# Prediction of International Roughness Index Based on Stacking Fusion Model

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## Abstract

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^{2}) reaching 0.974. However, the prediction accuracy varies in numerical intervals, with some deviations. The stacking fusion model with a powerful generalization capability is proposed to build a new prediction model using GBDT and XGBoost as the base learners and bagging as the meta-learners. The R

^{2}, RMSE, and MAE of the stacking fusion model are 0.996, 0.040, and 1.3%, which further improves the prediction accuracy and verifies the superiority of this fusion model in pavement performance prediction. Besides, the prediction accuracy is generally consistent across different numerical intervals.

## 1. Introduction

^{2}) of 0.995; the model validation using a different dataset also yielded highly accurate predictions (R

^{2}= 0.99) [5]. Although the prognosis of PCI by IRI reduces the detection and analysis work, it ignores the more critical pavement distress information, which has been mentioned by Kırbas [6]. This neglect may lead to a significant bias when applying this prognosis to the forecasting domain.

^{2}value of the ANN (Artificial Neural Network) model was 0.75. Riding index, cracking index, and rutting index for the three pavement types ACC, PCC, and COM were predicted, and compared to the multiple linear regression (MLR) model, the ANN model based on weather factors (i.e., temperature, precipitation, and freeze-thaw cycles), traffic load, pavement age, SN, layer thickness, and subgrade stiffness for the Iowa highway, future pavement conditions are more accurately predicted [18]. Hossain et al. [19] demonstrated that the ANN-based IRI prediction model is reasonable for short-term and long-term pavement observation IRI data, and the root mean square error (RMSE) value of the test results was as low as 0.027. A more accurate prediction was fine-tuned by a coupled use of RFR and ANN [20]. Choi and Myungsik Do [2] predicted the deterioration of pavement performance with a recurrent neural network algorithm with a high coefficient of determination of 0.71–0.87 by using monitoring data from the Korean National Highway Pavement Management System. Marcelino et al. [14] used a transfer learning approach based on a boosting algorithm to develop pavement performance regression models with limited data contexts achieving a prediction accuracy improvement of approximately 6%. Basher et al. [15] pointed out that ANN was considered an effective technique based on its accurate predictions of small and large samples. The gradient boosting machine (GBM) models were better than other machine learning methods [21,22].

^{2}and reduce the error. However, the role of rich and detailed parameters of structural and environmental features still cannot be ignored. The overall performances of ANN and RF are similar. When the dataset is the same one, RF usually performs better than ANN, XGBoost [3], GBM [22], and LightGBM [21], and all perform better than RF. In addition, the performance of SVM and MLR models based on the same dataset has achieved about 50% lower R

^{2}values than ANN.

## 2. Data Preparation

## 3. Methodology

#### 3.1. Feature Selection Based on RF Algorithm

#### 3.2. Accuracy Evaluation of MLR, GBDT, XGBoost, and SVM Models

^{2}were used to evaluate the machine learning models’ performance

^{2}is the expressiveness of the expected value to the actual value, and the larger R

^{2}means the higher prediction accuracy (not more than 1). The three evaluation indicators were calculated according to Equations (4)–(6).

#### 3.3. The Stacking Fusion Method

## 4. Results and Discussion

#### 4.1. Feature Selection Results

#### 4.2. Accuracy Evaluation Results of MLR, GBDT, XGBoost, and SVM Models

^{2}for the different prediction models are in Table 3. SVM and MLR perform even worse than the known datasets in the literature (Table 1), probably because the initial IRI data did not incorporate parameters. However, the prediction accuracy of GBDT and XGBOOST is significantly higher.

^{2}for GBDT and XGBoost are 0.974 and 0.925, and the R

^{2}values of SVM and MLR are almost 70% lower. We can indicate that the predicted values of GBDT and XGBoost are closer to the actual values in the prediction process of the IRI of pavement. Both the accuracies of GBDT and XGBoost can meet the requirements of net-level forecasting. However, MAE values (6.2% and 8.4%) for GBDT and XGBoost are close to 10%, and data on specific value intervals have relatively high absolute errors.

#### 4.3. Evaluation of the Stacking Fusion Model

^{2}) for the stacking fusion model are in Table 3. It is found that the stacking fusion model yields an improvement in each evaluation indicator.

