# Predicting Pavement Condition Index Using Fuzzy Logic Technique

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## Abstract

**:**

## 1. Introduction and Related Work

#### 1.1. Fuzzy Logic Approach

#### 1.2. Fuzzy Rule-Based System

## 2. Research Objective

#### Methodology and Data Collection

## 3. Fuzzy Inference System (FIS) and Membership Function

## 4. Mathematical Development

#### 4.1. Model Formulation

#### 4.2. Data Pre-Processing and Fuzzification

#### 4.3. Fuzzy Rule Generation

#### 4.4. Defuzzification Methods

**Failed, Very Poor, Poor, Fair, Good, Very Good, and Excellent**). The final outcome must be defuzzified to obtain crisp results. This is the aim of the defuzzification component of the fuzzy logic, which performs the defuzzification based on the membership function of the output variable. This implies that PCI will be in the range [0, 100], with 100 being the best possible value and 0 the worst [28]. In this study, four methods will be used for defuzzification, as follows.

- 1.
- Centroid method

- 2.
- Bisector Method

- 3.
- Largest of Maximum

- 4.
- Smallest of Maximum

#### 4.5. Evaluation of Model’s Performance

## 5. Results and Discussions

#### 5.1. Fuzzy Inference Systems’ Configurations for 120 Sections

**Centroid method**: The ${R}^{2}$ value was 97.3%, while the RMSE and MAE values were 5.28% and 4.617%.**Bisector method**: The ${R}^{2}$ value was 96.3%, while the RMSE and MAE values were 5.916% and 5.367%.**Lom method:**The ${R}^{2}$ value was 95.4%, while the RMSE and MAE values were 8.096% and 6.185%.**Som method:**The ${R}^{2}$ value was 95.8%, while the RMSE and MAE values were 6.696% and 5.567%.- The results showed the Centroid method gives a more accurate result (${R}^{2}$ = 97.3%, RMSE = 5.28%, and MAE = 4.617%) compared to other techniques.
- The results showed the Lom method gives the lowest accurate result (${R}^{2}$ = 95.4%, RMSE = 8.096%, and MAE = 6.185%) compared to other techniques.

#### 5.2. Fuzzy Inference Systems’ Configurations for 150 Sections

**Centroid method**: The ${R}^{2}$ value was 98.3%, while the RMSE and MAE values were 4.957% and 4.243%.**Bisector method**: The ${R}^{2}$ value was 96.9%, while the RMSE and MAE values were 5.499% and 5.347%.**Lom method:**The ${R}^{2}$ value was 98.2%, while the RMSE and MAE values were 5.042% and 4.487%.**Som method:**The ${R}^{2}$ value was 97.6%, while the RMSE and MAE values were 5.465% and 4.92%.- The results showed the Centroid method gives a more accurate result (${R}^{2}$ = 98.3%, RMSE = 4.957%, and MAE = 4.243%) compared to other techniques.
- The results showed the Bisector method gives the lowest accurate result (${R}^{2}$ = 96.9%, RMSE = 5.449%, and MAE = 5.347%) compared to other techniques.

#### 5.3. Sensitivity Analysis

#### 5.4. Comparison and Validation of the Models

**Centroid method**: The results of the statistical measures of 150 sections were improved by 1.03%, 6.12%, and 8.10% compared to 120 sections for ${R}^{2}$, RMSE, and MAE, respectively.**Bisector method**: The results of the statistical measures of 150 sections were improved by 0.62%, 7.01%, and 0.372% compared to 120 sections for ${R}^{2}$, RMSE, and MAE, respectively.**Lom method:**The results of the statistical measures of 150 sections were improved by 2.85%,37.72%, and 27.45% compared to 120 sections for ${R}^{2}$, RMSE, and MAE, respectively.**Som method:**The results of the statistical measures of 150 sections were improved by 1.84%,18.38%, and 11.6% compared to 120 sections for ${R}^{2}$, RMSE, and MAE, respectively.- The results show the Centroid method of 150 sections gave a more accurate result (${R}^{2}$ = 98.3%, RMSE = 4.957%, and MAE = 4.243%) compared to other techniques.

## 6. Conclusions

- This technique has a crucial advantage because it generates rules from large-scale distress data in a short time, especially when robust distress data are required, and the distress classification has become more consistent.
- As the FIS technique uses linguistic variables, this technique enables pavement engineers to identify pavement conditions and enhance decision-making processes, reduces human involvement in decision-making processes, and provides consistency to the process.
- Rutting and transverse cracking have the most influence on the FPCI calculation. Longitudinal cracking and fatigue cracking have some influence on the model, while patching, bleeding, and ravelling had only minor effects on the FPCI calculation.
- According to the results, the differences between the observed data and results from fuzzy logic system techniques were acceptable within allowed limits. The results also indicate that the models became more accurate as the number of road sections increased.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Rating scale used for pavement condition index (PCI) [3].

