Data-Driven Interpretable Machine Learning Prediction Method for the Bond Strength of Near-Surface-Mounted FRP-Concrete
Abstract
:1. Introduction
2. Construction of Bond Strength Database
2.1. Parameter Selection and Data Analysis
2.2. Sensitivity Analysis of Database Feature Parameters
3. ML-Based Predictive Models
3.1. DT
3.2. SVM
3.3. RF
3.4. XGB
4. Model Operation and Analysis
4.1. Data Normalization
4.2. Evaluation Indicators
4.3. Model Building Process
5. Model Training and Discussion of Results
5.1. Model Training
5.2. Comparison Analysis with Existing Empirical Models
6. Interpretability Analysis Based on SHAP
6.1. Introduction to SHAP
6.2. Feature Parameter Impact Analysis
7. Conclusions
- (1)
- By utilizing the database to train ML algorithms, an intelligent predictive model for the bond strength at the interface between FRP and concrete is established. The results demonstrate that the four ML models perform well, with the R2, RMSE, MAE, MAPE, and a20-index ranges for the training set being 0.9265–0.9695, 4.9608–7.79897, 3.1583–4.0759, 0.0519–0.0777, and 0.9097–0.9774, respectively. For the testing set, the ranges are 0.8190–0.9621, 4.4779–8.7680, 3.6252–6.1376, 1.0732–0.1013, and 0.8823–0.9705, respectively.
- (2)
- Among the selected four representative classical ML algorithms, namely DT, SVM, RF, and XGB, the performance of ensemble models (RF and XGB) is superior to that of individual models (DT and SVM), showing higher accuracy. Among all the models, the RF model performs the best.
- (3)
- Compared to the traditional empirical or semi-empirical models for predicting the bond strength at the interface between FRP and concrete proposed in the literature, the ML models consider the correlation between influencing parameters and can adapt to different experimental results, exhibiting higher accuracy and generality in bond strength prediction.
- (4)
- The SHAP method provides explanations for the prediction results from a global and local perspective. The results show that the width of the FRP bar (X2) and the thickness of the FRP bar (X3) have the most significant influence on the bond strength at the interface between FRP and concrete, while the width of the member section (X6) and the elastic modulus of the FRP bar (X4) have relatively smaller influences.
- (5)
- The SHAP method quantifies the influence of each input parameter on the prediction results. The SHAP feature dependence plots reveal how each individual feature affects the bond strength prediction. This provides useful ranges of values for individual features and their different combinations in influencing the bond strength, facilitating the development of improved bond strength models.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Classification | Variable | ID | Unit | Statistics | |||
---|---|---|---|---|---|---|---|
Min | Max | Mean | SD | ||||
Input | Lb | X1 | mm | 30.00 | 450.00 | 255.97 | 72.90 |
Input | tf | X2 | mm | 1.20 | 20.60 | 3.39 | 2.04 |
Input | bf | X3 | mm | 10.00 | 40.00 | 15.70 | 3.43 |
Input | Ef | X4 | GPa | 129.84 | 173.00 | 137.82 | 12.70 |
Input | fc | X5 | MPa | 11.85 | 64.80 | 33.76 | 8.79 |
Input | bc | X6 | mm | 150.00 | 220.00 | 180.65 | 29.81 |
Input | wg | X7 | mm | 3.00 | 35.00 | 11.17 | 5.93 |
