# Comprehensive Safety Evaluation of Corroded Circular Steel Tubes under Compression Based on Image Processing

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## Abstract

**:**

## 1. Introduction

## 2. Corrosion Image Acquisition

## 3. Image Preprocessing

## 4. Feature Extraction

#### 4.1. Image Features before Rust Removal

#### 4.1.1. Sub-Image Energy Value

_{w}denotes the corrosion depth and E

_{H1}, E

_{V1}, and E

_{D1}represent the sub-image energy values in the horizontal, vertical, and diagonal directions after application of the one-level wavelet transform, respectively. E

_{H2}, E

_{V2}, and E

_{D2}are the sub-image energy values after applying the two-level wavelet transform in the above-mentioned directions, while E

_{H3}, E

_{V3}, and E

_{D3}denote the sub-image energy values after application of the three-level wavelet transform in the directions explained above.

#### 4.1.2. Information Entropy Value

#### 4.2. Image Features after Rust Removal

#### 4.2.1. Sub-Image Energy Value

#### 4.2.2. Information Entropy Value

#### 4.2.3. Image Fractal Dimension

_{maxi,j}and z

_{mini,j}are the maximum and minimum elevations after rust removal, respectively. If lnN(ε) increases linearly with ln(1/ε), this indicates that the image features after rust removal have fractal characteristics, and the slope of the lnN(ε)~ln(1/ε) curve is the fractal dimension, D, of the image features after rust removal.

## 5. Comprehensive Safety Evaluation Method and Verification

#### 5.1. Establishment of the Comprehensive Evaluation Method

#### 5.2. Calculation Example

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Image acquisition equipment and schematic representation of members: (

**a**) Schematic representation of CCSTs, (

**b**) Canon EOS600D.

**Figure 2.**Preprocessing of the collected images: (

**a**) image normalization, (

**b**) Gaussian filter denoising, (

**c**) histogram equalization.

**Figure 3.**Relationship between energy values of the sub-images obtained after applying the three-level wavelet transform and corrosion depths: (

**a**) E

_{H3}-t

_{w}, (

**b**) E

_{V3}-t

_{w}, (

**c**) E

_{D3}-t

_{w}.

**Figure 5.**Relationship between energy values of the sub-images obtained after one-level wavelet transform and the corrosion depths: (

**a**) E

_{H1}-t

_{w}, (

**b**) E

_{V1}-t

_{w}, (

**c**) E

_{D1}-t

_{w}.

**Figure 7.**Fractal dimensions of images at various corrosion depths: (

**a**) t

_{w}= 0.096 mm, (

**b**) t

_{w}= 0.250 mm, (

**c**) t

_{w}= 0.387 mm, (

**d**) t

_{w}= 0.467 mm, (

**e**) t

_{w}= 0.609 mm, (

**f**) t

_{w}= 0.647 mm.

**Figure 9.**Morphology of each member before and after rust removal: (

**a**) C0–30, (

**b**) C35–90, (

**c**) C15–180.

**Table 1.**Corresponding energy value of sub-images and information entropy for various corrosion depths.

t_{w} (mm) | E_{entropy} | Energy Value/(×10^{−2}) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

E_{H1} | E_{V1} | E_{D1} | E_{H2} | E_{V2} | E_{D2} | E_{H3} | E_{V3} | E_{D3} | ||

0 | 4.930 | 7.328 | 7.364 | 7.288 | 7.293 | 7.311 | 6.790 | 7.484 | 7.506 | 7.348 |

0.096 | 5.195 | 7.368 | 7.379 | 7.319 | 7.390 | 7.408 | 6.989 | 7.517 | 7.529 | 7.363 |

0.250 | 5.271 | 7.367 | 7.380 | 7.139 | 7.395 | 7.401 | 6.981 | 7.536 | 7.554 | 7.429 |

0.423 | 5.507 | 7.447 | 7.443 | 7.058 | 7.462 | 7.459 | 7.157 | 7.569 | 7.572 | 7.496 |

0.647 | 5.591 | 7.459 | 7.452 | 7.029 | 7.447 | 7.450 | 7.142 | 7.588 | 7.582 | 7.531 |

0.805 | 5.631 | 7.473 | 7.473 | 7.208 | 7.450 | 7.446 | 7.116 | 7.593 | 7.583 | 7.531 |

**Table 2.**Fitting equation and significance test of the relationship between image features before rust removal and corrosion depth.

