Railway Axle Early Fatigue Crack Detection through Condition Monitoring Techniques
Abstract
:1. Introduction
2. Change Point Analysis (CPA) Methods
2.1. Unsupervised Learning Methods
Cluster Analysis with “k-means ++” Algorithm
- 1.
- The k initial centres are chosen arbitrarily C = { , , …, }.
- 2.
- For each i ∈ {1, …, k}, set the cluster Si to be the set of observations that is closer to one than they are to the other for all j ≠ i.
- 3.
- For each i ∈ {1, …, k}, set it to be the centre of mass of all points in Si.
- 4.
- Steps 2 and 3 are repeated until C no longer changes.
- 1.
- Initizalization:
- a.
- An initial centre is chosen uniformly at random from X.
- b.
- The next centre is chosen via a weighting based on probabilities selecting = x′ ∈ X, with probability D(x) being the shortest distance from a data point x to the closest centre previously chosen.
- c.
- Step 1b is repeated until a total of k centres is chosen.
- 2–4.
- Same steps as for the standard k-means algorithm.
3. Hypothesis and Methodology
- Hypothesis 1: in vibratory signals obtained during axle rotation, there are certain frequency bands where an increase in energy is produced when a crack appears. The energy increases due to cracking are experimentally detectable through vibration signals obtained from the bearing housing using energy analysis by means of WPT.
- Hypothesis 2: these frequencies can be associated with the theoretical fault frequencies reviewed in the state of the art (harmonics of the rotational speed and subharmonics of critical frequencies). Theoretical fault frequencies depend on the rotational speed and structural effects such as material and axle model. If energy increases are detected at these frequencies, it is known to be due to the occurrence of the crack and not to other causes.
- Hypothesis 3: the energy increases that occur at the theoretical defect frequencies are significant enough to be detected by these signals and these signal processing techniques, therefore allowing the presence of a crack to be diagnosed.
- Hypothesis 4: these energy surges do not manifest themselves when the axle is not damaged.
- 1.
- Design and performance of the experimental tests. Experimental tests are designed in such a way that the natural frequencies of the specimen to be tested are obtained in the first place. On the other hand, some fatigue tests are designed and carried out on a railway axle fatigue testing machine. A triaxial accelerometer to register vibration signals is set (), and two classes of test are conducted: one where the railway axles fatigue limit is exceeded and there is evidence that they have been cracked during the test (magnetic particle testing), as well as axles in which the fatigue limit is not exceeded and there is evidence that they have not been cracked during the test. The crack under study is transverse and subsurface. This is a fatigue crack and appears below a section change, which is a stress concentration zone. These cracks are the most common cracks within railway axles, and this is the area where fatigue cracks would appear in the railway axle fatigue test rig used, which operates to perform railway axle fatigue tests according to the standard EN 13261:2009+A1:2010.
- 2.
- Processing of the vibration signals obtained by calculating the WPT energy, using the Daubechies 6 function as the mother wavelet and with initial decomposition level k = 3 (then, the signal is divided in packets of the same resolution, that is, ). This makes it possible to increase the manageability of the signals while retaining valuable information about the defect. This mathematical tool was chosen because of the good results it has provided in previous work on the detection of cracks in axles. With respect to the mother wavelet, in previous work carried out in this field, the Daubechies 6 mother wavelet has traditionally been used due to its good results. However, recent studies have shown that the mother wavelet function chosen does not greatly affect the results obtained [52]. However, although recent studies have shown that the mother wavelet function chosen does not greatly affect the results obtained, according to [53], using the Daubechies 6 mother wavelet improves reliability when detecting incipient defects.
- 3.
- Pattern selection. When there is evidence that the axle is cracked during the test, an analysis of the evolution of the energy with the number of cycles by frequency bands or packages is carried out. The aim is to find the packages whose energy value is sensitive to the appearance of the defect. Those packages that show a change of trend or change point in the energy levels that allow the crack initiation to be detected are chosen as possible defect indicators.
- 4.
