Machine Learning Aided Design and Prediction of Environmentally Friendly Rubberised Concrete
Abstract
:1. Introduction
2. Materials and Methods
2.1. Data Collection
- Mandatory Elements (ME)
- Characteristic Elements (CE)
- Output Elements (OE)
2.2. Data Processing
2.2.1. Data Normalisation
2.2.2. Data Importation
2.3. The Optimum ANN Architecture Selection
2.3.1. Toolbox Selection
2.3.2. Hidden Layers and Neurons Determination
- The number of hidden neurons should be between the size of the input layer and the size of the output layer.
- The number of hidden neurons should be 2/3 of the size of the input layer plus 2/3 of the size of the output layer.
- The number of hidden neurons should be less than double the size of the input layer.
2.3.3. Algorithms Selection
- LM
- BR
- SCG
2.3.4. Performance Evaluation of ANN Architectures
3. Results and Discussion
3.1. Optimum ANN Architecture Determination
3.2. Comparative Analysis
4. Conclusions
- The ANN architecture with LM algorithm, two hidden layers and ten hidden neurons in each hidden layer is the optimal option for simultaneously predicting multiple mechanical properties of eco-friendly rubberised concrete.
- Based on the MSE (7.2420) and (0.9710) values of the optimal ANN architecture, excellent prediction accuracy of the machine learning can be attained.
- The value of MLR is relatively lower than that of the optimal ANN model. This traditionally implies that the prediction accuracy of the ANN model is relatively higher than that of MLR.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Training Group | ANN Architecture | MSE Value | Average Value | R2 Value | Average Value |
---|---|---|---|---|---|
LM-17-1-5 | LM-17-1-5-1 | 19.608 | 23.1850 | 0.915 | 0.9026 |
LM-17-1-5-2 | 27.179 | 0.889 | |||
LM-17-1-5-3 | 23.363 | 0.906 | |||
LM-17-1-5-4 | 20.507 | 0.907 | |||
LM-17-1-5-5 | 25.268 | 0.895 | |||
BR-17-1-5 | BR-17-1-5-1 | 24.124 | 26.4407 | 0.908 | 0.8955 |
BR-17-1-5-2 | 27.455 | 0.889 | |||
BR-17-1-5-3 | 26.468 | 0.889 | |||
BR-17-1-5-4 | 24.760 | 0.896 | |||
BR-17-1-5-5 | 29.395 | 0.895 | |||
SCG-17-1-5 | SCG-17-1-5-1 | 28.627 | 20.1789 | 0.880 | 0.9166 |
SCG-17-1-5-2 | 28.075 | 0.882 | |||
SCG-17-1-5-3 | 13.612 | 0.946 | |||
SCG-17-1-5-4 | 13.645 | 0.944 | |||
SCG-17-1-5-5 | 16.935 | 0.930 | |||
LM-17-5-5 | LM-17-5-5-1 | 45.467 | 17.7134 | 0.816 | 0.9281 |
LM-17-5-5-2 | 15.738 | 0.937 | |||
LM-17-5-5-3 | 9.336 | 0.961 | |||
LM-17-5-5-4 | 7.743 | 0.973 | |||
