the total fatigue damage. In Fig. 3a, the filled areas represent the segments which contribute to the minimal or no damage potential.
For the STFT analysis, the time history signal was separated into a number
of windows using the Gaussian window with 128 of window size. The Gaussian window
was used since one simultaneously achieves an optimal time and frequency resolution^{[24]}.
 Fig. 3: 
The analysis of SAESUS: (a) The 122second original time history
(b) The 65second edited time history 
Table 1: 
Mechanical properties of the SAE1045 steel 

The 120 number of overlaps were used in order to provide the high resolution
in the time representation. For each window, the Fourier transform was applied
for the calculation of the power spectral level contained in each window. The
power distribution was gained using the Power Spectral Density (PSD) that produced
the spectrogram of the STFT. For this case, the PSD is defined as the power
distribution of the signal and represent at με^{2}Hz^{1}
as the unit. The STFT plot of the original fatigue signal showed a twodimensional
view of the power distribution, as observed in the timefrequency plane. This
result was plotted in Fig. 4, showing the different colour
contours, i.e., the red colour for the highest energy content and followed by
yellow, green, blue and white.
According to the spectrogram parameter obtained in the STFT processing, the
power spectrum of the fatigue signal was decomposed into a time domain data
in order to represent the time history power spectrum distribution. The magnitudes
of time domain power spectrum were obtained from the accumulative power distribution
along the frequency band for each time interval.
 Fig. 4: 
The timefrequency localisation of the SAE fatigue signal
based on the STFT approach 
 Fig. 5: 
(a) SAESUS strain time history, (b) The power spectrum in
time history representation 
Thus, it’s provided the power level information at time location. The STFT
power spectrum distribution is illustrated in Fig. 5. The
figure shows the equality between magnitudes of power spectrum and strain magnitude
especially at 1, 10, 42, 55, 69, 115 and 120 sec time locations, where both
of the power spectrum and strain possess high magnitudes.
From the simulation of the fatigue history editing at 100% damage retained,
the output signal was separated into two new signals, i.e., the damage signal
and the nondamage signal. The damage signal is the signal that contained the
cycles associated to the fatigue damage. On the other hand, the nondamage signal
contained the cycles which were not damaging. For the validation purposes, the
power spectrum of each signal was also investigated in order to study the efficiency
of STFT parameter based on fatigue damage event.
 Fig. 6: 
Power spectrum at: (a) the damage segment (b) the nondamage
segment 
The power spectrum of each signal is shown in Fig. 6, for
which Fig. 6a shows that the power spectrum of the nondamage
signal that consist higher power spectrum level. The nondamage signal produced
the lower power spectrum level at the minimum value, as shown in Fig.
6b, which most of the power spectrum values were below 4×10^{5}
με^{2}Hz^{1}. The findings showed that the power
spectrum gained from the STFT method was enable us to detect the damage event
of the fatigue signal, as higher power spectrum presents the damage part.
The flowchart in Fig. 7 shows the process of fatigue data editing using the STFT method. The overall process consists of timefrequency transformation, time history power spectrum transposition and elimination of the low amplitudes cycles. The output of successive STFT can provide a timefrequency representation of the signal. Based on the spectrogram parameter obtained in the STFT processing, the power of the fatigue signal was decomposed into a time domain data in order to represent the power distribution in the time history. The power spectrum display in the time domain provided the time location containing the low power spectrum cycle. Accordingly, the low energy cycles will be eliminated for summarising the signal length without compromising the original fatigue damage potential. For a specific fatigue data, low energy cycles mean these cycles had a low amplitude strain which is not damaging.
