Stiffness Data of High-Modulus Asphalt Concretes for Road Pavements: Predictive Modeling by Machine-Learning
Abstract
:1. Introduction
2. Materials and Methods
High Modulus Asphalt Concrete Characterization
3. Methodology
3.1. Shallow Neural Networks with Backpropagation Algorithm
3.2. Bayesian Optimization
3.3. Input Features Selection and Models Evaluation
4. Discussion
5. Conclusions
- The IT-CY Stiffness Modulus of 115 Marshall test specimens of high-modulus asphalt mixtures prepared in the laboratory with reclaimed asphalt pavement or polymer-modified bitumen has been investigated, according to EN 12697-26 Annex C, as part of real case-mix design processes.
- There were good correlation strengths between the Stiffness Modulus and the Marshall test results, with high stiffness levels associated with high stability or quotient levels. Therefore, one of these empirical parameters could be used as an input feature, along with some parameters related to the HMAC composition, to improve the performance of a predictive model.
- Machine Learning approaches have been employed for the development of a predictive model of the HMACs’ stiffness modulus: the focus was particularly on Shallow Neural Networks, given their simple structure and good computational power even with respect to small data sets.
- A Bayesian optimization process was used to identify the neural topology, as well as the transfer function, optimal for the required modeling. In addition, a data augmentation strategy was designed for the case of the IT-CY test.
- By employing different performance metrics, it was possible to compare the optimal models obtained by varying the input feature related to the empirical Marshall test results. The SNN, which showed the best prediction accuracy of the average mechanical response of HMAC variants, receives as input a 6-component features vector, i.e., the Marshall stability (kN), the bitumen content (% by mass of mix), the air voids content (%), maximum and average bulk density (g/cm3), along with a categorical variable that distinguishes the bitumen type and RAP percentages (values from 0 to 10); such input features vector is processed by 6 neurons in the hidden layer characterized by a hyperbolic tangent activation unit.