LM-17-5-5-5 | 10.283 | 0.953 | |||
BR-17-5-5 | BR-17-5-5-1 | 13.150 | 12.7931 | 0.932 | 0.9437 |
BR-17-5-5-2 | 11.543 | 0.955 | |||
BR-17-5-5-3 | 11.961 | 0.950 | |||
BR-17-5-5-4 | 16.931 | 0.931 | |||
BR-17-5-5-5 | 10.381 | 0.950 | |||
SCG-17-5-5 | SCG-17-5-5-1 | 16.181 | 15.3224 | 0.927 | 0.9289 |
SCG-17-5-5-2 | 14.924 | 0.935 | |||
SCG-17-5-5-3 | 14.129 | 0.938 | |||
SCG-17-5-5-4 | 16.267 | 0.918 | |||
SCG-17-5-5-5 | 15.111 | 0.926 | |||
LM-17-10-5 | LM-17-10-5-1 | 6.384 | 10.9459 | 0.973 | 0.9560 |
LM-17-10-5-2 | 12.171 | 0.948 | |||
LM-17-10-5-3 | 8.397 | 0.964 | |||
LM-17-10-5-4 | 17.776 | 0.933 | |||
LM-17-10-5-5 | 10.002 | 0.963 | |||
BR-17-10-5 | BR-17-10-5-1 | 10.045 | 12.5805 | 0.956 | 0.9479 |
BR-17-10-5-2 | 12.745 | 0.946 | |||
BR-17-10-5-3 | 12.889 | 0.947 | |||
BR-17-10-5-4 | 12.937 | 0.945 | |||
BR-17-10-5-5 | 14.286 | 0.946 | |||
SCG-17-10-5 | SCG-17-10-5-1 | 14.474 | 16.4983 | 0.940 | 0.9317 |
SCG-17-10-5-2 | 20.373 | 0.915 | |||
SCG-17-10-5-3 | 15.608 | 0.944 | |||
SCG-17-10-5-4 | 13.072 | 0.945 | |||
SCG-17-10-5-5 | 18.964 | 0.914 | |||
LM-17-15-5 | LM-17-15-5-1 | 9.135 | 8.7459 | 0.965 | 0.9626 |
LM-17-15-5-2 | 9.664 | 0.958 | |||
LM-17-15-5-3 | 10.259 | 0.952 | |||
LM-17-15-5-4 | 6.710 | 0.973 | |||
LM-17-15-5-5 | 7.961 | 0.965 | |||
BR-17-15-5 | BR-17-15-5-1 | 20.356 | 32.3697 | 0.919 | 0.8795 |
BR-17-15-5-2 | 40.857 | 0.861 | |||
BR-17-15-5-3 | 22.650 | 0.920 | |||
BR-17-15-5-4 | 40.554 | 0.858 | |||
BR-17-15-5-5 | 37.433 | 0.839 | |||
SCG-17-15-5 | SCG-17-15-5-1 | 14.682 | 20.5665 | 0.946 | 0.9146 |
SCG-17-15-5-2 | 21.556 | 0.910 | |||
SCG-17-15-5-3 | 29.309 | 0.878 | |||
SCG-17-15-5-4 | 13.980 | 0.936 | |||
SCG-17-15-5-5 | 23.306 | 0.904 | |||
LM-17-20-5 | LM-17-20-5-1 | 10.841 | 11.0165 | 0.954 | 0.9509 |
LM-17-20-5-2 | 14.187 | 0.946 | |||
LM-17-20-5-3 | 9.020 | 0.956 | |||
LM-17-20-5-4 | 8.129 | 0.968 | |||
LM-17-20-5-5 | 12.905 | 0.930 | |||
BR-17-20-5 | BR-17-20-5-1 | 47.893 | 48.5124 | 0.840 | 0.8315 |
BR-17-20-5-2 | 54.524 | 0.813 | |||
BR-17-20-5-3 | 36.495 | 0.865 | |||
BR-17-20-5-4 | 39.970 | 0.858 | |||
BR-17-20-5-5 | 63.679 | 0.781 | |||
SCG-17-20-5 | SCG-17-20-5-1 | 22.263 | 17.2641 | 0.915 | 0.9315 |
SCG-17-20-5-2 | 13.949 | 0.946 | |||
SCG-17-20-5-3 | 21.249 | 0.914 | |||
SCG-17-20-5-4 | 17.420 | 0.935 | |||
SCG-17-20-5-5 | 11.439 | 0.948 | |||
LM-17-25-5 | LM-17-25-5-1 | 8.471 | 11.267 | 0.970 | 0.9522 |
LM-17-25-5-2 | 10.370 | 0.957 | |||
LM-17-25-5-3 | 14.410 | 0.931 | |||