 Fig. 7: 
The flowchart for fatigue data editing using STFTbased computational
algorithm 
In order to solve the subject matters of this paper, a STFTbased computational algorithm was developed in order to analyse the signal according to the fatigue damage calculation and also to remove cycles with low energy content. Thus, the cycles with higher energy content has been retained for further analysis. These cycles were then jointed to produce the new edited signal, which has shorter time length. In addition, this edited signal should also have equivalent fatigue damage to the original signal. The low energy cycles were removed from the time domain signal based on the location of low energy cycle in time history power spectrum distribution. A new parameter called CutOff Level (COL), which represents the minimum power value to be retained from the original signal was set. This means that, the cycles with power spectrum level below than COL value will be eliminated. Thus, a new shortened edited signal was generated which neglected low amplitude cycles.
For the validation purposes, the fatigue damage potential for both original
and edited signals were calculated in order to study the efficiency of the edited
signal based on the fatigue damage retention. The fatigue damage was calculated
based on strain life model which applied the CoffinManson strainlife relationship.
 Fig. 8: 
Time history signal of that was measured on the different
side of lower suspension arm of a car: (a) left lower suspension arm, (b)
right lower suspension arm 
In this study, the optimum edited signal was determined based on the shortest
signal with the minimal fatigue damage deviation when compared to the original
signal and that retains the original signal behaviour.
Two input signals were used to observe the efficiency of the newly developed fatigue data editing algorithm using the STFT approach. Both signals were measured on the left and right lower arm suspension of a car that was travelling on a country road. It was sampled at 200 Hz for 12,000,000 data points. The time history plots for the signals were shown in Fig. 8.
For the analysis purposes, two segments from the overall signal were selected
which contained of 30,000 data point for each segment. Those signals were selected
due to the highest fatigue damage content. The fatigue damage for each segment
was plotted in Fig. 9. The first selected signal, named as
D1 (Fig. 10a) was measured on the front left lower suspension
arm that contained the highest fatigue damage segment and the second signal,
D2 (Fig. 10b), was simultaneously measured with the D1 signal
on the front right lower suspension arm.
Using the STFTbased newly developed computational algorithm, the time history
D1 and D2 signal was then transformed into timefrequency representation.
 Fig. 9: 
Fatigue damage distribution calculated based on 30000 data
points for each segment: (a) signal measured on the left lower suspension
arm, (b) signal measured on the right lower suspension arm 
 Fig. 10: 
Time history signal of: (a) The D1 signal (b) The D2 signal 
Those signals were separated into a number of windows using the Gaussian window
with 64 of window size. The 60 number of overlaps were used in order to provide
the high resolution in the time representation where higher time resolution
provided better time information for further analysis. The timefrequency power
spectrum for both signals was plotted in Fig. 11.
 Fig. 11: 
The STFT localisation for: (a) D1 signal, (b) D2 signal 
As can be seen from this figure, higher magnitude distribution was observed
with low frequencies and lower magnitude distribution was observed with high
frequencies. The timefrequency power spectrum distribution was then converted
into time representation by accumulating the power spectrum at each time scale.
Thus, a set of power spectrum at particular time was gained. The power spectrum
in time history for D1 and D2 signals were plotted in Fig. 12.
As the STFT power spectrum has a significant relationship with the fatigue damage
potential distribution, the STFT spectrogram can be utilized as the parameter
for this fatigue data editing.
For the editing process, the power spectrum level was used as the parameter
to set the gate value (CutOff Level or also known as COL) for eliminating process.
The eliminating process was carried out by removing the low amplitude cycles
which contain the power spectrum lower than COL value. Various COL values were
used in order to exhibit the effectiveness of the edited signal with respect
to the fatigue damage retention.
 Fig. 12: 
Power spectrum in the time history representation for: (a)
D1 signal, (d) D2 signal 
The editing process at a particular COL value produced a new edited signal.
For each edited signal, the fatigue damage was determined and compared with
the original signal in order to obtain the optimum edited signal. The fatigue
damage was estimated by utilizing the CoffinManson, Morrow and SWT strainlife
models contained in the GlyphWorks^{®} software.
The simulation process provided the fatigue damage distribution for each cycles
as shown in Fig. 13. The fatigue damage of the signal was
the cumulative of the fatigue damage for each cycles contained in that signal.