- A worthwhile future development could be an in-depth investigation of aggregate grading curves’ influence on stiffness predictions by including additional inputs connected with mixture proportion. Another valuable alternative would be to replace during the modeling phase, variables referring to empirical properties (i.e., Marshall Stability) with those referring to pavement performance. In this way, it would be possible to predict by machine learning approaches fatigue life and/or permanent deformation resistance. Such an attempt would represent a significant step toward performance-based mixture design.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Mix | Bitumen Type | ID | Bulk Density | Max Bulk Density | Binder Content | Voids Content | Maximum Strength | Marshall Stability | Marshall Flow | IT-CY 15 °C |
---|---|---|---|---|---|---|---|---|---|---|
(g/cm3) | (g/cm3) | (%) | (%) | kN | kN | (0.1 mm) | (MPa) | |||
VMT 22 with 30% RA (Froněk-A) | 20/30 | M1 | 2.455 | 2.640 | 4.9 | 7.0 | 20.6 | 20.0 | 33 | 16,062 |
2.429 | 4.9 | 8.0 | 22.4 | 22.7 | 35 | 14,283 | ||||
2.456 | 4.9 | 7.0 | 21.6 | 23.1 | 28 | 16,078 | ||||
VMT 22 with 30% RA (Froněk-B) | 20/30 | M1 | 2.459 | 2.647 | 4.6 | 7.1 | 20.7 | 20.9 | 51 | 14,867 |
2.453 | 4.6 | 7.3 | 19.6 | 20.5 | 41 | 15,616 | ||||
2.456 | 4.6 | 7.2 | 21.0 | 21.4 | 43 | 14,350 | ||||
VMT 22 with 30% RA (Froněk-C) | 20/30 | M1 | 2.473 | 2.663 | 4.3 | 7.2 | 22.8 | 22.4 | 22 | 15,974 |
2.475 | 4.3 | 7.0 | 24.7 | 25.9 | 24 | 15,535 | ||||
2.485 | 4.3 | 6.7 | 24.1 | 24.6 | 27 | 15,452 | ||||
VMT 22 with 20% RA (Froněk-1) | 20/30 | M2 | 2.467 | 2.676 | 4.3 | 7.8 | 20.1 | 20.5 | 58 | 12,049 |
2.463 | 4.3 | 8.0 | 19.0 | 19.8 | 42 | 14,419 | ||||
2.461 | 4.3 | 8.0 | 20.2 | 21.0 | 30 | 13,003 | ||||
VMT 22 with 20% RA (Froněk-2) | 20/30 | M2 | 2.486 | 2.682 | 4.6 | 7.3 | 20.7 | 21.7 | 59 | 13,792 |
2.462 | 4.6 | 8.2 | 18.9 | 20.0 | 42 | 11,559 | ||||
2.480 | 4.6 | 7.5 | 19.6 | 19.8 | 47 | 12,452 | ||||
VMT 22 with 20% RA (Froněk-4) | 20/30 | M2 | 2.460 | 2.678 | 4.9 | 8.1 | 23.5 | 23.5 | 53 | 14,441 |
2.460 | 4.9 | 8.1 | 24.3 | 23.9 | 45 | 15,113 | ||||
2.443 | 4.9 | 8.8 | 23.9 | 24.6 | 30 | 16,558 | ||||
VMT 22 with 20% RA (Froněk-6) | 20/30 | M2 | 2.422 | 2.667 | 5.2 | 9.2 | 18.6 | 21.8 | 35 | 13,116 |
2.411 | 5.2 | 9.6 | 19.1 | 22.2 | 27 | 11,548 | ||||
2.422 | 5.2 | 9.2 | 22.3 | 25.4 | 34 | 12,370 | ||||
VMT 22 with 30% RA var. 5.1 | 50/70 | M3 | 2.547 | 2.617 | 5.1 | 2.7 | 17.1 | 19.7 | 71 | 13,171 |
2.554 | 5.1 | 2.4 | 17.2 | 20.0 | 55 | 11,659 | ||||
2.538 | 5.1 | 3.0 | 19.6 | 21.9 | 45 | 13,242 | ||||