^{2}is 2% higher than GBDT and 8% higher than XGBoost. The accuracy of the stacking fusion model is further improved compared with the GBDT and XGBoost models.

## 5. Conclusions

^{2}(0.974 and 0.925), which can meet the requirements of net-level forecasting. However, MAE values (6.2% and 8.4%) are close to 10%, and data on some specific value intervals have relatively high absolute errors.

^{2}is as high as 0.996, and the RMSE and MAE are only 0.04 and 13%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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No. | Models | Whether Pavement Distress or Rutting Indicators Are Used | Other Parameters | R^{2} (Testing) | RMSE | MAE (%) | Segments | Observations |
---|---|---|---|---|---|---|---|---|

1 [18] | MLR | N | Pavement age, previous IRI value (initial IRI), pavement thickness, subgrade stiffness, average rainfall, average temperature | 0.57 | 0.205 | / | 464 | 6222 |

ANN | 0.92 | 0.133 | / | |||||

2 [23] | ANN | N | Age, vehicle per direction heavy vehicle per direction, ESAL per direction | 0.86 | 0.369 | 9.8 | 204 | / |

3 [2] | RNN | N | AADT, ESAL, climate, equipment | 0.87 | 0.14 | / | 1880 | / |

4 [3] | XGBoost | N | Age (years), four specific climate and weather indicators, two specific traffic indicators, modified thickness | 0.7 | / | 12.6 | 1390 | 12,637 |

RF | 0.66 | / | 13.51 | |||||

SVM | 0.44 | / | 17.64 | |||||

5 [17] | ANN | Y | Initial IRI, age | 0.75 | / | / | 506 | 2439 |

6 [13] | RF | Y | Structure, total pavement thickness, initial IRI | 0.974 | 0.078 | / | / | 19,900 |

7 [24] | AdaBoost | Y | Pavement total thickness, initial IRI, AADT, ESAL, freeze precipitation | 0.9751 | 0.094 | / | / | 4265 |

8 [22] | GBM | Y | Structural number, KESAL, unbound granular base thickness, asphalt concrete thickness, temperature, precipitation, initial IRI, age | 0.86572 | 0.176003 | 12.6345 | 211 | / |

DL (deep learning) | 0.829877 | 0.198105 | 12.9814 | |||||

DRF (distributed random forest) | 0.795589 | 0.217154 | 14.5215 | |||||

GLM (Generalized linear model) | 0.824244 | 0.201358 | 15.1275 | |||||

9 [21] | LightGBM | Y | Total thickness, AC ratio, temperature, precipitation, KESAL, freeze index, wind speed, initial IRI time | 0.9 | 0.19 | 11 | 1781 | 100,000 |

ANN | 0.84 | 0.25 | 15 | |||||

RFR | 0.88 | 0.21 | 12 |

No | FIELD_NAME | FIELD_ALIAS |
---|---|---|

1 | GATOR_CRACK_A_L | Low-Severity Alligator Cracking Area |

2 | GATOR_CRACK_A_M | Medium-Severity Alligator Cracking Area |

3 | GATOR_CRACK_A_H | High-Severity Alligator Cracking Area |

4 | BLK_CRACK_A_L | Low-Severity Block Cracking Area |

5 | BLK_CRACK_A_M | Medium-Severity Block Cracking Area |

6 | BLK_CRACK_A_H | High-Severity Block Cracking Area |

7 | EDGE_CRACK_L_L | Low-Severity Edge Crack Length |

8 | EDGE_CRACK_L_M | Medium-Severity Edge Crack Length |

9 | EDGE_CRACK_L_H | High-Severity Edge Crack Length |

10 | LONG_CRACK_WP_L_L | Low-Severity Wheel Path Longitudinal Crack Length |

11 | LONG_CRACK_WP_L_M | Medium-Severity Wheel Path Longitudinal Crack Length |

12 | LONG_CRACK_WP_L_H | High-Severity Wheel Path Longitudinal Crack Length |

13 | LONG_CRACK_WP_SEAL_L_L | Low-Severity Well-Sealed Wheel Path Longitudinal Crack Length |