LM-17-25-5-4 | 10.994 | 0.950 | |||
LM-17-25-5-5 | 12.090 | 0.953 | |||
BR-17-25-5 | BR-17-25-5-1 | 69.336 | 49.6730 | 0.761 | 0.8305 |
BR-17-25-5-2 | 59.611 | 0.811 | |||
BR-17-25-5-3 | 43.495 | 0.846 | |||
BR-17-25-5-4 | 35.384 | 0.864 | |||
BR-17-25-5-5 | 40.540 | 0.870 | |||
SCG-17-25-5 | SCG-17-25-5-1 | 11.784 | 15.9628 | 0.944 | 0.9271 |
SCG-17-25-5-2 | 12.815 | 0.942 | |||
SCG-17-25-5-3 | 18.111 | 0.910 | |||
SCG-17-25-5-4 | 17.119 | 0.925 | |||
SCG-17-25-5-5 | 19.986 | 0.914 | |||
LM-17-30-5 | LM-17-30-5-1 | 20.039 | 29.3399 | 0.909 | 0.8847 |
LM-17-30-5-2 | 24.060 | 0.904 | |||
LM-17-30-5-3 | 29.875 | 0.871 | |||
LM-17-30-5-4 | 36.002 | 0.855 | |||
LM-17-30-5-5 | 36.724 | 0.884 | |||
BR-17-30-5 | BR-17-30-5-1 | 50.004 | 51.8540 | 0.828 | 0.8298 |
BR-17-30-5-2 | 54.383 | 0.819 | |||
BR-17-30-5-3 | 44.388 | 0.882 | |||
BR-17-30-5-4 | 52.017 | 0.824 | |||
BR-17-30-5-5 | 58.478 | 0.796 | |||
CG-17-30-5 | SCG-17-30-5-1 | 19.643 | 21.8357 | 0.916 | 0.9115 |
SCG-17-30-5-2 | 20.886 | 0.904 | |||
SCG-17-30-5-3 | 17.442 | 0.925 | |||
SCG-17-30-5-4 | 23.130 | 0.919 | |||
SCG-17-30-5-5 | 28.078 | 0.894 | |||
LM-17-1-1-5 | LM-17-1-1-5-1 | 23.061 | 21.5373 | 0.897 | 0.9078 |
LM-17-1-1-5-2 | 16.666 | 0.922 | |||
LM-17-1-1-5-3 | 15.999 | 0.940 | |||
LM-17-1-1-5-4 | 21.057 | 0.915 | |||
LM-17-1-1-5-5 | 30.904 | 0.865 | |||
BR -17-1-1-5 | BR-17-1-1-5-1 | 28.043 | 28.2334 | 0.895 | 0.8914 |
BR-17-1-1-5-2 | 26.079 | 0.903 | |||
BR-17-1-1-5-3 | 29.380 | 0.889 | |||
BR-17-1-1-5-4 | 31.593 | 0.886 | |||
BR-17-1-1-5-5 | 26.073 | 0.884 | |||
SCG -17-1-1-5 | SCG-17-1-1-5-1 | 29.392 | 25.4727 | 0.884 | 0.8937 |
SCG-17-1-1-5-2 | 22.598 | 0.892 | |||
SCG-17-1-1-5-3 | 21.492 | 0.904 | |||
SCG-17-1-1-5-4 | 26.143 | 0.896 | |||
SCG-17-1-1-5-5 | 27.738 | 0.892 | |||
LM-17-5-5-5 | LM-17-5-5-5-1 | 9.222 | 11.1077 | 0.958 | 0.9522 |
LM-17-5-5-5-2 | 11.546 | 0.945 | |||
LM-17-5-5-5-3 | 8.044 | 0.967 | |||
LM-17-5-5-5-4 | 14.946 | 0.933 | |||
LM-17-5-5-5-5 | 11.780 | 0.958 | |||
BR -17-5-5-5 | BR-17-5-5-5-1 | 6.122 | 9.1582 | 0.980 | 0.9623 |
BR-17-5-5-5-2 | 7.082 | 0.974 | |||
BR-17-5-5-5-3 | 7.614 | 0.966 | |||
BR-17-5-5-5-4 | 6.123 | 0.973 | |||
BR-17-5-5-5-5 | 18.850 | 0.919 | |||
SCG -17-5-5-5 | SCG-17-5-5-5-1 | 22.845 | 22.9340 | 0.912 | 0.9049 |
SCG-17-5-5-5-2 | 21.129 | 0.910 | |||
SCG-17-5-5-5-3 | 24.037 | 0.902 | |||
SCG-17-5-5-5-4 | 22.576 | 0.905 | |||
SCG-17-5-5-5-5 | 24.083 | 0.896 | |||
