# Comparative Analysis of Machine Learning Models for Prediction of Remaining Service Life of Flexible Pavement

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## Abstract

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## 1. Introduction

## 2. Literature Review

- First category: Models that predict the RSL based on the response (stress and strain) of pavement to the applied loads.
- Second category: Models that predict the RSL based on pavement quality indices.
- Third category: Models that predict the RSL based on the results of pavement non-destructive tests.

## 3. Methodology

#### 3.1. Pavement Condition Index (PCI)

_{i}) [22,34]:

#### 3.2. Remaining Service Life (RSL)

- The remaining time to reach a level of distress when the pavement needs to be rehabilitated or reconstructed. For example, the Minnesota Department of Transportation (MnDOT) defines the RSL as the time until the next major rehabilitation.
- The time until pavement conditions reach a specific condition index limit. For example, the Michigan Department of Transportation (MDOT) defines the RSL based on the Michigan Ride Quality Index, assuming an RSL of zero when the said index is 50.

_{i}) of the pavement is calculated by the following equation [41]:

_{i}and A

_{i}

_{+1}, c = electromagnetic wave speed through the vacuum, and ${\epsilon}_{r}$ = the relative dielectric constant of the layer. Table 4 shows the complete details of the GPR experiment carried out in this study.

#### 3.3. Machine Learning Techniques

#### 3.3.1. Gene Expression Programming (GEP)

#### 3.3.2. Support Vector Regression (SVR)

_{i}) and output (y

_{i}) [57]:

- $\epsilon $: this parameter supervises the width of the $\epsilon $-insensitive zone, used to fit the training data. The value $\epsilon $ can affect the number of support vectors used to build the regression function. For the bigger $\epsilon $, estimates are more ‘flat’, and the fewer support vectors are chosen.
- C: this parameter specifies the trade-off between the complexity of the model and the grade to which deviations larger than $\epsilon $ are bearable in optimization formulation.
- $\gamma $: this parameter determines the relation between error minimization and smoothness of the estimated function.

#### 3.3.3. Fruit Fly Optimization Algorithm (FOA)

**Step 1.**SVR parameters ($\epsilon $, c) initialization and kernel function determination.

**Step 2.**Parameter initialization; including the maximum number of iterations, location of initial population (X-axis, Y-axis), population size, and random flight distance domain:

**Step 3.**Population initialization

**Step 4.**Population evaluation

**Step 5.**Replacement

**Step 6.**Detect the maximal smell concentration

_{i}is identified and located within the population.

**Step 7.**Keep smell concentration

**Step 8.**Iterative optimization

**Step 9.**Output the optimum parameter of SVR.

## 3.4. Case Study

## 4. Results and Discussion

_{Oi}= observed RSL ith value, RSL

_{Pi}= predicted RSL ith value, and $\overline{{\mathrm{RSL}}_{Oi}}$ = average of RSL

_{Oi}.

**Blue contours**It shows the Pearson correlation coefficient.**Orange contours**It indicates the RMS error that is proportional to the distance from a green spot on the horizontal axis called observed.**Black contours**It indicates the standard deviation proportional to the radial distance from the center.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Acronyms

Abbreviation | Description |

RSL | Remaining Service Life |

PCI | Pavement Condition Index |

FWD | Falling Weight Deflectometer |

GPR | Ground Penetrating Radar |

SVR | Support Vector Regression |

SVR-FOA | Support Vector Regression Optimized by Fruit Fly Optimization Algorithm |