Feature Value | Fitting Equation | Coefficients | $\left|\mathit{R}\right|$ Value | Correlation | |
---|---|---|---|---|---|

Sub-image energy value | Horizontal | $y=A{e}^{\left(-{\scriptscriptstyle \frac{x}{t}}\right)}+{y}_{0}$ | A = −0.122, t = 0.348, y_{0} = 7.605 | 0.992 | Very significant |

Vertical | A = −0.082, t = 0.219, y_{0} = 7.586 | 0.997 | |||

Diagonal | A = −0.234, t = 0.362, y_{0} = 7.563 | 0.979 | |||

Information entropy value | A = −0.836, t = 0.438, y_{0} = 5.780 | 0.984 |

**Table 3.**Energy value and information entropy of sub-images corresponding to different corrosion depths.

t_{w}/mm | E_{entropy} | Energy Value/(×10^{−2}) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

E_{H1} | E_{V1} | E_{D1} | E_{H2} | E_{V2} | E_{D2} | E_{H3} | E_{V3} | E_{D3} | ||

0.096 | 5.344 | 7.272 | 7.272 | 6.536 | 7.464 | 7.462 | 7.199 | 7.571 | 7.570 | 7.491 |

0.250 | 5.404 | 7.296 | 7.281 | 6.530 | 7.474 | 7.467 | 7.198 | 7.572 | 7.569 | 7.494 |

0.387 | 5.701 | 7.452 | 7.465 | 7.112 | 7.453 | 7.456 | 7.116 | 7.579 | 7.582 | 7.497 |

0.467 | 5.846 | 7.467 | 7.464 | 7.015 | 7.466 | 7.471 | 7.134 | 7.577 | 7.582 | 7.502 |

0.609 | 5.307 | 7.256 | 7.220 | 6.510 | 7.457 | 7.437 | 7.112 | 7.573 | 7.563 | 7.479 |

0.647 | 5.175 | 7.206 | 7.184 | 6.572 | 7.434 | 7.419 | 7.043 | 7.568 | 7.558 | 7.463 |

**Table 4.**Fitting equation and significance test of the relationship between image features after rust removal (sub-image energy value, information entropy value) and corrosion depth.

Feature Value | Fitting Equation | Coefficients | $\left|\mathit{R}\right|$ Value | Correlation | |
---|---|---|---|---|---|

Sub-image energy value | Horizontal | $y={y}_{0}+\frac{A}{W\times \sqrt{{\scriptscriptstyle \frac{\pi}{2}}}}{e}^{-2{(\frac{x-{x}_{0}}{W})}^{2}}$ | A = 0.047, W = 0.158 y _{0} = 7.254, x_{0} = 0.428 | 0.983 | Very significant |

Vertical | A = 0.057, W = 0.168 y _{0} = 7.230, x_{0} = 0.414 | 0.966 | |||

Diagonal | A = 0.097, W = 0.061 y _{0} = 6.526, x_{0} = 0.425 | 0.997 | |||

Information entropy value | A = 0.082, W = 0.112 y _{0} = 5.327, x_{0} = 0.439 | 0.921 |

**Table 5.**Fitting equation and significance test of the relationship between image features after rust removal (fractal dimension) and corrosion depth.

Stage | Fitting Equation | Coefficients | $\left|\mathit{R}\right|$ Value | Correlation |
---|---|---|---|---|

Earlier stage | $y=A{e}^{\left(-{\scriptscriptstyle \frac{x}{t}}\right)}+{y}_{0}$ | A = 0.005, t = −0.199, y_{0} = 2.269 | 0.994 | Very significant |

Later stage | A = 0.827, t =0.261, y_{0} = 2.179 | 0.999 |

Types | R/(γ_{0}S) | |||
---|---|---|---|---|

Grade a_{u} | Grade b_{u} | Grade c_{u} | Grade d_{u} | |

Main components, nodes, and connection domains | ≥1.0 | ≥0.95 | ≥0.90 | <0.90 |

General components | ≥1.0 | ≥0.90 | ≥0.85 | <0.85 |

Objects | Grade | Grading Standards | Actions to Take |
---|---|---|---|

Individual steel member | a_{u} | The safety meets the requirements for grade a_{u}, and the member has sufficient load-carrying capacity | No action needed |

b_{u} | The safety is slightly lower than the requirements for grade a_{u}, and the member load-carrying capacity is not greatly affected. | No action necessary | |

c_{u} | The safety does not meet the requirements for grade a_{u}, and the member load-carrying capacity is affected. | Action needed | |

d_{u} | The safety does not meet the requirements for grade a_{u}, and the member load-carrying capacity is severely affected. | Immediate action needed |

Grade | Evaluation Standards |
---|---|

c_{u} | In the main loading part of the structure, the average corrosion depth of the member section 0.1 t < Δt < 0.15 t |

d_{u} | In the main loading part of the structure, the average corrosion depth of the member section Δt > 0.15 t |

Grades | Grade a | Grade b | Grade c | Grade d | Failure | |
---|---|---|---|---|---|---|

Item | ||||||

Load carrying capacity degradation/(%) | 0 | (0,5] | (5,10] | (10,15] | >15 | |

Corrosion depth/mm | 0 | (0,0.181] | (0.181,0.347] | (0.347,0.498] | >0.498 | |

Morphological features before rust removal | E_{H3}/(×10^{−2}) | ≤210 ho | (7.483,7.533] | (7.533,7.560] | (7.560,7.576] | >7.576 |

