BULLETIN OF THE CHINESE CERAMIC SOCIETY ›› 2026, Vol. 45 ›› Issue (8): 2711-2723.DOI: 10.16552/j.cnki.issn1001-1625.2026.0140
• Cement and Concrete • Previous Articles Next Articles
TIAN Shenhua(
), LI Beixing(
), XIAO Xiang, ZHOU Junkang
Received:2026-02-05
Revised:2026-03-17
Online:2026-08-15
Published:2026-09-01
Contact:
LI Beixing
CLC Number:
TIAN Shenhua, LI Beixing, XIAO Xiang, ZHOU Junkang. Machine Learning-Based Compressive Strength Prediction of Concrete: Model Screening and Performance Comparison[J]. BULLETIN OF THE CHINESE CERAMIC SOCIETY, 2026, 45(8): 2711-2723.
| Mix ID | Materials dosage/(kg·m-3) | ||||||
|---|---|---|---|---|---|---|---|
| CE | FA | GGBS | RS | LCS | Water | PCA | |
| F0S0 | 480 | 0 | 0 | 712 | 1 114 | 154 | 5.28 |
| F20S0 | 384 | 96 | 0 | 712 | 1 114 | 154 | 5.35 |
| F15S5 | 384 | 72 | 24 | 712 | 1 114 | 154 | 5.28 |
| F12S8 | 384 | 57.6 | 38.4 | 712 | 1 114 | 154 | 5.28 |
| F10S10 | 384 | 48 | 48 | 712 | 1 114 | 154 | 5.28 |
| F30S0 | 336 | 144 | 0 | 712 | 1 114 | 154 | 5.28 |
| F22.5S7.5 | 336 | 108 | 36 | 712 | 1 114 | 154 | 5.28 |
| F18S12 | 336 | 86.4 | 57.6 | 712 | 1 114 | 154 | 5.28 |
| F15S15 | 336 | 72 | 72 | 712 | 1 114 | 154 | 5.28 |
Table 1 Mix proportion of concrete
| Mix ID | Materials dosage/(kg·m-3) | ||||||
|---|---|---|---|---|---|---|---|
| CE | FA | GGBS | RS | LCS | Water | PCA | |
| F0S0 | 480 | 0 | 0 | 712 | 1 114 | 154 | 5.28 |
| F20S0 | 384 | 96 | 0 | 712 | 1 114 | 154 | 5.35 |
| F15S5 | 384 | 72 | 24 | 712 | 1 114 | 154 | 5.28 |
| F12S8 | 384 | 57.6 | 38.4 | 712 | 1 114 | 154 | 5.28 |
| F10S10 | 384 | 48 | 48 | 712 | 1 114 | 154 | 5.28 |
| F30S0 | 336 | 144 | 0 | 712 | 1 114 | 154 | 5.28 |
| F22.5S7.5 | 336 | 108 | 36 | 712 | 1 114 | 154 | 5.28 |
| F18S12 | 336 | 86.4 | 57.6 | 712 | 1 114 | 154 | 5.28 |
| F15S15 | 336 | 72 | 72 | 712 | 1 114 | 154 | 5.28 |
| Model | Evaluation metrics | Train | Test | Score | Overall score | Model | Evaluation metrics | Train | Test | Score | Overall score |
|---|---|---|---|---|---|---|---|---|---|---|---|
| LMR | MAE | 7.030 1 | 9.058 3 | 4 | 13 | DT | MAE | 2.012 4 | 4.719 3 | 11 | 44 |
| MAPE | 0.294 3 | 0.369 9 | 3 | MAPE | 0.068 8 | 0.180 7 | 11 | ||||
| RMSE | 10.009 9 | 11.835 0 | 3 | RMSE | 3.044 8 | 6.527 9 | 11 | ||||
