# Evolution of Rail Contact Fatigue on Crossing Nose Rail Based on Long Short-Term Memory

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## Abstract

**:**

## 1. Introduction

## 2. Features Acquisition and Methods

#### 2.1. A. Image Preprocessing

#### 2.2. Feature Extraction

#### 2.2.1. GLCM Feature Extraction

- Energy: It is the square sum of the element values of the gray co-occurrence matrix, so it is also called energy, which reflects the uniformity of the image’s gray distribution and the texture’s thickness.
- Contrast: it reflects the clarity of the image and depth of texture grooves.
- Correlation: It measures the similarity of the spatial grayscale co-occurrence matrix elements in the row or column direction. Therefore, the correlation value reflects the local grayscale correlation in the image.
- Entropy: It measures the amount of information an image has, and texture information belongs to the information of the image, which is a measure of randomness.
- Inverse differential moment: It reflects the homogeneity of the image texture and measures the local variation of the image texture. A significant value indicates no variation between different image text areas, and the local area is uniform.

#### 2.2.2. HOG Feature Extraction

#### 2.2.3. Gabor Feature Extraction

## 3. Regression Analysis

#### 3.1. Machine Learning Regression

#### 3.2. Deep Learning Regression

#### 3.3. Evaluation Indicators

^{2}[36] solves this problem. This article does not discuss their differences in detail and directly uses these data to measure the effect of regression models.

^{2}is, the higher the degree of explanation of the independent variable to the dependent variable. At the same time, the higher the percentage of the change caused by the independent variable to the total change. The scatter points are more clustered near the regression line (note that R

^{2}is not necessarily a 1:1 line), and in general, when R

^{2}is higher than 0.8, the fitting effect is better.

## 4. Results

^{2}has the opposite trend with these three values. They are reducing the number of features to reduce the calculation time. Eighteen principal components can be chosen for analysis when the data is vast because the R

^{2}value has exceeded 80%. However, to get the best results, this paper selects all 54 features for machine learning.

#### 4.1. Machine Learning Results

^{2}reaches the maximum, up to 0.91. This result can be fully applied to actual detection and prediction. The results in Table 1 and Table 2 also show that RSME is almost proportional to the other two indicators (MSE and MEA). Therefore, the authors only need to refer to one indicator. R

^{2}and RSME were applied as comparison metrics for neural network results.

#### 4.2. Long Short-Term Memory Results

#### 4.3. Results Evaluation

^{2}. The results of this paper have higher sensitivity than the results of [15]. The size of the main index proves that the result can evaluate and predict the damaged state of the track surface at any time. However, literature [15] can only expect in advance the surface damage of crossing nose tracks with a traffic volume of 10 Mt.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Feature No. | 6 | 12 | 18 | 27 | 35 | 44 | 48 | 52 | 54 |
---|---|---|---|---|---|---|---|---|---|

RSME | 7.314 | 6.2298 | 4.4361 | 4.1066 | 4.1909 | 3.9339 | 3.8559 | 3.8628 | 3.3273 |

MSE | 53.495 | 38.811 | 19.679 | 16.864 | 17.563 | 15.475 | 14.868 | 14.921 | 11.071 |

MEA | 5.2493 | 4.3527 | 3.1284 | 2.9974 | 3.0312 | 2.8421 | 2.8344 | 2.8266 | 2.3086 |

R^{2} | 0.58 | 0.7 | 0.85 | 0.87 | 0.86 | 0.88 | 0.88 | 0.88 | 0.91 |

GPR | Tree Ensemble | |||||
---|---|---|---|---|---|---|

Squared Exponential | Matern 5/2 | Rational Quadratic | Exponential | Bagged Trees | Boosted Trees | |

RSME | 3.5518 | 3.3739 | 3.3273 | 3.9627 | 4.9450 | 5.0920 |

MSE | 12.6160 | 11.3830 | 11.071 | 15.7370 | 24.4530 | 25.9290 |

MEA | 2.5092 | 2.3460 | 2.3086 | 2.8581 | 3.5040 | 3.8013 |

R^{2} | 0.90 | 0.91 | 0.91 | 0.88 | 0.81 | 0.80 |

SVR | ||||||

Linear | Quadratic | Cubic | Fine Gaussian | Medium Gaussian | Coarse Gaussian | |

RSME | 7.0201 | 28.528 | 21.025 | 8.7155 | 5.4601 | 8.3760 |

MSE | 49.282 | 62.847 | 42.199 | 73.787 | 27.408 | 68.912 |

MEA | 5.1181 | 3.6229 | 3.6891 | 7.2957 | 3.8202 | 6.0487 |

R^{2} | 0.62 | 0.51 | 0.67 | 0.43 | 0.79 | 0.46 |

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## Share and Cite

**MDPI and ACS Style**

Kou, L.; Sysyn, M.; Liu, J.; Nabochenko, O.; Han, Y.; Peng, D.; Fischer, S.
Evolution of Rail Contact Fatigue on Crossing Nose Rail Based on Long Short-Term Memory. *Sustainability* **2022**, *14*, 16565.
https://doi.org/10.3390/su142416565

**AMA Style**

Kou L, Sysyn M, Liu J, Nabochenko O, Han Y, Peng D, Fischer S.
Evolution of Rail Contact Fatigue on Crossing Nose Rail Based on Long Short-Term Memory. *Sustainability*. 2022; 14(24):16565.
https://doi.org/10.3390/su142416565

**Chicago/Turabian Style**

Kou, Lei, Mykola Sysyn, Jianxing Liu, Olga Nabochenko, Yue Han, Dai Peng, and Szabolcs Fischer.
2022. "Evolution of Rail Contact Fatigue on Crossing Nose Rail Based on Long Short-Term Memory" *Sustainability* 14, no. 24: 16565.
https://doi.org/10.3390/su142416565