14 | LONG_CRACK_WP_SEAL_L_M | Medium-Severity Well-Sealed Wheel Path Longitudinal Crack Length |

15 | LONG_CRACK_WP_SEAL_L_H | High-Severity Well-Sealed Wheel Path Longitudinal Crack Length |

16 | LONG_CRACK_NWP_L_L | Low-Severity Non-Wheel Path Longitudinal Crack Length |

17 | LONG_CRACK_NWP_L_M | Medium-Severity Non-Wheel Path Longitudinal Crack Length |

18 | LONG_CRACK_NWP_L_H | High-Severity Non-Wheel Path Longitudinal Crack Length |

19 | LONG_CRACK_NWP_SEAL_L_L | Low-Severity Non-Wheel Path Well-Sealed Longitudinal Crack Length |

20 | LONG_CRACK_NWP_SEAL_L_M | Medium-Severity Non-Wheel Path Well-Sealed Longitudinal Crack Length |

21 | LONG_CRACK_NWP_SEAL_L_H | High-Severity Non-Wheel Path Well-Sealed Longitudinal Crack Length |

22 | TRANS_CRACK_NO_L | Low-Severity Transverse Cracks Number |

23 | TRANS_CRACK_NO_M | Medium-Severity Transverse Cracks Number |

24 | TRANS_CRACK_NO_H | High-Severity Transverse Cracks Number |

25 | TRANS_CRACK_L_L | Low-Severity Transverse Crack Length |

26 | TRANS_CRACK_L_M | Medium-Severity Transverse Crack Length |

27 | TRANS_CRACK_L_H | High-Severity Transverse Crack Length |

28 | TRANS_CRACK_SEAL_L_L | Low-Severity Well-Sealed Transverse Crack Length |

29 | TRANS_CRACK_SEAL_L_M | Medium-Severity Well-Sealed Transverse Crack Length |

30 | TRANS_CRACK_SEAL_L_H | High-Severity Well-Sealed Transverse Crack Length |

31 | PATCH_NO_L | Low-Severity Patches Number |

32 | PATCH_NO_M | Medium-Severity Patches Number |

33 | PATCH_NO_H | High-Severity Patches Number |

34 | MRI | Mean Roughness Index |

35 | LLH_DEPTH_1_8_MEAN | Average Left Lane Half Depth From 1.8m Straight Edge |

36 | RLH_DEPTH_1_8_MEAN | Average Right Lane Half Depth From 1.8m Straight Edge |

37 | MAX_MEAN_DEPTH_1_8 | Maximum Average Depth From 1.8m Straight Edge |

38 | RLH_DEPTH_WIRE_REF_MEAN | Average Right Lane Half Depth From Wire Reference |

39 | MAX_MEAN_DEPTH_WIRE_REF | Maximum Average Depth From Wire Reference |

40 | AADTT_ALL_TRUCKS_TREND | Trend LTPP Lane Annual Average Daily Truck Traffic |

41 | ANNUAL_TRUCK_VOLUME_TREND | LTPP Lane Annual Truck Trend Estimate |

Algorithms | RMSE | MAE | R^{2} |
---|---|---|---|

GBDT | 0.096 | 0.062 | 0.974 |

XGBoost | 0.162 | 0.084 | 0.925 |

SVM | 0.541 | 0.350 | 0.161 |

MLR | 0.504 | 0.344 | 0.271 |

The stacking fusion model | 0.040 | 0.013 | 0.996 |

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**MDPI and ACS Style**

Luo, Z.; Wang, H.; Li, S.
Prediction of International Roughness Index Based on Stacking Fusion Model. *Sustainability* **2022**, *14*, 6949.
https://doi.org/10.3390/su14126949

**AMA Style**

Luo Z, Wang H, Li S.
Prediction of International Roughness Index Based on Stacking Fusion Model. *Sustainability*. 2022; 14(12):6949.
https://doi.org/10.3390/su14126949

**Chicago/Turabian Style**

Luo, Zhiyuan, Hui Wang, and Shenglin Li.
2022. "Prediction of International Roughness Index Based on Stacking Fusion Model" *Sustainability* 14, no. 12: 6949.
https://doi.org/10.3390/su14126949