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Probabilistic-based analysis for damaging features of fatigue strain loadings

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This paper presents the behaviour of fatigue damage extraction in fatigue strain histories of automotive components using the probabilistic approach. This is a consideration for the evaluation of fatigue damage extraction in automotive components
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    M.F.M. Yunoh et alii, Frattura ed Integrità Strutturale, 46 (2018) 84-93; DOI: 10.3221/IGF-ESIS.46.09 84 Developments in the fracture and fatigue assessment of materials and structures    Probabilistic-based analysis for damaging features of fatigue strain loadings  M. F. Mod Yunoh, S. Abdullah Centre for Automotive Research, Faculty of Eng. and Built Enviroments, Universiti Kebangsaan Malaysia  faridzyunus@gmail.com, shahrum@ukm.edu.my M. H. M. Saad, Z. M. Nopiah, M. Z. Nuawi, S. S. K. Singh Dept. of Mechanical and Materials, Faculty of Eng. and Built Enviroments, Universiti Kebangsaan Malaysia hanifsaad@ukm.edu.my, zmn@ukm.edu.my, mzn@ukm.edu.my, salvinder@ukm.edu.my  A  BSTRACT .  This paper presents the behaviour of fatigue damage extraction in fatigue strain histories of automotive components using the probabilistic approach. This is a consideration for the evaluation of fatigue damage extraction in automotive components under service loading that is vital in a reliability analysis. For the purpose of research work, two strain signals data are collected from a car coil spring during a road test. The fatigue strain signals are then extracted using the wavelet transform in order to extract the high amplitude segments that contribute to the fatigue damage. At this stage, the low amplitude segments are removed because of their minimal contribution to the fatigue damage. The fatigue damage based on all extracted segments is calculated using some significant strain-life models. Subsequently, the statistics-based Weibull distribution is applied to evaluate the fatigue damage extraction. It has been found that about 70% of the probability of failure occurs in the 1.0 x 10 -5  to 1.0 x 10 -4  damage range for both signals, while 90% of the probability of failure occurs in the 1.0 x 10 -4  to 1.0 x 10 -3  damage range. Lastly, it is suggested that the fatigue damage can be determined by the  Weibull distribution analysis K  EYWORDS .  Fatigue damage; Features extraction; Probabilistic; Wavelet;  Weibull distribution. Citation:  Yunoh, M. F. M., Abdullah, S., Saad, M. H. M., Nopiah, Z. M., Nuawi, M. Z., Singh, S. S. K., Determining probabilistic-based failure of damaging features for fatigue strain loadings, Frattura ed Integrità Strutturale, 46 (2018) 84-93. Received: 18.01.2018  Accepted: 20.05.2018 Published:  01.10.2018 Copyright:  © 2018 This is an open access article under the terms of the CC-BY 4.0,  which permits unrestricted use, distribution, and reproduction in any medium, provided the srcinal author and source are credited. I NTRODUCTION atigue life prediction under service loading remains a challenging problem in real life, especially in the automotive industry. In an automotive application, service loadings such as stress on a car wheel are in variable amplitude loading, as reported in Sonsino [1]. This situation leads to a need for developing a new approach to predict the reliability of F     M. F. M. Yunoh et alii, Frattura ed Integrità Strutturale, 46 (2018) 84-93; DOI: 10.3221/IGF-ESIS.46.09    85 the components that are subjected to the fatigue loading. The fatigue time histories often contain a major percentage of small amplitude cycles, and the fatigue damage for these cycles can also be small. Therefore, in many cases, the fatigue loading history is edited by removing these small amplitude cycles to produce representative and meaningful, yet economical testing, Stephens et al. [2]. Several fatigue data editing techniques have been developed for use in the time domain analysis, Abdullah et al. [3]. Some previous algorithms have been developed for eliminating low amplitude cycles in order to only retain the high amplitude cycles, El Ratal et al. [4]. In the frequency domain, the time history is a low pass filtered by the criterion that high-frequency cycles have small amplitude, which is are not damaging. The filtering method does not shorten the signal   because it does not provide the time-based information, Nizwan et al. [5]. In addition, Abdullah et al. [3] have developed a method for data editing to shorten the strain signal in the time-frequency domain. In fatigue data editing, the behaviour of extraction segments also needs to be studied because it contributes many bits of information that can improve fatigue life prediction.  To deal with uncertainties and variations in fatigue data, the statistical analysis, i.e. the probability analysis is the best approach that should be adopted. Zhao and Liu [6] use the approach of statistical aspects of the S-N curve by means of the  Weibull distribution. This approach indicates that an appropriate distribution determination is the primary task for a rolling contact fatigue analysis. Tiryakioglu [7] uses the Weibull analysis in fatigue data and predicts the failure mechanisms due to cracks initiating from surface and interior defects.  The evaluation of fatigue damage extraction for automotive components under service loading is vital in the reliability analysis. Very few analysis methods have been developed to evaluate the fatigue damage extraction. A consistent description of the probability of damage occurrences is possible only if the damage distribution function is known. In this paper, two sets of strain signals from the real component in service are used in the fatigue feature extraction. The feature extraction, i.e. fatigue damage, is analysed using statistical inferences. The objective of this study is to determine the probabilistic-based failure of damage featured in the strain signals, and at the same time, validate them through the extraction process. By considering the significant statistical tools, features extraction is combined with the Weibull distribution analysis in order to obtain a better evaluation.  