GEP | Gene Expression Programming |

CC | Correlation Coefficient |

NSE | Nash–Sutcliffe Efficiency |

SI | Scattered Index |

WI | Willmott’s Index of agreement |

PMSs | Pavement Management Systems |

MR&R | Maintenance, Rehabilitation, and Reconstruction |

IRI | International Roughness Index |

PSI | Present Serviceability Index |

PSR | Present Serviceability Ratio |

ANN | Artificial Neural Network |

SVM | Support Vector Machine |

RBF | Radial Basis Function |

GEP | Gene Expression Programming |

RT | Regression Tree |

RF | Random Forest |

GP | Genetic Programming |

AMS | Assessment Management System |

DV | Deduct Value |

CDV | Corrected Deduct Value |

TDV | Sum of DVs |

MnDOT | Minnesota Department of Transportation |

MDOT | Michigan Department of Transportation |

HWD | Heavy Falling Weight Deflectometer |

GA | Genetic Algorithm |

ETs | Expression Trees |

ORF | Open Reading Frame |

RRSE | Root Relative Squared Error |

RSE | Relative Square Error |

RMSE | Root Mean Square Error |

MSE | Mean Square Error |

SVM | Support Vector Machine |

SRM | Structural Risk Minimization |

ERM | Empirical Risk Minimization |

FOA | Fruit Fly Optimization Algorithm |

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**Figure 1.**The heavy falling weight deflectometer (HWD) used in this study for determining the remaining service life (RSL).

**Figure 2.**A sample of the genotype-phenotype structure in gene expression programming (GEP) [50].

**Figure 3.**The coding region (ORF), no-coding region, and expression tree in a gene [52].

**Figure 4.**The transformation process in the support vector regression (SVR) [58].

**Figure 5.**Fruit fly swarm optimization method [62].

**Figure 6.**The flowchart of the support vector regression optimized by the fruit fly optimization algorithm (SVR-FOA) method [62].

**Figure 10.**The scatter plots of calculated RSL by HWD and estimated RSL by SVR, SVR-FOA, and GEP models for test data.

Category | Model Inputs | Equation | Author |
---|---|---|---|

1. Based on pavement responses | ε_{t} = Tensile strain at the bottom of the asphalt layer,E _{1} = Elastic modulus of asphalt,f _{1}, f_{2}, and f_{3} = Regression coefficients. | ${\mathrm{RSL}}_{fatigue}={f}_{1}{\left({\epsilon}_{t}\right)}^{-{f}_{2}}{\left({E}_{1}\right)}^{-{f}_{3}}$ | Huang (1993) |

ε_{c} = Compressive strain at the top of the subgrade,f _{4} and f_{5} = Regression coefficients. | ${\mathrm{RSL}}_{rutting}={f}_{4}{\left({\epsilon}_{c}\right)}^{-{f}_{5}}$ | Huang (1993) | |

ε_{t} = Tensile strain at the asphalt layer bottom, M_{R} = Resilient modulus. | ${\mathrm{RSL}}_{fatigue}=0.1001\left({\epsilon}_{t}\right)-3.565{\left({M}_{R}\right)}^{-1.4747}$ | Das & Pandey (1999) | |

ε_{r} = Horizontal tensile strain at the bottom of the asphalt layer,E _{AC} = Modulus of asphalt,a, b, and c = Constant coefficients of regression. | $\mathit{ln}\left({\mathrm{RSL}}_{fatigue}\right)=a-b\mathit{ln}({\epsilon}_{r})-c\mathit{ln}({E}_{AC})$ | Hossain & Wu (2002) | |

ε_{t} = Tensile strain at the asphalt layer bottom,K and c = Regression coefficients. | ${\mathrm{RSL}}_{fatigue}=K{\left({\epsilon}_{t}\right)}^{-C}$ | Park & Kim (2003) | |

2. Based on pavement quality indices | IRI = International roughness index, a = Initial IRI (where age is zero), b = Curvature of performance line. | $\mathrm{RSL}=\frac{\mathit{ln}\left(\frac{{\mathrm{IRI}}_{terminal}}{a}\right)}{b}-\left(Currentage\right)$ | Al-suleiman & Shiyab (2003) |

PCI = Pavement Condition Index. | $\mathrm{RSL}=4.1872\mathit{ln}\left(\mathrm{PCI}\right)-14.728$ | Setyawan et al. (2015) | |

3. Based on the result of the non-destructive test | $\delta $ = Pavement surface curvature, $\delta ={D}_{0}-{D}_{20}$ $\alpha $ and $\beta $ = Material constants. | ${\mathrm{RSL}}_{fatigue}=\alpha {\left(\frac{1}{0.0023\delta +0.00002}\right)}^{\beta}$ | Saleh (2016) |

AUPP = Area under pavement profile, $\mathrm{AUPP}=\frac{5{D}_{0}-2{D}_{30}-2{D}_{60}-{D}_{90}}{2}$ $\alpha $ and $\beta $ = Material constants. | ${\mathrm{RSL}}_{fatigue}=\alpha {\left(\frac{1}{0.0000023AUP{P}^{0.912}}\right)}^{\beta}$ | Saleh (2016) |

_{i}= Deflection of pavement surface on distance i cm from the center of the loading plate in the FWD test.