Input | hg | X8 | mm | 11.00 | 51.00 | 26.60 | 6.96 |
Input | Ed | X9 | mm | 20.00 | 226.00 | 91.10 | 41.40 |
Output | Pu | Y | kN | 13.00 | 205.10 | 65.53 | 27.73 |
Parameters | Formula | Ideal Value |
---|---|---|
Coefficient of determination | 1 | |
Root mean square error | 0 | |
Mean absolute error | 0 | |
Mean absolute percentage error | 0 | |
a20-index | 1 |
Model | Hyperparameters | |
---|---|---|
Title | Value | |
DT | random_state | 65 |
max_depth | 43 | |
SVM | Kernel functions | RBF |
Regularization parameter | 1000 | |
Gamma | 0.00009 | |
RF | N estimators | 15 |
Max depth | 20 | |
XGB | N estimators | 75 |
Learning rate | 0.3 |
Data Type | Model | R2 | RMSE | MAE | MAPE | a20-Index |
---|---|---|---|---|---|---|
Training data | DT | 0.9435 | 6.8209 | 3.3922 | 0.0548 | 0.9474 |
SVM | 0.9265 | 7.7989 | 4.0032 | 0.0611 | 0.9097 | |
RF | 0.9695 | 4.9608 | 3.1583 | 0.0519 | 0.9774 | |
XGB | 0.9507 | 6.3696 | 4.0759 | 0.0777 | 0.9624 | |
Testing data | DT | 0.9043 | 7.0523 | 5.5013 | 0.0958 | 0.9117 |
SVM | 0.8190 | 8.7680 | 6.1346 | 0.1013 | 0.8823 | |
RF | 0.9621 | 4.4779 | 3.6252 | 0.0732 | 0.9705 | |
XGB | 0.9157 | 6.4673 | 5.0721 | 0.0935 | 0.9411 |
Researchers | Note | Formula | Equation |
---|---|---|---|
Reference [29] | M1 | (10) | |
Reference [30] | M2 | (11) | |
Reference [31] | M3 | (12) | |
Reference [32] | M4 | (13) | |
Reference [33] | M5 | (14) | |
Reference [34] | M6 | (15) | |
Reference [35] | M7 | (16) | |
Reference [36] | M8 | (17) |
Model | Max | Min | Mean | SD | C.V (%) |
---|---|---|---|---|---|
RF | 1.1709 | 0.6535 | 0.9895 | 0.0762 | 7.71 |
M1 | 3.4081 | 0.4145 | 1.7508 | 0.4751 | 27.14 |
M2 | 35.2400 | 4.6300 | 10.1311 | 3.4268 | 33.82 |
M3 | 15.1620 | 2.6178 | 6.7444 | 2.3414 | 34.72 |
M4 | 14.9916 | 2.7017 | 7.0281 | 2.3348 | 33.22 |
M5 | 2.8159 | 0.3425 | 1.4466 | 0.3925 | 27.14 |
M6 | 14.6710 | 1.3167 | 6.4836 | 1.8455 | 28.46 |
M7 | 6.1448 | 0.7474 | 3.1567 | 0.8566 | 27.14 |
M8 | 11.3512 | 1.2672 | 1.2672 | 1.4835 | 26.22 |
Model | R2 | RMSE | MAE | MAPE |
---|---|---|---|---|
RF | 0.9690 | 4.8664 | 3.2534 | 0.0563 |
M1 | −0.2253 | 33.2769 | 28.2303 | 0.4108 |
M2 | −0.7670 | 60.8606 | 55.3953 | 0.8315 |
M3 | −0.7581 | 60.3494 | 55.0615 | 0.8331 |
M4 | −0.7641 | 60.9050 | 55.5905 | 0.8413 |
M5 | 0.0522 | 26.5398 | 21.2689 | 0.3136 |
M6 | −0.6049 | 48.0253 | 42.2556 | 0.6282 |
M7 | −0.6070 | 48.1467 | 48.1467 | 0.6303 |
M8 | −0.7438 | 59.0602 | 53.8324 | 0.8084 |
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Gao, F.; Yang, J.; Huang, Y.; Liu, T. Data-Driven Interpretable Machine Learning Prediction Method for the Bond Strength of Near-Surface-Mounted FRP-Concrete. Buildings 2024, 14, 2650. https://doi.org/10.3390/buildings14092650
Gao F, Yang J, Huang Y, Liu T. Data-Driven Interpretable Machine Learning Prediction Method for the Bond Strength of Near-Surface-Mounted FRP-Concrete. Buildings. 2024; 14(9):2650. https://doi.org/10.3390/buildings14092650
Chicago/Turabian StyleGao, Fawen, Jiwu Yang, Yanbao Huang, and Tingbin Liu. 2024. "Data-Driven Interpretable Machine Learning Prediction Method for the Bond Strength of Near-Surface-Mounted FRP-Concrete" Buildings 14, no. 9: 2650. https://doi.org/10.3390/buildings14092650