- Study of the crack initiation or change point. Once the packets indicating the presence of the crack have been selected, the offline change point will be determined using the clustering algorithm based on k-means ++. Euclidean distances are used after checking that the method of distance measurement does not affect the results. In this way, the data are divided into two groups (cracked axle–non-cracked axle), and the transition determines the change point, which defines the point where the crack is detectable using these techniques. This would confirm Hypothesis 3. The change point may vary from one packet to another depending on the sensitivity of the packets to the occurrence of the crack. The determination of the change point will serve to indicate which of the packets affected by the crack has a higher sensitivity to the occurrence of the crack and can therefore provide earlier detection. The pattern that shows the changeover point earliest will be considered the optimum pattern. The change point estimated in this way will establish the transition energy value to be considered as the alarm value, which will be validated through statistical techniques.
- 5.
- Parameterization of the automatic adaptive alarm value. Once the final alarm value has been obtained in each case, a parameterisation of the same is studied to stablish an alarm value appropriate to the response of the machine that can be calculated during an online test. The parameterization is carried out according to the sample mean and standard deviation of the energies for a time window of size n, previous to the point analysed. This is in accordance with the recommendations given in [54] for automatic adaptive alarms, and it is also in line with the establishment of the threshold value for pattern selection in decision trees (step 3 of methodology). The parametric adjustment of the weight of these two parameters is performed by calculating the minimum norm least squares solution to the indeterminate equation that yields the value of as a function of the mean and standard deviation.
- 6.
- Verification that the selected fault indicators do not exceed the set alarm value for tests where the axle is not cracked.
4. Experimental Setup
5. Results
5.1. Experimental Tests
5.2. Signal Processing
5.3. Pattern Selection for Cracked Axle
5.4. Crack Initiation Point Estimation
5.5. Alarm Value Setting
5.6. Validation against Uncracked Axle
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Natural Frequencies N | Frequency [Hz] |
---|---|
fN1 | 194.2 |
fN2 | 485.2 |
fN3 | 886.0 |
fN4 | 1335.5 |
fN5 | 1857.2 |
Test | Speed (r.p.m.) | Load (kN) | Stopping Reason | Number of Cycles |
---|---|---|---|---|
1 | 509 | 216 | Number of cycles | 10,000,000 |
2 | 509 | 240 | Alarm values reached | 1,467,172 |
Sampling Frequency (Hz) | Signal Length (N) |
---|---|
6000 | 16,384 (214) |
Test | Speed (r.p.m.) | Number of Cycles | Number of Signals (M) |
---|---|---|---|
1 | 509 | 10,000,000 | 6550 |
2 | 509 | 1,467,172 | 960 |
Rotating Frequency (Hz) | 2X | Harmonics (Hz) 3X | 4X |
---|---|---|---|
8.48 | 16.97 | 25.45 | 33.93 |
1/2X | Subharmonics (Hz) 1/3X | 1/4X | |
194.2 | 97.1 | 64.73 | 48.55 |
Packet i | ||
---|---|---|
(9,11) | 3.7 | 1.12 |
(9,12) | 3.65 | 1.25 |
(9,13) | 3.33 | 1.2 |
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Gomez, M.J.; Castejon, C.; Corral, E.; Cocconcelli, M. Railway Axle Early Fatigue Crack Detection through Condition Monitoring Techniques. Sensors 2023, 23, 6143. https://doi.org/10.3390/s23136143
Gomez MJ, Castejon C, Corral E, Cocconcelli M. Railway Axle Early Fatigue Crack Detection through Condition Monitoring Techniques. Sensors. 2023; 23(13):6143. https://doi.org/10.3390/s23136143
Chicago/Turabian StyleGomez, María Jesús, Cristina Castejon, Eduardo Corral, and Marco Cocconcelli. 2023. "Railway Axle Early Fatigue Crack Detection through Condition Monitoring Techniques" Sensors 23, no. 13: 6143. https://doi.org/10.3390/s23136143
APA StyleGomez, M. J., Castejon, C., Corral, E., & Cocconcelli, M. (2023). Railway Axle Early Fatigue Crack Detection through Condition Monitoring Techniques. Sensors, 23(13), 6143. https://doi.org/10.3390/s23136143