LM-17-10-10-5 | LM-17-10-10-5-1 | 7.694 | 7.2420 | 0.970 | 0.9710 |
LM-17-10-10-5-2 | 6.067 | 0.974 | |||
LM-17-10-10-5-3 | 5.669 | 0.978 | |||
LM-17-10-10-5-4 | 8.088 | 0.964 | |||
LM-17-10-10-5-5 | 8.692 | 0.969 | |||
BR -17-10-10-5 | BR-17-10-10-5-1 | 26.057 | 25.1978 | 0.906 | 0.9071 |
BR-17-10-10-5-2 | 18.578 | 0.927 | |||
BR-17-10-10-5-3 | 35.363 | 0.877 | |||
BR-17-10-10-5-4 | 25.603 | 0.906 | |||
BR-17-10-10-5-5 | 20.387 | 0.919 | |||
SCG -17-10-10-5 | SCG-17-10-10-5-1 | 18.176 | 19.3592 | 0.934 | 0.9227 |
SCG-17-10-10-5-2 | 22.484 | 0.930 | |||
SCG-17-10-10-5-3 | 19.166 | 0.911 | |||
SCG-17-10-10-5-4 | 18.794 | 0.916 | |||
SCG-17-10-10-5-5 | 18.177 | 0.923 | |||
LM-17-15-15-5 | LM-17-15-15-5-1 | 29.132 | 30.3840 | 0.892 | 0.8923 |
LM-17-15-15-5-2 | 40.439 | 0.861 | |||
LM-17-15-15-5-3 | 15.351 | 0.941 | |||
LM-17-15-15-5-4 | 34.254 | 0.884 | |||
LM-17-15-15-5-5 | 32.744 | 0.884 | |||
BR -17-15-15-5 | BR-17-15-15-5-1 | 30.100 | 35.5664 | 0.908 | 0.8674 |
BR-17-15-15-5-2 | 48.677 | 0.824 | |||
BR-17-15-15-5-3 | 30.691 | 0.899 | |||
BR-17-15-15-5-4 | 43.835 | 0.791 | |||
BR-17-15-15-5-5 | 24.530 | 0.915 | |||
SCG -17-15-15-5 | SCG-17-15-15-5-1 | 12.935 | 11.6450 | 0.942 | 0.9500 |
SCG-17-15-15-5-2 | 11.981 | 0.951 | |||
SCG-17-15-15-5-3 | 7.689 | 0.970 | |||
SCG-17-15-15-5-4 | 12.935 | 0.940 | |||
SCG-17-15-15-5-5 | 12.687 | 0.946 | |||
LM-17-20-20-5 | LM-17-20-20-5-1 | 22.755 | 23.9056 | 0.903 | 0.9053 |
LM-17-20-20-5-2 | 29.075 | 0.885 | |||
LM-17-20-20-5-3 | 25.528 | 0.891 | |||
LM-17-20-20-5-4 | 25.748 | 0.911 | |||
LM-17-20-20-5-5 | 16.422 | 0.936 | |||
BR -17-20-20-5 | BR-17-20-20-5-1 | 60.931 | 54.9310 | 0.795 | 0.8179 |
BR-17-20-20-5-2 | 45.471 | 0.857 | |||
BR-17-20-20-5-3 | 70.394 | 0.796 | |||
BR-17-20-20-5-4 | 42.445 | 0.829 | |||
BR-17-20-20-5-5 | 55.414 | 0.813 | |||
SCG -17-20-20-5 | SCG-17-20-20-5-1 | 13.649 | 20.3014 | 0.939 | 0.9178 |
SCG-17-20-20-5-2 | 24.836 | 0.900 | |||
SCG-17-20-20-5-3 | 29.018 | 0.876 | |||
SCG-17-20-20-5-4 | 16.613 | 0.935 | |||
SCG-17-20-20-5-5 | 17.391 | 0.939 | |||
LM-17-25-25-5 | LM-17-25-25-5-1 | 29.484 | 18.4144 | 0.899 | 0.9285 |
LM-17-25-25-5-2 | 18.306 | 0.930 | |||
LM-17-25-25-5-3 | 16.619 | 0.933 | |||
LM-17-25-25-5-4 | 13.342 | 0.941 | |||
LM-17-25-25-5-5 | 14.321 | 0.940 | |||
BR -17-25-25-5 | BR-17-25-25-5-1 | 62.883 | 42.4919 | 0.768 | 0.8455 |
BR-17-25-25-5-2 | 48.863 | 0.804 | |||
BR-17-25-25-5-3 | 39.218 | 0.872 | |||
BR-17-25-25-5-4 | 35.220 | 0.882 | |||