VMT 22 with 30% RA. var. 4.8 | 50/70 | M3 | 2.538 | 2.607 | 4.8 | 2.6 | 17.4 | 19.9 | 58 | 12,739 |
2.535 | 4.8 | 2.8 | 14.8 | 16.9 | 47 | 13,287 | ||||
2.539 | 4.8 | 2.6 | 22.7 | 25.5 | 61 | 13,217 | ||||
VMT 22 with 30% RA (Froněk) | 50/70 | M3 | 2.549 | 2.602 | 4.8 | 2.0 | 17.4 | 20.2 | 53 | 13,025 |
2.539 | 4.8 | 2.4 | 15.3 | 17.9 | 63 | 14,267 | ||||
2.548 | 4.8 | 2.1 | 16.8 | 19.0 | 66 | 13,325 | ||||
VMT 22 with 30% RA (Froněk) | 50/70 | M3 | 2.553 | 2.626 | 4.6 | 2.8 | 20.6 | 20.7 | 51 | 15,871 |
2.548 | 4.6 | 3.0 | 18.6 | 21.0 | 54 | 15,666 | ||||
2.548 | 4.6 | 3.0 | 20.2 | 23.4 | 50 | 16,707 | ||||
VMT 22 with 20% RA (Froněk-3) | 50/70 | M4 | 2.473 | 2.639 | 4.8 | 6.3 | 18.1 | 19.0 | 34 | 12,729 |
2.495 | 4.8 | 5.4 | 20.2 | 21.6 | 34 | 12,282 | ||||
2.477 | 4.8 | 6.1 | 21.5 | 22.3 | 46 | 14,101 | ||||
VMT 22 with 20% RA (PKB-A) | 50/70 | M4 | 2.397 | 2.496 | 4.4 | 4.0 | 14.2 | 13.6 | 48 | 8666 |
2.421 | 4.4 | 3.0 | 13.4 | 13.4 | 50 | 9064 | ||||
2.412 | 4.4 | 3.4 | 12.2 | 12.4 | 51 | 8135 | ||||
VMT 22 with 10% RA (PKB-101) | 50/70 | M5 | 2.358 | 2.559 | 4.6 | 7.9 | 12.1 | 11.4 | 35 | 8950 |
2.351 | 4.6 | 8.1 | 15.3 | 14.1 | 37 | 9339 | ||||
2.355 | 4.6 | 8.0 | 12.8 | 14.5 | 34 | 9311 | ||||
VMT 22 with 10% RA (PKB-102) | 50/70 | M5 | 2.341 | 2.559 | 4.5 | 8.5 | 17.1 | 16.2 | 90 | 9203 |
2.343 | 4.5 | 8.4 | 17.1 | 16.1 | 80 | 9142 | ||||
2.323 | 4.5 | 9.2 | 15.1 | 14.2 | 96 | 9361 | ||||
VMT 22 NT | 20/30 | M6 | 2.362 | 2.490 | 4.7 | 5.1 | 18.9 | 17.1 | 46 | 14,357 |
2.409 | 4.7 | 3.2 | 21.4 | 20.3 | 56 | 14,601 | ||||
2.409 | 4.7 | 3.3 | 20.8 | 19.7 | 52 | 14,784 | ||||
VMT 22 NT | 20/30 | M6 | 2.296 | 2.490 | 4.7 | 7.8 | 19.4 | 16.3 | 84 | 13,653 |
2.313 | 4.7 | 7.1 | 20.8 | 18.8 | 84 | 15,529 | ||||
2.296 | 4.7 | 7.8 | 19.7 | 16.5 | 59 | 15,345 | ||||
VMT 22 (SK-1) | 20/30 | M6 | 2.330 | 2.449 | 4.6 | 4.9 | 25.4 | 24.1 | 26 | 12,102 |
2.324 | 4.6 | 5.1 | 24.5 | 23.2 | 20 | 12,027 | ||||
2.305 | 4.6 | 5.9 | 22.5 | 20.5 | 27 | 10,528 | ||||
VMT 22 (VIA-1) | 20/30 | M6 | 2.702 | 2.789 | 4.7 | 3.1 | 21.1 | 22.8 | 42 | 17,417 |
2.691 | 4.7 | 3.5 | 19.2 | 21.3 | 34 | 17,262 | ||||
2.680 | 4.7 | 3.9 | 20.5 | 23.0 | 29 | 17,478 | ||||
VMT 22 (SK-2) | 30/45 | M7 | 2.414 | 2.490 | 4.6 | 3.1 | 22.0 | 20.6 | 49 | 12,483 |
2.416 | 4.6 | 3.0 | 20.8 | 19.6 | 54 | 12,129 | ||||
2.396 | 4.6 | 3.8 | 21.7 | 20.6 | 59 | 11,734 | ||||
VMT 22 (VHS) | 30/45 | M7 | 2.641 | 2.747 | 4.7 | 3.9 | 11.5 | 14.7 | 38 | 12,136 |