The fatigue damage values for each edited signal were plotted in Fig.
14, showing the changes of fatigue damage against the COL values for all
strainlife fatigue damage models. The fatigue damage shows decrement when COL
values were ascending because of the departure of more low amplitude cycles.
In order to retain the originality of the signal, the statistical parameter
of the edited signal should be equivalent to the original signal.
 Fig. 13: 
The distribution of the fatigue damage potential for: (a)
D1 signal, (b) D1 edited signal, (c) D2 signal, (d) D2 edited signal 
Table 2: 
The compression characteristics between the original and
edited signals 

 Fig. 14: 
The fatigue damage changes over the COL values for: (a) D1
signal, (b) D2 signal 
For this case, the 10% difference in the rootmeansquare and kurtosis values
between the edited and the original signals was used for analysing experimental
road load data sets. This is important in order to retain the signal energy
and amplitude ranges^{[25,26]}.
From the result, the optimum COL value for D1 was 500 and 20 με^{2}Hz^{1}
for D2. Both of the edited signals gained from those COL value were retained
in the majority of the fatigue damage and were approximately same as the original
signal and they also retained the statistical parameters with below than 10%
deviation. Figure 15 represent the edited signal for both
D1 and D2 signals. The D1 edited signal recorded 126 seconds signal length which
reduced 16% of the original signal length, while the D2 edited signal was 84.67%
(127 sec) of the original signal.
 Fig. 15: 
The time history plots for: (a) the D1 edited signal, (b)
the D2 edited signal 
The compression characteristics between the original and edited signals were
shown in Table 2.
In overall, the analysis findings of this paper suggested that the STFTbased fatigue data editing can successfully remove the low amplitude cycles with respect to the power spectrum distribution, that retain higher fatigue damage segments in the time history. With the basis of the statistical parameter retention between the original and the edited signals, this technique produced the highly accurate edited signal which was similar to the original signal. The STFT power spectrum shows relatively adequate with damage event in the fatigue signal and is a very useful tool for damage detection in the fatigue signal. The extraction of damaging events successfully created a new edited signal which retained the majority of the fatigue damage. CONCLUSION This study discussed the study of a fatigue data editing technique in timefrequency domain by using STFT method. The STFTbased computational algorithm was developed to remove the low amplitude cycles which were contained in the original signal. The validation of the effectiveness of STFT was done by using the SAE data, called SAESUS. From the result, the damage segment contained high power spectrum and the nondamage segments were located in the lower part of the power spectrum. Obviously, the nondamage power spectrum has the power level below than 4×10^{5} με^{2}Hz^{1} which is close to the minimum value. It was shown that the power spectrum gained from the STFT algorithm has a significant relationship with the fatigue damage distribution. The editing process was performed based on the COL parameter which eliminated the cycle that contain power spectrum lower than COL value. In the presented case study, two new shortened edited signals, i.e., the D1 edited signal and the D2 edited signal were obtained. The edited signals gave conspicuous decreases of the signal length. The D1 edited signal had 126 sec of the time length, with the shortening of 16% of the original signal length. Similarly, the D2 edited signal was only 127 sec of the time length, which is about 15.3% reduction from the original signal length. Both of the signals also retained the major signal statistics with below than 10% of the rootmeansquare value (represents the vibration signal energy in a time series) and the kurtosis value (represent the amplitude range in a time series). In terms of the applicability of the shortened signal, this kind of signal can be normally used in the durability laboratory scale fatigue test. Such test is very important in the fatigue design criteria, especially for the task of accelerated fatigue testing. Finally, this method is suggested as an alternative technique in fatigue durability study, especially for the automotive engineering field. ACKNOWLEDGEMENT The authors would like to express their gratitude to Universiti Kebangsaan Malaysia and Ministry of Science, Technology and Innovation, through the fund of 030102SF0052, for supporting these research activities. " target="_blank">View Fulltext
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