# Evaluation of the Uniformity of Protective Coatings on Concrete Structure Surfaces Based on Cluster Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Infrared Imaging Detection of Silane Coatings

#### 2.1.1. Infrared Imaging Test Principle

#### 2.1.2. Infrared Imaging Test Program

_{14}H

_{32}O

_{3}Si. Silane is a colorless liquid at room temperature, and its boiling point is 236 °C. The test used an infrared bulb as a thermal excitation source to apply continuous heat flow excitation to the concrete structure. In addition, an infrared imaging system was constructed with an SC7000 infrared camera from FLIR.

_{1}and place it in the uniform temperature field formed by the two infrared bulbs to ensure the uniform heating of the specimen surface. The distance between the lens of the thermal imager and the test piece is about 1 m.

_{1}surface temperature drops to the initial temperature, the concrete surface is sprayed with silane. The concrete specimen after spraying silane is recorded as A

_{2}.

_{2}and specimen A

_{1}are tested under the same experimental environment. Repeat the above steps (1) to (7) to collect the infrared thermal image data of the concrete specimen A

_{2}sprayed with silane and save it.

#### 2.2. MATLAB-Based Infrared Image Processing

#### 2.2.1. Image Pre-Processing

#### 2.2.2. Concrete Surface Feature Recognition

#### 2.2.3. Morphological Processing of Images

#### 2.3. Evaluation of Uniformity Based on Cluster Analysis

#### 2.3.1. Clustering Analysis Algorithm

#### 2.3.2. Calculation of Pixel Point Affiliation Based on Bayes Discriminant

#### 2.3.3. Evaluation of Homogeneity of Silane Coating

_{i}is the total number of pixel points at Z = i; ω

_{1}, ω

_{2}, …, ω

_{i}are the corresponding weight values; ${\epsilon}_{j}$ denotes the affiliation degree corresponding to the jth pixel point; M denotes the total number of pixel points on the concrete surface.

## 3. Results

#### 3.1. Infrared Imaging Test Results

#### 3.2. Infrared Image Processing Results

#### 3.3. Cluster Analysis Results of Pixel Point Temperature Index

_{1}, y

_{2}, y

_{3}, and y

_{4}, respectively, as the indicator variables for each sample point. The final results of the pixel point temperature data statistics are obtained and shown in Table 2.

#### 3.4. Pixel Point Affiliation Calculation Results

_{1}, y

_{2}, y

_{3}, and y

_{4}values of the unknown pixel points are brought into the above equation. The values of T

_{1}, T

_{2}, T

_{3}, T

_{4}, and T

_{5}were calculated. Moreover, we compared the magnitude of these five values and took the category corresponding to the maximum value as the Bayesian discriminant result of the pixel point. The values were brought into the posterior probability calculation formula to obtain the posterior probability of each pixel point being discriminated into each category. To determine the cluster affiliation of any pixel point on the concrete surface, the maximum posterior probability value of the pixel point was taken as the affiliation of the pixel point belonging to the corresponding category. Figure 11 represents the two-dimensional distribution of clustering results for each pixel point.

#### 3.5. Coating Uniformity Analysis

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Concrete IR image pre-processing results: (

**a**) image quality evaluation; (

**b**) image noise removal; (

**c**) image sharpening.

**Figure 4.**Concrete infrared image processing results: (

**a**) edge detection processing; (

**b**) binarization processing; (

**c**) morphology processing.

Uniformity Grade | Very Even | More Uniform | Uneven | Very Uneven |
---|---|---|---|---|

Unevenness U | ≤0.1 | 0.1 < U ≤ 0.25 | 0.25 < U ≤ 0.4 | >0.4 |

Sample Pixel Dots | y_{1}/°C | y_{2}/°C | y_{3}/°C | y_{4}/°C |
---|---|---|---|---|