BR-17-25-25-5-5 | 26.276 | 0.902 | |||
SCG -17-25-25-5 | SCG-17-25-25-5-1 | 19.483 | 16.5416 | 0.926 | 0.9346 |
SCG-17-25-25-5-2 | 13.245 | 0.943 | |||
SCG-17-25-25-5-3 | 18.428 | 0.929 | |||
SCG-17-25-25-5-4 | 14.322 | 0.947 | |||
SCG-17-25-25-5-5 | 17.231 | 0.928 | |||
LM-17-30-30-5 | LM-17-30-30-5-1 | 6.665 | 19.0260 | 0.975 | 0.9247 |
LM-17-30-30-5-2 | 21.629 | 0.918 | |||
LM-17-30-30-5-3 | 25.859 | 0.892 | |||
LM-17-30-30-5-4 | 6.398 | 0.975 | |||
LM-17-30-30-5-5 | 34.579 | 0.864 | |||
BR -17-30-30-5 | BR-17-30-30-5-1 | 49.909 | 39.5577 | 0.823 | 0.8571 |
BR-17-30-30-5-2 | 31.449 | 0.874 | |||
BR-17-30-30-5-3 | 49.542 | 0.824 | |||
BR-17-30-30-5-4 | 31.739 | 0.893 | |||
BR-17-30-30-5-5 | 35.149 | 0.871 | |||
SCG -17-30-30-5 | SCG-17-30-30-5-1 | 20.650 | 22.2361 | 0.908 | 0.9074 |
SCG-17-30-30-5-2 | 18.320 | 0.921 | |||
SCG-17-30-30-5-3 | 23.257 | 0.903 | |||
SCG-17-30-30-5-4 | 15.679 | 0.935 | |||
SCG-17-30-30-5-5 | 33.275 | 0.869 |
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Number | Representation |
---|---|
1 | No special treatment |
2 | Pre-treated with NaOH |
3 | Pre-coated with limestone |
Number | Representation |
---|---|
1 | Portland Cement of Grade 32.5 |
2 | CEMI High Strength Portland Cement (52.5 MPa) |
3 | Ordinary Portland Cement grade 42.5 |
4 | ASTM C150 I (Ordinary Portland Cement Type I) |
5 | Portland Cement (42.5 MPa) |
6 | ASTM C150 II (Ordinary Portland Cement Type II) |
7 | AS 3972 for Type GB (Blended) cement |
Data Set Size | Cement Type | Replacement by Rubber | Reference |
---|---|---|---|
8 | 1 | 1%, 3%, 5%, 10%, 15%, 20% | [34] |
3 | 2 | 3%, 5%, 8% | [35] |
5 | 3 | 5%, 10%, 15%, 20%, 30% | [36] |
12 | 4 | 5%, 10%, 15%, 20% | [37] |
9 | 2 | 5%, 10%, 15% | [38] |
27 | 5 | 5%, 10%, 15%, 20%, 25%, 30% | [39] |
6 | 4 | 5%, 10%, 15% | [40] |
8 | 4 | 5%, 10%, 15%, 20% | [41] |
3 | 6 | 5%, 7.5%, 10% | [42] |
9 | 3 | 5%, 10%, 20% | [43] |
9 | 4 | 5%, 10%, 15% | [40] |
3 | 5 | 5%, 10%, 15% | [44] |
5 | 1 | 9%, 15%, 30%, 58.80%, 100% | [45] |
9 | 4 | 10%, 20%, 30% | [46] |
6 | 6 | 10% | [47] |
10 | 4 | 25%, 50%, 75%, 100% | [48] |
12 | 4 | 5%, 10%, 15%, 20% | [49] |
9 | 7 | 20% | [50] |
7 | 1 | 15%, 25%, 30%, 50%, 75%, | [51] |
48 | 4 | 2.5%, 5%, 10%, 15%, 25%, 50% | [52] |
24 | 1 | 5%, 10%, 15%, 25%, 30%, 40%, 50% | [53] |
9 | 1 | 10%, 20%, 30% | [46] |
11 | 4 | 5%, 10%, 15%, 20%, 40% | [54] |
5 | 4 | 5%, 10%, 15%, 20%, 30% | [6] |
5 | 5 | 20%, 40%, 60%, 80%, 100% | [55] |
