# Metro Track Geometry Defect Identification Model Based on Car-Body Vibration Data and Differentiable Architecture Search

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Traditional Train Vibration Data Analysis Methods

#### 2.2. ML-Based Train Vibration Data Analysis Method

#### 2.3. Network Architecture Search in the Field of ML

#### 2.4. Discussion of Existing Research

## 3. Problem Description

#### 3.1. Basic Problem

#### 3.2. Transformed Problem

**Design rules for CVD**–

**TGD example dataset generation**investigates the method of transforming the original data and prediction target in the CVD-based metro-TGD identification problem into input and output suitable for MTGDI-CNN. Moreover, it needs to consider 1) the method for transforming continuous CVD into discrete samples suitable for CNN input and 2) the heterogeneous factors between CVD and TGD that need to be introduced when generating the sample.

**MTGDI**-

**CNN architecture design**,

**training**,

**and evaluation**. The model architecture is designed according to the example dataset. CVD and TGD have a complex functional relationship that warrants an increase in the number of CNN layers to fit. However, adding layers to a CNN model with an ordinary simple architecture will lead to overfitting, thereby reducing the identification performance of the model [14]. Therefore, the NAS problem of MTGDI-CNN is a key problem to be addressed in the MTGDI-CNN development. This scheme must also consider (1) the reduction in the search space in Equations (1) and (2) the improvement of the training speed in Equations (2) and (3) the strategy to cope with the class-imbalance problem in the TGD dataset, and (4) the evaluation of the comprehensive performance of different model architectures in the context of the practical needs of metro management.

## 4. Metro Track Geometry Defect Identification Model and Its Optimization Method

#### 4.1. Example Dataset Design

#### 4.1.1. Sample Generation Rules

#### 4.1.2. Sample Labeling Rules

#### 4.2. MTGDI-CNN Based on DARTS

#### 4.2.1. Model Architecture

#### 4.2.2. Cell Architecture

#### 4.2.3. Computing Operation Architecture

#### 4.2.4. Cell Architecture Search Based on DARTS

#### 4.2.5. Coping with Dataset Class-Imbalance Problem

#### 4.3. Model-Performance Evaluation Metric

#### 4.3.1. Selection Principles of Model-Performance Evaluation Metrics

#### 4.3.2. TGD-Identification Performance-Evaluation Metric

## 5. Case Study

#### 5.1. Case Data Description

#### 5.2. Analysis of Identification Effect

#### 5.2.1. Setting of Model Parameters

**Computing operations**. According to the sample size, the kernel sizes were $3\times 3$, $5\times 5$, $7\times 7$ in 2D DSCB, $3\times 3$, $5\times 5$ in 2D DiSCB, $3\times 3$ in 2D MaxPool, and 2D AvgPool. Featuring the void operation, eight elements were present in the alternative computing operation set of the cell edges.

**CAS**. The number of stacked cells was eight, the channel number for the Init Conv was six, the batch size of each iteration was 128, and the number of training epochs was 50. The other parameters were in accordance with the DARTS basic setting [38]. Moreover, the number of intermediate nodes in the cells was four. The loss function was the cross-entropy loss function [53]. The inner optimization algorithm used was the stochastic gradient descent (SGD) [57], and the learning rate was updated via the non-restart cosine annealing method [58], with an initial value of 0.025, momentum of 0.9, and weight decay of 0.004. The outer optimization algorithm was Adam [59] with a learning rate of 0.004, momentum of $\left[0.5,0.999\right]$, and a weight decay of 0.001.

**FMV**. Different numbers of stacked cells and training epochs were set in this study to analyze the impact of these hyperparameters on the model performance, which is described in detail in later sub-sections. The number of channels for the Init Conv was six, and the batch size of each iteration was 512. The other parameters were in accordance with the DARTS basic settings [38]. The loss function employed was the cross-entropy loss function, and SGD was utilized as the optimization algorithm. To improve the training efficiency, cutout [60] and path dropout [61] with a probability of 0.2 were employed.

**Implementation and computing**. The models in this case study were all implemented via the PyTorch [62] ML framework and were trained on a single NVIDIA GeForce GTX 1080 8 gigabyte GPU.

#### 5.2.2. Model Identification Results

#### 5.3. Validation of the Effectiveness of Coping Strategies for Class-Imbalance Problem

#### 5.3.1. Setting of Validation

#### 5.3.2. Results of Validation

#### 5.4. Comparison with Other Models

#### 5.4.1. Comparison with the Model Constructed by 1D Convolution

- (1)
- Setting of 1D model parameters

- (2)
- Model validation results of 1D model

#### 5.4.2. Comparison with the Model Obtained by a Black Box Trial Method

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**(

**A**) CVD coordinate system; (

**B**) CVD acquisition location; (

**C**) structure of the portable detector.

**Figure 5.**(

**A**) ETI data; (

**B**) transformed EDI data; (

**C**) zoom-in ETI data; (

**D**) zoom-in transformed EDI data. (the RMS means root mean square).

**Figure 10.**(

**A**) Normal cell architecture obtained from CAS; (

**B**) reduction cell architecture obtained from CAS. (the transparent circles represent the input/output nodes, the normal circles represent the intermedia nodes, the arrows means the links between nodes and number 0-3 means the order of the intermedia nodes).