Parameters | Unit | Min Statistic | Maxi Statistic | Mean Statistic | Mean Std. Error | Std Statistic |
---|---|---|---|---|---|---|

PCI | - | 5.00 | 100.00 | 59.07 | 2.78 | 32.34 |

Rutting | (mm) | 0.0 | 135.9 | 23.6 | 3.1 | 37.7 |

Fatigue Cracking | (${\mathrm{m}}^{2}$) | 0.00 | 377.90 | 38.59 | 6.58 | 76.48 |

Block Cracking | (${\mathrm{m}}^{2}$) | 0.00 | 557.60 | 5.80 | 4.30 | 50.01 |

Longitudinal Cracking | (${\mathrm{m}}^{2}$) | 0.00 | 325.60 | 66.88 | 7.77 | 90.29 |

Transverse Cracking | (${\mathrm{m}}^{2}$) | 0.00 | 192.30 | 30.63 | 3.74 | 43.50 |

Patching | (${\mathrm{m}}^{2})$ | 0.00 | 45.80 | 1.52 | 0.67 | 7.73 |

Potholes | (Number) | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

Bleeding | (${\mathrm{m}}^{2}$) | 0.00 | 350.80 | 18.95 | 6.12 | 70.32 |

Ravelling | (${\mathrm{m}}^{2}$) | 0.00 | 564.30 | 44.98 | 10.62 | 122.05 |

Distress of Type | Category | Number of MF | Description |
---|---|---|---|

Rutting | Input | 3 | Extremely important |

Fatigue Cracking | Input | 3 | Relatively important |

Block Cracking | Input | 3 | Relatively important |

Longitudinal Cracking | Input | 3 | Important |

Transverse Cracking | Input | 3 | Important |

Patching | Input | 3 | Moderately important |

Potholes | Input | 3 | Moderately important |

Ravelling | Input | 3 | Relatively important |

Bleeding | Input | 3 | Relatively important |

PCI | Output | 7 | Extremely important |

Rule No. | Distress Type (Input) | FPCI (Output) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Rutting | Fatigue Cracking | Block Cracking | Longitudinal Cracking | Trans Cracking | Patching | Potholes | Bleeding | Ravelling | ||

1 | Minimal | Minimal | Minimal | Minimal | Minimal | Minimal | Minimal | Minimal | Minimal | Excellent |

2 | Minimal | Minimal | Minimal | Moderate | Minimal | Minimal | Minimal | Minimal | Minimal | Excellent |

3 | Minimal | Minimal | Minimal | Severe | Minimal | Minimal | Minimal | Minimal | Moderate | Very Good |

4 | Minimal | Minimal | Minimal | Minimal | Severe | Minimal | Minimal | Minimal | Minimal | Good |

5 | Minimal | Severe | Minimal | Moderate | Minimal | Minimal | Minimal | Minimal | Minimal | Good |

6 | Minimal | Moderate | Minimal | Minimal | Severe | Minimal | Minimal | Minimal | Minimal | Good |

7 | Minimal | Moderate | Minimal | Minimal | Minimal | Minimal | Minimal | Minimal | Minimal | Good |

8 | Minimal | Minimal | Minimal | Minimal | Minimal | Minimal | Minimal | Minimal | Moderate | Good |

9 | Minimal | Moderate | Minimal | Moderate | Severe | Minimal | Minimal | Moderate | Minimal | Good |

10 | Minimal | Moderate | Minimal | Moderate | Minimal | Minimal | Minimal | Minimal | Severe | Fair |

11 | Minimal | Minimal | Minimal | Moderate | Moderate | Minimal | Minimal | Minimal | Minimal | Fair |

12 | Moderate | Severe | Minimal | Minimal | Minimal | Minimal | Minimal | Moderate | Minimal | Fair |

13 | Moderate | Minimal | Minimal | Minimal | Minimal | Minimal | Minimal | Minimal | Severe | Poor |

14 | Minimal | Severe | Minimal | Minimal | Moderate | Minimal | Minimal | Minimal | Minimal | Poor |

15 | Moderate | Moderate | Minimal | Minimal | Minimal | Moderate | Minimal | Minimal | Minimal | Poor |

16 | Minimal | Minimal | Minimal | Moderate | Severe | Minimal | Minimal | Minimal | Minimal | Poor |

17 | Minimal | Minimal | Minimal | Moderate | Moderate | Minimal | Minimal | Minimal | Minimal | Very Poor |