| R2 | 0.637 35 | 0.514 92 | 3 | R2 | 0.966 45 | 0.852 42 | 11 | ||||
| LASSO | MAE | 7.940 2 | 9.061 2 | 3 | 9 | RF | MAE | 2.722 3 | 4.451 5 | 12 | 48 |
| MAPE | 0.294 5 | 0.370 2 | 2 | MAPE | 0.100 9 | 0.183 7 | 12 | ||||
| RMSE | 10.010 0 | 11.836 2 | 2 | RMSE | 3.749 1 | 5.900 0 | 12 | ||||
| R2 | 0.637 34 | 0.514 83 | 2 | R2 | 0.949 13 | 0.879 45 | 12 | ||||
| MRR | MAE | 7.956 3 | 9.071 8 | 1 | 12 | SVM | MAE | 7.766 3 | 9.065 4 | 2 | 9 |
| MAPE | 0.297 3 | 0.371 8 | 1 | MAPE | 0.282 2 | 0.356 4 | 5 | ||||
| RMSE | 10.017 4 | 11.827 2 | 5 | RMSE | 10.386 6 | 12.488 4 | 1 | ||||
| R2 | 0.636 81 | 0.515 56 | 5 | R2 | 0.609 54 | 0.459 88 | 1 | ||||
| LSBoost | MAE | 0.854 6 | 3.563 3 | 16 | 62 | XGBoost | MAE | 1.987 9 | 3.719 9 | 15 | 62 |
| MAPE | 0.030 6 | 0.139 63 | 16 | MAPE | 0.068 1 | 0.144 5 | 15 | ||||
| RMSE | 1.609 2 | 5.055 4 | 15 | RMSE | 2.850 9 | 5.049 2 | 16 | ||||
| R2 | 0.990 63 | 0.912 46 | 15 | R2 | 0.970 58 | 0.911 71 | 16 | ||||
| GPR | MAE | 2.999 2 | 4.074 9 | 13 | 53 | LGBM | MAE | 2.178 6 | 3.540 1 | 17 | 68 |
| MAPE | 0.103 0 | 0.150 97 | 14 | MAPE | 0.080 3 | 0.129 0 | 17 | ||||
| RMSE | 4.072 | 5.413 6 | 13 | RMSE | 3.113 2 | 4.674 3 | 17 | ||||
| R2 | 0.939 99 | 0.898 5 | 13 | R2 | 0.964 92 | 0.924 33 | 17 | ||||
| GKR | MAE | 4.859 0 | 6.191 7 | 8 | 32 | LSTM | MAE | 5.121 4 | 5.772 4 | 10 | 39 |
| MAPE | 0.180 9 | 0.253 34 | 8 | MAPE | 0.180 2 | 0.219 9 | 9 | ||||
| RMSE | 6.605 5 | 8.256 2 | 8 | RMSE | 6.656 1 | 7.508 3 | 10 | ||||
| R2 | 0.842 08 | 0.763 93 | 8 | R2 | 0.839 65 | 0.804 77 | 10 | ||||
| ELM | MAE | 7.939 1 | 9.058 3 | 5 | 17 | GRU | MAE | 5.141 7 | 5.832 6 | 9 | 37 |
| MAPE | 0.294 3 | 0.369 88 | 4 | MAPE | 0.178 7 | 0.219 7 | 10 | ||||
| RMSE | 10.009 9 | 11.835 0 | 4 | RMSE | 6.673 4 | 7.547 6 | 9 | ||||
| R2 | 0.637 35 | 0.514 92 | 4 | R2 | 0.838 82 | 0.802 72 | 9 | ||||
| GRNN | MAE | 7.615 7 | 8.476 6 | 6 | 24 | CNN | MAE | 6.884 7 | 7.774 4 | 7 | 28 |
| MAPE | 0.311 4 | 0.356 3 | 6 | MAPE | 0.277 0 | 0.325 0 | 7 | ||||
| RMSE | 9.558 6 | 10.867 8 | 6 | RMSE | 8.859 6 | 10.047 0 | 7 | ||||
| R2 | 0.669 31 | 0.590 97 | 6 | R2 | 0.715 91 | 0.650 42 | 7 | ||||
| GAM | MAE | 2.611 7 | 3.909 8 | 14 | 55 | ||||||
| MAPE | 0.097 7 | 0.154 2 | 13 | ||||||||
