# Accurate Detection Method of Aviation Bearing Based on Local Characteristics

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Overall Scheme Design and Principle Analysis

#### 2.1. Overall Scheme Design of Ball Detection in Aviation Bearing

#### 2.2. U-Net Network

#### 2.3. Hough Transform Principle

- (1)
- An accumulator array with $\left(a,b,r\right)$ parameter is obtained by quantifying the three-dimensional parameter space appropriately.
- (2)
- After edge extraction, all points $\left(a,b\right)$ whose distance from each pixel on the edge is r are calculated.
- (3)
- Let r change from 0 to 256, and then repeat the above steps.
- (4)
- The values of all accumulators of a three-dimensional array are checked. The coordinates of their peaks correspond to the center of the circle.

## 3. Segmentation Method Based on U-Net Network and Hough Circle Detection Algorithms

#### 3.1. Improved U-Net Network

#### 3.1.1. BN Layer

- (1)
- The sensitivity to parameter selection is reduced. The network can choose a larger learning rate to improve the training speed.
- (2)
- The loss process is smoother to prevent the disappearance of gradient and gradient explosion.
- (3)
- Reduce the need for dropout while resolving the over-fitting problem.
- (4)
- The noise mixed in the training process can not only regularize the model parameters, but also improve the generalization ability of the network.

#### 3.1.2. Network Structure

#### 3.2. Hough Circle Detection of Aviation Bearing Ball Based on Segmentation

^{6}to 10

^{4}, but the amount of calculation is also very large. Therefore, the gradient information of edge points can be used to change r along the normal direction of the edge point $\left({x}_{i},{y}_{i}\right)$, which not only reduces the invalid search of Hough circle detection, but also improves the accuracy of circle detection. The formula for calculating the center of a circle is as follows:

## 4. Experiments and Results Analysis

#### 4.1. Sample Creation

#### 4.2. Comparison of Ball Segmentation Algorithms for Aviation Bearing Based on Improved U-Net Network

#### 4.3. Experimental Result

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Aviation bearing image: (

**a**) Aviation bearing complete image; (

**b**) Aviation bearing part image.

**Figure 3.**Results of original U-Net network segmentation: (

**a**) First segmentation result; (

**b**) Second segmentation result; (

**c**) Third segmentation result; (

**d**) Forth segmentation result.

**Figure 4.**Relationship between a binary image plan and the Hough space: (

**a**) The circle in the image X-Y plane space; (

**b**) Representation of parametric space.

**Figure 8.**Training sample diagram: (

**a**) Sample diagram; (

**b**) Segmented diagram; (

**c**) Sample diagram; (

**d**) Segmented diagram.

**Figure 10.**Experimental result: (

**a**) test diagram; (

**b**) original U-Net network segmentation result diagram; (

**c**) improved algorithm segmentation result diagram.

Hough Test Results (μm) | Original U-Net Network | Improved U-Net Network |
---|---|---|

(0–30) | 47 | 153 |

(30–60) | 87 | 17 |

(60–80) | 46 | 26 |

(80–100) | 13 | 5 |

(100–120) | 6 | 0 |

Average of error | 49.8669 | 29.4792 |

standard deviation | 24.2230 | 20.5054 |

false reject rate | 9.5% | 2.5% |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xue, P.; Jiang, Y.; Wang, H.; He, H.
Accurate Detection Method of Aviation Bearing Based on Local Characteristics. *Symmetry* **2019**, *11*, 1069.
https://doi.org/10.3390/sym11091069

**AMA Style**

Xue P, Jiang Y, Wang H, He H.
Accurate Detection Method of Aviation Bearing Based on Local Characteristics. *Symmetry*. 2019; 11(9):1069.
https://doi.org/10.3390/sym11091069

**Chicago/Turabian Style**

Xue, Ping, Yali Jiang, Hongmin Wang, and Hai He.
2019. "Accurate Detection Method of Aviation Bearing Based on Local Characteristics" *Symmetry* 11, no. 9: 1069.
https://doi.org/10.3390/sym11091069