2.648 | 4.7 | 3.6 | 14.4 | 15.8 | 55 | 11,478 | ||||
2.650 | 4.7 | 3.5 | 14.2 | 15.6 | 42 | 12,566 | ||||
VMT 22 (VIA-2) | TSA 15/25 | M8 | 2.709 | 2.818 | 4.8 | 3.9 | 19.7 | 22.8 | 39 | 16,182 |
2.724 | 4.8 | 3.3 | 18.0 | 21.6 | 31 | 17,571 | ||||
2.712 | 4.8 | 3.8 | 18.4 | 22.3 | 31 | 17,227 | ||||
VMT 22 (TPA-1) | TSA 15/25 | M8 | 2.458 | 2.566 | 4.6 | 4.2 | 21.5 | 21.5 | 45 | 12,629 |
2.454 | 4.6 | 4.4 | 22.5 | 21.8 | 40 | 12,412 | ||||
2.460 | 4.6 | 4.1 | 23.5 | 23.0 | 52 | 13,627 | ||||
VMT 22 (EV) | PMB 25/55–60 | M9 | 2.574 | 2.655 | 4.9 | 3.0 | 24.8 | 25.1 | 81 | 13,203 |
2.567 | 4.9 | 3.3 | 23.2 | 23.6 | 71 | 11,688 | ||||
2.576 | 4.9 | 3.0 | 27.2 | 27.7 | 65 | 13,772 | ||||
VMT 22 (SK-3) | PMB 25/55–60 | M9 | 2.357 | 2.436 | 4.7 | 3.2 | 19.7 | 19.9 | 67 | 10,581 |
2.362 | 4.7 | 3.0 | 20.4 | 20.6 | 62 | 10,940 | ||||
2.363 | 4.7 | 3.0 | 20.9 | 21.1 | 76 | 10,505 | ||||
VMT 22 (SK-4) | PMB 25/55–60 | M9 | 2.366 | 2.436 | 4.9 | 2.9 | 11.8 | 18.5 | 34 | 6632 |
2.367 | 4.9 | 2.8 | 10.8 | 17.3 | 28 | 6001 | ||||
2.358 | 4.9 | 3.2 | 11.3 | 17.8 | 28 | 6699 | ||||
VMT 22 (TPA-2) | PMB 25/55–60 | M9 | 2.338 | 2.457 | 4.8 | 4.8 | 16.3 | 16.1 | 30 | 9024 |
2.329 | 4.8 | 5.2 | 20.2 | 20.4 | 31 | 9134 | ||||
2.334 | 4.8 | 5.0 | 17.6 | 17.4 | 39 | 9097 | ||||
VMT 22 (ESLAB) | PMB 25/55–60 | M9 | 2.476 | 2.558 | 4.7 | 3.2 | 18.4 | 19.5 | 31 | 9585 |
2.485 | 4.7 | 2.9 | 17.9 | 18.4 | 47 | 9322 | ||||
2.481 | 4.7 | 3.0 | 17.2 | 17.4 | 46 | 10,656 | ||||
VMT 22 (TPA-3) | PMB 25/55–60 | M9 | 2.415 | 2.632 | 4.9 | 8.3 | 20.8 | 19.7 | 53 | 7102 |
2.427 | 4.9 | 7.8 | 18.8 | 17.8 | 51 | 8203 | ||||
2.430 | 4.9 | 7.7 | 19.4 | 18.5 | 47 | 7986 | ||||
VMT 22 (TPA-4) | PMB 25/55–60 | M9 | 2.416 | 2.485 | 4.9 | 2.8 | 21.1 | 21.7 | 42 | 9174 |
2.408 | 4.9 | 3.1 | 19.4 | 19.6 | 39 | 10,245 | ||||
2.404 | 4.9 | 3.3 | 19.6 | 19.8 | 50 | 9421 | ||||
VMT 22 (VIA-3) | PMB 25/55–60 | M9 | 2.415 | 2.510 | 4.8 | 3.8 | 18.4 | 17.5 | 57 | 9731 |
2.416 | 4.8 | 3.7 | 18.1 | 16.9 | 45 | 10,044 | ||||
2.415 | 4.8 | 3.8 | 19.2 | 17.7 | 48 | 9446 | ||||
VMT 22 (TPA-5) | PMB 25/55–60 | M9 | 2.338 | 2.457 | 5.0 | 4.8 | 18.7 | 18.9 | 46 | 8691 |
2.329 | 5.0 | 5.2 | 20.7 | 20.9 | 36 | 8759 | ||||
2.334 | 5.0 | 5.0 | 17.4 | 17.6 | 34 | 8611 | ||||
VMT 22 (TPA-6) | PMB 25/55–60 | M9 | 2.335 | 2.467 | 4.8 | 5.3 | 18.2 | 18.8 | 36 | 9953 |
2.332 | 4.8 | 5.5 | 16.5 | 18.0 | 35 | 9018 | ||||
2.339 | 4.8 | 5.2 | 17.5 | 17.9 | 28 | 9884 | ||||