| RMSE | 3.482 7 | 5.274 4 | 14 | ||||||||
| R2 | 0.956 10 | 0.903 66 | 14 |
Table 2 Evaluation metrics of different models
| Model | Evaluation metrics | Train | Test | Score | Overall score | Model | Evaluation metrics | Train | Test | Score | Overall score |
|---|---|---|---|---|---|---|---|---|---|---|---|
| LMR | MAE | 7.030 1 | 9.058 3 | 4 | 13 | DT | MAE | 2.012 4 | 4.719 3 | 11 | 44 |
| MAPE | 0.294 3 | 0.369 9 | 3 | MAPE | 0.068 8 | 0.180 7 | 11 | ||||
| RMSE | 10.009 9 | 11.835 0 | 3 | RMSE | 3.044 8 | 6.527 9 | 11 | ||||
| R2 | 0.637 35 | 0.514 92 | 3 | R2 | 0.966 45 | 0.852 42 | 11 | ||||
| LASSO | MAE | 7.940 2 | 9.061 2 | 3 | 9 | RF | MAE | 2.722 3 | 4.451 5 | 12 | 48 |
| MAPE | 0.294 5 | 0.370 2 | 2 | MAPE | 0.100 9 | 0.183 7 | 12 | ||||
| RMSE | 10.010 0 | 11.836 2 | 2 | RMSE | 3.749 1 | 5.900 0 | 12 | ||||
| R2 | 0.637 34 | 0.514 83 | 2 | R2 | 0.949 13 | 0.879 45 | 12 | ||||
| MRR | MAE | 7.956 3 | 9.071 8 | 1 | 12 | SVM | MAE | 7.766 3 | 9.065 4 | 2 | 9 |
| MAPE | 0.297 3 | 0.371 8 | 1 | MAPE | 0.282 2 | 0.356 4 | 5 | ||||
| RMSE | 10.017 4 | 11.827 2 | 5 | RMSE | 10.386 6 | 12.488 4 | 1 | ||||
| R2 | 0.636 81 | 0.515 56 | 5 | R2 | 0.609 54 | 0.459 88 | 1 | ||||
| LSBoost | MAE | 0.854 6 | 3.563 3 | 16 | 62 | XGBoost | MAE | 1.987 9 | 3.719 9 | 15 | 62 |
| MAPE | 0.030 6 | 0.139 63 | 16 | MAPE | 0.068 1 | 0.144 5 | 15 | ||||
| RMSE | 1.609 2 | 5.055 4 | 15 | RMSE | 2.850 9 | 5.049 2 | 16 | ||||
| R2 | 0.990 63 | 0.912 46 | 15 | R2 | 0.970 58 | 0.911 71 | 16 | ||||
| GPR | MAE | 2.999 2 | 4.074 9 | 13 | 53 | LGBM | MAE | 2.178 6 | 3.540 1 | 17 | 68 |
| MAPE | 0.103 0 | 0.150 97 | 14 | MAPE | 0.080 3 | 0.129 0 | 17 | ||||
| RMSE | 4.072 | 5.413 6 | 13 | RMSE | 3.113 2 | 4.674 3 | 17 | ||||
| R2 | 0.939 99 | 0.898 5 | 13 | R2 | 0.964 92 | 0.924 33 | 17 | ||||
| GKR | MAE | 4.859 0 | 6.191 7 | 8 | 32 | LSTM | MAE | 5.121 4 | 5.772 4 | 10 | 39 |
| MAPE | 0.180 9 | 0.253 34 | 8 | MAPE | 0.180 2 | 0.219 9 | 9 | ||||
| RMSE | 6.605 5 | 8.256 2 | 8 | RMSE | 6.656 1 | 7.508 3 | 10 | ||||
| R2 | 0.842 08 | 0.763 93 | 8 | R2 | 0.839 65 | 0.804 77 | 10 | ||||
| ELM | MAE | 7.939 1 | 9.058 3 | 5 | 17 | GRU | MAE | 5.141 7 | 5.832 6 | 9 | 37 |
| MAPE | 0.294 3 | 0.369 88 | 4 | MAPE | 0.178 7 | 0.219 7 | 10 | ||||
