# A Machine Learning Approach to Determine Airport Asphalt Concrete Layer Moduli Using Heavy Weight Deflectometer Data

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Campaign

#### 2.1. In Situ Investigation

#### 2.2. Deflection Basin Parameters

- Surface curvature index (SCI) which provides information on changes in the near-surface layer’s relative strength.

- Deflection ratio (DR) which takes into account the type and quality of materials by relating them to the ratio of two deflections.

- Area under deflection basin curve (AREA) which relates the stiffness of the pavement structure to a shape factor. In fact, it is the partial area under the deflection basin curve normalized with respect to ${\mathsf{\delta}}_{0}$ using Simpson’s rule [48].

#### 2.3. Backcalculation Process

## 3. Theory and Calculation

#### 3.1. Neural Modeling

#### 3.2. Bayesian Regularization

^{®}Toolbox LM algorithm ($\mathsf{\mu},{\text{}\mathsf{\mu}}_{\mathrm{inc}},{\mathsf{\mu}}_{\mathrm{dec}},{\mathsf{\mu}}_{\mathrm{max}}$ and $\mathrm{E}$) were used, namely the initial $\mathsf{\mu}$ was set equal to 0.001, ${\mathsf{\mu}}_{\mathrm{inc}}$ to 10, ${\mathsf{\mu}}_{\mathrm{dec}}$ to 0.1, ${\mathsf{\mu}}_{\mathrm{max}}$ to $1\times {10}^{10}$, whereas the maximum number of training epochs $\mathrm{E}$ was 1000. As explained in Section 3.1, the size of the hidden layer together with its activation function were identified by performing a grid search. Moreover, one last parameter, ${\mathrm{w}}_{\mathrm{w}}$, was defined. It represented the number of re-trainings performed for each iteration and was set equal to 10. This was done in order to obtain the best network among the 10 fitted networks for every combination of neurons function as a result of a k-fold cross-validation partitioning.

#### 3.3. K-Fold Cross-Validation

#### 3.4. Data Augmentation

^{®}Toolbox, the comparison between this simplified model and the one proposed by the authors has been considered. Such comparison allows one to evaluate the improvement of stiffness values estimation given by the proposed model. Moreover, assuming that data augmentation implementation is nearly equivalent to a denser experimental campaign, it can be understood how the change of the HWD measurements resolution affects the modeling result.

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Inputs | Output | Activation Fun. | Best Architecture | $\mathbf{R}$ | $\mathbf{M}\mathbf{S}\mathbf{E}$ | ${\mathbf{R}}_{\mathbf{a}\mathbf{d}\mathbf{j}}^{2}$ |
---|---|---|---|---|---|---|

δ_{0}, HS, X, Y | ${\mathrm{E}}_{\mathrm{AC}}$ | ELU | 4-12-1 | 0.9673 | 0.0682 | 0.9231 |

ReLU | 4-27-1 | 0.9408 | 0.1309 | 0.8627 | ||

TanH | 4-25-1 | 0.9780 | 0.0494 | 0.9477 | ||

LogS | 4-22-1 | 0.9772 | 0.0474 | 0.9461 |

Inputs | Output | Activation Fun. | Best Architecture | $\mathbf{R}$ | $\mathbf{M}\mathbf{S}\mathbf{E}$ | ${\mathbf{R}}_{\mathbf{a}\mathbf{d}\mathbf{j}}^{2}$ |
---|---|---|---|---|---|---|

δ_{0}, δ_{2}, δ_{3,} δ_{4,} δ_{5,} HS, X, Y | ${\mathrm{E}}_{\mathrm{AC}}$ | ELU | 8-27-1 | 0.9805 | 0.0423 | 0.9368 |

ReLU | 8-3-1 | 0.9455 | 0.1217 | 0.8277 | ||

TanH | 8-9-1 | 0.9806 | 0.0437 | 0.9370 | ||

LogS | 8-13-1 | 0.9844 | 0.0370 | 0.9493 |

Inputs | Output | Activation Fun. | Best Architecture | $\mathbf{R}$ | $\mathbf{M}\mathbf{S}\mathbf{E}$ | ${\mathbf{R}}_{\mathbf{a}\mathbf{d}\mathbf{j}}^{2}$ |
---|---|---|---|---|---|---|

SCI_{1}, SCI_{2}, SCI_{3}, DR, AUPP, AREA, HS, X, Y | ${\mathrm{E}}_{\mathrm{AC}}$ | ELU | 9-18-1 | 0.9804 | 0.0501 | 0.9303 |

ReLU | 9-14-1 | 0.9555 | 0.0963 | 0.8441 | ||

TanH | 9-26-1 | 0.9807 | 0.0439 | 0.9312 | ||

LogS | 9-23-1 | 0.9864 | 0.0321 | 0.9516 |

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**MDPI and ACS Style**

Baldo, N.; Miani, M.; Rondinella, F.; Celauro, C.
A Machine Learning Approach to Determine Airport Asphalt Concrete Layer Moduli Using Heavy Weight Deflectometer Data. *Sustainability* **2021**, *13*, 8831.
https://doi.org/10.3390/su13168831

**AMA Style**

Baldo N, Miani M, Rondinella F, Celauro C.
A Machine Learning Approach to Determine Airport Asphalt Concrete Layer Moduli Using Heavy Weight Deflectometer Data. *Sustainability*. 2021; 13(16):8831.
https://doi.org/10.3390/su13168831

**Chicago/Turabian Style**

Baldo, Nicola, Matteo Miani, Fabio Rondinella, and Clara Celauro.
2021. "A Machine Learning Approach to Determine Airport Asphalt Concrete Layer Moduli Using Heavy Weight Deflectometer Data" *Sustainability* 13, no. 16: 8831.
https://doi.org/10.3390/su13168831