**Table 2.**PCI rating scale [22].

Rating Scale | 0–10 | 10–25 | 25–40 | 40–55 | 55–70 | 70–85 | 85–100 |
---|---|---|---|---|---|---|---|

Description | Failed | Serious | Very Poor | Poor | Fair | Satisfactory | Good |

**Table 3.**HWD test details [37].

Parameter | Value |
---|---|

Tension (kPa) | 600–900 |

Number of geophones | 9 |

Geophone distance from center of laoding plate (cm) | 0, 20, 30, 45, 60, 90, 120, 150, and 180 |

Number of weights falling | Four times |

Loading plate radius (mm) | 150 |

Parameter | Value |
---|---|

Antenna type | 1000 MHz |

Record speed (km/hr) | 10 |

Number of scanning (per meter) | 10 |

Maximum pulse penetrating depth (ns) | 32 |

Variable | Mean | Minimum | Maximum | Standard Deviation | Kurtosis | Skewness | Sig. in Kolmogorov–Smirnov Test | Correlation with RSL |
---|---|---|---|---|---|---|---|---|

PCI | 59.97 | 19.00 | 100.00 | 21.51 | −1.093 | 0.03 | 0.068 | 0.572 |

RSL | 17.77 | 0.00 | 40.00 | 15.04 | −1.393 | 0.50 | 0.000 | 1 |

Model | |||
---|---|---|---|

SVR | SVR-FOA | ||

SVR parameter | C | 1.0000 | 1.0022 |

$\mathsf{\epsilon}$ | 0.0100 | 0.2561 | |

$\mathsf{\gamma}$ | 0.0010 | 0.0760 |

Parameter | Quantity |
---|---|

Head size | 8 |

Number of Genes | 3 |

Chromosomes | 30 |

Linking function | Addition (+) |

One-point recombination rate | 0.3 |

Two-point recombination rate | 0.3 |

Inversion rate | 0.1 |

Gene recombination rate | 0.1 |

Mutation rate | 0.044 |

Gene transposition rate | 0.1 |

Used functions | +, −, ×, ÷, power |

Parameter | GEP | SVR | SVR-FOA |
---|---|---|---|

CC | 0.874 | 0.865 | 0.879 |

SI | 0.598 | 0.894 | 0.616 |

NSE | 0.601 | 0.110 | 0.577 |

WI | 0.807 | 0.369 | 0.786 |

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## Share and Cite

**MDPI and ACS Style**

Nabipour, N.; Karballaeezadeh, N.; Dineva, A.; Mosavi, A.; Mohammadzadeh S., D.; Shamshirband, S.
Comparative Analysis of Machine Learning Models for Prediction of Remaining Service Life of Flexible Pavement. *Mathematics* **2019**, *7*, 1198.
https://doi.org/10.3390/math7121198

**AMA Style**

Nabipour N, Karballaeezadeh N, Dineva A, Mosavi A, Mohammadzadeh S. D, Shamshirband S.
Comparative Analysis of Machine Learning Models for Prediction of Remaining Service Life of Flexible Pavement. *Mathematics*. 2019; 7(12):1198.
https://doi.org/10.3390/math7121198

**Chicago/Turabian Style**

Nabipour, Narjes, Nader Karballaeezadeh, Adrienn Dineva, Amir Mosavi, Danial Mohammadzadeh S., and Shahaboddin Shamshirband.
2019. "Comparative Analysis of Machine Learning Models for Prediction of Remaining Service Life of Flexible Pavement" *Mathematics* 7, no. 12: 1198.
https://doi.org/10.3390/math7121198