| RMSE | 10.009 9 | 11.835 0 | 4 | RMSE | 6.673 4 | 7.547 6 | 9 | ||||
| R2 | 0.637 35 | 0.514 92 | 4 | R2 | 0.838 82 | 0.802 72 | 9 | ||||
| GRNN | MAE | 7.615 7 | 8.476 6 | 6 | 24 | CNN | MAE | 6.884 7 | 7.774 4 | 7 | 28 |
| MAPE | 0.311 4 | 0.356 3 | 6 | MAPE | 0.277 0 | 0.325 0 | 7 | ||||
| RMSE | 9.558 6 | 10.867 8 | 6 | RMSE | 8.859 6 | 10.047 0 | 7 | ||||
| R2 | 0.669 31 | 0.590 97 | 6 | R2 | 0.715 91 | 0.650 42 | 7 | ||||
| GAM | MAE | 2.611 7 | 3.909 8 | 14 | 55 | ||||||
| MAPE | 0.097 7 | 0.154 2 | 13 | ||||||||
| RMSE | 3.482 7 | 5.274 4 | 14 | ||||||||
| R2 | 0.956 10 | 0.903 66 | 14 |
Fig.2 Relative magnitudes of evaluation metrics for each model on test set (the area of circle in figure represent relative magnitude of each evaluation metric)
| Model | Evaluation metrics | Train | Test | Score | Overall score | Model | Evaluation metrics | Train | Test | Score | Overall score |
|---|---|---|---|---|---|---|---|---|---|---|---|
| LSBoost-BO | MAE | 0.899 1 | 2.616 9 | 29 | 116 | RF-BO | MAE | 1.329 4 | 3.518 3 | 14 | 57 |
| MAPE | 0.032 1 | 0.096 1 | 29 | MAPE | 0.047 1 | 0.134 1 | 14 | ||||
| RMSE | 1.641 3 | 3.811 8 | 29 | RMSE | 2.099 0 | 4.835 5 | 15 | ||||
| R2 | 0.990 25 | 0.950 23 | 29 | R2 | 0.984 05 | 0.919 91 | 14 | ||||
| LSBoost-SSA | MAE | 0.851 6 | 2.544 6 | 30 | 120 | RF-SSA | MAE | 1.612 8 | 3.577 9 | 12 | 47 |
| MAPE | 0.030 3 | 0.093 9 | 30 | MAPE | 0.055 8 | 0.138 6 | 11 | ||||
| RMSE | 1.591 8 | 3.718 0 | 30 | RMSE | 2.427 1 | 4.924 1 | 12 | ||||
| R2 | 0.990 83 | 0.952 65 | 30 | R2 | 0.978 68 | 0.916 94 | 12 | ||||
| LSBoost-SCA | MAE | 0.768 4 | 2.895 9 | 23 | 90 | RF-SCA | MAE | 1.628 5 | 3.802 4 | 10 | 42 |
| MAPE | 0.027 4 | 0.108 5 | 21 | MAPE | 0.057 1 | 0.139 8 | 12 | ||||
| RMSE | 1.537 1 | 4.625 3 | 23 | RMSE | 2.585 9 | 5.308 0 | 10 | ||||
| R2 | 0.991 45 | 0.926 72 | 23 | R2 | 0.975 80 | 0.903 49 | 10 | ||||
| LSBoost-SA | MAE | 0.765 3 | 2.651 8 | 28 | 109 | RF-SA | MAE | 1.424 4 | 3.518 2 | 15 | 59 |
| MAPE | 0.027 3 | 0.102 6 | 26 | MAPE | 0.051 4 | 0.137 6 | 15 | ||||
| RMSE | 1.519 8 | 3.972 3 | 27 | RMSE | 2.186 6 | 4.888 5 | 14 | ||||
| R2 | 0.991 64 | 0.945 95 | 28 | R2 | 0.982 70 | 0.918 14 | 15 | ||||
| LSBoost-PSO | MAE | 0.847 7 | 2.705 3 | 26 | 103 | RF-PSO | MAE | 1.439 9 | 3.692 6 | 13 | 49 |