**Figure 11.**(

**A**) Comparison of ${F}_{2}^{\mathrm{TGD}}$ for models with different hyperparameter combinations; (

**B**) comparison of training time for models with different hyperparameter combinations.

Metric | No LLs | Level-I LL | Level-II LL |
---|---|---|---|

${P}^{\left(i\right)}$ | 0.9971 | 0.9392 | 0.6444 |

${R}^{\left(i\right)}$ | 0.9984 | 0.8528 | 0.8529 |

Mode | CAS Train | CAS Test | FMV Train | FMV Test |
---|---|---|---|---|

M-1 | ROS | ROS | ROS | ORI |

M-2 | ROS | ORI | ROS | ORI |

M-3 | ORI | ORI | ROS | ORI |

BASE | ORI | ORI | ORI | ORI |

Mode | $\mathbf{Avg}.{\mathit{F}}_{2}^{\mathit{T}\mathit{G}\mathit{D}}$ | $\mathbf{Avg}.{\mathit{F}}_{1}^{\mathit{T}\mathit{G}\mathit{D}}$ | $\mathbf{Avg}.{\mathit{F}}_{0.5}^{\mathit{T}\mathit{G}\mathit{D}}$ | Avg. Training Time (GPU Days) |
---|---|---|---|---|

M-1 | 0.8561 | 0.8346 | 0.8141 | 0.0669 |

M-2 | 0.8538 | 0.8367 | 0.8202 | 0.0755 |

M-3 | 0.8684 | 0.8428 | 0.8187 | 0.0655 |

BASE | 0.8043 | 0.8035 | 0.8029 | 0.0250 |

Mode | CAS Train | CAS Test | FMV Train | FMV Test |
---|---|---|---|---|

M-3-1D | ORI | ORI | ROS | ORI |

BASE-1D | ORI | ORI | ORI | ORI |

Mode | $\mathbf{Avg}.{\mathit{F}}_{2}^{\mathit{T}\mathit{G}\mathit{D}}$ | $\mathbf{Avg}.{\mathit{F}}_{1}^{\mathit{T}\mathit{G}\mathit{D}}$ | $\mathbf{Avg}.{\mathit{F}}_{0.5}^{\mathit{T}\mathit{G}\mathit{D}}$ | Avg. Training Time (GPU Days) |
---|---|---|---|---|

M-3 | 0.8684 | 0.8428 | 0.8187 | 0.0655 |

M-3-1D | 0.6516 | 0.6482 | 0.6456 | 0.0648 |

BASE-1D | 0.5286 | 0.5613 | 0.5997 | 0.0238 |

Metrics | ${\mathit{F}}_{2}^{\mathit{T}\mathit{G}\mathit{D}}$ | ${\mathit{F}}_{1}^{\mathit{T}\mathit{G}\mathit{D}}$ | ${\mathit{F}}_{0.5}^{\mathit{T}\mathit{G}\mathit{D}}$ |
---|---|---|---|

MTGDI-CNN Avg. metrics | 0.8684 | 0.8428 | 0.8187 |

$\mathrm{Wang}-\mathrm{model}\mathrm{Max}.\mathrm{Avg}.{F}_{2}^{\mathrm{TGD}}$ | 0.8142 | 0.7821 | 0.7681 |

$\mathrm{Wang}-\mathrm{model}\mathrm{Max}.\mathrm{Avg}.{F}_{1}^{\mathrm{TGD}}$ | 0.7924 | 0.8205 | 0.8144 |

$\mathrm{Wang}-\mathrm{model}\mathrm{Max}.\mathrm{Avg}.{F}_{0.5}^{\mathrm{TGD}}$ | 0.7900 | 0.8038 | 0.8180 |

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## Share and Cite

**MDPI and ACS Style**

Wang, Z.; Liu, R.; Gao, Y.; Tang, Y. Metro Track Geometry Defect Identification Model Based on Car-Body Vibration Data and Differentiable Architecture Search. *Appl. Sci.* **2023**, *13*, 3457.
https://doi.org/10.3390/app13063457

**AMA Style**

Wang Z, Liu R, Gao Y, Tang Y. Metro Track Geometry Defect Identification Model Based on Car-Body Vibration Data and Differentiable Architecture Search. *Applied Sciences*. 2023; 13(6):3457.
https://doi.org/10.3390/app13063457

**Chicago/Turabian Style**

Wang, Zhipeng, Rengkui Liu, Yi Gao, and Yuanjie Tang. 2023. "Metro Track Geometry Defect Identification Model Based on Car-Body Vibration Data and Differentiable Architecture Search" *Applied Sciences* 13, no. 6: 3457.
https://doi.org/10.3390/app13063457