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Image Recognition Method for Missing and Looseness of Hexagonal-Head Bolts Based on the Optimal Hexagon Rule
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Suyi MAO1, Xiaoheng ZONG2, Xiaoguang WEN3, 4, Xiaorui FENG5, Wenlong CHEN4, Guowei ZHANG6, Ji ZHANG5, Yingjie SUN4, Yongxing ZHANG2, Dongdong CHEN2
Industrial Construction | 2026, 56(5) : 239 - 247
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Industrial Construction | 2026, 56(5): 239-247
Image Recognition Method for Missing and Looseness of Hexagonal-Head Bolts Based on the Optimal Hexagon Rule
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Suyi MAO1, Xiaoheng ZONG2, Xiaoguang WEN3, 4, Xiaorui FENG5, Wenlong CHEN4, Guowei ZHANG6, Ji ZHANG5, Yingjie SUN4, Yongxing ZHANG2, Dongdong CHEN2
Affiliations
  • 1Jiangsu Expressway Company Limited， Nanjing210049， China
  • 2School of Civil Engineering， Nanjing Forestry University， Nanjing210037， China
  • 3China Railway Major Bridge Reconnaissance & Design Institute Co.， Ltd.， Wuhan430056， China
  • 4China Railway Bridge and Tunnel Technologies Co.， Ltd.， Nanjing210061， China
  • 5Beijing Jingneng International Integrated Smart Energy Co.， Ltd.， Beijing101204， China
  • 6Beijing Energy International Holding Co.， Ltd.， Beijing100020， China
Published: 2026-05-20 doi: 10.3724/j.gyjzG26033101
Outline
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A vision-based detection method for bolt missing and loosening using the optimal hexagon rule is proposed. High-quality images are obtained through preprocessing operations such as perspective transformation and distortion correction. Based on the optimal hexagon rule， combined with a regional attention mechanism and a residual efficient layer aggregation network， a keypoint detection algorithm based on YOLOv26 is developed to precisely locate the six vertex coordinates of the head of standard hexagonal-head bolts. The Graham scan algorithm is adopted to obtain the convex hull of the circumcircle of the six bolt vertices. Taking the centroid of the convex hull as the center， the sum of deviations between the actual and estimated values of the six vertices is minimized. The Broyden-Fletcher-Goldfarb-Shanno （BFGS） quasi-Newton optimization algorithm is used to adjust the vertex coordinates and generate optimized regular hexagon vertex coordinates. By comparing the coordinate states of bolts， the rotation angle of the bolt can be calculated. Bolt joint rotation tests using 16-hole three-color bolt heads （gray， blue， and red） showed that within the loosening angle range of 0–60°， the absolute error of the identified bolt loosening angle ranged from -2° to 2°， with a maximum relative error of 8%， demonstrating that the proposed optimal hexagon method provided high detection accuracy and stability.

bolt missing  /  bolt looseness  /  computer vision  /  image recognition  /  optimal hexagon rule
Suyi MAO, Xiaoheng ZONG, Xiaoguang WEN, Xiaorui FENG, Wenlong CHEN, Guowei ZHANG, Ji ZHANG, Yingjie SUN, Yongxing ZHANG, Dongdong CHEN. Image Recognition Method for Missing and Looseness of Hexagonal-Head Bolts Based on the Optimal Hexagon Rule[J]. Industrial Construction, 2026 , 56 (5) : 239 -247 . DOI: 10.3724/j.gyjzG26033101
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Year 2026 volume 56 Issue 5
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Article Info
doi: 10.3724/j.gyjzG26033101
  • Receive Date：2026-03-31
  • Online Date：2026-06-25
  • Published：2026-05-20
Article Data
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History
  • Received：2026-03-31
Affiliations
    1Jiangsu Expressway Company Limited， Nanjing210049， China
    2School of Civil Engineering， Nanjing Forestry University， Nanjing210037， China
    3China Railway Major Bridge Reconnaissance & Design Institute Co.， Ltd.， Wuhan430056， China
    4China Railway Bridge and Tunnel Technologies Co.， Ltd.， Nanjing210061， China
    5Beijing Jingneng International Integrated Smart Energy Co.， Ltd.， Beijing101204， China
    6Beijing Energy International Holding Co.， Ltd.， Beijing100020， China
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https://castjournals.cast.org.cn/joweb/gyjz/EN/10.3724/j.gyjzG26033101
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多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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