E_{V3}/(×10^{−2}) | ≤2106] | (7.504,7.550] | (7.550,7.569] | (7.569,7.578] | >7.578 | |

E_{D3}/(×10^{−2}) | ≤2108] | (7.329,7.421] | (7.421,7.473] | (7.473,7.504] | >7.504 | |

E_{entropy} | ≤4.944 | (4.944,5.227] | (5.227,5.401] | (5.401,5.512] | >5.512 | |

Morphological features after rust removal | E_{H1}/(×10^{−2}) | ≤7.254 | (7.254,7.256] | (7.256,7.394] | (7.394,7.414] | <7.414 |

E_{V1}/(×10^{−2}) | ≤21,230 | (7.230,7.236] | (7.236,7.427] | (7.427,7.393] | <7.393 | |

E_{D1}/(×10^{−2}) | ≤21,093 | (6.526,6.526] | (6.526,6.573] | (6.573,6.596] | <6.596 | |

E_{entropy} | ≤ntrop | (5.327,5.327] | (5.327,5.478] | (5.478,5.660] | <5.660 | |

D | ≤2.274 | (2.274,2.281] | (2.281,2.298] | (2.298,2.302] | <2.302 |

Objects | Grades | Grading Criteria | Actions to Take |
---|---|---|---|

Individual steel member | a | Impact of corrosion on the load-carrying capacity can be neglected, and the member is basically intact. | Rust removal and reinforcement measures not needed |

b | Impact of corrosion on the load-carrying capacity is not significant, and the member is slightly corroded. | Rust removal and reinforcement measures not necessary | |

c | Impact of corrosion on the load-carrying capacity is significant, and the member is moderately corroded. | Rust removal and reinforcement measures needed | |

d | Impact of corrosion on the load-carrying capacity is significant, and the member is severely corroded. | Immediate rust removal, reinforcement, or replacement measures needed | |

Failure | Impact of corrosion on the load-carrying capacity is extremely significant, and the member fails. | Replacement needed |

Grades | C0–30 | C35–90 | C15–180 | ||||
---|---|---|---|---|---|---|---|

Item | Result | Grade | Result | Grade | Result | Grade | |

Load carrying capacity degradation/(%) | 5.04 | Grade c | 5.83 | Grade c | 13.93 | Grade d | |

Corrosion depth/mm | 0.205 | Grade c | 0.243 | Grade c | 0.556 | Failure | |

Morphological features before rust removal | E_{H3}/(×10^{−2}) | 7.532 | Grade b | 7.539 | Grade c | 7.608 | Failure |

E_{V3}/(×10^{−2}) | 7.530 | Grade b | 7.525 | Grade b | 7.579 | Failure | |

E_{D3}/(×10^{−2}) | 7.411 | Grade b | 7.425 | Grade c | 7.567 | Failure | |

E_{entropy} | 5.030 | Grade b | 5.274 | Grade c | 5.434 | Grade d | |

Morphological features after rust removal | E_{H1}/(×10^{−2}) | 7.266 | Grade c | 7.286 | Grade c | 7.211 | Failure |

E_{V1}/(×10^{−2}) | 7.286 | Grade c | 7.280 | Grade c | 7.247 | Failure | |

E_{D1}/(×10^{−2}) | 6.543 | Grade c | 6.525 | Grade a | 6.463 | Failure | |

E_{entropy} | 5.422 | Grade c | 5.397 | Grade c | 5.368 | Failure | |

D | 2.277 | Grade b | 2.284 | Grade c | 2.263 | Failure | |

Final grade | Grade c | Grade c | Failure |

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**MDPI and ACS Style**

Wei, Y.; Li, Y.; Wu, Z.; Chen, J.; Jiang, S.-F.; Lin, D.; Xiao, X.
Comprehensive Safety Evaluation of Corroded Circular Steel Tubes under Compression Based on Image Processing. *Coatings* **2022**, *12*, 1690.
https://doi.org/10.3390/coatings12111690

**AMA Style**

Wei Y, Li Y, Wu Z, Chen J, Jiang S-F, Lin D, Xiao X.
Comprehensive Safety Evaluation of Corroded Circular Steel Tubes under Compression Based on Image Processing. *Coatings*. 2022; 12(11):1690.
https://doi.org/10.3390/coatings12111690

**Chicago/Turabian Style**

Wei, Yuan, Yingjie Li, Zhaoqi Wu, Jinyu Chen, Shao-Fei Jiang, Deyuan Lin, and Xianbiao Xiao.
2022. "Comprehensive Safety Evaluation of Corroded Circular Steel Tubes under Compression Based on Image Processing" *Coatings* 12, no. 11: 1690.
https://doi.org/10.3390/coatings12111690