T HEORETICAL BACKGROUND   The Global Statistic he time series contains an explanation of a set of variables taken at equally spaced time intervals. A statistical analysis is normally used to determine the random signals and monitor the pattern of the analysed signals. The calculation of the root-mean-square (r.m.s.) and the kurtosis is very important in the fatigue signals in order to retain a certain number of the signal amplitude range characteristics. The r.m.s. value is the 2nd statistical moment, is used to quantify the overall energy content of the signal. For discrete data sets the r.m.s. value is defined as: (1)  While kurtosis is the signal 4th statistical moment, is a global signal statistic which is highly sensitive to the spikiness of the data. For discrete data sets the kurtosis value is defined as: (2)  where  j  x   is the amplitude of signal, n   is number of data and x   is the mean value. The Wavelet Transform  The wavelet transform (WT) is defined in the time-scale domain and is a significant tool for analysing the time-localised features of a signal. It represents a windowing technique within the variable-sized region. A wavelet transform can be classified as either a continuous wavelet transform (CWT) or a discrete wavelet transform (DWT) depending on the discretisation of the scale parameters of the analysing wavelet. The DWT based on such wavelet functions is called the orthogonal wavelet transform (OWT). Orthogonal wavelet transforms are normally applied for the compression and feature 2/112 1..     n j j  xn smr       n j j  x x smr n  K  144 )..( 1  T    M.F.M. Yunoh et alii, Frattura ed Integrità Strutturale, 46 (2018) 84-93; DOI: 10.3221/IGF-ESIS.46.09 86 selection of signals. DWT is derived from discrete CWT, and it is shown as the following expression, Purushotham et al. [8]:   /2*000 (,)(), mm  Wmnxtaatnbdt              (3)  where a   and  j   are the scale factor, both b   and k are the position, and Ψ   is the mother wavelet. Oh [9] has previously conducted fatigue data analysis using the wavelet transform (WT) for spike removal, denoising, and data editing. Piotrkowski et al. [10] used the Wavelet Transform application in acoustic emissions to detect damage and corrosion. Fatigue Life Assessment  The Palmgren-Miner linear cumulative damaging rule is normally associated with the established strain-life fatigue models Sun et al., [11]. The fatigue damage caused by each cycle of repeated loading is calculated by reference to material life curves, such as SN    or  N       curves. The fatigue damage caused by multiple cycles is expressed respectively as: 1  f  D  N         (4) i  f   N D  N           (5)  where D   is fatigue damage for one cycle and D   is total fatigue damage i   N   is the number of cycles within a particular stress range and its mean and  f   N   is a number of cycles.  The strain-life model commonly used for the prediction of fatigue strain life is the Coffin-Manson relationship model. This model can provide a traditional prediction when there is more compressive load time history and the mean stress is zero.  The following equation can define this model:     '2'2 bc  f aff   NfN  E        (6)  E  is the material modulus of elasticity, a     is the true strain amplitude, 2  f   N   is the number of reversals to failure, '  f     is the fatigue strength coefficient, b   is the fatigue strength exponent, '  f     is the fatigue ductility coefficient, c   is the fatigue ductility exponent, m     is the mean stress, and max    is the maximum stress.  The inclusion of mean stress effects in the life prediction makes the process more complex. The Morrow mean stress model is given by Dowling [12]:     ''' 122 bc  f m afff  f   NN  E                 (7)  where is the total strain amplitude, '  f    , b, '    and c are considered to be material properties,  f   N    is the number of cycles to failure, and m      is the mean stress. Another strain life model dealing with mean stress effects is known as the Smith- Watson-Topper (SWT) model, and its equation is written as: 22 '(2)''(2)  f bbc amakffff   NN  E             (8)     M. F. M. Yunoh et alii, Frattura ed Integrità Strutturale, 46 (2018) 84-93; DOI: 10.3221/IGF-ESIS.46.09    87  The Coffin-Manson relationship only considers the damaging calculation at zero mean stress. However, in real-case scenarios, some of the realistic service situations involve nonzero mean stresses. For example, in a case of the loading being predominantly compressive, particularly for wholly compressive cycles, the Morrow mean stress correction effect provides more realistic life estimates and seems to work reasonably well for steels, Ince & Glinka [13]. The Weibull Distribution In terms of the statistical analysis used in engineering, the Weibull distribution is a theoretical model that has been successfully used to model the life data. The Weibull distribution is described by the shape, scale, and threshold parameters.  The Weibull distribution model is a tool to develop the probabilistic analysis because of its ability to provide reasonably accurate failure analysis and failure forecasts with extremely small samples, Sivapragash, [14]. The 2-P Weibull distribution function is shown in Eqn. 7: (9)  where  f (x: θ  :  β   ) represents the probability of strain-life being equal to or less than x  , θ   is a scale parameter, and  β   is a shape parameter.   θ   and  β   are estimated by observation.  