1 | 34.01 | 35.22 | 35.27 | 35.29 |

2 | 30.76 | 32.11 | 32.44 | 32.64 |

3 | 28.47 | 29.85 | 30.41 | 30.85 |

4 | 26.72 | 28.14 | 28.87 | 29.48 |

5 | 25.46 | 26.93 | 27.80 | 28.51 |

6 | 24.60 | 26.08 | 27.05 | 27.81 |

7 | 23.75 | 25.26 | 26.29 | 27.15 |

8 | 23.01 | 24.53 | 25.65 | 26.57 |

9 | 22.87 | 24.36 | 25.55 | 26.45 |

10 | 22.43 | 23.99 | 25.25 | 26.16 |

⋮ | ⋮ | ⋮ | ⋮ | ⋮ |

17,098 | 27.97 | 28.35 | 29.11 | 29.56 |

Indicators | Final Clustering Center | ||||
---|---|---|---|---|---|

I | II | III | IV | V | |

y_{1}/°C | 29.64 | 26.58 | 24.93 | 23.92 | 22.70 |

y_{2}/°C | 31.11 | 28.15 | 26.56 | 25.54 | 24.33 |

y_{3}/°C | 32.27 | 29.41 | 27.92 | 26.93 | 25.75 |

y_{4}/°C | 33.11 | 30.35 | 28.93 | 27.97 | 26.82 |

Sample Pixel Dots | y_{1}/°C | y_{2}/°C | y_{3}/°C | y_{4}/°C | Clustering Results |
---|---|---|---|---|---|

1 | 34.01 | 35.22 | 35.27 | 35.29 | I |

2 | 30.76 | 32.11 | 32.44 | 32.64 | I |

3 | 28.47 | 29.85 | 30.41 | 30.85 | II |

4 | 26.72 | 28.14 | 28.87 | 29.48 | II |

5 | 25.46 | 26.93 | 27.80 | 28.51 | III |

6 | 24.60 | 26.08 | 27.05 | 27.81 | IV |

7 | 23.75 | 25.26 | 26.29 | 27.15 | IV |

8 | 23.01 | 24.53 | 25.65 | 26.57 | V |

9 | 22.87 | 24.36 | 25.55 | 26.45 | V |

10 | 22.43 | 23.99 | 25.25 | 26.16 | V |

⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |

17,098 | 27.97 | 28.35 | 29.11 | 29.56 | II |

Sample Pixel Dots | Pre-Painting Results | Results after Spraying | Affiliation |
---|---|---|---|

1 | I | II | 1 |

2 | I | I | 1 |

3 | II | I | 0.99985 |

4 | II | IV | 0.99830 |

5 | III | V | 0.87697 |

6 | IV | V | 0.80302 |

7 | IV | V | 0.62214 |

8 | V | V | 0.96985 |

9 | V | V | 0.98881 |

10 | V | V | 0.99867 |

⋮ | ⋮ | ⋮ | ⋮ |

17,098 | II | II | 0.99431 |

Experimental Group | N1 | N2 | N3 |
---|---|---|---|

Unevenness U | 0.122 | 0.298 | 0.415 |

Homogeneity evaluation grade | More uniform | Uneven | Very uneven |

Actual painting situation | More uniform | Uneven | Very uneven |

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**MDPI and ACS Style**

Liu, D.; Zhang, W.; Tang, Y.; Jian, Y.; Gong, C.; Qiu, F.
Evaluation of the Uniformity of Protective Coatings on Concrete Structure Surfaces Based on Cluster Analysis. *Sensors* **2021**, *21*, 5652.
https://doi.org/10.3390/s21165652

**AMA Style**

Liu D, Zhang W, Tang Y, Jian Y, Gong C, Qiu F.
Evaluation of the Uniformity of Protective Coatings on Concrete Structure Surfaces Based on Cluster Analysis. *Sensors*. 2021; 21(16):5652.
https://doi.org/10.3390/s21165652

**Chicago/Turabian Style**

Liu, Dunwen, Wanmao Zhang, Yu Tang, Yinghua Jian, Chun Gong, and Fengkai Qiu.
2021. "Evaluation of the Uniformity of Protective Coatings on Concrete Structure Surfaces Based on Cluster Analysis" *Sensors* 21, no. 16: 5652.
https://doi.org/10.3390/s21165652