18 | Moderate | Moderate | Minimal | Minimal | Moderate | Minimal | Minimal | Moderate | Minimal | Very Poor |

19 | Moderate | Moderate | Minimal | Moderate | Severe | Minimal | Minimal | Moderate | Moderate | Very Poor |

20 | Minimal | Minimal | Minimal | Minimal | Moderate | Minimal | Minimal | Minimal | Severe | Very Poor |

21 | Minimal | Severe | Minimal | Severe | Severe | Minimal | Minimal | Moderate | Minimal | Very Poor |

22 | Moderate | Moderate | Minimal | Moderate | Moderate | Minimal | Minimal | Minimal | Moderate | Very Poor |

23 | Minimal | Minimal | Minimal | Severe | Severe | Minimal | Minimal | Minimal | Minimal | Very Poor |

24 | Minimal | Moderate | Minimal | Minimal | Moderate | Minimal | Minimal | Minimal | Minimal | Failed |

25 | Moderate | Severe | Minimal | Moderate | Severe | Minimal | Minimal | Minimal | Minimal | Failed |

26 | Severe | Moderate | Minimal | Moderate | Severe | Minimal | Minimal | Minimal | Minimal | Failed |

27 | Severe | Severe | Minimal | Moderate | Moderate | Minimal | Minimal | Moderate | Minimal | Failed |

Inference | Number of Sections | Defuzzification | Statistical Measures | ||
---|---|---|---|---|---|

${\mathit{R}}^{2}$ | RMSE | MAE | |||

Mamdani (Triangular) | 120 | Centroid | 97.3 | 5.28 | 4.617 |

Bisector | 96.3 | 5.916 | 5.367 | ||

Lom | 95.4 | 8.096 | 6.185 | ||

Som | 95.8 | 6.696 | 5.567 |

Inference | Number of Sections | Defuzzification | Statistical Measures | ||
---|---|---|---|---|---|

${\mathit{R}}^{2}$ | RMSE | MAE | |||

Mamdani (Triangular) | 150 | Centroid | 98.3 | 4.957 | 4.243 |

Bisector | 96.9 | 5.499 | 5.347 | ||

Lom | 98.2 | 5.042 | 4.487 | ||

Som | 97.6 | 5.465 | 4.92 |

Independent Variable | ${\mathit{R}}^{2}$ | |
---|---|---|

120 Sections | 150 Sections | |

Rutting | 45.1 | 46.5 |

Fatigue | 27.9 | 28.4 |

Block Cracking | 0. 1 | 0. 2 |

Longitudinal Cracking | 26.6 | 26.6 |

Transverse Cracking | 35.5 | 39.9 |

Patching | 5.1 | 0.6 |

Potholes | - | - |

Bleeding | 9.6 | 7.2 |

Ravelling | 6.5 | 7.1 |

Inference | Number of Sections | Defuzzification | Statistical Measures | Improvement (%) | ||||
---|---|---|---|---|---|---|---|---|

${\mathit{R}}^{2}$ | RMSE | MAE | R^{2} | RMSE | MAE | |||

Mamdani (Triangular) | 120 | Centroid | 97.3 | 5.28 | 4.617 | - | - | - |

Bisector | 96.3 | 5.916 | 5.367 | - | - | - | ||

Lom | 95.4 | 8.096 | 6.185 | - | - | - | ||

Som | 95.8 | 6.696 | 5.567 | - | - | - | ||

150 | Centroid | 98.3 | 4.957 | 4.243 | +1.03 | +6.12 | +8.10 | |

Bisector | 96.9 | 5.499 | 5.347 | +0.62 | +7.01 | +0.372 | ||

Lom | 98.2 | 5.042 | 4.487 | +2.85 | +37.72 | +27.45 | ||

Som | 97.6 | 5.465 | 4.92 | +1.84 | +18.38 | +11.6 |

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**MDPI and ACS Style**

Ali, A.; Heneash, U.; Hussein, A.; Eskebi, M.
Predicting Pavement Condition Index Using Fuzzy Logic Technique. *Infrastructures* **2022**, *7*, 91.
https://doi.org/10.3390/infrastructures7070091

**AMA Style**

Ali A, Heneash U, Hussein A, Eskebi M.
Predicting Pavement Condition Index Using Fuzzy Logic Technique. *Infrastructures*. 2022; 7(7):91.
https://doi.org/10.3390/infrastructures7070091

**Chicago/Turabian Style**

Ali, Abdualmtalab, Usama Heneash, Amgad Hussein, and Mohamed Eskebi.
2022. "Predicting Pavement Condition Index Using Fuzzy Logic Technique" *Infrastructures* 7, no. 7: 91.
https://doi.org/10.3390/infrastructures7070091