The Weibull distribution has been widely utilised to develop a model of extreme values, such as failure time and fracture strength, Shalabh et al. [15]. The Weibull distribution is a probabilistic analysis which has been used for the determination of static and dynamic mechanical properties of materials. This distribution has the capability to model experimental data  with different characters, Li et al. [16]. METHODOLOGY    n this work, the strain signal has been collected from the coil spring in the car suspension system during a road test as shown in Fig. 1 which is collected in macrostrain (  e     ). An established signal, known as SAESUS, is the typical strain history for the suspension system, developed by the Society of Automotive Engineers (SAE), as reported in Oh [9].  Another signal, S1, is a set of experimental strain signals measured at 500 Hz sampling rate using a strain gauge that is positioned on the coil spring component of a car being driven on a rural road at a velocity of 50 to 60 km/h. The measurement procedure is reported in their previous work by Yunoh et al. [17].    The fatigue signal was measured at the car coil spring which subjected to the road load service. All data were recorded as strain time histories and Fig. 2 shows the set-up of fatigue data measurement during the process. The strain value was measured using strain gauge and it was connected to the specific data logger, for data acquisition purpose. Experimental parameters such as sampling frequency and type of output data were then set using the common data logger interface. (a) (b) Figure 1: The strain signals used for the work: (a) SAESUS, (b) An experimental measured data, S1.   The extraction algorithm of the strain signal is developed for fatigue data editing purposes. The discrete wavelet transform is utilised to identify the high amplitude segments in the fatigue signal due to the high-energy coefficients magnitude. The magnitudes of the wavelet energy coefficients in the time-frequency domain are transposed into time histories representations to trace the location of the high amplitude segments. The respective magnitudes are obtained from the accumulation of wavelet transform magnitude distributions along the frequency band at each time interval. Thus, the energy coefficients in time representation are gained, and these signals are used to detect the presence of high amplitude events in the fatigue signal.                       x x x f   exp),:( 0 20 40 60 80 100 120-1,000-800-600-400-20002004006008001,000Time (s)    A  m  p   l   i   t  u   d  e   (  u  e   ) 0 20 40 60 80 100 120-500-400-300-200-100100200300400500Time (s)    A  m  p   l   i   t  u   d  e   (  u  e   ) I    M.F.M. Yunoh et alii, Frattura ed Integrità Strutturale, 46 (2018) 84-93; DOI: 10.3221/IGF-ESIS.46.09 88  The Cut-off Level (COL) needs to be set up for the elimination process in a high amplitude event extraction process. The COL is the minimum percentage of the wavelet energy coefficients to be retained and the segments with magnitudes lower than the COL value will be removed. The retained segments are then sliced from the srcinal signal. The sliced segment identification is performed by means of a search which identifies the point at which the signal envelope inverts from the decay behaviour. The two inversion points, one on either side of the peak value, define the temporal extent of the sliced segment. The srcinal strain signal is then edited to remove the low amplitude cycle contained in the signal based on the time location of the wavelet transform spectrum-sliced segment. The fatigue damage for every retained segment is then calculated for the probabilistic analysis. Figure 2: A diagrammatic process flow for fatigue signal collection   The fatigue damage for all segments is further analysed using the 2-P Weibull distribution to evaluate the segments’ extraction results. The advantage of using this distribution lies in its ability to explain the simple function. This approach is often used in assessing the fatigue life of the material based on its simple calculation, Glodez et al. [18]. All the fatigue damage of the retained segments is incorporated into the Weibull distribution, and as has been later suggested, based on the probability distribution, the resultant significant findings are utilised to reveal the inferences of this study. RESULTS AND DISCUSSIONS   irst, the strain signals were evaluated by observation based on statistics characteristics, i.e. number of cycles counted, root-mean-square (r.m.s), kurtosis and total damage as tabulated in Tab. 1. According to the results, the SAESUS signal produced higher values of r.m.s and kurtosis. This is due to the higher amplitude segments existing in the SAESUS signal compared to the S1 signal. Higher amplitude segments contributed more energy in the oscillatory signals.  The value of kurtosis for the SAESUS strain signal was found to be 4.32, which indicates that the spike and extreme values exist in the signal. This result was consistent with the r.m.s value for SAESUS, which is found to be 246.6 με , higher when compared to S1. The kurtosis value for both strain signals was not found in a Gaussian distribution because in a stationary Gaussian process, the kurtosis value is approximately 3.  The fatigue damage for both signals was calculated based on three strain-life models as tabulated in Tab. 1. The values of the fatigue damage based on the three models were close to each other with minor differences. The fatigue damage values for SAESUS were found to be higher compared to S1. The existence of the higher amplitude segments in the SAESUS signal contributed more fatigue damage compared to S1. F Strain GaugeStrain gauge position   Strain gauge connect to   data acquisition   Data transfer from data acuisition to comuterStrain signal in time domain  
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