| MAPE | 0.030 4 | 0.097 8 | 27 | MAPE | 0.052 5 | 0.142 7 | 10 | ||||
| RMSE | 1.597 6 | 4.289 2 | 24 | RMSE | 2.211 4 | 4.999 4 | 13 | ||||
| R2 | 0.990 76 | 0.936 98 | 26 | R2 | 0.982 30 | 0.914 38 | 13 | ||||
| GPR-BO | MAE | 2.666 0 | 4.169 5 | 8 | 33 | XGBoost-BO | MAE | 0.526 2 | 2.661 2 | 27 | 102 |
| MAPE | 0.091 0 | 0.138 7 | 9 | MAPE | 0.017 8 | 0.108 0 | 22 | ||||
| RMSE | 3.688 3 | 5.677 3 | 8 | RMSE | 1.364 7 | 3.887 5 | 26 | ||||
| R2 | 0.950 76 | 0.889 59 | 8 | R2 | 0.993 26 | 0.948 23 | 27 | ||||
| GPR-SSA | MAE | 2.999 2 | 4.420 3 | 5 | 20 | XGBoost-SSA | MAE | 0.981 1 | 3.133 8 | 16 | 61 |
| MAPE | 0.103 0 | 0.150 4 | 5 | MAPE | 0.033 7 | 0.122 3 | 13 | ||||
| RMSE | 4.072 0 | 5.850 5 | 5 | RMSE | 1.724 0 | 4.534 0 | 16 | ||||
| R2 | 0.939 99 | 0.882 75 | 5 | R2 | 0.989 24 | 0.929 58 | 16 | ||||
| GPR-SCA | MAE | 2.999 2 | 4.169 5 | 5 | 20 | XGBoost-SCA | MAE | 0.981 1 | 3.133 8 | 16 | 61 |
| MAPE | 0.103 0 | 0.150 4 | 5 | MAPE | 0.033 7 | 0.122 3 | 13 | ||||
| RMSE | 4.072 0 | 5.850 5 | 5 | RMSE | 1.724 0 | 4.534 0 | 16 | ||||
| R2 | 0.939 99 | 0.882 75 | 5 | R2 | 0.989 24 | 0.929 58 | 16 | ||||
| GPR-SA | MAE | 2.999 2 | 4.169 5 | 5 | 20 | XGBoost-SA | MAE | 0.981 1 | 3.133 8 | 16 | 61 |
| MAPE | 0.103 0 | 0.150 4 | 5 | MAPE | 0.033 7 | 0.122 3 | 13 | ||||
| RMSE | 4.072 0 | 5.850 5 | 5 | RMSE | 1.724 0 | 4.534 0 | 16 | ||||
| R2 | 0.939 99 | 0.882 75 | 5 | R2 | 0.989 24 | 0.929 58 | 16 |
Table 3 Evaluation of model after hyperparameter optimization
| Model | Evaluation metrics | Train | Test | Score | Overall score | Model | Evaluation metrics | Train | Test | Score | Overall score |
|---|---|---|---|---|---|---|---|---|---|---|---|
| LSBoost-BO | MAE | 0.899 1 | 2.616 9 | 29 | 116 | RF-BO | MAE | 1.329 4 | 3.518 3 | 14 | 57 |
| MAPE | 0.032 1 | 0.096 1 | 29 | MAPE | 0.047 1 | 0.134 1 | 14 | ||||
| RMSE | 1.641 3 | 3.811 8 | 29 | RMSE | 2.099 0 | 4.835 5 | 15 | ||||
| R2 | 0.990 25 | 0.950 23 | 29 | R2 | 0.984 05 | 0.919 91 | 14 | ||||
| LSBoost-SSA | MAE | 0.851 6 | 2.544 6 | 30 | 120 | RF-SSA | MAE | 1.612 8 | 3.577 9 | 12 | 47 |
| MAPE | 0.030 3 | 0.093 9 | 30 | MAPE | 0.055 8 | 0.138 6 | 11 | ||||
| RMSE | 1.591 8 | 3.718 0 | 30 | RMSE | 2.427 1 | 4.924 1 | 12 | ||||