2.330 | 4.8 | 5.5 | 16.3 | 16.4 | 26 | 9521 | ||||
VMT 22 (Chvaletice) | PMB 25/55–60 | M9 | 2.392 | 2.532 | 4.7 | 5.5 | 28.3 | 26.3 | 47 | 16,134 |
2.397 | 4.7 | 5.3 | 25.6 | 23.8 | 41 | 15,808 | ||||
2.386 | 4.7 | 5.8 | 28.3 | 26.8 | 33 | 15,855 | ||||
VMT 22 (SK-5) | PMB 25/55–60 | M9 | 2.373 | 2.460 | 4.9 | 3.5 | 14.5 | 12.9 | 37 | 5685 |
2.362 | 4.9 | 4.0 | 14.2 | 12.0 | 34 | 5636 | ||||
2.378 | 4.9 | 3.3 | 15.2 | 13.7 | 52 | 5991 | ||||
VMT 22 (TPA-7) | PMB 25/55–65 | M10 | 2.439 | 2.610 | 5.1 | 6.6 | 15.1 | 14.8 | 85 | 6686 |
2.441 | 5.1 | 6.5 | 15.8 | 14.9 | 90 | 6223 | ||||
2.433 | 5.1 | 6.8 | 14.1 | 13.6 | 76 | 6848 | ||||
VMT 22 (TPA-8) | PMB 25/55–65 | M10 | 2.553 | 2.648 | 4.8 | 3.6 | 19.8 | 19.2 | 79 | 11,989 |
2.556 | 4.8 | 3.5 | 21.8 | 22.0 | 61 | 12,075 | ||||
2.545 | 4.8 | 3.9 | 18.9 | 19.1 | 58 | 11,958 | ||||
VMT 22 (TPA-9) | PMB 25/55–65 | M10 | 2.554 | 2.629 | 5.0 | 2.8 | 21.8 | 22.7 | 54 | 11,849 |
2.548 | 5.0 | 3.1 | 19.8 | 20.2 | 59 | 11,603 | ||||
2.543 | 5.0 | 3.3 | 19.5 | 19.3 | 56 | 12,071 |
ID | Features | N | MAE | RMSE | R2 | R2adj | ||
---|---|---|---|---|---|---|---|---|
MIXSNN | 5 | 6 | TanH | 12.093 | 209.12 | 293.56 | 0.9909 | 0.9894 |
MSSNN | 6 | 6 | TanH | 11.856 | 160.17 | 241.54 | 0.9938 | 0.9923 |
MQSNN | 6 | 8 | LogS | 12.373 | 174.91 | 272.61 | 0.9922 | 0.9902 |
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Baldo, N.; Miani, M.; Rondinella, F.; Valentin, J.; Vackcová, P.; Manthos, E. Stiffness Data of High-Modulus Asphalt Concretes for Road Pavements: Predictive Modeling by Machine-Learning. Coatings 2022, 12, 54. https://doi.org/10.3390/coatings12010054
Baldo N, Miani M, Rondinella F, Valentin J, Vackcová P, Manthos E. Stiffness Data of High-Modulus Asphalt Concretes for Road Pavements: Predictive Modeling by Machine-Learning. Coatings. 2022; 12(1):54. https://doi.org/10.3390/coatings12010054
Chicago/Turabian StyleBaldo, Nicola, Matteo Miani, Fabio Rondinella, Jan Valentin, Pavla Vackcová, and Evangelos Manthos. 2022. "Stiffness Data of High-Modulus Asphalt Concretes for Road Pavements: Predictive Modeling by Machine-Learning" Coatings 12, no. 1: 54. https://doi.org/10.3390/coatings12010054
APA StyleBaldo, N., Miani, M., Rondinella, F., Valentin, J., Vackcová, P., & Manthos, E. (2022). Stiffness Data of High-Modulus Asphalt Concretes for Road Pavements: Predictive Modeling by Machine-Learning. Coatings, 12(1), 54. https://doi.org/10.3390/coatings12010054