# Effective Crack Detection in Railway Axles Using Vibration Signals and WPT Energy

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Prototype Description

## 3. Experimental System Description

#### 3.1. Bogie Test Rig

#### 3.2. Measurement Chain and Acquisition System

#### 3.3. Tests Description

#### 3.4. Data Processing

## 4. Results

#### 4.1. Feature Selection

#### 4.2. Neural Networks

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Bogie test rig with bogie Y21 Cse installed on it (

**1**), tested wheelset (

**2**), fixed wheelset (

**3**), left-hand-side (LHS) axle box (

**4**), right-hand-side (RHS) axle box (

**5**), driving system (

**6**), and driving roller (

**7**).

**Figure 8.**Example of decomposition in approximation (A) and detail (D) for a signal with a frequency range of $\pi $ Hz.

**Figure 10.**Evolution of energies (units: V${}^{2}/$s) versus crack levels D0, D1, D2, and D3 for features selected at WS2 LHS ccw 4 t–50 km/h at the vertical acceleration.

**Figure 11.**Evolution of energies (units: V${}^{2}/$s) versus crack levels D0, D1, D2, and D3 for features selected at WS1 RHS ccw 10 t–50 km/h at the vertical acceleration.

**Figure 13.**POD curves at 95% confidence for load and speed conditions at: (

**a**) 4 t–20 km/h; (

**b**) 4 t–50 km/h; (

**c**) 10 t–20 km/h; (

**d**) 10 t–50 km/h; (

**e**) 16 t–20 km/h; (

**f**) 16 t–50 km/h.

Maximum load (t) | 60 |

Maximum weight (t) | 20 |

Brake | Pneumatic |

Maximum speed (km/h) | 120 |

Width (m) | 2.1 |

Length (m) | 4 |

Sampling Frequency Fs (kHz) | Acquisition Time for Each Signal (s) | Number of Points N |
---|---|---|

12.8 | 1.28 | 16,384 (${2}^{14}$) |

D0 | 0 mm (healthy) |

D1 | 5.7 mm |

D2 | 10.9 mm |

D3 | 15 mm |

Packet Number | Related Frequency Band (Hz) |
---|---|

1 | 0–100 |

2 | 100–200 |

37 | 3600–3700 |

46 | 4500–4600 |

47 | 4600–4700 |

50 | 4900–5000 |

51 | 5000–5100 |

54 | 5300–5400 |

60 | 5900–6000 |

61 | 6000–6100 |

**Table 5.**Design parameters for the radial basis function artificial neural network (RBF-ANN). MSE: mean squared error.

Number of neurons at input | 32 | |

Normalization of input values | Between [−1;1] | |

Number of neurons at output | 1 | |

Normalization of output values | [−1,1] | |

Input data distribution | Training | 75% |

Test | 25% | |

Stopping criteria | MSE | 0.1–0.2 |

Number of neurons at hidden layer | 700 | |

Spread | 0.2–2 |

Spread Value | Neurons at Hidden Layer | MSE |
---|---|---|

1 | 201 | 0.1 |

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## Share and Cite

**MDPI and ACS Style**

Gómez, M.J.; Corral, E.; Castejón, C.; García-Prada, J.C.
Effective Crack Detection in Railway Axles Using Vibration Signals and WPT Energy. *Sensors* **2018**, *18*, 1603.
https://doi.org/10.3390/s18051603

**AMA Style**

Gómez MJ, Corral E, Castejón C, García-Prada JC.
Effective Crack Detection in Railway Axles Using Vibration Signals and WPT Energy. *Sensors*. 2018; 18(5):1603.
https://doi.org/10.3390/s18051603

**Chicago/Turabian Style**

Gómez, María Jesús, Eduardo Corral, Cristina Castejón, and Juan Carlos García-Prada.
2018. "Effective Crack Detection in Railway Axles Using Vibration Signals and WPT Energy" *Sensors* 18, no. 5: 1603.
https://doi.org/10.3390/s18051603