# Deep-Learning and Vibration-Based System for Wear Size Estimation of Railway Switches and Crossings

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Deep-Learning Algorithms for Feature Learning

#### 2.1. Long Short-Term Memory (LSTM) for Feature Learning

_{f}, b

_{i}, b

_{o}, and b

_{c}are the biases matrices and they are not time-dependent, this implies that these matrices do not update from one-time step to another.

_{t}, h

_{t−}

_{1}, and c

_{t−}

_{1}are the inputs from the previous timestep LSTM. o

_{t}illustrate the output of the LSTM cell for the current timestep. The LSTM also produces the c

_{t}and h

_{t}for the feeding of the next time step LSTM. Based on the present input x, the internal state c and the hidden state h, the internal gates will decide as to the amount of information that can be updated into the hidden state h and the cell state c. This behavior grants the LSTM cell the ability to uncover new key features and remove irrelevant information.

#### 2.2. The Residual Neural Network (ResNet) for Feature Learning

## 3. Materials and Methods

#### 3.1. Experimental Set Up and Sensors Placement

#### 3.2. Data Aquisition for Vibration and Speed

#### 3.3. Wear Severity Classification Using LSTM and RESNET

#### 3.3.1. LSTM Model for Wear Severity Classification

#### 3.3.2. ResNet Model for Wear Severity Classification

## 4. Results and Discussion

#### 4.1. Vibration Measurements

#### 4.2. Wear Measurement

#### 4.3. Wear Measurement Using LSTM Model

#### 4.4. Wear Measurement Using ResNet Model

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Principle sketch of the test switch (bogie picture: courtesy of Igor Antolovic at Kockums Industrier AB).

**Figure 5.**(

**a**) Bogie with two winches and an electrical power supply, (

**b**) remote control unit, and (

**c**) tachometer.

**Figure 13.**Spectrograms obtained from the vibration data for different level of wear: (

**a**) no wear, (

**b**) first level, (

**c**) second level, (

**d**) third level.

Position | Accelerometer | Frequency (kHz) | Direction |
---|---|---|---|

C | KS91C1 | 37 | Z |

A | 608A11 | 10 | X |

A | 608A11 | 10 | Y |

A | 608A11 | 10 | Z |

B | SKF 2310T | 10 | Y |

D | SKF 2310T | 10 | Y |

Features | Formula |
---|---|

Root Mean Square (RMS) | ${X}_{rms}=\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}{x}_{i}{}^{2}}$ |

Skewness | ${X}_{skew}=\frac{{{\displaystyle \sum}}_{i=1}^{N}{\left({x}_{i}-m\right)}^{3}}{\left(N-1\right){\sigma}^{3}}$ |

Kurtosis | ${X}_{kurt}=\frac{{{\displaystyle \sum}}_{i=1}^{N}{\left({x}_{i}-m\right)}^{4}}{\left(N-1\right){\sigma}^{4}}$ |

Shape factor | ${X}_{shape}=\frac{\sqrt{\frac{1}{N}{{\displaystyle \sum}}_{i=1}^{N}{x}_{i}^{2}}}{\frac{1}{N}{{\displaystyle \sum}}_{i=1}^{N}\left|{x}_{i}\right|}$ |

Crest factor | ${X}_{crest}=\frac{max\left|{x}_{i}\right|}{\sqrt{\frac{1}{N}{{\displaystyle \sum}}_{i=1}^{N}{x}_{i}^{2}}}$ |

Impulse factor | ${X}_{impl}=\frac{max\left|{x}_{i}\right|}{\frac{1}{N}{{\displaystyle \sum}}_{i=1}^{N}\left|{x}_{i}\right|}$ |

Clearance (Margin) factor | ${X}_{clear}=\frac{max\left|{x}_{i}\right|}{{\left(\frac{1}{N}{{\displaystyle \sum}}_{i=1}^{N}\sqrt{\left|{x}_{i}\right|}\right)}^{2}}$ |

When | Repetition |
---|---|

Orig. wear level ^{1} | 4 |

1st wear level | 3 |

2nd wear level | 3 |

3rd wear level | 3 |

^{1}The original condition of the S&C.

Tool Position | Orig. Wear Level | 1st Wear Level ^{1} | 2nd Wear Level ^{1} | 3rd Wear Level ^{1} |
---|---|---|---|---|

X0 | 0.51 | 1.31 | 2.62 | 3.82 |

X3 | 1.63 | 2.36 | 4.48 | 5.92 |

X6 | 4.30 | 4.54 | 6.54 | 8.00 |

Z0 | 0.96 | 0.94 | 0.96 | 0.96 |

^{1}All measurements are in millimeters.

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**MDPI and ACS Style**

Najeh, T.; Lundberg, J.; Kerrouche, A. Deep-Learning and Vibration-Based System for Wear Size Estimation of Railway Switches and Crossings. *Sensors* **2021**, *21*, 5217.
https://doi.org/10.3390/s21155217

**AMA Style**

Najeh T, Lundberg J, Kerrouche A. Deep-Learning and Vibration-Based System for Wear Size Estimation of Railway Switches and Crossings. *Sensors*. 2021; 21(15):5217.
https://doi.org/10.3390/s21155217

**Chicago/Turabian Style**

Najeh, Taoufik, Jan Lundberg, and Abdelfateh Kerrouche. 2021. "Deep-Learning and Vibration-Based System for Wear Size Estimation of Railway Switches and Crossings" *Sensors* 21, no. 15: 5217.
https://doi.org/10.3390/s21155217