15 | 5 | 5%, 10%, 15%, 20%, 25% | [56] |
4 | 4 | 10%, 20%, 30%, 40% | [57] |
16 | 4 | 5%, 10%, 15%, 20% | [58] |
4 | 3 | 4%, 4.5%, 5%, 5.5% | [59] |
53 | 4 | 5%, 10%, 15%, 20%, 25% | [60] |
Parameter | Unit | Minimum | Maximum |
---|---|---|---|
RR | (%) | 1.00 | 100.00 |
PSR | (mm) | 0.00 | 21.50 |
FA | (kg/m3) | 0.00 | 1116.00 |
MCFA | (%) | 1.00 | 9.00 |
PSFA | (mm) | 2.00 | 5.00 |
R | (kg/m3) | 9.00 | 549.00 |
PR | |||
C | (kg/m3) | 280.00 | 540.00 |
CT | |||
W | (kg/m3) | 115.00 | 453.00 |
WRM | (kg/m3) | 0.00 | 15.00 |
SG | (kg/m3) | 0.00 | 165.00 |
FA | (kg/m3) | 0.00 | 156.00 |
SF | (kg/m3) | 0.00 | 362.80 |
CA | (kg/m3) | 0.00 | 1493.00 |
CAPS | (mm) | 6.00 | 20.00 |
WCR | 0.25 | 0.70 | |
CS28 | (N/mm2) | 0.37 | 79.10 |
CS7 | (N/mm2) | 0.20 | 48.30 |
FS | (N/mm2) | 0.04 | 10.65 |
STS | (N/mm2) | 0.15 | 14.80 |
EM | (kN/mm2) | 1.10 | 40.90 |
ANN Architecture | Output | Statistical Index | Ref |
---|---|---|---|
(2-5)-(4-6)-1 | Compressive strength | R, MSE | [68] |
16-40-1 | Elastic modulus | R2, RMSE, MAPE | [69] |
8-9-8-2 | Tensile strength | RMSE, R2, MAPE | [32] |
6-15-1 | Compressive strength | R2 | [70] |
8-17-17-17-1 1 | Compressive strength | R2, RMSE, MAPE | [71] |
6-10-1 | Compressive strength | R, R2, RMSE, MAPE | [72] |
4-5-1 | Compressive strength | R2, RMSE, MAE | [73] |
Parameter | Value |
---|---|
Training function | LM, BR, SCG |
Hidden layer | 1;2 |
Hidden neurons | 1,5,10,15,20,25,30 |
Epochs | 1000 |
Performance evaluation | MSE, |
Transfer function | Tansig 1 |
Performance goal | 0 |
Predicted Mechanical Properties | MLR | ANN (LM-17-10-10-5) |
---|---|---|
CS7 | 0.660 | 0.9552 |
CS28 | 0.673 | 0.9641 |
FS | 0.601 | 0.8493 |
STS | 0.460 | 0.6545 |
EM | 0.773 | 0.9576 |
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Huang, X.; Zhang, J.; Sresakoolchai, J.; Kaewunruen, S. Machine Learning Aided Design and Prediction of Environmentally Friendly Rubberised Concrete. Sustainability 2021, 13, 1691. https://doi.org/10.3390/su13041691
Huang X, Zhang J, Sresakoolchai J, Kaewunruen S. Machine Learning Aided Design and Prediction of Environmentally Friendly Rubberised Concrete. Sustainability. 2021; 13(4):1691. https://doi.org/10.3390/su13041691
Chicago/Turabian StyleHuang, Xu, Jiaqi Zhang, Jessada Sresakoolchai, and Sakdirat Kaewunruen. 2021. "Machine Learning Aided Design and Prediction of Environmentally Friendly Rubberised Concrete" Sustainability 13, no. 4: 1691. https://doi.org/10.3390/su13041691