| R2 | 0.990 83 | 0.952 65 | 30 | R2 | 0.978 68 | 0.916 94 | 12 | ||||
| LSBoost-SCA | MAE | 0.768 4 | 2.895 9 | 23 | 90 | RF-SCA | MAE | 1.628 5 | 3.802 4 | 10 | 42 |
| MAPE | 0.027 4 | 0.108 5 | 21 | MAPE | 0.057 1 | 0.139 8 | 12 | ||||
| RMSE | 1.537 1 | 4.625 3 | 23 | RMSE | 2.585 9 | 5.308 0 | 10 | ||||
| R2 | 0.991 45 | 0.926 72 | 23 | R2 | 0.975 80 | 0.903 49 | 10 | ||||
| LSBoost-SA | MAE | 0.765 3 | 2.651 8 | 28 | 109 | RF-SA | MAE | 1.424 4 | 3.518 2 | 15 | 59 |
| MAPE | 0.027 3 | 0.102 6 | 26 | MAPE | 0.051 4 | 0.137 6 | 15 | ||||
| RMSE | 1.519 8 | 3.972 3 | 27 | RMSE | 2.186 6 | 4.888 5 | 14 | ||||
| R2 | 0.991 64 | 0.945 95 | 28 | R2 | 0.982 70 | 0.918 14 | 15 | ||||
| LSBoost-PSO | MAE | 0.847 7 | 2.705 3 | 26 | 103 | RF-PSO | MAE | 1.439 9 | 3.692 6 | 13 | 49 |
| MAPE | 0.030 4 | 0.097 8 | 27 | MAPE | 0.052 5 | 0.142 7 | 10 | ||||
| RMSE | 1.597 6 | 4.289 2 | 24 | RMSE | 2.211 4 | 4.999 4 | 13 | ||||
| R2 | 0.990 76 | 0.936 98 | 26 | R2 | 0.982 30 | 0.914 38 | 13 | ||||
| GPR-BO | MAE | 2.666 0 | 4.169 5 | 8 | 33 | XGBoost-BO | MAE | 0.526 2 | 2.661 2 | 27 | 102 |
| MAPE | 0.091 0 | 0.138 7 | 9 | MAPE | 0.017 8 | 0.108 0 | 22 | ||||
| RMSE | 3.688 3 | 5.677 3 | 8 | RMSE | 1.364 7 | 3.887 5 | 26 | ||||
| R2 | 0.950 76 | 0.889 59 | 8 | R2 | 0.993 26 | 0.948 23 | 27 | ||||
| GPR-SSA | MAE | 2.999 2 | 4.420 3 | 5 | 20 | XGBoost-SSA | MAE | 0.981 1 | 3.133 8 | 16 | 61 |
| MAPE | 0.103 0 | 0.150 4 | 5 | MAPE | 0.033 7 | 0.122 3 | 13 | ||||
| RMSE | 4.072 0 | 5.850 5 | 5 | RMSE | 1.724 0 | 4.534 0 | 16 | ||||
| R2 | 0.939 99 | 0.882 75 | 5 | R2 | 0.989 24 | 0.929 58 | 16 | ||||
| GPR-SCA | MAE | 2.999 2 | 4.169 5 | 5 | 20 | XGBoost-SCA | MAE | 0.981 1 | 3.133 8 | 16 | 61 |
| MAPE | 0.103 0 | 0.150 4 | 5 | MAPE | 0.033 7 | 0.122 3 | 13 | ||||
| RMSE | 4.072 0 | 5.850 5 | 5 | RMSE | 1.724 0 | 4.534 0 | 16 | ||||
| R2 | 0.939 99 | 0.882 75 | 5 | R2 | 0.989 24 | 0.929 58 | 16 | ||||
| GPR-SA | MAE | 2.999 2 | 4.169 5 | 5 | 20 | XGBoost-SA | MAE | 0.981 1 | 3.133 8 | 16 | 61 |
| MAPE | 0.103 0 | 0.150 4 | 5 | MAPE | 0.033 7 | 0.122 3 | 13 | ||||
| RMSE | 4.072 0 | 5.850 5 | 5 | RMSE | 1.724 0 | 4.534 0 | 16 | ||||
| R2 | 0.939 99 | 0.882 75 | 5 | R2 | 0.989 24 | 0.929 58 | 16 |
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