# Supervised Machine Learning–Based Detection of Concrete Efflorescence

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Research Methods and Materials

#### 3.1. Machine Learning Classifiers

#### 3.1.1. Support Vector Machine (SVM)

_{i}, y

_{i}}; yi = {−1, + 1} and w = (w

_{1}, w

_{2}, …, w

_{n}) represent normal vectors, and they can determine the direction of hyperplanes. b represents the bias value and can determine the distance between the hyperplane and original point (0, 0). The distance between any point in the sample space and the hyperplane is r.

^{T}+ b = 1 and w

^{T}+ b = −1 (Figure 1). The area between hyperplanes is known as the margin, and the distance is 2/‖$w$‖. To maximize the distance between hyperplanes, the ‖$w$‖ must be minimized. The hyperplane in the middle of the maximum margin is the “Optimal hyperplane”. To ensure that the sample data points are all outside the margin area of the hyperplanes, a researcher must ensure that all training samples fulfill one of the conditions stated in Equation (1). To find the maximum margin hyperplane, parameters w and b fulfilling Equation (2) must be obtained, and the value of 2/‖$w$‖ must be maximized.

#### 3.1.2. Maximum Likelihood (ML)

_{i}) is the probability that category ω

_{i}appears in the image, and all categories are assumed to be equal. |Σi| is the determinant of the covariance matrix of category ωi data. Σi

^{−1}is the inverse matrix, and m

_{i}is the mean vector. These training pixels can provide the mean values and covariance of spectrum bands used for estimation. These data are then used to assign pixels to a category.

_{0}, P(x|j) > (x|i), x is then classified into the j category. (2) When x < x

_{0}, P(x|j) < (x|i), x is then classified into the i category. (3) When x = x

_{0}, P(x|j) = (x|i), the probability of classifying x into either i or j categories is equal.

#### 3.1.3. Random Forest (RF)

_{2}d [53].

#### 3.2. Material and Image Processing

## 4. Model Evaluation Indicators

#### 4.1. Accuracy

#### 4.2. Precision and Recall

#### 4.3. F1

#### 4.4. ROC, AUC, and Gini Coefficient

#### 4.5. Kappa

_{0}represents overall agreement probability (i.e., accuracy), and Pe represents agreement probability occurring by chance. The Kappa coefficient ranges between +1 (completely consistent) and −1 (completely inconsistent). A zero value indicates random classification [67]. Therefore, the Kappa value is regarded as an effective method for analyzing a single confusion matrix or comparing differences between various confusion matrices [68,69]. In addition, it can be used to explain the accuracy of CE and OE in classification [70].

#### 4.6. Gain Chart

## 5. Results and Discussion

#### 5.1. Evaluation of Classification Models

#### 5.2. Efflorescence Detection Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**SVM and hyperplane [51].

**Figure 7.**Scalar and vector of the spectrum of SVM-based efflorescence detection. (

**a**) The scalar of the spectrum and detection image and (

**b**) The vector of the spectrum and the detection image.

**Figure 8.**SVM detection results under different light source conditions: (

**a**) natural light source, (

**b**) fluorescence light source, (

**c**) nonuniform light source, (

**d**) SVM efflorescence detection under natural light source, (

**e**) SVM efflorescence detection under fluorescence light source, and (

**f**) SVM efflorescence detection under nonuniform light source.

Actual | Classification Results (Predicated) | PA (%) | OE (%) | |
---|---|---|---|---|

A | B | |||

A | True Positive (TP) | False Negative (FN) | TP/(TP + FN) (Sensitivity) | FN/(TP + FN) |

B | False Positive (FP) | True Negative (TN) | TN/(FP +TN) (Specificity) | FP/(FP +TN) |

UA (%) | TP/(TP + FP) (Precision) | TN/(FN + TN) | AUC = Mean PA | Accuracy = (TP + TN)/(TP + TN + FP + FN) |

Number | Indicator | Formula |
---|---|---|

(a) | Accuracy | $\frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}}$ |

(b) | Precision (P) | $\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}}$ |

(c) | Recall (R) | $\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}$ |

(d) | F1 | $\frac{2\times P\times R}{P+R}$ |

(e) | ROC | X-axis: FP Ratio (1-Specificity); Y-axis: TP Ratio (Sensitivity) |

(f) | AUC | $\frac{1}{2}(\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}+\frac{\mathrm{TN}}{\mathrm{FP}+\mathrm{TN}})$ |

(g) | Gini coefficient | 2 × AUC − 1 |

(h) | Kappa | $\begin{array}{l}\mathrm{Kappa}=\frac{Po-Pe}{1-Pe};Po=\mathrm{Accuracy};\\ Pe=\frac{\left[\right(\mathrm{TP}+\mathrm{FP})\times (\mathrm{TP}+\mathrm{FN}\left)\right]+\left[\right(\mathrm{FN}+\mathrm{TN})\times (\mathrm{FP}+\mathrm{TN}\left)\right]}{{(\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN})}^{2}}\end{array}$ |

(i) | Gain | X-axis: Percentage of dataset; Y-axis: Cumulative precision |

Truth | Predicated | PA (%) | OE (%) | |
---|---|---|---|---|

Efflorescence | Normal | |||

efflorescence | 272 | 30 | 90.1 | 9.9 |

normal | 19 | 179 | 90.4 | 9.6 |

UA (%) | 93.4 | 85.6 | Accuracy = 90.2% | |

CE (%) | 6.6 | 14.4 | n = 500 |

Truth | Predicated | PA (%) | OE (%) | |
---|---|---|---|---|

Efflorescence | Normal | |||

efflorescence | 271 | 31 | 89.7 | 10.3 |

normal | 20 | 178 | 89.9 | 10.1 |

UA (%) | 93.1 | 85.2 | Accuracy = 89.8% | |

CE (%) | 6.9 | 14.8 | n = 500 |

Truth | Predicated | PA (%) | OE (%) | |
---|---|---|---|---|

Efflorescence | Normal | |||

efflorescence | 264 | 38 | 87.4 | 12.6 |

normal | 27 | 171 | 86.4 | 13.6 |

UA (%) | 90.7 | 81.8 | Accuracy = 87.0% | |

CE (%) | 9.3 | 18.2 | n = 500 |

Accuracy | F1 | AUC | Gini | Kappa | Gain | |
---|---|---|---|---|---|---|

SVM | 0.902 | 0.880 | 0.902 | 0.805 | 0.797 | 0.774 |

ML | 0.898 | 0.874 | 0.898 | 0.796 | 0.789 | 0.771 |

RF | 0.870 | 0.839 | 0.869 | 0.738 | 0.731 | 0.751 |

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**MDPI and ACS Style**

Fan, C.-L.; Chung, Y.-J.
Supervised Machine Learning–Based Detection of Concrete Efflorescence. *Symmetry* **2022**, *14*, 2384.
https://doi.org/10.3390/sym14112384

**AMA Style**

Fan C-L, Chung Y-J.
Supervised Machine Learning–Based Detection of Concrete Efflorescence. *Symmetry*. 2022; 14(11):2384.
https://doi.org/10.3390/sym14112384

**Chicago/Turabian Style**

Fan, Ching-Lung, and Yu-Jen Chung.
2022. "Supervised Machine Learning–Based Detection of Concrete Efflorescence" *Symmetry* 14, no. 11: 2384.
https://doi.org/10.3390/sym14112384